Nov 22T

   

OAK RIDGE NATIONAI. I.ABORATORY
U operated by L

UN!ON CARBIDE CORPORATION E UNiON
- NUCLEAR DIVISION b e
U S.;'*ATOMIC ENERGY COMMISSION |
B o ORNL TM 2029 o

 

CAREIDE

   

 

 

 

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

W K Crowley
J.R ,Rose '

 

 

- 'm"cEThts document contains - informohon of o prehmmory nuture S
- ond was prepured primarily -for ‘internal ‘vse at the Ock Ridge Nationa! -~ - - .

- Laboratory. It is subject to revision or correction und therefore does '_ S
' nof rcpresent c flnni rapofl SIS LA e _ :

   
 

i o i i ey g e

Bt ot eyt AT S e ot e e

 

 

 

L-EGAL,NOT!_C.E

) This report was propcrod as an cccount ol Government sponsoud work. N-Iflur fho United States,
" nor -the Commission, nor any person acting on behalf of the Commissiont - '

A. Makes any warranty or reprasentation, expressed or implied, with respect to the uccumcy,

_completeness, or usefulness of the information contained in this report, or that the use of

ony information, -apparatus, method, or ‘process du:!osod in_this report may not Infringe
_ privately owned rights; or

B. Assumes any licbilities with respect lc fho vse of or for dumugn rnulting from the use of

any information, apparctus, method, of process disclosed in this report,
As used in the above, "person acting on behalf of the Commission® includes any smployee or
contractor of the Commission, or amployes of such contractor, to the extent that such employes
or contractor of the Commission, or employse of such contractor prepares, disseminates, or
provides access to, any information pursuant to his employment or contract with the Commission,

or his employment with such contractor.

 

 

 

|
|

 

 

 

 
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) (‘ )

 

rye

( - ,  ORNL TM-2029
Contract No. W=7405-eng-26

General Engineering Division

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

'W. K. Crowley
J. R. Rose

- NOVEMBER 1967

' OAK RIDGE NATIONAL LABORATORY .
- 0ak Ridge, Tennessee . - .
-~ operated by ‘
UNION CARBIDE CORPORATION
for the ,
U. S. ATOMIC ENERGY COMMISSION

 
 

 

 

 

e
 

£ 5‘ 3’1-’.

Abstract . . s ¢ .
1. INTRODUCTION . o o s o ¢ o« ¢ o« o ¢

2, SUMMARY

3. DEVELOPMENT OF ANALYTICAL METHODS
Steadyfstate'Cohditibn e e ee e e e

‘CONTENTS

» * -0 s s e 9

B N . . . . e * »

Derivation of Equations .

Calculational Prdcedure .

TraHSient.CaS-e :.'- ¢ s & e . .
4. PARAMETRIC STUDIES ¢ o« « o «

Cases Studied for Steady#State Condition
Case Studied fot_Transient Condition . .
'50\ CONCLUSIONS ) lc.o.'o' .., o * *+ o 9 ¢ s @® o-

EQUATIONS NECESSARY TO CONSIDER
GAMACURRENTgo o--‘u . -.—o n

'EVALUATION OF THE CONVECTIVE HEAT

Appéndix A,

Appendix B.

Appendix C.

Appendix D.
Appendix E.

141

A MULTIENERGETIC

COEFFICIENT « 4 o o o « o = » o o
VALUES OF PHYSICAL CONSTANTS USED
TSS COMPUTER PROGRAM . o v o o + o « o o + o &
NOMENCLATURE o & o + o o o o o s o o o o o o

- -

. * » o * 2

TRANSFER

»

¢ 5 8 " e ® ®

IN THIS STUDY

Page

X N NP =o

15
17
20
20
29
35

41

4t
46
47
60
 

 

Qo
A...»s 8..%‘

 
 

Table

Number

“k.

£y e

D.1
D.2

.3

&}

oh

LIST OF TABLES

.Title

Results of Investigation of First Steadyestate Case

Results of Investigation of Second Steady-State Case

Resuits.of_Investigation ef Third Steady-State Case

Results OfCInvestigation'of Fourth Steady-State Case

-Results'of Investigation of Fifth Steady-State Case

Resfilts of Investigation of Sixth Steady-State Case
Results of Investigation of Seventh Steady-State Case

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

Rénge of Parameters of Interest in Studies Made of
Proposed Wall With An Incident Gamma Current of
1x 1012 photons/cu? sec

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

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

1TSS Output Data at the Top of the Air Channel for One[

Case

Page

Number

22
23
24
25
26
27
28

31

36

54

58

59

 
 

 
 

»

F oL

Figure

Number

‘D.1

- vii

LIST OF FIGURES

Title
Proposed Configuration of Reactor Room Wall

Proppséd'COnfiguration bf Reactor Room Wall With
Corresponding Terminology

‘Designations Given Segments of Reactor Room Wall for

Study of Transient Conditions

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

' Temperature Distribution in Proposed Reactor,Roofi_

Wall With No Internal Heat Generation During the
Loss-o0f-Wall-Coolant Transient Period

Assembly of Data Cards for TSS Computer Program

Page
" Number

2
6_
18

33
34

53

 
 

{ix

 
 

 

“C

hf’

£

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

; °Abétraet!'

° !‘ L =
LT

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 con-
figuration of a laminated shielding wall proposed for
‘the reactor room was studied to determine (1) its abil-

1ty to maintain the bulk temperature of the concrete
and the maximum temperature differential at levels be-
low the allowable maximums, (2) whether or not the con-
duction 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 102 photons/cu? .sec 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.

1. INTRODUCTION

.

Thermal-energy molten-salt breeder reactors (MSBR) are being studied

. to: assess their economic and nuclear performance and to identify ‘important

i,:design problems One design problem identified during the study made of

_b'a conceptual 1000~Mw(e) MSBR power plant® was that there will be a rather
;;intense gamma current in the room in which the molten-salt breeder reactor
is housed The concrete wall providing the biological. shield around the

reactor room must be protected from this intense gamma current to. limit

 

1P ‘R. Kasten, E. S Bettis, and R C Robertson, "Design Studies of

© 1000-Mw(e) Molten-Salt Breeder Reactors," USAEC Report 0RNL-3996 Oak
- Ridge National Laboratory, August 1966.

 
 

 

gamma heating‘in the concrete. Further, ‘the concrete must be protected ' ¥
from the high ambient | ‘temperature in ‘the reactor room. " One possible

method of protecting the concrete is the application of layers of gamma

and thermal shielding and insulatingmeteriels on the reactor side of the

concrete, A proposed configuration”of the'leyered-type wall for the

reactor room is illustrated in Fig. 1.

- ORNL Dwg 67-I2000

- :s'xm'-\ msuumou] /—sren.——\ /—coucnera o

  

s
"
e

CURRENT . AR

\
rr\/\.,‘_\\

\"

\

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)

‘Fig. 1. Proposed Confignretion'ofrkeactor Room Wall. -

The . study reported here was made to investigate this proposed con-
figuration of a reactor room wall for the modular concept1 of a 1000-Mw(e)
MSBR power plant. This modular plent would‘have four separate and identi-
cal 250-Mw(e) reactors with their seperete selt circuits_and heat-exchange
loops. This preliminary investigation was made to determine whether or
not the proposed configuration for the reactor room wall will ¢
‘1.  maintain the bulk temperature of the concrete portion of the wall at

levels below 212°F, ' ' o
2. maintain the temperature differential in the concrete lamination at

 less than 40°F (a fairly conservative value), and -
3. maintain the conduction loss from a reactor room at 1 Mw or less.
This study was. also pexrformed to determine whether or not air is a suit-
able medium for cooling the reactor room wall and to determine the length

of time over.which theAlose of.this air‘flow can be tolerated_before the Qfij

‘). )

 
Cfi)(;

£31

 

 

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bulk temperature of the concrete lamination exceeds the maximum allowable

temperature of 212°F | |
‘Analysis of the proposed configuration for the wall of the reactor

Lroom was based on an investigation of the ‘heat transfer and shielding S

properties of the composite wall shown in Fig 1. Equations were devel-_

."oped that would allow these properties to be examined parametrically for

various combinations of 1amination materials and thicknesses in the wall.

 
‘2, SUMMARY

VMethods were devised to“parametrically'analyzefa composite plane wall
with internal heat generation produced by the attenuation of the _gamma
curreat from the reactor room., Both steady state and transient conditions
were considered Thirty-one equations were derived and a computer pro-
gram was written to examine the heat transfer and shielding properties of
the proposed wall for various combinations of lamination materials and
‘thicknesses. Incident monoenergetic'(lrMev) gamma currents of 1 x 102
~ photons/cn? *sec through 3 x 10*2 photons/cuf "sec were examined. A finite
difference‘approach,_with the differencing with respect to-time, was -
used in the transient-condition analysis to obtain a first_approrimation
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 10'%

)

photons/cnf +sec end a firebrick insulation lamination of 5 in. or more.
Under these conditions, a total of approximately 4 in. of steel is suffi-
cient for gamma shielding. The best results are obtained when the thick-
nesses 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 102 photons/enf - sec. |
With an incident monoenergetic (1 Mev) gamma current of 1 x 102
photons/cof *sec, the proposed laminated wall will masintain 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 15°F 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 — \ \Ej:

room have the same laminated configuration as the walls, the proposed

. Cl
 

 

»

w ( -~y

wall will allow the conduction loss from the reactor room to be maintained

at a level below 1 Mw for an'incident'monoenergetic‘(l Mev) gamma current

~of 1 x 10'2 photons/cnfa +sec 1if the thickness of the firebrick insulation

lamination iz 5 in. or more and if at least 4 in; of mild-steel gamma
shielding is inciuded ) o LT e T e
‘With a coolant air channel width of 3 in. and an air velocity of
50 ft/sec, air is an acceptable medium for cocling the proposed reactor
room wall. 1f the ambient temperature of the reactor room remains at
approximately 1100°F and if the’ gamma’ current is maintained at 1 x 102
photons/cn? sec, the temperature of the concrete will remain below the
critical 1eve1 (212°F) for approximately one hour after a loss of the

coolant air flow. If a zero incident gamma current is assumed the

“"permissible" loss-of-coolant-air-flow time is greater than one hour but

less ‘than two hours.

To determine whether or not a conduction loss of l Mw will permit

'maintenance of the desired ambient temperature within the reactor room

without the addition of auxiliary cooling or heating systems, an overall
energy balance should be performed vhen sufficient information becomes

available. This balance should start with the fissioning process in the

" reactor and extend out through the wall of the reactor room to an outside

surface.

 

 
 

3. DEVELOPMENT OF ANALYTICAL METHODS

In the modular concept of a IOOO-Mw(e) MSBR power plant,1 the four U
identical but separate ZSO-Mw(e) molten-salt breeder reactors would be
housed in four separate reactor rooms. One primary fuel-salt-to-coolant-
. salt heat exchanger and one bianket-salt-to-coolant-salt heat exchanger__

would also be housed in each reactor room along with the reactor. These

items of equipment are to be located 11 ft from each other in the 52 ft-‘

long reactor room that is 22 ft wide and 48 ft high The reactor and the
primary fuel-salt-to-coolant-salt heat exchanger are reSponsible for the
gamma current in each of the reactor rooms. The proposed configuration
of the laminations devised to protect the concrete from the gamma current
in the reactor room is shown in Fig. 2 with the corresponding terminology

used in the parametric studies made of the composite wall

 

1P. R. Kasten, E. S. Bettis, and R. C. Robertson, "Design Studies of
1000-Mw(e) Molten-Salt Breeder Reactors," USAEC Report 0RNL-3996 Oak
Ridge National. Laboratory, August 1966.

ORNL Dwg. €7-12001

 

AR

 

 

 

 

 

 

 

 

 

 

e
NI\ |

To, T T | s T | T B

 

 

SKIN ~ INSULATION ——STEEL CONCRETE

Fig. 2. Proposed Configuration of Reactor Room Wall With Corres- -
ponding Terminology.

)
»

ad

W

w) ( o

"In the direction from_the interior of the reactor room out to the
outer surface of the wall (left to right in Fig. 2), the layers of mate-

~rial comprisingtthe-wallQare-atStainless steel skin, firebrick insulation,

a miidesteel,gammajshield;;an;air channel, a mild-steel gamma shield, and

the concretevbiological shield."~Therthicknesses ofstheifirebrick-insula-
tion and each of the two mild-steel gamma shields are considered to be
the:variable*parameterssin this study.  The thickness of the stainless
steel skin is fixed at 1/16 in., the thickness of the concrete is either

8 ft for an exterior wall or 3 ft for an interior wall and the width of

the air channel is fixed at '3 in.

- The temperature of . the interior surface of the reactor room ‘wall’ is

‘considered to be uniform over the surface and constant at 1100°F. The
‘temperature of the exterior surface of the wall is considered to be uni-

form over the surface and . constant at . 50°F for the 8-ft thickness of

concrete (the temperature of ‘the earth for an exterior wall) or at 70°F

‘for the 3-ft thickness of concrete (the ambient temperature of an adjoin-

ing room withinrthe_facilit§,for!an interior wall). The temperature of

the coolant'airhisfassumed to be 100°F at the bottom (entrance) of the
air channel, and the velocity of the air is assumed to be 50 ft/sec.

The situation examined is basically one involving & composite plane
wall with internal heat generation caused by the attenuation of the gamma
current from the reactor room. Two conditions were considered the

steady-state condition and the transient condition. The steady-state

f?condition was considered first and the transient condition was considered

; later when the problem of a loss of wall ‘coolant was examined

v“SteadyestatefCondition,

Equations were deve10ped to allow the heat transfer and shieIding

1~:properties of the composite wall, shown in Fig. 2,_to be examined para-

'-Qmetrically for various combinations of lamination materials and thick-

nesses. A one-dimensional analysis was used, assuming that the tempera-
tures of the interior and exterior surfaces of the wall were constant and

uniform.

 
 

Derivation of Equations

A steady-state energy balence on & differentisl element of the reactor
room wall ‘can-be expressed semantically as follows. The ‘heat conducted
into the element through the left face during the time A6 plus the heat
generated by sources in the element during the time A8 equals the heat
conducted out of the element through the right face- during the time A8,
This 1s expressed. algebraically in Eq. 1. . L '

-ki, AB + Q(A; AX)ND = -kAl - N8, - (D
dx ax| L. o
where | | | o ] '
k= thermal.conductivity,_Btu/hrjit-°F,:
A = unit area on wall, ft?,
T = temperature, °F, - L - _
x = distance perpendicular to surface of the wall, ft, .
@ = time, hours, and :
Q = volumetric gamma heating rate, Btu/hr ft" | o
Application of the mean-value theorem to dT/dx gives the expression of ,
| T o | |
g, -8 8w
_ x + Ax , L G

where M 1is a point between x and x + Ax. Equation 2 is substituted into
Eq. 1 and AB is canceled '

— dT| . Q(Alox) i} -kA1 dTl [d dT

_ ‘ dx‘é;E]MAx e
‘The common term -kAl'-—| is canceled, and it is noted that----(d )

= £T/d®. The resulting expression is given in Eq. 4,

QAan -kAl—kr\ "-.-(4')_."

Dividing Eq. 4 by A Ax and allowing‘Ax to approach zero as a limit go

that a value at M becomes a value at x, the volumetric gamma. heating rate,

Q = .k«gzg - T 'i:*i;fl, (5)

W Cl

x)

"

 

 
124

oy

X

 

oy ( »y

4

Equation 5 is integrated twice, and if Q # Q(x),
T(x) = 0 @ + Gx + G . - (6)

The applicable boundary conditions for anylparticular laminationvin the
wall are T=T, at x =0 and T = TL at x = L, where Tg = the temperature
of the lamination interface at zero location designated in Fig. 2 and
L = the thickness of the material in a lamination in feet. Tkese con-

ditions are applied to Eq. 6.
T =T + AT - B) ¢ R(x - ) . S m
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 atten-

uated by the materials-iu.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 gamma current where buildup and exponential attenuation are

considered, the equation for Q(x) becomes

Ax) = & [Aeo‘“‘ + (1 - A)e'B“"]e“”" , o ®
where S o : o ' '
| A, Q, and B = dimensionless constants used in the Taylor buildup
| equation ' |
~and p = the total gamma attenuation coefficient, ft'1
When . o .,[l'i _f o o |
s Bhoty » -
| Q) = -q,[ px@ - 1) (L ge(B 1’] (9
where - : j R | '_’h o
V'iQ,cé the volumetric gamma heating rate at the surface on the reactor
’77i ‘side of the stainless steel skin, Btu/hr-ft‘3 o o |
E = energy of the incident gamma current,. Mev,
%, = incident gamma current, photons/cn? ~sec, and
hg = gamma energy attenuation_coefficient, fe-t,

 
 

ST R | | cr

Substituting Eq. 9 into Eq. 5,

£, % (4@ D, o pe=® n] o W

Equetipn 10'ie'integrated twice to yield'

_ % A ux(a-* 1) IV—A '-ux(fi+1)
TG = - 9’1‘? -7 Eé(a o | |
+ ('ax + G = o | (11)

The previously stated boundary conditions are still applicable, and the
result of applying these conditions to Eq. 11 is that

,T.(,‘;A)_;-T6+-§(T.-To) | N -
ux(a - 1)) 1 - A (1 -ux(B + 1))]

kuz{[W (1 | *’(‘;‘3‘?1')"5 -
-_[W(l uL(o.' )) +Té"i'%'2'(i |J.L(B+ 1))] Caz

The temperature distribution in any particular lamination of the wall
is given by Eq. 12 when the apprOpriate constants for that lamination are

used. Equation 12 is ‘used primarily to determine the maximnm 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
obtaified gives the distance from the concrete-steel interface to the
position of the maximum temperature in the concrete. |

o, - )

el Mgt (o oo )

(¢ - 1)

- %[—————(af 1)3(1 - em‘(a -_1.)) (514--1?3 (1 e HL(P + D)]} =0, (13)

4 Equatien 13 is a transcendentsl equation in x, and as such, it must

 

‘be solved by using a trial-andferror technique. There are only two terms
in Eq. 13 that contain x, and these terms are rearranged to put Eq. 13

in a2 form more easily solved by trial and error. o o | ]

i

 

 
 

 

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-

 

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¥

£

11

     

HX(as?-l)

BB m T
;%(To : TL)+ 1(‘%)[(“ )5 (1 ”L(a 1)) )
e ) e

- All of the coefficients on the left side of Eq. 14 are known, and all of

the terms on the right srde are known Therefore, Eq. 14 may be written :

in the form

fi,'xew,+ae%*;t;3 L
where the K's and a's are calculable numbers. When Eq. 14 is solved for
x, this value of x is called B fiéx .1The value x = Xy oo 18 substituted

into Eq. 12 to obtain the maximum temperature of the concrete.
To determine the. magnitude of the conduction 1oss, q*, from the
reactor room, equations were written to give the temperature drops across

each separate lamination in, the wall These equations are simple con-

‘duction and convection equations in which all of the heat generated in a

particular lamaination is assumed to be conducted through a length equal
to two-thirds of the thickness of the particular lamination. The total
amount of gamma heat, qT, deposited per unit area in a direction normal to
the face of the wall is found for any particular 1amination by integrating
Eq. 9 over the length L, of the particular lamination._'

0 f* . [Aeux(ot n. “ (1 A) ~ux(B + 1)] x . ae
5 o, e 1 A FT S |
Q:[.(E.g..r). ML(Q_‘__"__ 1’ 1) 4 A( '”L(B * 0 1)] an

where QG is the incident volumetric gamma heating rate.grf*

There are two possible ways to evaluate the incident volumetric

ggamma heating rate at some particular material interface, which shall be
-referred to as. the "j th" interface.! The first way is to calculate the

'gamma current, (j)’ at each interface. To obtain Q’(j)’ this calculated

value of § is substituted into the equation

o(3)
5 = Bohke

 
 

12

The second method of evaluating the incident volumetric gamma heating
rate involves subtracting the total ‘amount of gamma heat deposited per
unit area in the j-th lamination, qJ, from the gamma energy current per
unit area incident upon the j -th lamination, q (j)’ to approximate the
gamma energy current per unit area incident upon the face of the follow-

‘ing lamination q (j + 1)

The volumetric gamma heating rate incident upon a particular lamination, |
Q (j)’ and the gamma energy current per unit area incident upon the j -th
'lamination, q o(4)’ are related by the following equation.(. o
Y1) = o(j)/“E(j) - (188)
Therefore, : v P
(g + 1 - % + DPEG + D

These two methods are in fairly good agreement, and since the values for -
‘the various materiel constants were not well fixed at this point in the i
design for the reactor room wall, the ‘second method of evaluating the f"'
incident volumetric gamma'heating'rate?was"usedin thiS'study;.‘The ' |
second method is simpler to use and easier to calculate. o

The equations for the steady-state temperature drOps across each of
the material laminations on the reactor side of the air channel are given

below and the temperature points are as 1llustrated in Fig._2 ’

(gx + 3q )L o
T -T =-—-—e-;:-—-- , . (19)

where o o , c - | L
' gq* = heat conduction rate out of the reactor room;'Btu/hr £t2,

q, = gamma heat.deposition: rate in the:stainless steel outer skin,

- Btu/hr- £, | | | o
:*L§,= ‘thickness of the-stainless*steel skin, ft, and
'k = thermal conductivity of the stainless steel skin, Btu/hr-ft-oF;

© (18b)

 
 

 

A e e g e A i vl

"

w)

a

wi

"}

 

o AsEETT (20)
where the subscript 1 refers to the insulation lamination shown in Fig. 2.

L2

o (4* +q  + Qp *+ 34 )Lpe o r

BT - I_ 3ESE @y
' o , FS

vhere the subscript FS refers to the first mild-steel gamma shield (on

 

the reactor side of the air channel)

- q* + q + qp + 9pg - .
L - T, = - 2, | (22)

 

where | ‘ .
T, = temperature of the air in the channel, °F, and

" h = convective heat transfer coefficient, Btu/hr-£t?.°F.

‘The ‘average convective heat transfer coefficient across the walls of the

air channel is evaluated in Appendix B, and the value of 5 was determined
for a mean temperature of from 130 to 150°F. It was assumed that the
gamma heating in the air channel is negligible. ‘Equations 19, 20, 21,
and 22 were added and the resulting equation was solved for q*. The heat

conduction rate’ out of the reactor room to the air ohannel,

 

. (z,.‘.:z Les 1] .. [j2yles, 1
| 3, T TR Us (3) . ' h o
q* = L L. L. .1 - ‘ (23)
s, I, CFS 1} : ;
1. ° k"+'E—7:f h
s _I o FS_

is the maximum temperature of the concrete, Tmax’: This temperature may be
'jdetermined by using Eqs 12 and 14 but the temperature of the steel-.. .

concrete interface, Tg, must be known before these equations can be used.

' The simple conduction and convection equations for the laminsted wall on

the concrete side of the air channel are given below.

L % R |
L fflra;?‘*f'—fif"'*f“’ o S (2%)

 
14

 

where S o _
| qgg = gamma heat deposition rate in the second mild-steel gamma shield
 Btu/hr- £, ; R o
qé: rate at which the gamma heat generated in the concrete 1is
- conducted back toward the air channel, Btu/hr:£ft®, and
qR_=_radiant heat transfer rate between the walls of the air channel,
| Btu/hr-fta | ' |
g = 7 (B* - T*)
et
-whete
o = Stefan-Boltzmann constant -
= 0.1714 x 10~ |
€ = surface emiSSiVity.of.air'channellwalls,.aesumed.to-the"
same for both surfaces. el
(e +g“ss”‘ss o o
k- L= R o
- 88 IR e . _
In this study, there is a point in the concrete at which the tempera- | -

ture of the concrete 1is a maximum. All of the gamma heat generated on

the air channel side of that point will be conducteditoward”thezair channel;
that is, in the direction of decreasing temperature. Thie amonnt ofheat,
q;, may be calculated by evaluating dT/dx in the concrete at x = 0, using

 

.1 » [ o @-D) . _,1|;Lc(a_+',,1)
(cx et +W(1'e o dp
| o + o ey
-.recognizing that . : S AR
R w-vd . ew

c Cdx_ =0 -

vhere the subscript ¢ denotes concrete. The right side of Eq. 28 is

positive rather than negative.becauseiEq. 27 makes positive conduction

—

in the direction from the air channel toward the concrete, but q; 1is . O/
 

 

 

"

T W

142

oy

15

to be made positive in the:direction from the concrete:toward'the'air

channel. Equations 24, 25, 26, 27, and 28 were combined to yield one
equetion in which the only unknown is T;, The value for T, can ‘be calcu-

lated from the equations for the reactor side of the air channel.

| | 1“

 

 

 

 

L+ Tih + '
(’2"1} i _I_‘_s__s_ +.,_L_C o
k k.
SS - L .
e o(e SS °SS
=(2 )T34+hT +qSS L TLL. ) -.(29)
- -1 ' _S_§ + _.E
;g_; e T e kSS k-
. - : €
B! p(l 'Al pA B 1' A 1 -_ eu,
2 B+ 1 _(a-l) (a-""'fil)' e
o “uL (B + 1) B
- oo . e

The constants in Eq. 29a that have no identifying subscripts are understood
to be for concrete., Equation 29 is also a transcendental equation. VThere-

fore, a trial and-error method must be used to solve for T,. Once l; and

. qc are known, lg can be calculated by using Eq. 25.

‘Calculational Procedure

Since the calculation of certain of the desired: quantities requires

':that the value of other desired quantities be known, there: is a certain
. order in which the problem must be worked For a particular case, - the
';thickness of each of the laminations in- the wall is- selected, and the. o

'_inside (reactor room) and outside (earth or internal) wall- ‘temperatures

are specified. ‘The - incident gamma current and the temperature of the.

- cOolantrair are also specified.; Ihe constants for the various equations

are selected, and those used are given in Appendix C.

 
16

With the prqpercenstants_foreachdiffereht,lamination, Eq. 17 is
first used to calculate the gamma heat depbaitions in,each'of the sepa-
ratelaminations (qs, g qFS,‘qSS,_anq‘qc). Equation 23 is then used
to calculate the conduction loss from the reactor room q*.. The tempera-
ture drops and the interface temperatures on the reactor side of the air
channel are calculated by using Eqs. 19, 20, 21,,and 22. Equation 29 is .
used tc calculate the value of T;, and then the value of qR is calculated
by using Eq. 25. Then q; is calculated by using Eq. 24, and the value
of Tz is calculated by using Eq. :26. Once the value of Tg is knowm,
is obtained by using Eq. 14, and the maximum temperature of the

T max

concrete is calculated by evaluating Eq.712 at X = xT max’
At this point, it is possible to calculate the vertical temperature

gradient (°F/ft) in the coolant air. This temperature gradient,

Qg + 9p * Apg *'9gg t 97 * G+ 4,

 

’ G0

AT = 360006 Ly Cp
where , _ R
| U = bulk relocity of coolant air, ft/sec,
P, = density of air, 1b/ft®, ) |
Ly = width of air channel (distance between steel laminations), ft,
Cpa = specific heat of air at constant pressure, Btu/lb °F.,

The temperature of the air at the t0p of the channel,
T . . .
Ty = T, + AI(H) o @G

where H = the vertical length of the air channel in feet.

The entire-calculational procedure can now be repeated usifigithe7

new air. temperature at the top of the air channel, T'.‘ This calculation o

of the temperature of the air at the top of the channel is necessary
because & higher T causes the maximum temperature of the concrete to be
higher, and the magnitude of this maximum temperature 1s one of the
constraints in this study.

- A program was developed for the CDC 1604-A computer to solvé’qu;”Bf
through 31 for the steady-state condition.  The TSS (Thermal Shield Study)"

a4y
 

 

r

b )

¥

 

17

computer program is described in Appendix D. The program performs the
calculations in the order described above, and it will handle up to five

‘material laminations (excluding,the,air channel) in the proposed reactor

room wall and up to eightvenergyrgronps for the incident gamma current.

Transient Case

The problem of the loss-of coolant forrthe reactor room wall is
basically a transient heat conduction problem with internal heat genera-
_tion. If the flow of cooiant air through the channel in the wall is lost
for an appreciable length of time, the temperature‘in;the concrete and/or
the steel laminations may become excessive To investigate this situation

with the goal of obtaining a first approximation of the amount of time

‘that such & loss of air flow could beksustained safely, a finite differ-

ence approach was taken.- Thefldifferencing‘is with respect to time and
the superscript nin'the_followingequstions denotes values after the
n-th time interval. . | e

. The proposed configurstion’of the reactor room wall was broken into
segments of given lengths with nodal points locatediat the Center of each
segment, as shown in Fig. 3. Each segment in the concrete region of the
wall was essumed to be 1 ft thick, each segment in the mild-steel gamma
shields and- in the firebrick insulation was assumed to be 1 in. thick,

the entire stainless steel skin was treated as a single segment 1/16 in.

thick, and the air channel was treated as a single segment 3 in.-thick

The energy balance for a particular segment can be expressed seman- .

_f-tically as follows._ ‘The heat conducted into a segment during the time AB
.';_plus the heat generated in the segment during the time AB _equals. ‘the heat
?stored in the segment during the time A8 plus the hest conducted out of the
| _segment during the time A®. The corresponding algebraic equation for a
:typical segment of the composite wall is given. below with Segment 4

selected for illustrative purposes

k A o pcALccp B . kA

 

(%" - “)+q4,A- = (m“*l TY + S-(n" - Y.

c c

(32)

 
 

18

. - -1
STAINLESS STEEL . ORNL pug 7:87 12002
: SKIN

FIREBRICK -

INSULATION
o / FIRST MILD-STEEL

GAMMA SHIELD

AIR CHANNEL

  

SECOND MILD-STEEL
GAMMA SHIELD

—{ CONCRETE

 

 

7 CURRENT

uoom./ : 1 11

POINT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SEGMENT 2019 18 ITIG IS4 1312H 109 B 7T 654 3 21

Fig. 3. Designations Given Segfients of Reactor Room Wall for Study
of Transfent Conditions. _ _

Rearranging Eq. 32,

T4,“+1—T4 +—i—q—('r5n;2n +Ta“)+——. O (39)
pCC p | S pCCp . Lo :

A characteristic equation at an interface ‘between two different

materials is given in Eq. 34

kAB k,_ 00 @ 3

n+1 . n. S=C _
- Ve’ p_ ss¢p 5P,

- (358)
where the subscript s denotes the stainless steel skin, the subscriptic
denotes the concrete, and'is_c is an equivalentconductfyity~giveh by
Eq. 35. | k@ fL). |

kyp = ik:b: kb: ’ | e
a a | ,

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

 

 

 

 
3§

o | 19
-

Eighteen equations similar to those just given were derived to carry

o

the analysis across the entire reactor room wall, and a‘simple computer -
program was written to perform the calculations required for one specific
transient cbndition;r B - o

 

 

4

Ay

 
 

 

20
4. PARAMETRIC STUDIES

The parametric:studies“ofsthepfoposedconfigorstioo-of:e laoinated
walllfor the reactor rOom,_shown in Fig. 2, to protect the concrete bio-
logical shield from the gamma current within the room were made for two
conditions: the steady-state condition and the transient coodition.
Parametric studies of the material laminations for the steady-state con-
dition were made to determine whether or not |
1. the bulk temperature of the conc:ete portion of the wall could be

| maintained at levels below 2129F, N

2. the temperature differential in the concrete could be maintained at
less than 40°F, and |

3. the conduction loss for a reactor room could be maintained at 1 Mw
or less.

A transient condition was investigated to.determine the length of time

~ over which the loss of coolant air flow could be tolerated before the

temperature of the concrete would exceed the maximum allowable tempera-

ture of 212°F. |

Cases Studied for Steady-State Condition

For the parametric analysis of the composite plane wall with internal
heat generation for steady-state conditions, the air channel was not con-
sidered as a material lamination but rather as having a fixed width of
3 in. between the first and second mild-steel gamma shields. The tempera-
ture of the incoming cooling air at the bottom of the air channel wss
essumed to be 100°F, and the velocity of the air was set at 50 ft/sec.

The thickness of the stainless steel skin on the reactor side or interior
surface of the wall was fixed at 1/16 in., and the temperature of the
interior surface of the reactor room wall was considered to be uniform
over the surface and constant at 1100°F. Equations 8 through 31 derived
‘in Chapter 3 were used with the TSS eomputer program described in
Appendix D to examine the steady-state effects of ehanging the

i
f

 
 

 

 

 

o

"

21

1. thickness of the firebrick insulation,
total amount of mild steel used for the gamma shields,
3. ratio of-the amount-ofnsteel On‘the reactor side of the air channel

to the amount of steel on the concrete side of the air channel

‘4. thickness and outside temperature of the concrete wall, and the

5. magnitude of the incident monoenergetic (1 Mev) gamma current.
Sixty-four’Separate cases were analyzed for the steady-state con-
dition-to;determinejtheeffects of changing those parameters of interest,
Data illustrative of the typical 'ef'fects of varying the parameters were
selected from the results of these analyses and are compiled in Tables 1
through 7. The effects of changing the parameters are given for 1ncident
gamma currents of 1 x 10'2 and 2 x 10°2 photons/cnf3 -sec in all of these
tables, and the conditions at the bottom (entrance) -and top (exit) of
the air channel are given for both magnitudes of incident gamma current.
For cases with an incident gamma current of 1 x 10'2 photons/caf - sec,
the maximum temperature of the concrete increases approxlmately 50°F from
the bottom of the air channel to the top. For cases with an incident
gamma current of 2 x 103 photons/cma-sec and no conduction back to the
reactor room, the makimum temperature of the concrete increases approxi-
mately 80°F from the bottom to the top of the air channel. For a given
gamma current and insulation thickness, the conduction loss changes very
1ittle (about O. 04-Mw)-between the bottom and the'top of the air channel.
The largest value for the maximum temperature of the concrete at

the top of the air channel in those cases with an incident gamma current

of 1 X 1012 photons/cn? sec and an insulation thickness of 5 in. or more
s approximately 200°F On ‘the other hand, the smallest value for the
. maximum ‘temperature of ‘the concrete at the top of the air channel in
_'those cases with an incident gamma current of 2 x 10la photons/cnP-sec

‘and an insulation thickness of 5 in. or more is greater than 250°F

 
 

 

 

 

22

- Table 1. Results of Investigation of First Steady-State Case
‘Case Conditions Studied

- 7.0 . = = o
T, = 1100°F L =8 ft . Te = SO°F

 

=2 in,

L, = 1/16 in, Ly =5dn.. Leg = 4 in, Lgg

¢, = 1 X 10*2 photons/cuf - sec ¢, = 2 X 102 photons cuf . 8ec
‘ . o

 

 

 

Bottom of Top of -~ Bottom of = Top of
, , Channel Channel Channel ___Channel =
q,, Btufhr:f£t? 16.57. 1657 3.6 36
qq Btufbref® 75.47 1547 _ 151.0 151.0
qpgs Btujhre£e3 o 30.6 306 T4L2 741.2
qgq, Btufbre£e? 11.69 ©11.69 23,38 23,38
 q, Btufnr-ft? 33,65 33.65 . . 67.30 - 67.30
q ', Btu/hr-fe? 25.84 - 22.04 - .§5.31 . 48,99
Ggs Btufhre £t 0.6 1312  198.9  253.9
MWL, Mw 0.5812 0.5382 0.3520 0.2838
n, % 1099.9 1099.9 ©1099.9  1099.9
T, OF 247.9 2971 326,6 4027
B, °F 260.5 289.9 314.1 - 392,5
T, °F 100.0 153.0 100.0  184.0
T, °F 129.6 186.0 155.5 . 249.3
T, °F 129.8 186.2 . 156.0 . 249.7
=Ty, °F 0.1018 . 0.0946 0.0679 0.0565
T-T, °F 852.0 802.8  775.3 . 697.3
LT, °F 7.412 7.185 10.55 - 10.19
Ta~T,s °F 140.5 - 136.9 214,1  208.5
T-T, F '29.63 32,98 55.52  65.25
T-%, °F 0.216 0.1916  0.4556  0.4148
Toaxr F 0.5 1936 181.3  268.5
Xy gays 0.5422 - 0.4083 0.6343  0.4887

ar/e, °F/ft 1.104 1.103 1.751 1,777 -

 

 
 

 

i

»)

23

' Table:2. Results of invéstigatibn of Second Steady-State Case -

.Case Conditions Studied

T, = 1100°F L =3 ft Te = 70%F

 

L, = 1/16 in. | L,

¢ =1X lola'fihotona/bmfiosec gy =2 X% 1012 photons /cu® . sec

 

 

 

 

- Bottom of Top of . ‘Bottom of ~ Top of
: .~ Channel . Channel Channel Channel
q,, Btufhr-£e 16,57 . 16.57 33,14 . 33.14
qps Btufnr:fe? L 15,47 715,47 151.0  151.0
qpgs Btu/hreft® 3706 370.6 o 761.2  741.2
qggs Btufhrefe?  11.69 11.69 23,38 - 23.38
q.» Btufnr-f® . 3365 33.65 = 67.30 67,30
q.’, Btufhr-£e3 18,33 8.446 42,64  26.19
qg» Btu/hre £t? uL6e 133.3 ~200.8 - 258.2
ML, Mw ~ 0.5812 0.5385 0.3520 0.2845
%, F 1099.9 1099.9 1099.9 1099.9
T, °F w19 296.7 . 32.6 402.1
T, F ©200,5 - 289.5 3141  391.9
T,, °F 1000 152.6 100.0 183.4
%, °F 128.3 183.3 153.6 244.9
T, °F 128.5- - 183.4 ©153.7 245.2
BT, F 0.1018  0.0947 . 0.0679 0.0566
T-Ta, °F . 852.0 803,2 775.3 o 697.9
| LT, °F S 7.412 7,187 1055 10,19
Ta-T, F 140,570 0 T °136.9 2161 208.5 -
5-T,, °F. 28,32 . 30.68 53.36 - 60.55
. Tk, °F 0 0.1678  .0.1043 0.3740  0.2683
O Tgae F 1334 1844 1674 250.0
C Xp e £t .0.3126 - 0:1276 - 00,3878 - 0.2061
- ar/m, °F/te 91,096 . 1.088 L7 1,756

 
 

 

24

 

- Table 3. Results of Investigétionj of Third Steady-State Case

 

T = 1100°F
o -

L = 1/16 {in,

b = 1 X 1022 photdns/cmg-cec

I"I = 5 in.

‘Case VCondu:lonés ‘Studied
= 8 ft |
Lc | |

|
|

,Lrs['_' 2':ln.

Te = SOOF

Ls

s = 4 111._

¢, = 2 X 10*2 photons/cu® -sec

 

 

 

. Bottom of “Top of . 7 Bottom of “Top of
o .~ Channel = Channel Channel Channel
q,s Btufhreft® - 16.57 16.57 . 33,14 33,14
qy, Btufhre £t - 75.47 75.47 - 151.0 - 151.0
Qpgs Btufhr £t 299.6 299.6 $599.2 599.2
qgqr Btufhr-£e? 82.69 +82.69 165.4 165.4
q,, Btu/hreft® 133,65 33.65 167.30 - 67.30
q ', Btu/hr-fe 25.15 21.50 54,08 T 48,21
qp, Btufbrefed - 87.31 - 102,6 141.5 177.6
ML, Mw '0.5960 0.5538 -0.3799 0.3139.
5, °F 1099.9 1099.9 1099.9 1099.9
T, °F 1230.9 279.2 292.7 368.2
T, °F 227.5 275.9 288.0 363.6
T,» F 100.0 151.9 100.0 181.1
%, °F 1139.0 193.3 172.2 259.3
%, °F 140.1 194.2 174.3 261.4
T-T, °F 0.1043 0.0972 0.0276 0.0616
T,-Ts, °F 869.0 820.7 807.2 731.7
-, °F 3.452 13,341 4,754 4,580
Ta-Tps °F 127.5 126.0 188.0 182.5.
T-T,ys °F 39.03 41.35 72,19 78,26
Te=L, °F: 1.028 © 0.9814 © 2.105 2.030
Ty F 150.1 201.2 1198.2 279.5
X pax? £t 0.5139 -0.3927 '0.6004 0.4745 -
- arfu, °F/ee 1.081 1,074 1.689 1694

 

 

 

 
 

 

e

25

Table 4., Results of Investigation of Fourth Steady-State Case
Case Conditions Studied
Lc = 3 ft

 

"'ro = 1100°F Te = 70°F

L, = 1/16 in, Ly = 5 in. Lgg = 2 in. Lgg = 4 in.

| "o = 1 X 10*? photons/cuP - sec '

 

¢, = 2 X 10*2 photons/cof . sec

 

 

1.673

. Bottom of Top of Bottom of Top of
-Channel Channel ~ Channel Channel
q,, Btu/hre£ed - 16.57 16.57 33.14 33.14
qys Btu/hrefe® 75.47 75.47 151.0 151.0
Qpgs Btufhr. €43 299.6 299.6 599.2 599,2
qgqs Btu/hr-£62 - 82.69 82.69 165.4 165.4
‘g, Btufnrefe? 33.65 33.65 67.30 67.30
q.'s Btu/hr-fe? 16.53 7.048 39.42 24,17
qgs Btu/hre fe? 88,49 104.9 143.8 182.4
MWL, Mw 0.5960 0.5543 0.3799 0.3146
T, °F 1099.9 1099.9 11099.9 1099.9
T, °F 230.9 278.8 292.7 367.5
T, °F 227.5 275.5 288.0 362.9
T, °F © 100.0 151.4 100.0  180.3
T, °F 1137.5 190.4 169.7 2547
T, °F 138.5 191.2 171.6 256.4
To~T, °F 0.1043 0.0973 0.0726 0.0617
T, Tz, °F 869.0 821.1 - 807.2 732.4
T-Ts, °F 3.452 3342 4.754 4,581
Ta=T, °F 127.5 1240 188.0 . 182.6
L-T,, °F 37.54 . 38,93 69.71 74,40
Te-T, °F 0.9178  ~  0.7963 1.917 1.722
T, °F 12,4 192.8 183.1 2605
X pay £t ©0.2726 . 0.1052 ©0.3454 - 0.1881
arfu, °rffe 1.072 - 1,058 1,669

 

 
 

 

26

Table 5. Results of Investigation of Fifth Steady-State Case
Case Conditions Studied
T, =1100°° L =8ft Te = SO°F

 

L, = 1/16 in, 1 =5 1n. L = 2 in. - Lgg 52'111.

& =1 x 1082 photons /cuf « sec 8, = 2 X 10*2 photons/cuf . sec

 

 

 

Bottom of ~ Top of - . Bottom of Top of

: Channel Channel Channel Channel
q s Btufhre£e? 16.57 16.57 33,14 33,14
qys Btu/hre £6° - 75.47 75.47 | '151.0 151.0 -
Qg Btu/hr. ££2 299.6 _ 299.6 599.2 . 5¢9.,2 .
Qggs» Btufbrefe 71.15 71.15 © 142.3 Cc 142,30
q_, Btu/hr- £t3 - 45,19 45.19 90,38 - 0.38
q.'s Btufhre £t ~ 35.90 32.24 75.58 69,71
Qs Btufhr-fe? 87.42 - 102.7 141.7 177,99
MWL, Mw 0.5960 0.5538 0.3799 0.3141
5, % 1099.9 1099.9 ©1099.9 1099.9
T, °F 230.9 279.2 '292.7 368.1
T, °F - 227.5 275.9 288.0 - 363.6
T, °F 100.0 151.9 100.0 181.0
%, °F 138.9 193.1 ' 171.9 259,0
1, °F 139.4 193.6 173.0 260.1
=Ty, °F 0.1043 0.0972 . 0.0726 0.0616
T,~Tz, °F 869.0 820.7 - 807.2 731.8
T.-Ts, °F 3.452 3.341 4,754 . 4,580
Ty-T,, °F 127.5 124.0 188.0 182.6
L-T,, °F - 38.89 41.22 C71.92 . 77.%9
To-%, °F 10,5353 0.5118 1.095 1.057
T, F 155.0 205.6 208.6 289.1
Xp gax? f€ 0.5851 0.4716 0.6638 0.5484

 

arfu, °rfft 1.080 1.073 1.688 1.692

 
 

 

-

N

27

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

 

 

 

 

 

T = 1100°F L =8 fr Ts = SOOF
L, = 1/16 in, L, = 7.5 in. Lyg = 4 in. Ly = 2 in.
. 4 =1 X 10' photons/c? -sec fg = 2 X 10*2 photons/cof . sec
- Bottomof . . Top of - ___Bottom of - Top of
— — __ Channel - _Channel Channel __Channel
q Btufbr g 16;:57 16.57 3314 |
9y, Btu/hre £e° 11,9 - 111.9 223.8
Gpgs Btufhref® - 338.1 33841 676.2
9ggs Btu/href£e? 10,69 10.69 21.38
q., Btu/hreft3 £ 30.70 30.70 61.40 §
q.', Btufhr- 63 23.47 20.35 '"50.39 :
qgs Btu/hr- £13 86.60 101.1 164.5 g
MWL, Mw 0.2891 0.2649 0.0245 o
T, °F 1099.9 ©1099.95 ' 1099.99 2
T, °F 223.2 265.1 297.9 »
T, °F 217.2 259.2 288.7 =
T,, °F 100.0 144.0 100.0 g
%, °F 124.1 170.5 147.2 7
T, °F 193.6 1706 147.7 'g
To-To, °F 0.0529 0.0488 " 0.0131 °
T-Tz, °F | 876.7 834.8 802.1
T-T,, °F  6.0600 5,931 9.195
=Ty, F. U2 Cus.2 . 1887
L-T, ¢ 2600 - 2642 47.24
Te-L, F 0.1965 0.1764 .0.4150
Tax’ T %0 e w0
X maxr ££8 0.5375.  0.4162  0.6322 B
oT/e, °Ffte o017 es19% . 152 .. Y

 
 

 

28

Table 7. Results of Investigation of Seventh Steady-State Case

 

O
T, = 1100°F

, c
I:'I = 10 in.

Lpg = 4 1in.

Case Conditions Studied
L = 8 ft

¢ =1 X 10*® photons/cuf «gec

 

Te = 50°F

. Lgg

= 2 in.

- by =2 X 102 photons/cu® - sec

 

 

 

 

Bottom of - . Top of  Bottom of Top of
' - Channel Channel ' Channel  Channel
9, Btu/hf' ftz : 16.57 16,57 . 33.14 .. — 33. %
qps Btu /hr- £t 146.7 146.7 1293.4 293.4
9pgs Btu/hreft? 307.1 307.1 . 614.2 - 614.2
qggs Btu/hre £t 9.689 . 9.689 19,38 ©19.38
qs Btu/nrefe? 27.89 27.89 55.78 5578
- q,', Btufhr £ 21,08 18.35 l L
Qps Btufhref£e? 73.58 84.92 |
WL, Mv. 0.1118 0,0955 : "
%, °F 1099.98 1099.98 & S
T, :F 1208.6 245.9 8 8
T, F 203.3 240,.7 9 8
o L2 o o
T, F 100.0 138.7 o .
T, °F 120.9 161.3 £ g
Ts, °F 121.0 161.5 x »
. . o 9
Ty, °F 0.0232 0.0205 2 &
T,-T,, °F - 891.4 854.1 & 8
T,-T., °F '5.304 5.218 g g
Ty-T,, °F 103.3 102.0 | § :'é,
u-T,, °F 20.87 22.59 | -
Ts=Ta, °F 10.1769 0.159
Tooxr F 129.6 167.6
Xp oay? £€ ~ 0.5256 0.4117 - :
arfa, °p/fe 0.8064 0.8088 ¥ v

 

 
 

 

 

'

29

Tables 1, 6 and 7 may be compared for the effects of changing the
thickness of the firebrick insulation from 5 in, to 7.5 in. and 10 in.
The addition of 2.5 in. of insulation decreases the conduction loss by
about a factor of 2, ‘and this addition also decreases the maximum temper-

ature of the concrete by approximately 15°F in those cases with an inci-

dent gamma current of 1 x 10'% photons/cu? sec.

Tables 1 and 5 may be compared for the effects of changing the
total thickness of the steel in the two gamma shields. Decreasing the
total thickness from 4 to 2 in. causesonly-a'siight_increase in the
conduCtioallcss.mrThe maximum temperature of the concrete is increased
approximately 10°F for the cases with an'incident gamma'current‘of'l'x 102
photons/cut'a sec and by approximately 20°F for the cases with an incident
gamma current of 2 x 102 photons /cnf - sec.:

Tables 1 and 3 and Tables 2 and 4 may be compared for:the*effects of
changing the ratio of the-thickfiess-of the steel on the reactor side of
the air channel to theithickness:of the steel on the cencrete gide of the
air-channel."Changingrfrom-4fin.,on the reactor side and-2 in. on the
concretefside to 2 in. on the reactor side and 4 in.'on'the-cthrete side
increases the conductionzloss:only'slightly and increases the maximum
temperature of the. concrete approximately 10°F.

| .Tables 1 and 2 and Tables 3 and 4 ‘may be compared for the effects of
changing the thickness of the concrete and the temperature over the cut-
side surface ofithe'concrete“wali; Changing the thickness of the concrete -

from 8 to 3 ft and the temperature on the outside surface from 50 to 700F

. decreases the‘maximum temperature- of therconcrete about 10°F but the

conducticn loss'is'cotfaffectéd;gppreciably. -
'LCaseeStsdied for Transient Conditicn,g_;i;-'

Eighteen finite difference equations, with the differencing with

: respect to time, similar to Eqs. 32 through 35 discussed in Chapter 3

were written to analyze the proposed configuration of the reactor room

wall for one transient-condition case, The analysis was performed to

 
 

30

determine the iength of time 6vér which a loss of coolant air flow could

be tdlerated before the temperature ofrthe concfete would gxcéedrthe
maximum_allowable temperature.of.212°F. Such 2 loss of coolant air flow
ucould_arise.as a result of a malfunction in. the blower systém supplying the
coolant air. Although natural convection currents would cause some cir-
culation of the cbolant air during 8 blower failure, it was asspmed that
the coolant air was stagnaht during the failure so that the worst case
could be analyzed. Under this assumption, the air channel_séfves-only

as an insulating materialjand-temoves no heat from the wall. .

" The conditions_established;for the analysis of this particular case
were 8 5-in.-thick layer of firebrick inSulatioh,_a,4-1n.-thick.1ayer of
mild steel for the first gamma shield, the 3-in.-wide air channel, a 2-
in.-thick layer of mild steel for the second gamma shield, and a 6-ft-
thick cqncréte wall for the biologicalrshield, A simple cbmputet program
was written to perform the calculations, but the zero-time temperatures
and heat depositions for each segment in the composite wall were calcu-
lated by hand and used as fixed numbers in the program. This computer
program was used only to obtain a first_approximafiion 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 =3.0hr, t = 4.0 hr, and tr= 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 interfial heat generation (reactor shutdown
simultaneous with blower failure) during the transient period. The
éomputer program used to analyze the condition for internal heat genera-
tion is given in Table 8. To analyze the condition of no internal heat
generation, Q2C thrqugh-Q19SS-inTab1e 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 ghown in Fig. 4, and the temperature distributibn,in
~ the wall with‘no internal heat generation during the transient period is
illustrated in Fig. 5. | | -

 
 

 

n

R

- -—————— K . . v e ik mmmr—— e —— e -

  
 

e TiuB & T!0A¢69.6325

31

Table 8. Computet Program Used to Analyze the PrOposed Reactor Room Wall for
the Condition of Internal Heat Generation

 

uuaznju_ILc -

T = 0.001 . -
‘T) & 86,35 o
T2A ' 109,65 o
T&‘ = |32.95
TR T THR02S
7 TS54 = 179,42 '
T OT6A @ 9TRBQ T TS TSI s s s e
T7A = ]H&p|4 . :
 T6A & |B6.D4 T emmemmeme e
TYA = 153, a0
T TTiRA=¢ Wy
TIIA gggoos S
" TIEA 294,94 T T T s s "“”'“ff‘f*f‘f—“‘“""””
) TIEA 296i50 . . -
TUTI4A B IB5L9R T T e e
_TIEA- _553090 ) -
TTER & 728,60
‘ TI7A = 880,72
TTTTIERA ' 1030 48 7
TISA 8 099,90 -
TITTT20 TN I00.00 T T
' Q2C = pg.255 :
Q4C = 0,255
_‘””05C g |32
Q6C = 29,99 7
T R78 ® 2.46. ““f““ —
OBS X 059
UTOS & 2T 11
QIS ® 49,62 : : .
-- - n!'zs B 'ng.ea‘ TOOTTTT OTTTTT O D T T M St emems ST S s e e s o =
RI3IS = 190,084

 

 

 

T QIS o ® '5,09_f'f"ifj; #ff*”*““f“f““*"““-““?_ " T s

Q)1sSS = lfi.b?

 

EPSIL = U, 7 | |
QRAD = (SlGMA/(?-l&PSIL'I,))'!(T|0A+460.D"4 (TflA0400,)"4)

TTR2E ® TRA40. )1 B405° T ITIAS2,*T2A¢Y|)eTj,034083%2C ~ = o
T3IE u T3Ae .oifl405'7'(TdA-20’T3A*TEA!*T’U 034083°Q3C

’ ' ’ . U@'Ulb““

 

 

TS5E = TS5A+0,01B405°T*(TEA2, *TSAeT4AI*T*0,034085°Q5C

TGE = T6A+Q, 066747'T'tT7A-T6A)+0.n|8405'7'(T5A'76A)*T'0r034u83'06c
T7E & T7A469,63252T4(TBA=T7A)¢0,24062°T(TOA=T7A)*T%0,223]8,%Q7S
TEE & TBA4D, ualu7't'tT9A~taA:+59.5325'1-cr7a~raaaoonan-r-o.gzanaa
A ATe0,2231H8)°08S . _

 

   

_ _ A ‘3
T'!TltA*TnnAi¢nvns|o?*r'¢T9A-1lnAt*T'u-eeslal‘
I Cius e

o Tilp = TI{A*69 6325'7'(Tl2A 2.'71lA’TiBA)#T'G.ZZSIBl'OIIS
12 TI28 8 T12A%69, 6325’7 (TIBARR, 97124671 1A)+T 022318128 T
48 TI36 £ TI3A+0+798)0 ST4CTIAAT [3A)469,6325°T(T|2AeT 3A)+T 0, 223181

 

¥ 'uloa .

N4 TI4B & TI4A®3 4TAAST AT 5AT 14A)06,902485T*(T|3AeT 4A) 4T o}, y3gz2*

 
 

32 - _ _ N
Table 8 (contlnued) ) k | o ‘ S .

1> Tisu & T|5A¢3.4744'l'tT|eA-2.'r|sgoT|4A)¢T' 0 93022°QINS -
TiGA*3+4744°To T 7A=2, TI6A+T|HA)¢T*| +93(22°0INS
17 T178 & T17A¢304744°TS0T[BA=2,°T 1 7AeT 0AYST*)s93U22°0INS
18 TIEH & T1BA+6:93245° T (T 9ATBAYSYT, 4744'T'QT|7A'TIBA)‘T' -93022'

°
-y
-
o

"

20V & K B s
201 TIVEW & Vo7
21 TirveM = TIMEH®6),
IF(veR) 29,22,35
3 IFtVvsZ Y RYr297 22731
A1 IF V=3, *R) 26+22,32 o , I SRS
32 IF(Vaq,*R) 26s22,38° — - 0 © T ot
38 IF(V=D,%R) 29,22,34 | L - |
- 34 lF‘v'O 'R’ 29.?2‘35 . i & e s m——— e - - h emr. -——— b — 8 - - - -7-- . m—— e - Ee A A e o 4 . ox
3o IFIV-I.‘R) 290122:36 o , _
— SO IF V=0, "R 293227 37 , | , !
87 IF(Ve9,%R) 29,722,308 o T
“TSHTIF (Ve 0y YR) 39,22y 29 7T T S e e e
22 WRITE(S5],108002(K»TIMEH,THEN)
‘23 WRITE5],20000 ¢T s T2B, 13857485 TSR T6Bs T785T88; 19Bo?TGfl¢TTTfl‘T]28‘
I 7I1B¢TI4BoTl580TleoTl?BcTIBBoT|9807203
2% WRITELST» 3TN0 7 TURAD? —
 IF(v=10+*R) 29,25,2% , | . o .
29 K € K¢ —orm— T ——— s e e ety '
T24 = ¥28 ' , .
"TSA & TR o mrs g o e e o
T4h = T48 | | | e .
—T% Y58 _
T62 = Te8 | o T
T7‘ ‘ 778 - - [ - ——— . i w o mer ba e T w f e — A.-......f..».‘--,“_‘.A.A,‘A.V-._.:......
THs & TBB ’ ' ! : ‘
Tv‘ l TgB - - © - e e rm————— e —— - Lk s s e e———— e e ————- o .._...-7._.. .- PR .
TIOA = TIiIgB ' ,
THA =718
Tiea & TI28 _ o - I
TIZA 3 TIIB - = om o s oo L e
_TI14A = T14B : S |
T |‘A T ISR 0 e emmmeniem e sl e e s
TI€A TiéB : ' ' '
—F 178
TIEA = T}86 | - SR
.T'GA. = T'ga Sl e -— vam = ....-_:-_...—— —— e s wm——n & w _..T — ..._.--—-‘--'.-a.u.‘.-_ - . -
G 70 100 ' | o S
29 CONTINUE
ooy FOFHAT(24H|NUMBER ek ITERATIUNS e .16/?4H ELAPS&D Tth (HOUNS) 2,
T U A7 2R EERPSENTIHEtHIRUTES Y T T T 67772
200U FORMAT(IGHKCELL TEMPERATURES (DEGREES-F)/6HgT| 5 2FB8:323Xs5HT2 8
IFB.343Xs5HTI £ ,FBe3s3XoS5HTE £ ,FB,3,3Xs5HTS & 2FB.,3/6N T6 & ,FB,3
" 293%Xe5HT7 = LFB8,3528Xe5HTE & ,F8, 3.3XJSHT9 & pF8y3»3X)SHT 0% »FB.3/
SOH TIHIE sFB.3o3Xs5HT 128 ,FBs3,3X,5HT |32 1F8-333XO§HT|4' oFB,3,3Xs"
ASHT 5% »F8, 3/6H Tifi' 2FB.3+3Xs5HT 72 oFG.So&X;SH?IB' »F8, a.ax.
Y ORTT T i F BT S IoKsORTE0T FF 833)
J0uv tOFMATCBHEQRAD g 0F|0Q4l|5H (BTUIHR-SO FT)}

 

 

 

 

 

 

 

 

e e B e kn o b - A T T Tt e i i 78—

 
 

 

 

ot marn st Pl - BB i s - P

 

 

et oo

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

33
ORNL Dwg. 67-12003
800
400 } :
LEGEND _ 7
(D TEMPERATURE OISTRIBUTION AT T= 0.0 HRS.
(@ TEMPERATURE DISTRIBUTION AT Ts 1.0 HRS.
(@ TEMPERATURE OISTRIBUTION AT T» 2.0 HRS.
- (¥ TEMPERATURE DISTRIBUTION AT T= 3.0 HRS.
s (® TEMPERATURE DISTRIBUTION AT Ts 4.0 HRS.
w ~ (© TEMPERATURE DISTRIBUTION AT T = 5.0 HRS.
300 —t :
g
&=
at
®
&
W
=4
200
- 100 - , ;
: T_ T : o | s 20 28 30 33 40 4
' m_k fia\' .. _ [concrete eiorocicar smiELDl
: T CHANNELE - . e
FIRST STEEL | - , -
GAMMA SHIELD! - IGAMMA SHIELDl = .+ .
| f'w"ALL' fmcxnss'ses UINCHES)
Fig. 4. . Temperature Distribution in: Proposed Reactor Room Wall

With Internal Heat. Generation Rate Mainteined During I.oss-of-Wall-Cool- :
ant Transient Period. ' . _

 

 

 

   
 

   

 

 

 

 

 
 

34

- ORNL Dwg - €7-12004
T 7 1 T § 7 VT T O o

 

$00 11

 

    
  
   

. 400

 

 

 

 

 

 

LEGEND

TEMPERATURE DISTRIBUTION AT T # 0.0 HRS.
TEMPERATURE DISTRIBUTION AT Te 1.0 HRS.
TEMPERATURE DISTRIBUTION AT Te® 2.0 HRS. |
TEMPERATURE DISTRIBUTION AT T » 3.0 HRS.
TEMPERATURE DISTRIBUTION AT T e 4.0 HRS.
- TEMPERATURE DISTRIBUTION AT T s 5.0 HRS.

 

 

©EEEEO

 

300

 

TEMPERATURE (°F)

200

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

WALL THICKNESSES (INCHES)

‘Fig. 5. Temperature Distribution in Proposed Reactor Rob@:Wéll_
With No Internal Heat Generation During the Loss-of-Wall-Coolant
Transient Period. ' S T
 

 

35
5. CONCLUSIONS
Two basic conclusions may be drawn from the results of the parametric

studies made in this investigation of the proposed configuration of a

laminated wall to protect the concrete biological shield from the gamma

.current within the room housing a 250-Mw(e) molten-salt breeder reactor, a

fuel-salt-to-coolant-salt heat exchanger, and a blanket-salt-to-coolant-

- salt heat exchanger. The’first basic conclusion is that with air used

as the wall coolant, the proposed configuration is acceptable for an

incident monoenergetic (1 Mev) gamma current of 1 x 10'® photons/enf - sec
for all cases considered in which the thickness of the firebrick insula-
tion was 5 in.,or'more. Arsecond'basic conclusion is that the proposed

configuration is nct acceptable for those cases considered with an

incident monoenergetic (1 Mev) gamma current of 2 x 1012 photons/cdaosec

because the maximum allowable temperature of the concrete (212°F) is
exceeded by 50 to 100°F. The values of several of the parameters of
interest in this'study-that were obtained from the cases analyzed for
a gamma current of 1 x 102 photons/cda-sec are given in Table 9.

Based on the assumption that the floor and ceiling of the reactor room
have the same laminated configuration as the walls, giving a total "wall"
surface area of 8276 ftZ, the proposed wall‘ccnfigurationrwili allow the
conduction loss from the reactor room to be maintained at a level below
1 Mw if the thickness'of the”insuleticn is 5 in. or more. Further,

~ based on an air velocity of 50 ft/sec and an air coolant channel width

”; of 3 in., air is an acceptable medium for cooling the wall. L

A general conclusion that may be drawn from the 1imited analysis
made of one transient-condition case is that if the ambient temperature

of the reactor room remains at approximately 1100 F, the proposed con-

",figuration of the reactor room wall studied in this case can sustain a
r'loss of coolant air flow under the conditions described in Chapter 4. for
:'approximately 1 hour before the temperature of the concrete begins to

",exceed 212°F, If a zero incident gamma current is assumed the

"permissible" loss-of-coolant-air time is greater than one hour but less

than two hours.

 
~

Table 9. Range of Parameters of Interest in Studies Made of Proposed Wall With An .
Incident Gamma Current of 1 x 1012 photonslcuf3 sec

Parametric Conditions

 

 

VariaBIe of ' - Minimum_ - Maximum LI | L?S _'LSS j _Lc T
Interest ' Value Value (in.) (in.) (in.)  (ft) - (°®)
Skin AT,°F | | 0.021 10 4 2 a a
S . . | - 0.22 2,5 2 4 - a a
Insulation 726 2,5 4 2 '8 50
AT, °F | A f 906 10 2 -a a a
First steel 2,38 10 = 2 a - a a
shield AT, F | | - 10.9 2.5 4 2 . a a
Second steeleo | | ~0.08 ‘- 2.5 4 2 3 70
Air vertical tempera- f 0.77 _ 10 ¢ 2 -2 .3 70
- ture gradient, F/ft - o 1.57 2,5 . &4 2 .8 50
T L,°F 126 10 4 2 3 70
¢ max’ - | | e | T B | g
- (12%%) - - 205.6 5 2 2 8 50
% maxs £ o ) o s 2 4 3
(T . < 212°F) o 0.58 7.5 2 -2 8 50
MWL, Mw S 0.096 - 10 4 2 8 50
- : o ) | 132 2.5 -2 a a a

 

This parameter has little effect in combination'with the other parameters given, and

the values of the variables of interest are essentially the same for various values of this
: parameter. : :

9¢

 
 

 

"

Ly

37

If a wall of the type proposed is used, the temperature of the con-

crete, T c? ©OF 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 con-
duction 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 10*3 photons/cuf -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-
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 solotion than increasing the thickness of the wall
laminations for gamma currents greater than 1 x 10*% photons/enf - 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 is 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 or heating systems. o

 
 

wi

39

- APPENDICES

 
-y

 

 

41

Appendix A

EQUATIONS NECESSARY TO CONSIDER A MULTIENERGETIC GAMMA CURRENT

'The equetionsrderiVed 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 current
can be represented as a multigroup Current. The equations in which an
incident multigroup gamma Current appears, either directly or indirectly,
must be written to account for this segmentation in gamma energy. - This
multigronp modificatiOn'has beentmade 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.

 

 

_x e |
Q) = ZQ [ s-ape Ph]e (A.8)
- H x(d - i) . x(B, + 1)
Q(x) = ‘;Qoi[Aie P T a-ape U ] : (A.9)
Q= VK8 : - (A.9a)
o é; i.oqui .
T(x) _"r'o + =(T '_To)_ .
Tl Ay A )
e (1 -A) | - x(B, + 1)1
S '_'_,*--z'(ei""“+ 1)“3,‘»,1__-;3' e T T )]
oA L(Q: -1 1- 4, e, L(B, + 1)
oxl_Ti | ”1 MyL(By + 1)]
AR 1)4i1 — o ) O 1)5 (1 e i

(A.12)

 
 

 

42

Q - . - | . . | | —7.—,7 V - -,
o1 Aiui ( nyx(@, - 1)\_ ny (1 - A) g -pi#-(Bi + 1))]
E—— -e ; + T ————— \+e

'.1,‘ Ai Sy uiL(O!i - 1) ' 1 - A uiL(Bi + D0 -
"ii(a - 1)5( L ) B, + 1)2(1 ) . (A.13)

[Q (1 A ) -p.ix(fii + 1) - Qoi s uix(a - 1)]

 

o ZQ il1 .'.';'A . uiL(a ' ) e e
=1(To =T kui [W(l -el T )
A-4)  ule - -l
+ W(l - e ) | .7 (A.14)
a1 e v Dy |
ap = };{j: :Qoi[Aie- | +Q-age T OE Jox b - (A.16)
Q, A i L»(a .=1) , (1-4 ) -p. L(B + i)
q =ZJ-—1-[ L et o) et ]fl (A.17)
T i ! By (ai - 1) B ) ( + 1) -

+1, 7 %W, Y,

Y1 PUey T PGm ) (2.18)
(Qo \
(j) ’
Yo e(3) | ‘
4 Ta = D[ D) L (A.182)
o()) qo(J)i it“g(j)_f ’ | e

 
 

 

 

g

 

43
o QO(j + 1) (qO(j + 1) )(”E(j + 1), )

o(j + 1) Qo(j . 1) o (qo(j + 1)1)(|J'E(j + 1)1) (A.18b)

 

de;'A" . =.'- j #y By (L - A)
-&;x; =-I:- 'T5)+Zkui L (a -1) (Bi+1)

1' Ay {Lo(e - 1)
' [m(“e ]

 

 

B (1 - A, ) -uil‘é(fii + Dl : -
2 ’ 'I:a.4 + Tq, h + .1”
-l Lss | L
€ T T

 

 

 

g e s c TUMH [ ss o
=[5 To* + hT_ + q. + — = - (A.29)
1‘.gr; 1} a sS ~ Lgg - L, - ’
e ! Tt
. 1 c
where
[ mA-A) A g A - uL (o, - 1))
i) B+ T @ -D) |- "¢
(L -A)  euL (B, + D)
' . i i

 
 

 

&4

- 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
~ Kreith.! | ‘ o | |

= k s 5.8‘ 3
b= 0:0% g R Cpefe

wvhere

k = thermal cbnductiyity;of air,'Btu/hr-ft-oF, |

H = vertical length of the air channel, ft,
ReH = Reynolds number evaluated at the_tdp of the air channel, snd.
Pr = Prandtl number evaluated for air.

The Reynolds number evaluated at the top of the eir-ehannel,'

ReH =-H&E ’
where | | R
" U = the bulk air velocity, ft/sec, B
p = density of the air, 1b/ft®, and
B = viscosity of air,llb/ft'sec.
The Prandtl number evaluated for air,
Pr -'E;B s

where Cp = the specific heatrof air at a constant pfessure, Btu/lb*oF.

In the range of temperatures considered, Pr is approximately constant

and equal to 0.72, Kreith's' expression for h wss evaluated for various
‘air-wall meen temperatures in the air channel, and the results are

on the following page.

 

! Frank Kreith, p. 286 in Principles of Heat Transfer, International
Textbook Company, Scranton, Pennsylvania, 4th printing, 1961.

 
 

 

fa

T
100
130
150

 

45

 h
(Btu/hr: £t2 -°F)
. 5.15
5.04
5.04

The meéhvtempététhfe of';he walls_of.théiair channel is expected to
be approximately 130 to 150°F, and a value of 5 was used for the convective

heat transfer coefficient at the walls of the air channel.

 
 

 

 

46
Appendix C

VALUES OF PHYSICAL CONSTANTS USED IN THIS STUDY

Values for the gamma energy attenuation coefficient, ""E’ the total gamma attenuation
'coefficient, B, and the dimensionless constants &, £, and A used :ln the Iaylor bu:l.ldup
fomuln for a gamma energy of 1 Mev are tabulated below. " '

 

 

Materiel (££72) - (£r71) o _PB A
Type 347 stainless . 6.28" '14.08%  0.0895¢  0.04¢ 8¢
steel ' d . d ) d ’ a
Keolin insulating ~ 0.367 . 0.838 0.088 0.02¢¢ 10¢
brick : .
Mild steel 6.302 14.02*  .0.0895° 0.04¢ g¢c
Concrete 1.994 4,554 0.088d 0.0294 104

Values for the density, p, specific heat, C_, thermal conductivity, k, and equivalent
thermal conductivity at interfaces of adjacent mterials, k, for materials in the proposed

laminated wall in their order of occurrence from the relctor cutward are tabulated below.

 

 

' -2 (1b_/ie) (nm/‘:g °p kK K
Material (g/en® ) m n (Btu/hr. ft-ogl (Btu [hr'fl:-"g!
Type 347 stain- 7.8° 486.9" 0.11¢ 12.8¢
less steel ' 0.159
Kaolin insulat- 0.433% 27.03¢ 0.23¢ 0.15¢ S
ing brick ' 0.298
Mild steel 7.83b 488.6b 0.11¢ 26.0° |
| . - 0.0232
Alx 0.060% 0.241¢ © 0,0174¢
0.0232
Mild steel 7.83% 488.8Y 0.11¢ 26.0°
. 0.584
Concrete 2,35¢ 146,749 0.20¢ - 0.54¢ '

 

“E. P. Blizard lnd L. S. Abbott, editors, p. 107 in Resctor Randbook, Vol. 3,
Part B, Johh Wiley and Sons, Kew York, 1962,
hn. M. El-Wakil, p. 223 in Nuclear Power Engineering, McGraw-Hill Book Company, Inc, »
First Edition, Rew York, New York, 1962,

“E. P. Blizard and L. S. Abbott, editors, p. 116 in Reactor Handbook, Vol. 3,
Part B, John Wiley and Sons, New York, 1962. ,

. d"Reactor Physics Constants," USAEC Report ANL-5800, Argonne National Laboratory,

¢Frank Kreith, pp. 533-535 fn Principles of Heat Transfer, International Textbook
Company, 4th printing, Scranton, Pennsylvania, 1961. ° _

¥

 
 

 

 

as

47

Appendix D

" 7SS COMPUTER PROGRAM

- A program. ‘was developed for the CDC 1604-A computer to solve the
equations. (Eqs. 8 through 31) necessary to evaluate the proposed con-

figuration of the-reactor"room wall for the steady-state conditions. As

‘written,sthe TSS (Thermal Shield Study),program”will handle up to five

material laminations, excluding the air channel, and up to eight energy
groups for the incident gamma current. The calculations are performed
inzthesorder described in Chapter 3. For arproblem‘with.five-energy,
groups and sixteen different combinations of laminations (cases), the
machine time LS'one minute and 45 seconds and the compilation time is
56 seconds.; : ,

A Newton-Raphson iteration scheme is used to evaluate T, and Xp max’
The convergence criterion for T, is that the right and left sides of
Eq; 29 must agree;to within_0.0S, and the criterion for X max is that the
right and left sides of Eq. 14 must agree to within 0.10. These conver-
gence criteria could be made smaller with a corresponding increase in |
machine time, but very little more - real accuracy would be obtained be-
cause the program uses the approximate method to calculate the incident
gamma current at each material interface. If more real accuracy is

required, the program could be- modified to calculate the attenuated gamma

| current at each interface and to calculate from this information the -

.incident gamma current at the material interfaces.

"If a vertical temperature profile were known for the interface of

'3f;pithe reactor room and the skin, the - program “could be modified to do calcu-
v*lations at several points up the air channel rather than Just at the top
z.and bottom as it does at present.. Both the setup of. the program and the
-mmanner in ‘which the necessary input data are prepared are explained in

" the following discussion.;qj

The TSS computer program is set up for a given physical situation
with a given photon current incident upon the reactor room wall. The

temperature of the inside surface of the wall is fixed at a given value.

 
 

 

48

The composite wall is composed of;five,matefial regions, and progressing

from the inside surface outward, these regions are (1) a thin steel skin,

(2) an insulating material, (3) thé first steeligamma shield, (4) the

second steel gamma shield, and (5) the concrete biological shield with a

fixed temperature on the outside surface. The 3-in.-wide air channel

placed between the first and secbnd,gammajshields 1s not considered a

'material”region. By calculating a vertical temperature gradient ih-the.'

air channel, the program will calculate at both the bottom and top of °

the reactor room wall the RRE

1, gemma heat generation rate in each materieal,

2. temperafifire'at each material interface and temperature changes across:
each material, | | | RN

3. conduction heat loss from the reactor room to ‘the air channel,

4, radiation heat transfer rate between the walls of the air channel,

5. heat in the concrete conducted both toward and away.ffom the air
channel, and the | '

6. maximum temperature in the concrete and its corre3pond1hg'location.

- The program input deck allows the use of any material in ‘any region
of the composite wall., For a fixed incident photon current, a fixed
inside wall temperature, a fixed inlet air velocity and temperature, and
fixed wall materials, the calculation of a particular case is done by'~‘
selecting all material thicknesses and the temperature of the outside
surface of the concrete wall. At present, the program will allow a maxi-

mum of 32 cases to be run, but it can easily be expanded to handle more.

Preparation of Input Data

~ The first set of input data consists of energy-dependent information
pertaining to the incident photon current and to the nuclear properties
of the materials chosen for each region in the wall. The order in which

the information is supplied is given on the following pége.'

 
 

L1

49

‘Card 1. QSI(I);7Q81(2); e+ QSL(B). - The incident photon current
(Btu/hr-£ft?) for each of eight possible energy groups. o '

Card 2. EMUl(l), EMUl(Z), +e+, EMU1(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(1), AMU1(2), ..., AMU1(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(1), ALPHA1(2), ..., ALPHA1(8). The dimensionless
constant ¢ used in ‘the Taylor buildup formula in the first region of the
wall (the inner skin) for»eéch-of eight poseible energy groups.

Card 5. BETAl(l); BETAL(2), ..., BETAL(8). The dimensionless con-

~stant B used in the Taylor buildup formula in the first region of the

wall (the inner skin) for each of eight possible energy groups.

Card 6. CAl1(1), A1(2), eeey . A1(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., N

Card 7. EMUZ(I), EMU2(2), ..., EMU2(8). The same as Card 2 except
for the second region of the wall (insulation).

Card 8. AMU2(1), AMU2(2),;..., AMU2(8). The same as Card 3 except
for the second region of the wall (insulation)

Card 9. ALPHA2(1), ALPHAZ(Z), ceey ALPHAZ(S) The same as Card 4

except for the second region‘of the wall (insulation),

 card 10. BETA2(1), BETAZ(Z), e ' BETA2(8). The same as Card 5

)-except for the second - region of the wall (insulation)

g Card 11. A2(1), A2(2), eeay A2(8) The same as Card 6 except for

the ‘second region of the wall (insulation)

- Card 12. EMU3(1), EMUB(Z), oy EMU3(8) The same as Card 2 except

~ for the third region of the wall (the first gamma shield)

Card 13. AMU3(1), AMU3(2), ces AMU3(8) The same as Card 3 except

'ffor the third region of the wall (the first gamma shield)

- Card 14, ALPHAB(l), ALPHA3(2), .., ALPHA3(8). The same as Card &

-exCept for the third region of the wall_(the first gamma shield).

 
 

50

- Card 15. BETA3(1), BETA3(2), ..., BETA3(8). The same as Card 5 except

for the third region of the wall (the first gamma_shield). -

Card 16. A3(1), A3(2), ..., A3(8). The same as Card 6 for the third
‘region of the wall (the first gamma shield). o ;- o

Card 17. EMU4(1), EMU4(2),-...;,EMU4(8).'.The same aspCard.Z-except
for the fourth region of the wall (the'second_gamma shield). L

Card 18. AMU4(1), AMU4(2), ..., AMU4(8). The same,as;Cardi3fiexCept
for the fourth region of the wall (the second gamma shield). L |

Card 19. ALPHA4(1), ALPHA4(2), ... 3 ALPHAA(S) The same as Card 4
except for the fourth region of the wall (the second gamma shield)

Card 20, :BETAA(I), BETA4(2), ..., BETA4(8). The same as Card 5
except for the fourth region of the wall (the second gamma. shield)

Card 21. A4(1l), A4(2), ..., A4(8). The same as Card 6 except for
the fourth region of the wall (the second gamma shield). . e

Card 22. EMUS(1), EMUS(Z), caey EMUS(S) The same as Card 2 except
for the fifth region of the wall (the biological shield). ‘

Card 23. AMU5(1), AMUS(Z), ..., AMU5(8). The same as Card 3 except
for the fifth region of the wall (the biological shield). - -

Card 24. ALPHA5(1), ALPHA5(2), ..., ALPHAS(8). The same as Card 4
except for the fifth region of the wall (the biological shield)

Card 25. BETA5(1l), BETA5(2), ..., BETA5(8). The same as Card 5
except for the fifth region of the wall_(thebiological-shield)

Card 26, AS(1), A5(2), ..., A5(8). The same as Card 6 except for
the fifth region of the wall (the biological shield)

The format statement for gll of the above cards is 8F9;0.5”Since'
only the first 72 spaces on each data card-are'used5sthe_last‘eight'may
be used for identification purpoées.' If fewer than eight energy groups
are used,:the unused data fields may either be punched with a zero or
left blank. In either case, the energy-summing DO loops subscripted
J, K, L, and N must be changed to correspondttO'the number of energy
groups used; that is, if there are six energy groups, DO 100 I = 1,6;
and K, L, and N are also 1,6. If the DO loops are not changed to. corres-

pond to-the number of energy groups used, division by zero will occur. ©

 

 
 

 

Ǥ

 

51

- The next set of data-entered'isuenergy'independent'and is’assumed
to be constant'overfthe'rangedof'temperatures'covered in the program.
This information should be given on the two following cards.

" Card 27. CON1, CON2, CON3, CON4, CON5, TO, HT, and HF. The thermal
conductivities (Btu/hr-ft?offi'Of the meterialsrin'eachdofithe five regions
should be entered in the first five data fields. The temperature on the
inside surface of the reactor room wall, TO in OR, the height of the
reactor room, HT in ft, and;thedtilm coefficient on the sides of the air
channel HF in Btu/hr £t2 - F, should be entered in data fields six through
eight. The format for this card is the same as that for the previous
26 cards (8¥9.0). | ' o

Card 28, TA EPSIL, VEL, ACHAN, CP, RHO, and SIGMA are respectively
the inlet air temperature, R the emissivity of the surface of the air
channel (dimensionless and assumed to be equal for both sides of the air
channel), the velocity of the air, ft/sec, the width of the air channel,
ft?, the specific heat of air, Btu/lb F, the density of air, 1b/ft®, and
the Stefan-Boltzmann constant (Btu/hr-ffia-oR?). These values must be
entered according to format 6F9.0, F18.0. Again, the last eight spaces

can be used for identification.

Preparation of Case Data

Once the input data hayefheen supplied, one card must be prepared
for each case to be run. ,This;cerd;COntainszELl, EL2, EL3, EL4, ELS,

-and'TG' ELI through ELS-correspond to the material'thicknesses (ft) to
,be used for each of the five regions in ‘the wall, and T6 is the tempera-

ture of the externel surface of the concrete biological shield in °Rr.
The. format 8F9. 0 allows nine ~spaces for each data field and the last eight

spaces for identification.. For 16 cases, the cards could be numbered

29 through 44. Numbering is for the user s convenience and is not re-

'—quired; fThe first DO loop in the program must’ always be changed to DO

5000 I = 1,N where N is the number of cases to be run. All cases must

have the same air temperature, TA, and the statement immediately

 
 

 

52

following DO 5000 I = 1,N must be written to correspond to the air
temperature used. The DIMENSION statement containing EL1(I) through
EL5(I), T6(I), BOP(I), and BAM(I) must be checked to see that .a sufficient
dimension size is given to allow all of the cases to be run, BOP(i) ond

BAM(I) are dummy variables and may be left blank.
'Typioai.bomouter Sheets

The assembly of the control cards, deck, input data, and case data
cards for the TSS computer program is illustrated in Fig. D.l. Typical |
data for 32 cases to be run with one _energy group are given in Table D.1l.
The output data at the bottom of the air channel for one case are given
in Table D.2, and the output data at the top of the air channel for the

case are given in Table D.3.

f

 
  

  

53

 

ELI(IG) ELZ(IG) EL3(I6) EL4(16) ELS(16), TE(16)

ELIUIS), EL2(15), EL3(15), EL4(15), ELS(I15), T6(I15)
ELI(14), EL2{I4}, EL3(14), EL4(14), EL5(14), TE(I4)

ELI(I3), EL2113), EL3{i3), EL4{13), ELS{13), T6l13)

. _JELA(IR), EL2(12), EL3(12), EL4(12), EL5{I2), T6(I2)
ELI(1N), EL2(I0), EL3Q11), EL&(1), ELS(11), TE(11)
‘] EL1(10), EL2(10), EL3{10), EL4(10), EL5(I0), T6(10)

ELI(9), EL2{S), EL3(9), EL4(9), EL5(9), TE(9)

. ORNL Dwg 67-12005
44
43

42

4
40
39

38

37

 

ELt(8), EL2

8), EL3(8), EL4({8), EL5(8), T6(8)

36

 

 

 

ELI(T), EL2(7

LEL3(7), EL4(T), ELS(7), T6(7)

33

 

  
   

ELI(6), EL2(6) ELS

 

 

LAS{), AS{2)
BETA 8(1), BETA 8(2),

TARU ST, AMU 5(2)

. [EMU (i), EMU 5(2),
- {asm), ae(2),
[BETA 4111, BETA 4(2),

6), EL4{€), EL3{6)}, T6(6)
ELI{S), EL2(5), EL3(5), EL4{5), EL5(5), T6(5)

JEL {4}, EL2{4),EL3(4),EL4{4),ELS(4), T6(4)

-JELI(3),EL2(3), EL3(3), EL4(3), ELS(3), T6(3)
EL1(2), EL2(2), EL3(2), EL4(2), EL5(2), TE(2)

ELI1), EL2(1), EL3(1), EL4(1), ELS(1), TE())

| TA, EPSIL, VEL, ACHAN, CP, RHO, SIGMA _

CONI, CON2,CON 3, CON4, CONS, TO, HT, HF

 [ALPHA 8{1), ALPHA B(2), — — — ALPHA 5(8)
EMUS(8

----- BETA4(8)

34
33
- 32
3t
30

BETA 5(8) -

AMUS(8)

 

JALPHA 4(1), ALPHA 4(2), — - = ALPHA

4(8)

 

 

JAMU 4 1),

AMU 4(2), = = =~ = = ~AMU4(8)

 

 

 

A3, A3(2), — —.
BETA 3(i), BETA 3{2), = — — — - BETA 3(8
JALPHA 3(1), ALPHA 3{2), = — — ALPHA 3(8)
AMU 3(1}, AMU3(2), = = = = = = AMU 3(8)
TEMU 30}, EMU3(2), ~ - — = = = EMU 3(8)
A2(1), A2(3), = = ~ = = ~ — — — -A2(B)
8ETA 2(i), BETA 2(2), = — — — — BETA 2(8)

 

JEMU4(1), EMU 4(2), ~ - — — ~ -EMU 4(8)
- A 3(8)

 

2(1}, ALPHA 2(2), — — —ALPHA 2(8)
), AMU 2(2)
, EMY 2(2),

 

 

 

JAI), AH{2),

AMU 1{1}), AMU §(2)
EMUIN, EMUI(2), = = = = = . EMU I(8)

 

—————————— Al(B)
|BETAI{l), BETAI{2), — — — — — ~BETAI(8)
JALPHAI{1), ALPHA 1(2), — — — -ALPHA I{8)

 

 

 

 

— [asin,qsH2), = — — = = = -~ ~ @S 1(8)

 

/ : [% Execute

JAAAAAA END

 

 

 

 

 

 

 

 

 

 

 

 

   
    

  

 

-
]
b
1
I
!f
J_AAAMA PR(D—GRAH AAAA
o FIN, LA E,G. I--I-—-Pabsnm NAME ,
7 c@@P AAAA, AAA, AAA, AR o
cuanez ' fi|:m.u= Rzauzsrso' o
NUMBER . PROGRAM NAME @ - -
St useu‘s lNlTlALS R
"Fig. D.1.

'Aissembl_;.y of Data Cards for TSS ,Compu'tef Progrém.

 
 

 

 

54

. -
- —~ Nt e o s an a t o h e i e e o Ak e = tham e et — C e e o e w
- -

_m_.-Ihble_n.l.m_lypicalwnata Ior 32 Cases Witk One Energy Group for the. ISS _ -
Computer Prqgglm ' '

T PREGRANYSS

‘ "“"‘%*!E5%l%%‘%gE}§lglEHUTTBT"IFU’F"“‘IFHT‘r :
- VENST 1T8Y, T(B8¥, & i * R .
"rj;“]EHLZGB)c AMU2(R), ALPHA2(8Y, BETA2(8)s A2(B)» EMUZ(B)s AMUI(8Y,
~ 2ALPHA3(8Y, BETA3(g)e A3(8)s EMU4IB), AMUG(B)» ALPuuqtaa. BETA4(8),
o 3AG(BYs _ENUSEB), AMUS(B), ALPHAS(8Y, BETAS(8)s AS(E)
- DIVEMSTON ELJ($2), EL2€32), ELstszf’“ELacsz)c EC?T3§70'13‘325.
. BGF (32), BAM(S3 ,
IFENS]EN QDEP g 6)s QVItai. 206 2Té7, 3
_._ ._10V3(&), ODEP3(g)s 054(51- 0V4le), QDEP4(s), 055(6). ovstgio -
20DEP5(8). B(&), Di(63s ET(E), p2te), E2¢6)s Fil6), F2UEI. FSl6Ye |
__3FTR(6)s SUM(g), SUHPsgii_RI(E).Vflfillé)n_flg(éfo RE2(6) o
READ tspg, luflfl, tas} ¢ ERUE ., aMU| e ALPHA] ljtfll ’
tA| o ENU2  , AMU2 o ALPHA2 , BETA2 o+ A2 , EMUY .,

2AMLI o _ALPHAS HETA; ¢+ A3 _ o ERUCT ARUE o ALPHAG o

38E1A4 s A4, EMUS » ANUS - , ALPHAS + BETAS , a5 ' o o
READ (50, 1Qr0Y(CONT, CONZ, cuus. CONd, CONSe YO, WY HFY 7T -
__READ (5g4 1001)¢Tae EPSILe -VEL, ACHANe CP, RWO, SIGMA) = - C
T READ(Sps TOO0OVTELTCIY s ELZUT)» ELI(DY ¢ EL4111. ELSTIY,
1BOFCY), BAM(1), l=(s32)
c BEGIM MAIN FROGRAM
De 5q0p 1=1.32 '
TA = 540,
ELX] = ELI(])
ELx2 = ELE(])
ELX3 = EL3(])
EL¥4 = EL4(])
ELXS & EL5(])
Téx = T&E(1Y
QDEPT! O
ODEPYT2
QDEPYT3
QDEPTY = . i
' _QDEPTS =
c gALcuE‘Yfufi“?r“EfiURcE_YE‘ Nn‘GIH?K‘HEKT'DEFBSITTBN"TERRS‘—“—‘““‘
8 180 Jt T,

T avi(y) & aSI (Y ENUTTIY

2 ODEFTlJi € 0V|(J"‘((AI‘J"EKPF(ANUI(J"ELtl'(ALPHA[(J"].}),/

1CAYUT LI (A Al "l 1e®A

ngjjjffajgjjJ"(BE?AI!J"l 1)e GIAI(J)!ItAFUIIJ)'(ALPHAIlJ)-|.!)-

30|.-AttJ!)ItshuutJl'tBEfaltdiol.t)s)

3 052()) = 0S)tJ)«0DEP)EN)

4 GVz(J) = 0S2(J) *Emli2(J}

5 QODEP2(J) = uvzlJ)'ttcaalJ)'ExPrtAMU:(J)'Esz‘(ALPHAZGJ)-|.))}I
1CAarvu2TOY*CalPHAZT T vy, teobcly (=A
e...:a)g(nnuthi'tegtsth)ol.fi)s-t(aatJ)alcnnuztdi'tsLPHAth)-|.)!
3-(|.-Az(J)’lcanu2tdl'teETA2(J)¢s.l)i) _

©_0S3I(J) = 0S){JIn0BEPILJ)=0DEP2(Y) o
7 GVItJ) & QSI(J)EMUILS) -
8 GDEP3()) = OV3t )'t(!AS(J)'EXPF(:MUS(J)'ELXS‘(!LPHAStJ)-|.))!I :
TCAMUSCUY *CALPHAZTE LI | o))l ) o=a3t ) ) EXPF(=aMUIT ) PELXI*IBETAS(J
2%, )))I(AHU}(J!‘CBEIASQJS*L-))!'tCASGJD)I!AHUS(JI‘(ALPHA;(J)-;.)i

 

  
  
 

     

   
 

82,

 

 

 

        

1/1

 

 

 

 

      

 

3-(l.-AS(J))I(AuUSlJ)'!BEYASlJ)ol.ill)
_,_PLYA___ELxANELK!
QDFTS(Y)Y = QVS(J)'(((A4!J)'EXPF(IMU4(J)'ELXG‘(ALPHA4(J!'|.)l)l
LCAVUAC )Y *CALPHAGC IR o))l il ,=Adt ) ) EXPF(eAMU4( ) *ELXC*(BETAL(J)

2+|.)3)/(1HUQ!J!'(BE714(J)¢3o)))-((14(4))I(ANU4€J)'(ALPHA4(JI-I.))
eha 1 JS(REYAL(J)el, )’)’
oaep4tJ) = QDPTS{J)sQDEPILY)
e _ELX4 T _ELX4eELYXY
12 0S%tY) = 05|tJa-nnEPl(4)-GDEchaa-nDEFstJ:-anEP4¢J!
_____ LS_0VELJ) & QSSCJYEMUSLS) ' o :
I; onspstJ) £ 0SS : ' s

pYj«0DEP] (D)
Y6 ODEFTZ & GDEPT240DEF2LJY o/

 

 

 

 
 

 

 

 

-

.3

€. _1VeRaTjoy PRUcESS ruR Te.

G2-F T cr1't1t'v11tcvz'ttwtrt't1a-fa1-Hrfttwofifip%q-era————————~»fw-

55

Table D.1 {continued)

_17 ODEPYI3 = GDEPT3+ODEP3(J)
18 ODEPTA = QDEPT4+QDEF4(J) , _ ,
19 QDEPtfi_fi_flDER.E*BDEPB‘J! : — o .
108 CEATINUE ' o _
20 K7=0
¢ BEG]WM CALCULAT!ON Ffln THE REACTOR SIDE 6F THE CHaNNEL
21 GCEN = ((Tp~TAYeQDEPT {2, *ELXI/13.%CON|IeELX2/CON2SELXI/CONI® ./
THFY=NDEPT2% (2, ELX2/ (3, *CONZI*ELXI/CON3® | /HF )*QDEPTI® (2, 9ELX Y/
_*gts.'cou3i¢1-(@5)!/!5inlcen1oepr/ceuatELxSIcunsol /WPy
22 DELT) = tGCBN*?.'GDEPTtls.)'ELIIIcHNl '
€ {N¢ CARD NO, 23)
24 TOF = TO=460,
_._25 TiF_=_TDF-DELT)
26 DELTD = CQCGN+ODEPT1*2.'QBEPTEIS.)‘EszlCONa
_ 27 _T2F = Y F=DELT2 T
26 DELY3 = cocun*nnEPT|woneprzoz.-ooeptsls.)'Eanlcens

e e e e r .+ r——— At wat R T e s e

 

; 29 T3IF = Y2F=DELTS
: 30 DELT4 = (QCON*QDEP T+uUpD P ZOODEPTsilHF

31 _TAF ® TAw4b0,. o
c CHECK FOR UNACCEPTABLE HEAY connucTIsN cuan! NS

32 _IFCOCON) 3005033.33

33 CONTINUE .

34 JF(DELT|) 3005,35,35

35 CONTINUE o

36 IF(DELT2)Y 3005,37,37

37 CONTINUE .

38 IFCDELTI) 3005,39,39

39 CONTINUE .

40 1F(DELY4) sonsiql 4l

41 CONYINUE

42 BT = U, e
€ BEGIM CALCULATION™ FHR THE concneve STDE ur THE CHANNEL
A3 DB 200 kst
44 B(x) = tavstk)lthnustx)"2))'((CAHU5¢K30¢|.-A5tK)))ltl *BEYAS(K)l

w(AMYSIK) "ASE{K) )/ (ALPHASIKI®] ,3)e (T o ZELXS) 2CLASCK)Z(ALPHAS(K)»i,)
2%%2) (| =EXPFLANUS(K) ELxS'tALPHA5¢K: |.:):o TeohS(K Te®

 

 

 

 

 
          

T 45 BY = BT¢B(K)

__200 CONTINUE .

46 CF| s S13MA/t2, /EPleni.) ,

47 CFz = HFol.ltELx4IcUN4+ELXSIc0N51

46 CFY « (TGX*ELXS'BTIGON5!2-‘ELX4'ODEPT4733;‘EUH?TT7TECY?7EEF3*EL25
LCENS ) .

49 K9 = 0

50 T4 = T
51 13 = 13F*460,

53 FT4P & 4,°CFi®(742°3)¢CF2
54 TF(ABSF(FT4)=0,05) 58+58,55
55 T4 = T4eFT4/FT4p
56 K9 & K9ej
57 GO 168 51 -
- 58 COATINUE
59 ORAD = cra'173'04-14-'a)
60 OCCP = HF‘(T‘PTAJ-ODEFTQ-QRAD
61 DELYTS = (T4=YA)

~""62 DELTe ¥ tELx4'nccpicoN4)oz.'Equ-anEPTazcs.'canfr“‘““"“““‘“"“*‘*

__ 63 TAF & T4e4&D, - —
T 64 75 @ T4«DELTE "
_ 65 T5F = THe46Q,

¢6 TéxF & YéXedagl,

 

 

- € _(NC CARD NUMBERS 67'73)

7 ' cmt s i e - e e e feeee e o mmmme— e

X =z 0,
72 K3 = 0 e e e
78 FYy = @, - ‘ T - _ - T——

 
 

 

 

 

56

Table D.1 (continued)

7‘ SUMY E O,
75 SUMPT = O,
C_ _‘CALCNLATIUN raR LOCATIUN _OF ugx;uun concnste teflpgagtung
76 Do 300 LE{.T
77 DIELY = =(QVSIL) *ASILII/ZCANUS(L) “(ALPHASIL) =1, n
T8 ETCLY £ AKUSILYC(ALPHAS{L)~1 42
7% D2eL)Y = GVSGL"Cl.'ASCLiiltlfiustL)'l|o0BFTA§¢L”)
U0 E2CLY ® *AMUSTL)®( 1+ *BETAS(L)) - ,
CBE FJCLY = QVSILIZ(CANUSIL)®*2)*ELXS) . .
82 F2(L)Y = AstL"texPrtEi(t"ELxs’-u.s/ttALPuast‘i-n.#"zi
___“ggmgslgl;gkgllzigng)'texpr¢52lL’°ELxs>-| )I¢t|.¢BETAs¢L)$"2’ -
B4 FTYFIL) = FIILIS(F2ELYCF3(L))
E5 FT = FT oFTPIL)Y
“"‘E3‘§UfiTtT‘?‘ETTITTEYFFTETTrTTYT?EfiTti?EiPrteatL:-x:
_ B7 SUMT = SUMT e SUM(L)

e i it

 

—— . p— ittt

 

B 1 surpiCT"i“EutEi*DllL)'ExPrtél(L)°x:4E§¢LS'Dth1'EXPrrEéTtT‘iT“*“‘-

£9 SUMPY = SUMPY*SUMP(L)

300 CONTINUE _
$0 FX = !ctexors)IELxsioGSUnT‘FT)ICHus
§1 FXF s SUMPFY/CONE .
$2 !F(ABSF(FX!'Q}ln’ 95096!93-

93 K3 = K3¢] :
___ 94 X = X~FX/FXP_
T 95 Ge T8 73
$6 CONTINUE
Y7 XTrAX & K
98 SEnMT = 0, -

C CALanITon er"naxlnun CONCRETE rgupengrune
9% Do 4p0 Nei, )

101 RjINY = nvscnl'Asffi)7(iAuu5¢N:"aj-tflLPuasifl)-i )"2))
182 REIC(N) & (T.eEXPFLEJEINY® XTMAX))

i (N} & AVS(NTS(l,~ N} . _

104 REZAN) & (j,eEXPF(E2(NI® XTHAX)) -

105 SOMT £ ssnronstufinelI“T"RaiN)-fiszth’trTP(ui' xrnax :

400 CONTINUE .

IB6 THMAX & TS5+XTMAX '(Téx-TS’IELXSOSGntIcONS -

107 THAXF = TMAXed6D,

€ CALCULXTION ®F ATR TEMPERATURE AT TUP OF XIRCRANNEL

ip8 DELTeL = (ODEPTIODDEPTQ*QDEPTSOCPEPTQ'OCCP‘URAD'OCON’/(VEL'ACRAN'
ICP*3600, *RHO)
106t WRITE(51,2007)¢1) -
, IF (x7=1) 1121,499904999
3000 MRITE(S{»2000) CELX1eELX2,ELXS,ELY4,ELXSs TEXFoTAFY
3001 wn:tstsg.2gg9:cnoept;.onspra.unenr,.nneprq.QDEPTsoocfirifih“b.E oNT
2 W )¢ TiFeT2F,T3F,Y4F, I5F) ;
3063 HR!TF(SI-2004 (DELTI- ;
__3DD4_WRITE(S), znn;)L]HAXF.XTMIX-DELTUL)
109 K7 =2 KT+
41D IF(K7=2) 11155000,5000
T NIY TA = TaeDELTOLOKT
112 6o Te 2|
$121 WRITE (51,2008}
— 60 _Yn 3000
4999 WRITE(S1,2009)
Go_Ye 3000
3005 WRITF(S|+2007)())
IF (w7+1) 4nn515096040fl6
4005 WRITE(S1,200R) -
___w___HBJTE_51!Znfl§"EL_lifiL!aoEL*S-EL!4-ELXB'T6xf_I_£
Ge Tm S00D
4006 WRITE(51,2009)
' #RITFtsl.zuue’csLxloEan.ELxs.ELX4.ELKS.Taxrarnrfi
5000 COMTINUE - :
1000 FornaT(8F9,0,8X)

10D} _FORMATCEFS,0,FiBe0o8X)

 

 

 

 

 

 

   
       
 

 

. e . P - A B MV am

 
 

 

57

Table D 1 jpontinued)
2000 FORMAT(SIHKTKIS CASE HAS THE FULIUH!HG PHYSICAL CHARACTER[ST!CS ’
_A/77 30K LAMINATION THICKNESSES (FEET) / BHOSKIN & ,F6,3,5X,9H INSU
2L.8 ,F6,305Xs15H FIRST STEEL = 2F§,3:5%s j6H SECOND STEEL £ ,F6.3s
____ 35X.)2H CONCRETF ® sF6430 /77 26H EXTERIOR CONCRETE TEMP 3 ,FS,. 10

T 42X.12 (nEGREEfiirT"TdX.zuH EfioLANT ATR TEMP ® ,F5,1+2Xs I2H (DEGREE
- 5SeF) /77)

2002 FflRHAT(béHKGAHMA HEAT nhPUSITluws IN EACH SEPARATE LAHINATION (BTU
_§/HReS0 FT) /RHOSKIN = sF0,3,2X,9H INSUL £ ,F9.3,2X,I5H FIRST STEEL
T2 5 2F9,322Xs 6K SECBND STEEL = ,F9.3,2Xs |8H CONCRETE (TOT) = ,F9.3
3/24H RETURN FROM CONCRETE = ,F9,X,2X,27H RADIATION HEAT TRANSFER =
4 ,F9.3,2%+37H COGNDUCTION LASS FRAM REACTAR ROGM = ,F9.3 777)

2003 FORMAT (35HKINTERFACE TEMPERATURES (DEGREES=F) /2 HOREACTAR RAOMASK
1IN = 2F9.3,15X,14H SKIN=INSUL « .r9.3a|5x.2|H INSULFIRST STFEL =

.. .2sFS,3 /19K FIRST STEEL=AIR = ,F9,3,13X,20H AIR=SECAND STEEL e,
3F9,.3,13Xs25H SECHBND STEEL~CONCRETE ® »F9,3 //77):

2004 FORMATIS2HKTEMPERATURE DROP ACROSS EACH LAMINATIAN (F-DEGRFeS) /
IFHOTO=T| & oF7,4+2X0 9H T|=12 & qu 412Ks9H T2oT3 € +F94422Xs6H 13
2°TA & ,F9,4,2X,9H T4=TA 3 ,F9,4,2X.9H T50T4 & ,FG,4 #//)

200% FGFMATCSZHKHAXlMUH CONCRETE TEMPFRATURF * ,F9.3,2X,|2H (DEGREES»F)

1 /8SH DISTANCE FROM CGNCRETE-GTEEL INTERFACE TO LOCATION OF MAXIMUM

"2 TEMPERATURE IN CONCRETE = #F7,4,2%,7H (FEET) /48H VERTICAL TEMPER™

. 3ATLRE GRADIENT OF COBLANT AIR = ,FA.4+2X,|5H (DEGRFES/FOBT) ) .

2006 FORMAT(S53HITHIS CASE HaAS THE FOLLAWING PHYSTCAL CHARACTERISTICS »

.. Vll7 30K LA"INATIUN THICKNESSES (FEET) /BHOSKIN % »F6.3/5Xs0H 1~suL

: T2 SF6,325Xs 15H FIRST STEEL ® ,F6.3+5Xs|6H SECOND STEEL ® ,F6.3»

3%Xs|2H CONCRETE & 4F&,34 /7/ 26K EXTERIOGR CONCRETE TENP ® ,£S, |,

: 42X, |24 (DEGREES»F) s 14X,20H COOLANT AIR TEMP = 2F8, 1 s2Xsi2H (DEGREE™
5SwF)-/// 93Ho THIS CASE GIVES WEAT CONDUCTION BACK INTO THE REACTO

"'””'6R FUHN—INB“TS'THEREFGRE"NUT fiCCEFTIHLE'i T

- 2nn? anfig;gbg|gg§ ,13[
2008 FORMAT(JI7HKCALCULA T BOTTEM OF: Alfi_EHANNEL)

zonv EURHAT¢34HKCALCULA?10N AT 6P Uf‘jlfi CHANNELY = . . . .

 

 

 

 
e

e e et e oo imm amnTADL@ Do2...TS8. Output .Data.at the Bottom of the Air Chamnel for.One Case ' e,
CALCULATION AT BOTTOM OF AJR CHANNEL -

 

h mes e e am p mem Semm ik el e AR ERAY B - 2w AN g e el ¥ e Bar R ds s m il o e S deo Smmp—— A AR el 4 e e tme . = e - A —

'TflIS“CISE”HKS"fFE'FULfiOH1NG"PHYSICAEmCHARACTER!ST!CS'" -

e et e n - T e eaee e e e mmen L e e e me e e 4 ey e eSe  m  n eeee R e L S e L s e 7T e ——" s o 1 e | 20 4 A+ vt i e e s e i e S e

LAMINATION THICKNESSES CFEEY): . . ‘ :
SKIN = ° ,008 INSUL = 0208 FIRST STEEL » .250 SECOND STEFL . 250 CUNCRETE»- ‘8000

¢ b 4 7 i o e A e ¢ s 4 4 e o Frder b e e . S s o o i mem k£ o e b gt bt ol i e—————— - B - A Al el e 2 S S 4

 

—— - AR dres hmam = A R e

"EXTERIOR CONCRETE TEMP & 53,0 ~ (DEGREESF) COBLANT WIRTéMp % Tg0TE TDEGREES-F)‘ '

 

 

—— Cerrrem 4 e e . - .- e e ke e . . C—

 

“BAMMA“HEAT DEPOSTYIONS™ TN EXCH SEPARATE CAMINATION (BTUZHReSE-FT)—— — ==~ ——— T e
St T N3 T RO R —— RO A TR 3O TR 3G EOMN DS TR —e——— 357723 —CONCRETE—TOTe—36v 705
_RETURN FROM CONCRETE ® 27,470 RADIATION HEAT TRANSFER ® __ 172,6(8 _ CONDUCTION (OSS FROM REACTOR ROOM = 5334620

 

8¢

- o o - o —— w1 m e mmtem s e s e e = e i v s v Sream C % n - e et o - Ml rilh sk ke b R £ L . A 8 AR B o M - Ll g % R LG mep Mt W amermmi o

 

— ARl £ i

 

- e e oy o e

 

 

_INTERFACE_YEMPERATURES (DEOREESeFY I e
REACTOR ROOMWSKIN = {100,000 SK‘N'lNSUL . I099g779 - !NSUL"!RST STEEL s 3010936
FIRST STEEL=AIR s 293,888 7T UilAeseconp STEEL = ja¥iis2 T ‘“?"T*‘"‘“.‘f‘““.‘.‘9_sco~b“srfisf‘cofié'fls75" TYATEss T

 

et . et Y A A e '

 

 

 

 

TEMPERATUAE DROP ACROSS EAGH LAMINATIGN (FeDEGREES)

 

 

 

i ot - s . i s s e 8 o B e b S Pl o AR e PO

 

“WAXTHUM CONCRETE YEHPERAYURE ¥ T158,818 wEGREEa-r) .
DISTANCE FROM CENCRETE~STEEL INTERFAGE TO LACATION OF HA&IHUH TEMPERATURE IN CONCRETE =  ,5153  (FEET)
"VERTICAL TEMPERATIRE GRADIENT OF COOLANT AIR & ™ |+5649 (DEGREES/FOOT)

'} (f. ‘_ ’ ’ . ‘ e S - - o I o o - '(0’._-f‘ )

 

 

 
 

e (m . _ ) : A n (‘3

 

CALCULATION AT Y0P OF HR CHlNNEL

S

 

Tablo D.3. '1'88 Ougput Data at the Top of the Air Chanmel for One Cue

THIS CASE HA’S’ T!-'& FOLLQWING' PHVSIGA“L""CHKflACfEfii”STiCS’ e

LAMINATION THICKNESSES (FEET) ‘ L 4 _
SKIN = 4005 INSUL ® 208 FIRSY STEEL w250  SECOND STEEL » ,250  CONCRETE &: 6,000

—_— i mm—— ke s . [ fa e cesae h e e MR L etk e e a

 

 

 

"Ei?éfiiifi'Eoflcnsvefjéfifif-‘ 500  C(DEGREESsF) TEOBLANT ATR TeMP # (75,1 (DEGREESSF)

 

 

it -
. e . gy s - et 4 -

 

GRHHA HEAY DEPOSTFTONS YN EACH SEPARATE LAKINKT{ON tBTUZHRSSO FTy— =~

"t

   

  

. -

RETURN_FR®M CONCRETE 3 21,989  RADIATION HEAT TRANSFER % 209,017 _ CONDUCTION L 0SS FROM REACTOR ROOM ¥ 48as574

———— e e i - - 4 v dme wmr o e s amamen s s i mm——dn = N i e ¢ s R A G £ A b s am s aARA A b mcke o . e e skt Mo oo e i

 

INTERFACE TEHPER ATURES (DFGREES'F’

REACTOR RAOMsSKIN ® 100,000 __SKiN®INSUL 8 1099,798 ____INSULTFIRSY STEEL 5 367,192
FIRST s1'EEI.....AIR 5 359,547 j AJReSECOND STEEL = 228,462 . SECOND STEEL-CONCRETE 8 2284902

 

 

 

 

 

 

 

‘RIYTEHE"EENUFETE“?EflFERTTUFF‘““‘“F35'TUS"“TUF§WEEs-r)
DISTANCE FROM CPNCRETE«STEE|L INTERFACE YO LACATION OF nAx!HUH TEHPERA?URE IN_CONCRETE =  ,3568 (FEET)
VERT]CAL TEMPERATURE GRADIENT OF COOLANT AIR »  |.5440 (DEGREES/FOOT)

 

66

 
 

O

el

a-b

ch

o and B

o it a;'m

® oo o

60 , : _nwgf

Appendix E o - | ?f?‘

NOMENCLATURE

dimensionless constant used in the Taylor buildup equation

unit area of reactor room wall, ft2 |

specific heat at constant pressure, Btuf1b:°F

energy of incident gamma curtent, Mev

vertical length of air channel, ft

convective heat transfer coefficient, Btu/hr -£t2 -°F

thermal conductivity, Btu/hr - £t-°F

equivalent conductivity where the subscripts a and b refer to

any two adjacent materials

thickness of a material lamination

width of air channel (distance between adjacent Surfaces of -

first and second steel gamma shields), ft _ |
heat conduction rate out of the reactor room to the air channel, £
Mw o

volumetric gemma heating rate, Btu/hr:ft®

heat conduction rate out of the reactor room tcithe air channel,
Btu/hr- £t3 - - |
rate at which the gamma heat generated in the concrete is con-
ducted back toward the air channel, Btu/hr- £t2

rate of radiant heat transfer between the walls of the_air cfiannel,
Btu/hr- £t2 | N
temperature, °F L

bulk velocity of coolant air, ft/sec | | |
distance perpendicular to the surface of the reactor rcom wall,
t | o | o o o
dimensionless congtants used 1n ‘the Taylor builkup equation
surface emissivity of walls of air channel'

time, hours | _ .

total gamma attennation coefficient, ft-!

gamma energy attenuation coefficient, ft-! :-17 | f i | &;Jh
 

- 61

* p = density, 'lb"/‘_r"ta- 7_
0 = Stefah-BOlthann constant
$o = incident gamma current, photons/cuf *sec

| '-SubScripté-Used With Terms

0 through 6 = numbers;denotifigra lamination interface as illustrated
| in Fig. 2 and usually associated with temperature, T
= air - | | |

= cohcrete |

= insulatiofi-?-

= energy group 

= lamination

? e -0 P
|

| o = skin lamination on reactor side of wall
- o FS ='first-éfeel;gamma'shield |

_, 8§ =Secbnd'5teei_gamm§ fleld
total |

3
0

 
 

e
 

 

 

wi

. w7

FL

24,

11.

13.

14.

15,
16.
17.
18,
19.
20,
21.
22,
23,

2.

61,

62,

18.

63

 

ORNL TM-2029

Internal Distribution

Bender . o 26.

R.V

L.

 

_Tennessee, Knoxville, Tennessee

M. Moore

C. E. Bettis | 27. H. A, Nelms

E. S. Bettis 28, E. L. Nicholson

E. G. Bohlmann 29, L, C. Oakes

R. B. Briggs ' 30. A. M. Perry

W. K. Crovley 31, T.W. Pickel

F. L. Culler : 32-33. J. R, Rose
8. J. Ditte 34-35. M. W. Rosenthal

H. G. Duggan | ~ 36. Dunlap Scott

D. A, Dyslin ~ 37. W, C, Stoddart

D. E. Ferguson 38. D. A, Sunberg

W. F. Ferguson 39. R. E. Thoma

. C. Fitzpatrick = : 40; - H. K. Walker

C. H. Gabbard 41. J. R. Weir

W. R. Gall 1 42, M. E. Whatley

W. R. Grimes"- o | 43, J. C. White

A, G. Grindell . 44, W, R. Winsbro

P. N, Hanbenreicnu'“_ 45-46. Central Research Library
H.”W. Hoffman - | 47, Document Reference Section

P. R. Kasten =~ *-'7,'_ 48. GE Division Library

R. J. Kedl: "; _E_f ;_f_,49f58; Eaboratorv'Records Departnenti
G. H, Llewellyn = 59, Laboratory Records, ORNL R. C.
R. E. MacPherson ~ 60. ORNL Patent Office

H. Ei'McCoyiiiu'"' T e

'EHErternsirDistribution'
_P F. Pasqua, Nuclear Engineering Department, University of o+

‘L. R. Shobe, Engineering Mechanics Department University of

63-77.

Tennessee, Knoxville, Tennessee

Division of Technical Information Extension 7
Laboratory snd University Division, USAEC, ORO