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i I
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i
1 i
OWL, TM-2029
Contract No. W-7405-eng-26
General Engineering Division
INVESTIGATION OF ONE CONCEPT OF A THERMAL SHIELD FOR THE ROOM M U S I N G A MOLTEN-SALT BREEDER REACTOR
W. K. Crowley J. R. Rose
NOVEMBER 1967
OAK RIDGE NATIONAL LABORATORY
UNION CARBIDE CORPORATION for the U. S. ATOMIC ENERGY COMMISSION
”
.
3
c
iii
CONTENTS Page
.......................... .. SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . DEVELOPMENT OF METHODS . . . . . . . . . . . . . Steady-State Condition . . . . . . . . . . . . . . . . . . . D e r i v a t i o n of Equations . . . . . . . . . . . . . . . . . C a l c u l a t i o n a l Procedure . . . . . . . . . . . . . . . . . T r a n s i e n t Case . . . . . . . . . . . . . . . . . . . . . . . . . PARAMETRIC STUDIES . . . . . . . . . . . . . . . . . . . . Cases Studied for Steady-State Condition . . . . . . . . . Case Studied f o r T r a n s i e n t Condition . .. . ... CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . .
Abstract..
1. 2.
3.
4.
INTRODUCTION.
0
0
ANALYTICAL
0
5.
Appendix A. Appendix B. Appendix C. Appendix D. Appendix E.
EQUATIONS NECESSARY TO CONSIDER A MULTIENERGETIC G A M M A C U R R E N T e . * o . o o . . o . . . . . . . . EVALUATION OF THE CONVECTIVE HEAT TRANSFER COEFFICIENT
.
.................... VALUES OF PHYSICAL CONSTANTS USED I N THIS STUDY . . TSS COMPUTER PROGRAM . . . . . . . . . . . . . . . NOMENCLATURE . . . . . . . . . . . . . . . . . . .
1
1 4 6
7 8
15 17 20 20 29
35
41
44 46 47 60
3
?
'c c:
I
V
LIST OF TABLES. Table Number
Title
Page Number
1
Results of Investigation of First Steady-State Case
22
2
Results of Investigation of Second Steady-State Case
23
3
Results of Investigation of Third Steady-State Case
24
4
Results of Investigation of Fourth Steady-State Case
25
5
Results of Investigation of Fifth Steady-State Case
26
6
Results of Investigation of Sixth Steady-State Case
27
7
Results of Investigation of Seventh Steady-State Case
28
Computer Program Used to Analyze the Proposed Reactor Room Wall for the Condition of Internal Heat Generation
31
Range of Parameters of Interest in Studies Made of Proposed Wall With An Incident Gamma Current of 1 x lola photons/cn? *sec
36
D. 1
Typical Data for 32 Cases With One Energy Group for the TSS Computer Program
54
D.2
TSS Output Data at the Bottom of the Air Channel for One Case
58
D. 3
TSS Output Data at Case
59
Top of the Air Channel for One
vii
$ 2
W
e
LIST OF FIGURES Figure Number
Title
Page Number
1
Proposed Configuration of Reactor Room Wall
2
2
Proposed Configuration of Reactor Room Wall With Corresponding Terminology
6
3
Designations Given Segments of Reactor Room Wall for Study of Transient Conditions
18
4
Temperature Distribution ' in Proposed Reactor Room Wall With Internal Heat Generation Rate Maintained During Loss-of-Wall-Coolant Transient Period
33
5
Temperature Distribution in Proposed Reactor Room Wall With No Internal Heat Generation During the Loss-of-Wall-Coolant Transient Period
34
Assembly of Data Cards for TSS Computer Program
53
D.1
7 f
z
INVESTIGATION OF ‘ONE CONCEPT OF A THERMAL SHIELD FOR THE ROOM HOUSING A MOLTEN-SALT BREEDER REACTOR
‘ :
Abstract’:’ !C. 3
The concrete providing the biological shield for a 250~Mw(e) molten-salt breeder reactor must be protected from the gamma current within the reactor room. A configuration of a laminated shielding wall proposed for the reactor room was studied to determine (1) its ability to maintain the bulk temperature of the concrete and the maximum temperature differential at levels below the allowable maximums, (2) whether or not the conduction loss from the reactor room will be kept below a given maximum value, (3) whether air is an acceptable medium for cooling the wall, and (4) the length of time that a loss of this coolant air flow can be sustained before the bulk temperature of the concrete exceeds the maximum allowable temperature. Equations were developed to study the heat transfer and shielding properties of the proposed reactor room wall for various combinations of lamination thicknesses. The proposed configuration is acceptable for (1) an incident monoenergetic (1 Mev) gamma current of 1~ x 1012 photons/c& see and (2) an insulation thickness of 5 in. or more. The best results are obtained when most of the gamma-shield steel is placed on the reactor side of the cooling channel. l
1.
INTRODUCTION t
Thermal-energy to assess design /
.
their
intense is
housed.
reactor
economic
problems.
a conceptual
molten-salt
gamma current The concrete room must
and nuclear
One design
10001Mw(e) in
breeder-reactors performance
problem,identified
MSBR power
plant1
the-room
in-which
wall.providing
be protected
(MSBR) are
fromthis
and
to
during was that the
the
there
intense
identify the
made of
be a rather
breeder shield
gamma current
: ‘P. R. Kasten, E. Si Bettis, and R. C. Robertson, lOOO-Mw(e) Molten-Salt Breeder Reactors, ” USAEC Report Ridge National Laboratory, August 1966.
studied important
study
will
molten-salt
biological
being
reactor
around to
the
limit
“Design Studies ORNL-3996, Oak
of
2
gamma h e a t i n g i n t h e concrete.
Further, the c o n c r e t e must be p r o t e c t e d
from t h e high ambient temperature i n t h e reactor room.
One p o s s i b l e
method o f p r o t e c t i n g t h e c o n c r e t e is t h e a p p l i c a t i o n of l a y e r s o f gamma and thermal s h i e l d i n g and i n s u l a t i n g materials on t h e r e a c t o r s i d e of t h e concrete.
A proposed c o n f i g u r a t i o n o f t h e layered-type w a l l f o r t h e
r e a c t o r room i s i l l u s t r a t e d i n Fig. 1. ORNL
SKIN7
7
INSULATlON
r STEEL 7
OW#
61-12000
rCONCRElE
AIR
3
Fig. 1. Proposed Configuration of Reactor Room Wall. The study r e p o r t e d h e r e was made t o i n v e s t i g a t e t h i s proposed conf i g u r a t i o n of a r e a c t o r room w a l l for t h e modular concept? of a 1000-Mw(e)
MSBR power p l a n t .
This modular p l a n t would have f o u r s e p a r a t e and i d e n t i -
cal 250-Mw(e) r e a c t o r s w i t h t h e i r s e p a r a t e s a l t c i r c u i t s and heat-exchange loops.
T h i s p r e l i m i n a r y i n v e s t i g a t ’ i o a was made t o determine whether o r
n o t t h e proposed c o n f i g u r a t i o n f o r t h e reactor room w a l l w i l l
1. maintain t h e bulk temperature o f t h e c o n c r e t e p o r t i o n o f t h e w a l l a t l e v e l s below 212’F, 2.
maintain t h e temperature d i f f e r e n t i a l i n t h e c o n c r e t e lamination a t l e s s than 40°F (a f a i r l y c o n s e r v a t i v e value), and
3,
maintain t h e conduction loss from a r e a c t o r room a t 1 Mw o r less.
This study w a s a l s o performed t o determine whether o r n o t a i r i s a s u i t a b l e medium f o r c o o l i n g t h e reactor room w a l l and t o determine t h e l e n g t h o f t i m e over which t h e l o s s o f t h i s a i r flow can be t o l e r a t e d b e f o r e t h e
3
i 2
u b
bulk temperature of the concrete lamination.exceeds the maximum allowable
w
temperature of 212'F. Analysis of the proposed configuration for the wall of the reactor room was based on an investigation of the heat transfer and shielding n Fig. 1.
properties of t
osite wall sho
Equations were devel-
oped that would
these properties to be examined parametrically for
various combinations of lamination materials and thicknesses
L r
c
4
2
I?
w 2.
s
SUMMARY
\
Methods were devised to parametrically analyze a comp with internal heat generation produced by the attenuation current from the reactor room. Both steady state and tran were considered.
Thirty-one equations
gram was written to examine the heat transfer and shielding properties of the proposed wall for various combinations of lamination materials and Incident monoenergetic (1 MeV) gamma currents of 1 x
thicknesses. photons/ca?
sec through 3 x 10”
photons/ca? *sec were examined.
le2
A finite
difference approach, with the differencing with respect to time, was used in the transient-condition analysis to obtain a first approximation of the amount of time that the proposed wall could sustain a loss of coolant air flow. The results of these studies indicate that the proposed configuration of the laminated wall in the reactor room is acceptable for the cases considered with an incident monoenergetic (1 MeV) gamma current of 1 x 1Ol2 photons/ca?*sec and a firebrick insulation lamination of 5 in. or more. Under these conditions, a total of approximately 4 in. of steel is sufficient for gamma shielding. The best results are obtained when the thicknesses of the mild-steel gamma shields are arranged so that the major portion of the steel is on the reactor side of the air channel.
However,
the proposed configuration of the laminated wall for the reactor room does not protect the concrete from excessive temperature when the incident monoenergetic gamma current is 2 x lola photons/ca? osec. With an incident monoenergetic (1 MeV) gamma current of 1 x 10’” photons/c$
sec, the proposed laminated wall will maintain the temperature
differential in the steel to within 10°F or less for all the cases studied. The differential between the temperature of the steel-concrete interface and the maximum temperature of the concrete is less than 1S0F for all the cases studied.
The values of both of these temperature differentials are
well below a critical value. Based on the assumption that the floor and ceiling of the reactor room have the same laminated configuration as the walls, the proposed
w L
5
wall
will
allow
at a level of
below
1 x 10la
is
1 Mw for
With
5 in.
if
or more
a coolant
50 ft/sec,
air
room wall. approximately
9set,
the
air
flow.
nperu&ssibleii than
and if
of
least
of
room
the
4 in.
3 in.
for
to be maintained
(1 Mev)
gamma current
firebrick
insulation
of mild-steel
the
gamma
the
concrete
approximately a zero
incident
is
maintained will
reactor
at
remain
after
gamma’current
is
is
of
room remains
one hour
time
velocity
the.proposed
reactor
the. gamma’current of
and an air
cooling
of
loss-of-coolant-airiflow
greater
at
1 x lOla
below
a loss
of
the the
assumed,.the than
one hour
but
two hours.
maintenance
of
without
the
energy
balance
and
whether-or
not
desired
ambient
the
addition
of
should This
available.
surface.
at
medium
temperature
If
To determine
reactor
if
temperature
level.(212oF)‘for
coolant
reactor
thickness
channel’width
ambient
1106OF
photons/&
and
the
monoenergetic
the
an acceptable
the
from
_ air
is
If
critical
loss
an incident
is ikiuded.
shielding
4
conduction
photons/ct#*sec
lamination
less
the
balance
extend-out
a conduction temperature
auxiliary
cooling
be performed
when
should through
loss
start the
wall
of
within
the
or heating sufficient
with of
1 Mw will
permit
reactor
systems,
an overall
information
the
fissioning
the
reactor
room
becomes process
room
in
the
to an outside
6
3.
DEVELOPMENT OF ANALYTLCAL METHODS
I n t h e modular concept o f a 1000-Mw(e) MSBR power plant,'
the four
i d e n t i c a l b u t s e p a r a t e 250-Mw(e) molten-salt breeder r e a c t o r s would be One primary f u e l - s a l t - t o - c o o l a n t -
housed i n four s e p a r a t e r e a c t o r rooms. s a l t h e a t exchanger and one blanke
alt-to-coolant-salt
h e a t exchanger
would a l s o be housed i n each r e a c t o r room along with t h e reactor.
These
items o f equipment are t o be l o c a t e d 11 f t from each o t h e r in t h e 52-f long r e a c t o r room t h a t i s 22 f t wide and 4 8 - f t high. primary f u e l - s a l t - t o - c o o l a n t - s a l t
The r e a c t o r and t h e
h e a t exchanger are respons
gamma c u r r e n t i n each o f t h e r e a c t o r rooms.
The proposed c o n f i g u r a t i o n
t i o n s devised t o p r o t e c t t h e c o n c r e t e from t h e gamma c u r r e n t
r room i s shown i n Fig. 2 w i t h t h e corresponding terminology used i n t h e parametric s t u d i e s made o f t h e omposite w a l l .
'P. R. Kasten, E. S. Bettis, and R. C. Robertson, "Design S t u d i e s o f lOOO-Mw(e) Molten-Salt Breeder Reactors," USAEC Rep0 ORNL- 3996, Oak Ridge National.Laboratory, August 1966. ORNL Dug. 67-10001
I
AIR
-4
Fig. 2. Proposed Configuration o f Reactor Room Wall With Corresponding Terminology.
U *
7
2 lj ‘i
In
the
direction
outer
surface
of
rial
comprising
the-variable
wall,are
8. ft
for air
is
an exterior
-considered
fixed
of
over
the
concrete
ci
of
the
the
thickness
ing
room within
the
facility
the
coolant
is
assumed
air
channel,
air and
the
velocity
heat
current.
from
the
steady-state condition later
was considered problem
of
properties
of
metrically
for
i
nesses.
LJ
tures
E
uniform.
were
of
the
interior
(the
mate-
insulation,
the
and
insulato be
stainless
concrete
is
and the
either
width
of
interior
the
room wall
is
is
first
and the
a loss
of
combinations analysis and exterior
of
or of
at
70°F
an adjoin-
(entrance) to’be
of
the
SO ft/sec.
attenuation
were
of
a composite of
plane the
considered:
condition.
gamma
the
The steady-state
transient
condition
was considered
was examined.
Condition
.to mallow wall,
to be uni-
thickness
involving
coolant
The
The temperature
assumed
by the
wall
1100’F.
wall)
bottom
one
transient
8-ft
wall).
air
and the
at
temperature
be lOOoF at the the
reactor
is -considered
ambient
Two conditions
\
the
an exterior
room.
A one-dimensional
of
shield,
of
the
wall
for
is>basically
the--compositevarious
the
earth
of
develoPed
the
considered
wal.1,
SOoF for
Steady-State : Equat,ionk-
to
firebrick
and constant
caused
. of
the
are
of
generation
reactor
condition
when the ,’ 1
surface
at
the
to
with
internal
‘the
for’an
examined
firebrick
of
of
surface
concrete
The situation
layers
a mild-steel-gamma
an interior
interior
of of
the
skin,
thickness
for
and constant
the
2),
The thickness
the
surface
for
wall
3-ft
study.
room out
in.
over
temperature
Fig.
gamma shields
3 ft
exterior
surface
(the
channel,
in.,
at.3
to be uniform
temperature form
l/16
wa.ll:or
is
in
reactor
The thicknesses
this
at
The temperature
cc
an air
the
steel
two,mild-steel
fixed
channel
to right
shfeld:
of, the
of
a-stainless
parametersin
skin
interior
(left
gamma shield,
and each
steel
the
wall
concrete;biological
tion
the
the the
a mild-steel the
from
shown of
the
heat
transfer
in
Fig.
2,
lamination
was used, surfaces
materials
the
shielding
to be examined
assuming of
and
wall
para-
and thick-
that were
the
tempera-
constant
and
8 Derivation o f Equations
A s t e a d y - s t a t e energy balance on a d i f f e r e n t i a l element o f t h e r e a c t o r room w a l l can be expressed s e m a n t i c a l l y as follows.
The h e a t conducted
i n t o t h e element through t h e l e f t f a c e during t h e time A0 p l u s t h e h e a t generated by sources i n t h e element d u r i n g t h e t i m e A0 e q u a l s t h e - h e a t conducted o u t of t h e element through t h e r i g h t f a c e d u r i n g t h e time 08. This i s expressed a l g e b r a i c a l l y i n Eq. 1.
where
k = thermal conductivity, Btu/hr*ft*'F, A,.
= u n i t a r e a on wall, f t a ,
T = temperature,
0
F,
x = distance perpendicular t o surface o f the w a l l , f t , 0 = time, hours, and Q = volumetric gamma h e a t i n g rate, Btu/hr*ft?.
Application of t h e mean-value theorem t o dT/dx g i v e s t h e e x p r e s s i o n o f
Eq. 2.
where
M i s a p o i n t between x and x + Ax.
Equation 2 i s s u b s t i t u t e d i n t o
Eq. 1 and A0 i s canceled.
The common term '
= @T/d$.
-&
:Ix
i s canceled, and i t i s noted t h a t
The r e s u l t i n g expression i s given i n Eq. 4. Q 4 & = - krtaT p,gl&.
M Dividing Eq. 4 by &Ax and a l l o w i n g & t o approach zero a s a l i m i t so t h a t a value a t M becomes a v a l u e a t x, t h e volumetric gamma h e a t i n g r a t e ,
CPT Q = - k q ,
-
9
L
u c Âś
A
Equation 5 is integrated twice, and if Q T(x) =
3
# Q(x),
+ G x + C,
x?
.
(6)
The applicable boundary conditions for any particular lamination in the at x = 0 and T = T at x = L, where T, = the temperature wall are T = ‘I& L of the lamination interface at zero location designated in Fig. 2 and
L = the thickness of the material in a lamination in feet. ditions are applied to Eq. 6.
Tkese con-
The internal heat generation encountered in this study is caused by a deposition of energy in the form of heat when the gamma rays are attenuated by the materials in the wall of the room.
Because of this atten-
uation of the gamma rays, the volumetric gamma heating rate, Q, is a function of the distance perpendicular to the surface of the wall, x. The equations derived in this study are based on the assumption that the incident gamma current is monoenergetic, but appropriate equations for a multi-energetic gamma current are given in Appendix A.
For a mono-
energetic g a m a current where buildup and exponential attenuation are considered, the equation for Q(x) becomes Q(x) = Q[Aewx
+ (1
- A)e -PPX],-Px ,
where
A,
(31,
and p = dimensionless constants used in the Taylor buildup enuation coefficient, ft-1.
When
= the volumetric
te at the surface on the reactor n, Btu/hr*ft?, current, MeV,
go = incident gamma current, photons/cn? i
%
sec, and
= gamma energy attenuation coefficient, ft-1.
10 Substituting Eq. 9 into Eq. 5,
-
Equation 10' is integrated twice to yield
+c;x+cq=o. (11) The previously stated boundary conditions are still applicable, and the result of applying these conditions to Eq. 11 is that
The temperature distribution in any particular lamination o f the wall is given by Eq. 12 when the appropriate constants for that lamination are used.
Equation 12 is used primarily to determine the maximum temperature
in the concrete and to determine the location of this maximum temperature.
To locate the position of the maximum temperature in the concrete, Eq. 12 is differentiated with respect to x, the resulting derivative (dT/dx) is set equal to zero, and the equation is solved for X. The value of x obtained gives the distance from the concrete-steel interface to the position of the maximum temperature in the concrete.
Equation 13 is a transcendental equation in x, and as such, it must be solved by using a trial-and-error technique.
There are only two terms
in Eq. 13 that contain x, and these terns are rearranged to put Eq. 13 in a form more easily solved by trial and error.
All
of
the
terms
in
the
the
= $6 - TL>+ +(YC k
A (a - l)=
+ (B1+-lfa
11 - e
coefficients on the
on the
right
side
are
x,
the
this
into
K’s
value
Eq.
and a’s
are
of
called
x is
12 to obtain
To determine reactor each
room, separate
duction
of
the
face
Eq.
9 over
the
14 are
Therefore,
Eq.
.
(14)
known,
and all
of
14 may be written
written
lamination
in
the~wall.
thickness
the
gamma heat, the the
wall
is
There gamma heating referred.
to
gamma current, of
ip o(j)
is
assumed
which
L,
the
the
- ‘)
)
incident two possible
rate as the
at “j-th”
ways
in
to
E@o(j)%
generated
in
a length
equal
a
The total
a direction
-PUB 1e _-
- ++
normal
to
by integrating
.
+ 0
incident
which
way is ~to calculate
To obtain
l
(17)
’
volumetric
interface,
equation
-113
(16)
rate.
the
The first.
=
con-
+ ‘)] dx
material
@ at each’interface. o(J)’ is substituted into the
across
lamination.
evaluate
interface.~
.
lamination
gamma heating
some.particular
‘(3
area
+-. (1 - A)e”~x(p ._~~~ .-. -
volumetric
simple
heat
through
the
drops
are
the
any particular
A eCrL(a - 1) _ .---:ll - 1)(
from
lamination.
unit
particular
q*,
equations of
for
substituted
temperature
particular
per
for
of
the
all
solved
concrete.
loss,
to be conducted
of
found
L & [Aepta
are
in
the
conduction
These
14 is
= xT max is
of
to give
q TI deposited
length,
the
the
(15)
When Eq.
The va1ue.x
of
equations
,;
temperature
were
=Sro2 Q
maximum
magnitude
= k
numbers.
equations
J
value
-cl.L(cr - 1)
of Eq.
=%kx
xT.max;
of
of
ke
calculable
is
qT =
where
known.
-a,x;
Lamaination
two-thirds
amount
1L
the
and convection
particular to
side
I
form %e
where
left
pL(c%- 1) il - e
Q
W’
this
shall
be the
calculated
12 The second method o f e v a l u a t i n g t h e i n c i d e n t volumetric gamma h e a t i n g
rate involves s u b t r a c t i n g t h e t o t a l amount o f gamma h e a t d e p o s i t e d p e r u n i t area i n t h e j - t h lamination, q
.I
from t h e gamma energy c u r r e n t p e r
u n i t area i n c i d e n t upon t h e j - t h lamination
qo(j),
t o approximate t h e
gamma energy c u r r e n t p e r u n i t area i n c i d e n t upon t h e f a c e of t h e followi n g lamination qo(j
+
1) * “(j-
+ 1) =
qo(j)
- qj
The volumetric gamma h e a t i n g rate i n c i d e n t upon a p a r t i c u l a r lamination, Qoij)
, and
lamination
t h e gamma energy c u r r e n t p e r u n i t area i n c i d e n t upon t h e j - t h qo(l)y
are r e l a t e d by t h e following equation. qo(3)
= Qo(j,/h(J)
There f o r e (18b)
Qo(j + 1)
These two methods are i n f a i r 1
i n c e t h e v a l u e s for
t h e v a r i o u s material c o n s t a n t s were n o t w e l l f i x e d a t t h i s p o i n t i n t h e design f o r t h e reactor room w a l l ,
t h e second method o f e v a l u a t i n g t h e
i n c i d e n t volumetric gamma h e a t i n g rate was u s e d i n t h i s study.
The
second method i s simpler t o u s e and easier t o c a l c u l a t e . The equations f o r t h e s t e a d y - s t a t e temperature drops a c r o s s each o f t h e material laminations on t h e reactor s i d e o f t h e a i r channel are given below and t h e temperature p o i n t s are as i l l u s t r a t e d i n Fig. 2.
where
q* QS
E
h e a t conduction rate o u t o f t h e r e a c t o r room, Btu/hr*ft?,
E
gamma h e a t d e p o s i t i o n rate i n t h e s t a i n l e s s steel o u t e r s k i n , Btu/hr*f?,
Ls = t h i c k n e s s o f t h e s t a i n l e s s steel skin, f t , and kS
= thermal c o n d u c t i v i t y o f t h e s t a i n l e s s s t e e l s k i n , Btu/hr*ft*’F.
13
(cp + 4,
TL - Ta = where
the
subscript
I refers
(20)
?
to
kI insulation
the
lamination
shown
in
Fig.
2.
(q* + q, + 41 + &LFS Y
-T3.=
%
: where the
the
subscript
reactor
FS refers-to
side
of
the
(21)
kFS
air
the
first
mild-steel
gamma shield
(on
channel).
%
- T, =
of
the
q* + q, + qI + qFS Y h
(22)
where Ta = temperature h=
convective
heat
The ‘average
convective
air
channel
is
for
a mean temperature
gamma heating and 22 were conduction-
heat
added rate’
air
and out
channel,
transfer
of
across
B, and the
130 to
channel
is
150’F.
It
room
the
walls
air
of
the
off 5 was determined
was assumed
was solved
to
the
Equations
equation
reactor
value
negligible.
resulting
the
Btu/hr=ft?*OF.
coefficient
from
the
OF, and
coefficient,
in Appendix of
the
in-the
transfer
evaluated
in
air
that 19,
for
the
20,
21, The heat
q*.
channel,
:. (&
- Ta)
2 Ls LI J~+F+-+[o 8 .I
-‘qs
Lps
1
kFS
h
1 ..
q* E
(23)
On the is
the
side .of- the air channel, the TV- ~ temperature of the concrete, Tmax.
maximum
-determined concrete
by using
Eqs.
interface,
The simple the
concrete
concrete
Tn,
conduction side
.of
12 and must
14,
but
be known
the before
air-channel
.are
these
of
equations
for given
.of primary
interest
This-temperature
temperature
and convection’equations the
value
the
the
may be steel-!
can be used.
laminated
wall
on
below.
Qss + 4; + QR Q
- Ta 4
h
Y
(24)
~
14
..r
‘I
where qss = gamma h e a t d e p o s i t i o n r a t e i n t h e second m i l d - s t e e l gamma s h i e l d , Btu/hr*ft? qr
,
= rate a t which t h e gamma h e a t generated i n t h e c o n c r e t e is conducted back toward t h e a i r channel, B t u / h r - f e , and
QR
= r a d i a n t h e a t t r a n s f e r rate between t h e walls of t h e a i r chan Btu/hr f t?
,
where t
Stefan-Boltzmann c o n s t a n t
= 0.1714 x E
loa
= s u r f a c e e m i s s i v i t y o f a i r channel w a l l s , assumed t o t h e same for both s u r f a c e s .
% - % =
+
2
yss)Lss
kSS
.
(26)
I n t h i s study, t h e r e is a p o i n t i n t h e c o n c r e t e a t which t h e temperat u r e of the concrete
i s a maximum.
A l l of t h e gamma h e a t generated on
t h e a i r channel s i d e o f t h a t p o i n t w i l l be conducted toward t h e a i r channel; t h a t is, i n t h e d i r e c t i o n o f d e c r e a s i n g temperature. q’, C
This amount o f h e a t ,
may be c a l c u l a t e d by e v a l u a t i n g dT/dx i n t h e c o n c r e t e a t x = 0, u s i n g
Eq. 13.
~-
recognizing t h a t .
9; = kc
dx
dTI x = o
where t h e s u b s c r i p t c denotes concrete.
?
The r i g h t s i d e o f Eq. 28 i s
p o s i t i v e r a t h e r than n e g a t i v e because Eq. 27 makes p o s i t i v e conduction i n t h e d i r e c t i o n from t h e a i r channel toward t h e concrete, b u t q; is
..
. I
j
15
:
&Iii 5
to be made positive
in
channel.
24,
Equations
equation lated
i
in which from
the
the
the
direction
25,
26,
only
equations
from
27,
unknown for
the
and 28 were is Q.
the
concrete
reactor
‘toward~the
combined
The-value side
of
to
for
air
yield
one
T3 can be calcu-
the-air
channel.
where B’ =
. 11
‘i.qB + 1) + (pl+-l+i1.- e The constants to be for fore,
in
Eq.
concrete.
29a that
have
Equation
29.is
also
.must
be used
a trial-andferror
method
qk are known,
% can be calculated
Calculational
Procedure
Since
the.calculation
that
the
order
value
in which
thickness inside are
specified. air
selected,
other
the
of.each (reactor
coolant are
of
of
of
the
room)
are
also
used
For the
is
(earth,or
internal)
current
and the
given
&.
quantities there
for
in Appendix
There-
Once ‘J& and
requires is
a particular
wall
The constants are
for
be known,
in
ganrna
specified..
and those
desired
the
understood
equation.
solve
of
be worked.
and -outside
The incident
to
Eq.- 25.
laminations
are
a transcendental
quantities
must
subscripts
by using
certain
desired
problem
no identifying
(294
a certain case)
-the
selectedi
and
wall
-temperatures
temperature
of
the
-equations
C:
various
the
the
16 With t h e proper c o n s t a n t s f o r each d i f f e r e n t lamination, Eq. 17 is f i r s t used t o c a l c u l a t e t h e gama h e a t d e p o s i t i o n s i n each o f t h e sepaEquation 23 i s then used rate laminations (qs, qI, qFs, qss, and 9,). to c a l c u l a t e t h e conduction l o s s from t h e r e a c t o r room q*. The temperat u r e drops and t h e i n t e r f a c e temperatures on t h e r e a c t o r s i d e o f t h e a i r channel a r e c a l c u l a t e d by u s i n g Eqs. 19, 20, 21, and 22.
Equation 29 is
used t o c a l c u l a t e t h e value o f %, and then t h e v a l u e o f qR is c a l c u l a t e d by u s i n g Eq. 25.
Then q:
i s c a l c u l a t e d by u s i n g Eq. 24, and t h e v a l u e
o f & i s c a l c u l a t e d by u s i n g Eq. 126. Once t h e v a l u e o f Ts is known,
i s obtained by u s i n g Eq. 14, and t h e maximum temperature of t h e T max c o n c r e t e is c a l c u l a t e d by e v a l u a t i n g Eq. 12 a t x = xT max.
X
A t t h i s p o i n t , i t is p o s s i b l e t o c a l c u l a t e t h e v e r t i c a l temperature
g r a d i e n t (OF/ft)
i n t h e coolant a i r .
T h i s temperature g r a d i e n t ,
where Ua = bulk v e l o c i t y o f c o o l a n t a i r , f t / s e c ,
Pa
= d e n s i t y o f a i r , lb/ft?,
Lch = width o f a i r channel ( d i s t a n c e between steel laminations), f t , C = s p e c i f i c h e a t o f a i r a t c o n s t a n t p r e s s u r e , Btu/lb*OF. Pa The temperature o f t h e a i r a t t h e top of t h e channel,
where H = t h e v e r t i c a l l e n g t h o f t h e a i r channel i n f e e t . The e n t i r e c a l c u l a t i o n a l procedure can now be repeated u s i n g t h e new a i r temperature a t t h e t o p of t h e a i r channel, Ti.
This c a l c u l a t i o n o f t h e temperature o f t h e a i r a t t h e t o p o f t h e channel is n e c e s s a r y because a h i g h e r T c a u s e s t h e maximum temperature o f t h e c o n c r e t e t o be a
higher, and t h e magnitude o f t h i s maximum temperature is one of t h e c o n s t r a i n t s i n t h i s study. A program was developed f o r t h e CDC 1604-A computer t o s o l v e Eqs. 8
through 31 f o r t h e s t e a d y - s t a t e condition.
The TSS (Thermal S h i e l d Study)
17
z LJ
computer
4
program
is
in
the
calculations material
described order
laminations
room wall
in
Appendix
described
(excluding
and up to eight
air
basically
of
a transient If
tion.
the
an appreciable
the
steel
with
the
that
such
ence
approach
the
superscript
of
groups
for
of n in
segment,
as shown
given
was assumed and
entire
thick,
and
plus
the
in
in
3.
Fig.
firebrick
stainless
steel
the
air
the
temperature
up to
proposed
five
reactor
gamma current.
room wall
internal
channel
excessive.
the
the
be sustained equations
with
the
amount
is
to
values
lost
and/or situation
of
a finite
respect
denotes
wall
this
safely,
is
genera-
concrete
To investigate of
is
heat
in in
approximation
balance
in
the
selected
for kCA
+TSn C
nodal Each
thick,
skin
reactor
points
each
time differ-
time
and
after
the
the
time
of
the
time
wall
the
segment into
+q+=
each
region
of
the
gamma thick,
segment
segment
l/16
3 in.
a segment
during
in.
thick.
can be expressed
seman-
the
time
A0
during
the
time
A6 equals
the
heat
A6 plus
the
heat
conducted
out
of
5s given
algebraic below
equation with
Segment
for
the
a
4
‘,
purposes. W=ccp ne
of
mild-steel
a single
into
center
to be 1 in.
as a single
The corresponding
composite
illustrative
- G.“)
the
concrete in
was treated’as
then segment
A0.
the
was broken the
was assumed
The heat~conducted
during
in
segment
a particular
in
room wall located.at
segment
was treated for
segment
segment
the
insulation
channel
generated
segment-during
b f
with
time,
of
with
the
heat
typical
reactor
the
could
lengths
as follows.
stored
the
through
following
to be 1 ft
The energy tically
for
The differencing
the
incident
air
configuration
of
the
flow
the
the
interval.
segments
shields
air
in
handle
the
problem
a first
was taken.-
The proposed
wall
coolant
may become
obtaining
a loss
time
of
will
performs
Case
conduction
length
of
of
coolant
laminations goal
loss
heat
flow
for
n-th
the
it
channel)
Transient
The problem
The program
and
above,
the
energy
D.
?T4
n+l-
T4n)
kCA
+ +T4”
- %“I*
C
(32)
18
<
6T-12002
ORNL O r g
/STAINLLSS STELL \ SKIN FIREBRICK INSULATION
<
FIRST MILD-STEEL BAMYA SHIELD r(AIR
CHANNEL SECOND MILD-STEEL GAMMA SHIELD CONCRETE
i
z
0
+ 1
f CURRENT
.....
NODAL WIN1
SEGMENT
ZC
I I7 16 I!
I
I1
I 6 4 5 9 1
Fig. 3. Designations Given Segments of Reactor Room Wall for Study of Transient Conditions.
Rearranging Eq. 32,
A characteristic equation at an interface between two different
materials is given in Eq. 34. l+"
+
1
-
qn
+
-
p ksm L Z C (Gn T7n) 6 s Ps
+
-k
s-cA0
p sLsLcCp S
G n-
%
T79
+
c
L s
8
,
Ps
(34) where the subscript s denotes the stainless steel skin, the subscript'c
-
denotes the concrete, and ks-C is an equivalent conductivity given by
where the subscripts a and b refer to any two adjacent materials,
19 Eighteen equations similar t o those j u s t given were derived t o carry the a n a l y s i s across the e n t i r e reactor room wall, and a simple computer program was written t o perform the c a l c u l a t i o n s required f o r one s p e c i f i c transient condition.
I
\
*
20
hd i.
4. PARAMETRIC STUDIES
The parametric s t u d i e s of t h e proposed c o n f i g u r a t i o n of a laminated w a l l f o r t h e r e a c t o r room, shown i n Fig. 2, t o p r o t e c t t h e c o n c r e t e biol o g i c a l s h i e l d from t h e gamma c u r r e n t w i t h i n t h e room were made f o r two conditions: t h e s t e a d y - s t a t e c o n d i t i o n and t h e t r a n s i e n t c o n d i t i o n . Parametric s t u d i e s o f t h e material laminations f o r t h e s t e a d y - s t a t e cond i t i o n were made t o determine whether o r n o t
1.
t h e bulk temperature o f t h e c o n c r e t e p o r t i o n o f t h e w a l l could be maintained a t l e v e l s below 212'F,
2.
t h e temperature d i f f e r e n t i a l i n t h e c o n c r e t e could be maintained a t
less than 40째F, and 3.
t h e conduction loss f o r a r e a c t o r room could be maintained a t 1 Mw o r less.
A t r a n s i e n t c o n d i t i o n was i n v e s t i g a t e d t o determine t h e l e n g t h o f time
over which t h e loss o f c o o l a n t a i r flow could be t o l e r a t e d b e f o r e t h e temperature of t h e c o n c r e t e would exceed t h e maximum allowable temperat u r e o f 212'F.
Cases Studied f o r Steady-State Condition
For t h e parametric a n a l y s i s of t h e composite p l a n e w a l l w i t h i n t e r n a l 3:
h e a t g e n e r a t i o n f o r s t e a d y - s t a t e c o n d i t i o n s , t h e a i r channel was not cons i d e r e d as a m a t e r i a l lamination b u t r a t h e r a s having a f i x e d width o f
3 i n . between t h e f i r s t and second m i l d - s t e e l gamma s h i e l d s .
The tempera-
t u r e of t h e incoming c o o l i n g a i r a t t h e bottom o f t h e a i r channel was assumed t o be 100째F, and t h e v e l o c i t y of t h e a i r w a s set a t 50 f t l s e c . The t h i c k n e s s o f t h e s t a i n l e s s steel s k i n on t h e r e a c t o r s i d e o r i n t e r i o r s u r f a c e of t h e w a l l was f i x e d a t 1/16 in.,
and t h e temperature o f t h e
i n t e r i o r s u r f a c e o f t h e r e a c t o r room w a l l was considered t o be uniform over t h e s u r f a c e and constant a t 110O0F.
Equations 8 through 31 d e r i v e d
i n Chapter 3 were used w i t h t h e TSS computer program d e s c r i b e d i n
c; ?
Appendix D t o examine t h e s t e a d y - s t a t e e f f e c t s o f changing t h e , i
21
1.
thickness
2.
total
amount
of mild
steel
3.
ratio
of
amount
of~steel
to
of
the
the
the
amount
firebrick
of
steel
4.
thickness
and outside
5.
magnitude
of
the
Sixty-four dition
to
Data
selected
from
through
the
gamma currents
of
tables,
and
the
channel
air For
the
the
maximum
the
bottom
with
of
the of
reactor
the
room, 80°F
from and
little
0.04
The largest the
top
of
the
of
1 x 101s
is
approximately
maximum those
temperature cases
with
and an insulation
both
the
of
parameters
varying
the
and are
compiled
(entrance)
the
thickness
.in Tables
all
top
of
these
(exit)
of
1 x 1012
photons/cu?*sec,
increases
the
top.
For
top
the
of
the
the
bottom
maximum
concrete air
with
other at
gamma’current 5 in.
top
of
of
the
the
top of
or more
the
of
the
2 x 10la is
greater
air
very
channel, at
gamma current 5 in.
value air
a given
concrete
of
smallest
the
changes
an incident
the
from
approxi-
For
loss
thickness
hand,
to
increases
conduction
temperature
cases
back
channel.
and the
50°F
an incident
and no conduction of
the
approximately cases‘with
1
for.incident
of
concrete
of
and
were
gamma current
and an insulation
an incident
parameters
gamma current.
those
On the
interest.
incident
the
in
the
of
of
to
to
con-
magnitudes
concrete
Mw)between
ZOOoF,
steady-state
in
thickness,
photons/cn?*sec
the
*set
bottom
the
gamma current.
bhotons/cn?
insulation
channel
and
and 2 x 10la
temperature
for
wall,
given
the
channel
channel,
those
analyses
air
air
are
bottom
value air
of
2 x 101s photons/ca?*sec maximum
the
parameters
channel
the
gamma current (about
air
for
the
the
for
of
of
(1 Mev)
effects
an incident
temperature
of
concrete
changing
these
at
given
the
analyzed
changing
conditions
gamma current
mately
of
1 x 10’s
are
cases
typical
side
side
of
of
of
The effects
7.
reactor
concrete
were
effects
results
gamma shields,
monoenergetic
cases
the
the
on the
incident
of
for
temperature
the
illustrative
used
on the
separate
determine
insulation,
or more for
channel
photons/& than
250’~.
the in *set
22
- .?
w
.
Table 1. Results of Investigation of First Steady-State Case Case Conditions Studied Tg = 50째F Lc = 8 ft To = llOO째F
$=
Ls = 1/16 in. 0,
Ss= 4 in.
5 in.
P 1 x Ida photons/& -see Bottom of Top of Channel Channel 16.57 16.57 75.47 75.47 370.6 370.6 11.69 11.69 33.65 33.65 22.04 25.84 131.2 110.6 0.5382 0.5812
4,
Lss = 2 in.
le8photons/d *bee
o 2 X Bottom of Channel 33.14 151.0 741.2 23.38 67.30 55.31 198.9 0.3520
Top of Channel 33.14 151.0 741.2 23.38 67.30 48.99 253.9 0.2838
1099.9 247.9 240.5 100.o 129.6 129.8
1099.9 297.1 289.9 153.0 186 60 186.2
1099.9 324.6 314.1 100.o 155.5 156 .O
1099.9 402.7 392 5 184.0 249.3 249.7
0.1018 852.0
7.412 140.5 29.63 0.216
0.0946 802.8 7.185 136.9 32.98 0.1916
0.0679 775.3 10.55 214.1 55.52 0.4554
0.0565 697.3 10.19 208.5 65.25 0.4148
140.5 0.5422 1.104
193.6 0.&83 1.103
181.3 0.6343 1.751
268.5 0.4887 1.777
c; i
23
Table 2.
Results of Investigation of Second Steady-State Case Case Conditions Studied Lc = 3 ft T6 = 70째F
To = llOO째F La = 1/16 in.
LFS = 4 in.
LI = 5 in. 0, = 1 X
leaphotoncl/cn? rsec
Bottom of Channel 16.57 75.47 370.6 11.69 33.65 18.33 111.6 0.5812
Top of channel 16.57 75.47 370.6 11.69 33.65 8.446 133.3 0.5385
0 ,
Lss = 2 in.
leaphotons/d -8ec
a 2 X Bottom of Channe1 33.14 151.0 741.2 23.38 67.30 42.64 200.8 0.3520
Top of Channel 33.14 151.0 741.2 23.38 67.30 26.19 258.2 0.2845
1099.9 247.9 240.5 100.0 128.3 128.5
1099.9 296.7 289.5 152.6 183.3 183.4
1099.9 324.6 314.1 100.o 153.4 153.7
1099.9 402.1 391.9 183.4 244.9 245.2
0.1018 852.0 7.412 140.5 28.32 0.1678
0.0947 803.2
0.0566
30.68 0.1043
0.0679 775.3 10.55 214.1 53.36 0.3740
697.9 10.19 208.5 60.55 0.2683
133.4
184.4
0.3124
0.1276
167.4 0.3878
250.o 0.2061
24
Table 3. Results .of Investigation of Third Steady-State Case Case Conditions Studied
L~
To = 1lOOOF
TU = 50째F
8 ft I
5 = 5 in.
L, = 1/16 in. 0,
$s
E 1 X Id2 photonr/cl$ - r e c Bottom of Top of Chainel Channel 16.57 16.57 75.47 75147 299.6 299.6 82.69 82.69 33.65 33.65 25.15 21.50 87.31 1002.6 0.5960 0.5538
Lss
= 2 in. 0,
= 4 in.
le2photons/crdaarec
= 2x Bottom of Channe 1 33.14 151.0 599.2 165.4 67.30 54.08 141.5 0.3799
Top of Channel 33.14 151.o 599.2 165.4 67.30 48.21 177.6 0.3139
1099.9 230.9 227.5 100.o 139.O 140.1
1099.9 279.2 275.9 151.9 193.3 194.2
1099.9 292.7 288.0 100.o 172.2 174.3
0.1043 869 .O 3.452 127.5 39.03 1.028
0.0972 820.7 3.341 124.0 41.35 0.9814
0.0276 807.2 4.754 188 .O 72.19 2.105
0.0616 731.7 4.580 182.5 78.24 2 .om
1m.1 0.5139
201.2 0.3927 1.074
198.2 0.6004 1.689
279.5 0.4745 1.694
1.081
*
1099.9 368.2 363.6 181.1 259.3 261.4
25
Table 4. Results of Investigation of Fourth Steady-State Case Care Conditions Studied Lc 3 ft Te = 70째F
To = llOO째F
Ls = 1/16 in.
Btu/hr'fe qIO Btu/hr*fI? qFsO Btu/hr*fl? qss, Btu/hr-f@ qcO Btu/hr*fP qc ' 9 Btu/hr*ft? qRO Btu/hr*fP HWL, Mu 0
LFS =
LI = 5 in. 4,
q,
P
= 1 X lea photone/ca? osec Bottom of Top of Channel Channel 16.57 16.57 75.47 75.47 299.6 299.6 82.69 82.69 33.65 33.65 7.048 16.53 88.49 104.9 0.5543 0.5960
Lss
2 in.
e,, = 2
X lOla
Bottom of Channel 33.14 151.0 599.2 165.4 67.30 39.42 143.8 0.3799
=
4 in.
photone/ca? -set Top of Channel 33.14 151.0 599.2 165.4 67.30 24.17 182.4 0.3146
1099.9 230.9 227.5 100.o 137.5 138.5
1099.9 278.8 275.5 151.4 190.4 191.2
1099.9 292.7 288.O 100.o 169.7 171.6
1099.9 367.5 362.9 180.3 254.7 256.4
~ 3 0 ~ aOF0 %-Tar OF 0 6-%,F
0.1043 869.O 3.452 127.5 37.54 0.9178
0.0973 821.1 3.342 124.0 38.93 0.7963
0.0726 807.2 4.754 188.O 69.71 1.917
0.0617 732.4 4.581 182.6 74.40 1.722
T-0
142.4
192.8
260.5
0,2724 1.072
0.1052 1,058
183.1 0.3454 1.673
T10 F h8 OF 6 ,OF 0
Tar F 0 t r F 0 b r F %-T10 T1-Tar
OF
%-Tar
OF
9
OF
xTmlax8
ft
D/H0 OF/ft
0.1881 1.669
26
Table 5.
To
6
Results of Investigation of Fifth Steady-State Case
(b
qI, Btu/hr*f3 q*s,
Bm/hr*f?
qss, Btu/hr*f@ qc, Btu/hr*fe qc
@
8
Btu/hr*ft?
qR, Btu/hr'fP W JMW
le3 photons/cu? -see
P 1 x Bottom of Channel
0
F
OF
T1-%8
%-6,OF TS-T,,
OF
t o T ~ 8 OF
OF
Tg't,
T-8
OF
xr alax, AT/&
ft
OF/ft
Top of Channel
3
50째F
2 in.
Lss = 2 in.
= 2 x lo1* photons/& OBec Bottom of Top of
@o
Channel
Channel
16.57 75.47 299.6 71.15 45.19 35.90 87.42 0.5960
16.57 75.47 299.6 71.15 45.19 32.24 102.7 0.5538
33.14 151.0 599.2 142.3 90.38 75.58 141.7 0.3799
33.14 151.0 599.2 142.3 90.38 69.71 177.9 0.3141
1099.9 230.9 227.5 138.9 139.4
1099.9 279.2 275.9 151.9 193.1 193.6
1099.9 292.7 288.O 100.o 171.9 173.0
1099.9 368.1 363.6 181.0 259.0
0.1043 869.O 3.452 127.5 38.89 0.5353
0.0972 820.7 3.341 124.0 41.22 Q.5118
0.0726 807.2 4.754 188.O 71.92 1.095
0.0616 731.8 4.580 182.6 77.39 1.057
155.O 0.5851 1.080
205.6
208.6 0.6638 1.688
289.1 0.5484 1.692
NO .o
%-T1,
LFS =
5 = 5 in.
La = 1/16 in.
qs, Btu/hr'ft?
Case Conditions Studied Lc = 8 ft T6
llOO째F
0.4716 1.073
260.1
27
Table 6. Results of Investigation of Sixth Steady-State Case Case Conditions Studied To = l1OOOF
L~ = 1/16 in.
'& = 50째F
Lc = 8 ft
LFS = 4 in.
LI = 7.5 in.
e,, = 1 X lOla photons/cu? esec
Tl-%D
OF
OF
b-T,,
qCT,D %-%I
0
F
OF
OF
= 2 X lOla photons/d ~ s e c Top of Bottom of Channe1 Channel 33.14 223.8 676.2 21.38 61.40 50.39 164.5 0.0245
Bottom of Channel 16.57 111.9 338.1 10.69 30.70 23.47 86.60 0.2891
Top of Channel 16.57 111.9 338.1 10.69 30.70 20.35 101.1 0.2649
1099.9 223.2 217.2 100.0 124.1 193.6
1099.95 265.1 259.2 144.0 170.5 170.6
1099.99 297.9 288.7 100.0 147.2 147.7
0.0529
0.0488
0.0131
876.7 6.060 117.2 24.10 0.1965
834.8
802.1
115.2 26.42 0.1764
7 47.24 0.4150
134.o
177.6
170.7
1
%-%9
4o
Lss = 2 in.
5.9
5
28
_ _ e
W Table 7.
Results of Investigation of Seventh Steady-State Case Care Conditions Studied
To = llOO째F
La = 1/16 in.
leaphotons/ca? =see
Bottom of
Btu/hr*fi? qI, Btu/hr*ft? qFs, Btu/hr-ft? qsss B-u/hr*f@ qc, Btu/hr*f@
Tan OF t r
0
F
LFS = 4 in.
5 = 10 fn. 0, = 1 x
q,
& = 5O0F
Lc = 8 ft
Channel 16.57 146.7 307.1 9.689 27.89 21.08 73.58 0.1118
Top of Channel 16.57 146.7 307.1 9.689 27.89 18.35 84.92 0.0955
1099.98 208.6 203.3 100.o 120.9 121.0
1099.98 245.9 240.7 138.7 161.3 161.5
0.0232 891.4 5.304 103.3 20.87 0.1769
0.0205 854.1 5.218 102.0 22.59 0.1594
129.6 0.5256 0.8064
167.6 0.4117 0.8088
0,
Lss = 2 in.
E 2 X 10la photons/& =rec Bottom of Top of Channel Channel 33.14 33.14 293.4 293.4 614.2 614.2 l9.38 19,38 . 55.78 55.78
29
6, i Tables
1, 6,
thickness
of
the
The addition
firebrick
of
about
a factor
ature
of
dent
2.5 of
the
total
thickness
of
total
thickness
from
photons/ca?*sec of
Tables
air
air
channel.
ratio
channel
concrete
side
increases
the
temperature Tables
in
the
2 in,
on the
conduction
loss
surface
of
from
8 to 3 ft the
of
the and
respect iid i
to
were
written-to
wall
for
time,
one
analyze
for
with
by temper-
an inci-
changing
the
increase
concrete
the
is
cases
the
in
the
increased
gamma current
steel
with
of
1 x 10la
an incident
side
for
on the
on the
reactor
and
side
effects
reactor
side side
and 2 in. on the
increases
of of
of
on the
concrete the
Changing on the
side
maximum
the
for
temperature
the
effects
over
the
the
thickness
of
outside
surface
from
concrete
about
the
of out-
concrete
50 to 700F
1OoF but
the
appreciably,
Transient
equations,
case,
Condition
with
32 through
proposed
the
lOoF.
and the
of
the
concrete
and 4 in.
slightly
for
: to Eqsi
transient-condition
the
steel
on the
temperature
the
the
wall;
difference similar
loss
Decreasing
a slight
the
concrete
affected
finite
of
3 and 4 may be compared
is
10 in.
maximum
cases
effects
of
of
only
the
the
*sec.
of
Case Studied
Eighteen
those
an incident
reactor
temperature
not
the
2 and 4 may be compared
maximum
loss
the
approximately
concrete the
in
20°F
4 in.
the. concrete
15’F
only
with
thickness
to
and
conduction
two gamma shields.
thickness
from
the
decreases
temperature
cases
Changing
thickness
side
conductian
the
photons/en?
the
in.
also
for
causes
1 and 2 and Tables
the
decreases
of to
of
changing
steel
2 x 1012
to
7.5
changing
photons/ca?*sec.
1 and 3 and Tables
the
the
addition
and by approximately
gamma current
changing
this
the
5 in.
decreases
4 to 2 in.
for
of
insulation
The maximum lOoF
effects
from
1 x 10la
the
the
insulation
5 may be’compared
loss.
for
by approximately of
1 and
approximately
of
2, and
gamma current
conduction
:
in.
concrete
Tables
;
and 7 may be compared
the
differencing
35 discussed
configuration The analysis
of
in the
with Chapter
reactor
was performed
3 room to
-
30
hd
determine the length of time over which a loss of coolant air flow could be tolerated before the temperature of the concrete would exceed the Such a loss of coolant air flow maximum allowable temperature of 212'F. could arise as a result o f a malfunction in the blower system supplying the Although natural convection currents would cause some circulation of the coolant air during 8 blower failure, it was assumed that coolant air.
the coolant air was stagnant during the failure so that the worst case could be analyzed. Under this assumption, the air channel serves only as an insulating material and removes no heat from the wall. The conditions established for the analysis of this particular case were a S-in.-thick layer of firebrick insulation, a 4-in.Othick layer of mild steel for the first gamma shield, the 3-in.-wide air channel, a 2in.-thick layer of mild steel for the second gamma shield, and a 6-ftthick concrete wall for the biological shield. A simple computer program
t
was written to perform the calculations, but the zero-time temperatures and heat depositions for each segment in the composite wall were calculated by hand and used as fixed numbers in the program.
This computer
program was used only to obtain a first approximation to the transient situation for one particular case, and the details of the program are not presented here. The program was run for elapsed times of t = 1.0 hr, t = 2.0 hr, t = 3.0 hr, t = 4.0 hr, and t = 5.0 hr for the condition of internal heat
generation (reactor at power during blower failure) during the transient period.
The program was then run again for the same elapsed times but
for the condition of no internal heat generation (reactor shutdown simultaneous with blower failure) during the transient period.
The
computer program used to analyze the condition for internal heat generation is given in Table 8. To analyze the condition of no internal heat generation, Q2C through Ql9SS in Table 8 are set equal to zero.
The
resulting temperature distribution in the proposed reactor room wall
-
analyzed for the condition of internal heat generation during the transient period is shown in Fig. 4, and the temperature distribution in the wall with no internal heat generation during the transient period is illustrated in Fig. 5.
--
P
cbt
31 i
.
,
Table 8. Cdmputer Program Used to Analyze the Proposed Reactor Room Wall for the Condition of Internal Heat Generatfon
32 Table 8 (continued)
4
33
ORNL Dug. 67-12003
soa
roa
LEQENO
L
@ @ @ @
TEMPERATURE DISTRIBUTION AT 1. 0.0 HRS.
@ @
TEMPERATURE DISTRIBUTION AT T TEMPERATURE DlStRlaUTlON AT T
TEMPERATURE DISTRIBUTION AT 1. 1.0 HRS. TEMPERATURE DISTRIBUTION AT 1. 2.0 HRS. TEMPERATURE DISTRIBUTION AT T 8 3.0 HRS. 4.0 HRS. 5.0 HRS.
200
IO0
30
g.
I-)
.
4. Temperatu rnal Heat Gene ient Period.
35
40
bution i n Proposed Reactor Room Wall te Maintained During Loss-of-Wall-Cool-
34
II ORNL 0-
80f
400
I
6 @
LEGEND
8T-ILDM
TEMPERATURE OlSTRlBUTlON AT T
0.0 HRS.
T
-
@
TEMPERATURE OlSTRlBUTlON AT t
@
TEMPERATURE DISTRIBUTION AT t
1.0 HRS. 0.0 HAS. S.0 HRS.
0
@
TYPERATORE OISTRIBUTION AT t
4.0 WRS.
L
0 TEMPI
u
.
TEMPERATURE OISTR18UTION AT
soa
L
U
s
U
t
200
1
IO0
1 1 1
WALL THICKNESSES t INCHES 1
F i g . 5. Temperature Distribution i n Proposed’Reactor Room Wall With No Internal Heat Generation During the Loss-of-Wall-Coolant Transient Period.
!
i
35 5.
CONCLUSIONS
Two b a s i c conclusions may be drawn from t h e r e s u l t s o f t h e parametric s.tudies made i n t h i s i n v e s t i g a t i o n of t h e proposed c o n f i g u r a t i o n of a laminated wall t o p r o t e c t t h e c o n c r e t e b i o l o g i c a l s h i e l d from t h e gamma c u r r e n t w i t h i n t h e room housing a 250-Mw(e) molten-salt breeder r e a c t o r , a h e a t exchanger, and a b l a n k e t - s a l t - t o - c o o l a n t -
fuel-salt-to-coolant-salt s a l t h e a t exchanger.
The f i r s t b a s i c conclusion i s t h a t w i t h a i r used
as t h e w a l l coolant, t h e proposed c o n f i g u r a t i o n i s a c c e p t a b l e f o r an i n c i d e n t monoenergetic (1 MeV) gamma c u r r e n t of 1 x lola photons/cn?*sec f o r a l l c a s e s considered i n which t h e t h i c k n e s s o f t h e f i r e b r i c k i n s u l a t i o n was 5 i n . o r more.
A second b a s i c conclusion i s t h a t t h e
proposed
c o n f i g u r a t i o n i s n o t a c c e p t a b l e f o r those c a s e s considered w i t h an i n c i d e n t monoenergetic (1 MeV) gamma c u r r e n t o f 2 x 1Ol2 photons/ca? . s e c because t h e maximum allowable temperature o f t h e c o n c r e t e (212OF) i s a
exceeded by 50 to 100째F.
The v a l u e s o f s e v e r a l of t h e parameters o f
i n t e r e s t i n t h i s study t h a t were obtained from t h e cases analyzed f o r a gamma current o f 1 x ' ' 0 1
photons/cnP*sec a r e given i n Table 9 .
Based on t h e assumption t h a t t h e f l o o r and c e i l i n g o f t h e reactor room have t h e same laminated c o n f i g u r a t i o n as t h e walls, g i v i n g a t o t a l llwallll s u r f a c e a r e a of 8276 f ?
, the
proposed w a l l c o n f i g u r a t i o n w i l l allow t h e
conduction l o s s from t h e r e a c t o r room t o be maintained a t a l e v e l below
1 Mw if t h e t h i c k n e s s o f t h e i n s u l a t i o n i s 5 i n . or more.
Further,
based on an a i r v e l o
c and an a i r c o o l a n t channel width
o f 3 in.,
m f o r cooling the wall.
a i r i s an a c c e p t a b l e
A g e n e r a l conclusion t h a t may be drawn from t h e l i m i t e d a n a l y s i s
made o f one t r a n s i e n t - c o n d i t i o n case i s t h a t i f t h e ambient temperature of t h e r e a c t o r room rema
a t approximately llOO째F, t h e proposed con-
f i g u r a t i o n of t h e r e a c t o
om w a l l s t u d i e d i n t h i s c a s e can s u s t a i n a
loss o f c o o l a n t a i r flow under t h e c o n d i t i o n s described i n Chapter 4 f o r approximately 1 hour bef exceed 212'F.
t i
I f a zero
re. of t h e concrete begins t o
a current is assumed, t h e
llpermissiblell l o s s - o f - c o o l a n t - a i r time i s g r e a t e r than one hour b u t less than two hours.
. . .
. Table 9. Range o f Parameters of I n t e r e s t i n S t u d i e s Made of Proposed Wall With An I n c i d e n t Gamma Current of 1 x lora photons/ct#*sec Parametric Conditions LI 5s Lss Lc li3 Variable o f Minimum Maximum I n teres t Value Value (in.) (in.) (in.) (ft) (OF) Skin AT,'F
F i r s t steel s h i e l d AT,
4.
2.5 10
4
906
2
2 a
10.9
10 2.5
2 4
2
2.5 2.5
4 2
2
1.1 1.57
10 2.5
a a
a a
8
50
a a a
a
4
3 8
70 50
2 4
2 2
3 8
70
10
4
2
3
70
5
2
2
8
50
5
2
4
70
0.58
7.5
2
2
3 8
1.32
10 2.5
4 2
2 a
8 a
50 a
2.38 F
Second steel s h i e l d AT, OF
0.08
A i r v e r t i c a l temperat u r e g r a d i e n t , OF/ft
0.77
Tc max' (Q12'F)
2
2
726
Insulation AT, OF
0
10 2.5
4
0.22
0.021
F
124 205.6
T max, f t (Tmax < 212'F)
0.11
m, Mw
0.096
X
a
a
a
50
w
OI
50
~-
a
This parameter h a s l i t t l e e f f e c t i n combination with t h e o t h e r parameters given, and t h e v a l u e s o f t h e v a r i a b l e s of i n t e r e s t are e s s e n t i a l l y t h e same f o r v a r i o u s v a l u e s o f t h i s parameter
.
e:.
37
If a wall of the type proposed is used, the temperature of the conCrete,
TCâ&#x20AC;&#x2122;
or the conduction loss, or both, can be controlled to some
extent by varying the physical characteristics of the wall.
The thickness
of the insulation can be increased, but the desirable effect approaches a limit rather rapidly.
As the results of our parametric studies have
indicated, an insulation thickness can be reached that will cause conduction back into the reactor room.
The total thickness of the mild-
steel gamma shields can be increased with good results up to the point where the gamma current is reduced by several orders of magnitude. After this point is reached, adding more steel for gamma shielding does not produce sizable changes in the maximum temperature of the concrete. A total of approximately 6 in. of steel is sufficient for an incident
monoenergetic (1 MeV) gamma current of 1 x 10â&#x20AC;?
photons/cu?*sec.
The
thickness of the mild-steel gamma shields should be arranged so that the major portion of the steel is on the reactor side of the air channel. Placing the major portion of the steel on the concrete side of the air channel results in the undesirable effect of raising the maximum tempera-
j
.
ture of the concrete.
Shadow shielding of the particular components
within the reactor room that may be causing a large gamma current appears to be a better solution than increasing the thickness of the wall laminations for gamma currents greater than 1 x 10la photons/ca?*sec. When sufficient information becomes available, an overall energy balance should be written, starting with the fissioning process in the reactor and extending out through the wall of the reactor room to an outside surface.
This balance i s necessary to determine whether or not a conduction loss of 1 Mw will permit maintenance of the desired ambient temperature within the reactor room without the addition of auxiliary cooling ar heating systems.
39
APPENDICES
41 Appendix A EQUATIONS NECESSARY 'ID CONSIDER A MULTIENERGETIC GAMMA CURRENT
The equations derived in Chapter 3 of this report were based on the assumption that the incident gamma current is monoenergetic. If the energy distribution of the incident gamma current is known, this curr,ent can be represented as a multigroup current.
The equations in which an
incident multigroup gamma cur nt appears, either directly or indirectly, must be written to account fo this segmentation in gamma energy. This multigroup modification has been made in the following equations, and they are to be used in place of the correspondingly numbered equations in Chapter 3 when the energy distribution of the gamma current is known. The subscript i denotes the energy group, and the terms are defined in Appendix E.
(A.9a)
42 dT = -(T 1 - To) dx L L
J
(A. 13)
(A.
',pie
PiX(cri
'T
=
- 1) + (1 - Ai)e
14)
(A. 16) e
,
(A. 17)
Q j += l
=i
Q j+ li =
i
(QO(j),
-
Sji)
(A. 18)
(A. 18a)
(A. 18b)
(CJ Q( 44 +
i
where
1 +
-Lss +-
k Lc
kSS
c
)
44 Appendix B . EVALUATION OF THE CONVECTIVE HEAT TRANSFER COEFFICIENT
The average convective heat transfer coefficient, h, for the walls of the air channel was evaluated by using the expression published by ~~
Kre ith
. h = 0.036
Ek :eR
* 8 p S/3
,
where 0
k = thermal conductivity of air, Btu/hr*ft* F,
H = vertical length of the air channel, ft, ReH = Reynolds number evaluated at the top of the air channel, and Pr = Prandtl number evaluated for air. The Reynolds number evaluated at the top of the air channel,
where .
- -
U = the bulk air velocity, ft/sec, p = density of the a i r , lb/ft?, and = viscosity of air, lb/ft*sec. The Prandtl number evaluated for air,
where C = the specific heat of air at a constant pressure, Btu/lb*OF. P In the range of temperatures considered, Pr is-approximately constant and equal to 0.72.
Kreith'2
expression for h
was evaluated for various
air-wall mean temperatures in the air channel, and the results are on the following page. lFrank Kreith, p. 286 in Principles of Heat Transfer, International Textbook Company, Scranton, Pennsylvania, 4th printing, 1961.
45
I
-T
.h
0
(Btu/hr*ft? 'OF)
100 130 150
5.15
5.04 5.04
The mean temperature of the walls of the air channel is expected to be approximately 130 to 150째F, and a value of 5 was used for the convective heat transfer coefficient at the walls of the air channel.
i
i
46 Appendix C
VALUES OF PHYSICAL CONSTANTS USED IN THIS STUDY
Values f o r the gamma energy attenuation coefficient, %, the t o t a l gamma rttenuatiou coefficient, p, and the dimensionless constants a, @, and A used i n the Taylor buildup formula f o r a gamma energy of 1 Hev are tabulated belov.
%? Material Type 347 atainleas steel Kaolin insulatingbrick Mild steel Concrete
P
L(ft-11
(ft-1)
a
p
6.28.
14.0ab
0.0895'
0.04C
0.088'
O.02gd
aC lod
0.0895' 0.0886
0.04C 0.029'
lod
0.367' 6.30. 1.99d
0.83Sd 14.02. 4.55d
BC
Values f o r the density, p # Specific heat, c thermal COndUCtiVitp, k, ant equivalent P' thermal conductivity a t interfaces of adjacent materials, f o r materiala in the proposed laminated wall i n t h e i r order of occurrence from the reactor outward a r e tabulated below.
E,
1
0
Material Type 347 rtainless s t e e l Kaolin insulatlag brick Mild steel
l & a lbm/ft3) ( 7.Bb
b86.gb 0.159
0.433' 7.83b
27.03e uq.ab
0.29 0.11e
0.15"
0.298
26.0e 0.0232
Air
0.060e
0.241e
0.0174e 0.0232
Mild steel
7.83b
488Ab
0.lP
Concrere
2.3Sd
146.7d
0.20e
26.0' 0.584 0.W
*E. P. Blizard and L. S. Abbott, editors, p. 107 i n Reactor Handbook, Vol. S, Part B, Johh Uiley and Sons, New York, 1962. bM. M. El-Uakil, p. 223 i n Nuclear Power Engineering, McGraw-Hill Book C~IU~UII~, be., F i r s t Edition, Nev York, N w York, 1962.
%. P. Blizard m d L. S. Abbott, editors, p. 116 i n Reactor Randbook, Vol. S, Part B, John Wiley md Sons, New York, 1962. dnReactor Physics Constants," USAEC Report ANL-5800, Argonne National Laboratory, pp. 653-6578 July 1963. 'Frank Kreith, pp. 533-535 in Principles of Heat Transfer, International Textbook Company, 4th printing, Scranton, Pennsylvmia, 1961.
c
47
Appendix
D
TSS COMPUTER PROGRAM
A program-was
developed 8 through
equations-(Eqs. figuration writ
of
material for
in
order
groups
incident
sixteen
Shield
to
for
Study) the
in Chapter
air
to
the
handle
For
a problem of
and 45 seconds
conAs
up to
and up to eight
The calculations
3.
the
conditions.
will
channel,
solve
proposed
steady-state
program
combinations
one minute
computer
evaluate
the
gamma current.
different
is
CDC 1604-A
necessary
excluding
described
time
the
room wall
TSS (Thermal
the
and
machine
31)
reactor
laminati.ons,
groups the
the
the
ten,
for
five energy
are
performed
five
energy
with
laminations
(cases),
and the
compilation
used
evaluate
the
time
is
56 seconds. A Newton-Raphson The convergence Eq.
29 must
iteration
criterion
agree
for
to within
right
and left
sides
of
gence
criteria
could
machine cause
time, the
but
program
Eq.
with
very
little
more
uses
the
gamma current a vertical
reactor
lations
at
and bottom manner the
,interface
room and several as it
in which
following
the
a given
temperature
for
to within
0.10.
accuracy method
to
If
material
up the
were
necessary
known
program air
present.
increase
in
the
this
the
conver-
calculate
be-
incident
accuracy
the
that
These
be obtained
real
of
is
attenuated
information
gamma the
interfaces.
profile
points
xT max is
would
more
from
and xT max, sides
a corresponding
and to calculate the
&
and left
to calculate
skin,~the
at
right
be modified
the
does
to
criterion
interface.
temperature
could
channel Both
input
data
for
the
be modified
rather
the are
interface
than
setup
of
to do calcu-
just
the
at
program
prepared-are
of
the
top
and
the
explained
in
discussion.
The TSS computer with
at
real
approximate
c0ul.d
the
and the
smaller
program
If
the
be made
required,
incident
that
agree
material
each
is
is
14 must
at each
current.at
Q 0.05,
gamma current the
scheme
photon of
the
program current inside
is
set
incident surface
up for upon
of
the
a given the
wall
..
physical
reactor is
fixed
situation
room wall. at
a given
The value.
48 The composite w a l l i s composed o f f i v e m a t e r i a l regions, and progressing
.
from t h e i n s i d e s u r f a c e outward, these regions are (1) a t h i n s t e e l skin, (2) an i n s u l a t i n g m a t e r i a l , (3) t h e f i r s t steel gamma s h i e l d , (4) t h e second steel gamma s h i e l d , and (5) t h e concrete b i o l o g i c a l s h i e l d with a f i x e d temperature on t h e o u t s i d e surface.
The 3-in.-wide
a i r channel
placed between t h e f i r s t and second gamma s h i e l d s i s n o t considered a
material region.
By c a l c u l a t i n g a v e r t i c a l temperature g r a d i e n t i n t h e
a i r channel, t h e program w i l l c a l c u l a t e a t both t h e bottom and top of t h e r e a c t o r room w a l l t h e
1, gamma h e a t generation r a t e i n each m a t e r i a l , 2. temperature a t each m a t e r i a l i n t e r f a c e and temperature changes a c r o s s each m a t e r i a l ,
3. 4.
conduction h e a t l o s s from t h e r e a c t o r room t o t h e a i r channel,
5.
h e a t i n t h e concrete conducted both toward and away from t h e a i r
r a d i a t i o n heat t r a n s f e r rate between t h e w a l l s of t h e a i r channel, channel, and t h e
6.
maximum temperature i n t h e concrete and i t s corresponding l o c a t i o n . The program i n p u t deck allows t h e use of any material i n any region
of t h e composite wall.
*
For a f i x e d i n c i d e n t photon c u r r e n t , a f i x e d
i n s i d e w a l l temperature, a f i x e d i n l e t a i r v e l o c i t y and temperature, and fixed w a l l m a t e r i a l s , t h e c a l c u l a t i o n o f a p a r t i c u l a r case i s done by s e l e c t i n g a l l material t h i c k n e s s e s and t h e temperature o f t h e o u t s i d e s u r f a c e of the concrete w a l l .
A t p r e s e n t , t h e program w i l l allow a maxi-
mum of 32 cases t o be run, b u t i t can e a s i l y be expanded t o handle more.
P r e p a r a t i o n o f Input Data
The f i r s t set of input d a t a c o n s i s t s o f energy-dependent information p e r t a i n i n g t o t h e i n c i d e n t photon c u r r e n t and t o t h e n u c l e a r p r o p e r t i e s of t h e m a t e r i a l s chosen f o r each region i n t h e wall.
The o r d e r i n which
t h e information i s supplied i s given on t h e following page. - e
Ld *
49
m &i 0
Card 1.
The incident photon current Qslil), Q=(2), . ..> QSl(8). (Btu/hr*ft?) for each of eight possible energy groups. Card 2. EMUl(l), EMLl1(2), . . . . EMIJl(8). The energy absorption coefficient (l/ft) in the first region of the wall (the inner skin) for each of eight possible energy groups. Card 3. AMUl(l), AMU1(2), . . . . AMul(8). The mass attenuation coefficient (l/ft) 'in the first region of the wall (the inner skin) for each of eight possible energy groups. Card 4. ALPHA(l), ALPHA1(2), . . . . ALPHAl(8). The dimensionless constant Q used in the Taylor buildup formula in the first region of the wall (the inner skin) for each of eight possible energy groups. Card 5. BETAl( BETA1(2), . . . . BETAl(8). The dimensionless constant 8.used in the Taylor buildup formula in the first region of the wall
s
(the inner skin) for each of eight possible energy groups. Card 6. Al(l), A1(2), . . . . Al(8). The dimensionless constant A used in the Taylor buildup formula in the first region of the wall (the inner skin) for each of eight possible energy groups. Card 7. EMlJ2(1), EMU2(2), . . . . EMU2(8). The same as Card 2 except for the second region of the wall (insulation). Card 8. AMUP( AMU2(2), . . . . AMJP(8). The same as Card 3 except for the second region of the wall (insulation). Card 9. ALPHA;!(l), ALPHA2(2), . . . . ALPHA2(8). The same as Card 4 except for the second region of the wall (insulation). Card 10. BETA2(1), BETA2(2), . . . . BETA2(8): The same as Card.5 except for the second region of the wall (insulation). Card 11. A2(1), A2(2), . . . . A2(8). The same as Card 6 except for the second region of the,wall (insulation). Card 12. EMU3(1), EMU3(2), . . . . EMID( The same as Card 2 except for the third region of the wall-(the first gamma shield). Card 13. AMU3(1), AMU3(2), ..,, AMU3(8). The same as Card 3 except for the third region of the wall (the first gamma shield)., Card 14. ALPBA3(1), -ALPIiA3(2), .*., ALPHA3(8). The same as Card 4 except for the third region of the wall (the first gamma shield).
50 Card 15.
BETA3(1), BETA3(2),
..., BETM(8).
The same as Card 5 except
f o r t h e t h i r d region of t h e w a l l ( t h e f i r s t gamma s h i e l d ) . Card 16.
A3(1),
A3(2),
.,., A3(8).
The same a s Card 6 f o r t h e t h i r d
region of t h e w a l l ( t h e f i r s t gamma s h i e l d ) . Card 17.
EMU4(1), EMU4(2),
..., EMU4(8).
The same as Card 2 except
f o r t h e f o u r t h region of t h e w a l l ( t h e second. gamma s h i e l d ) . Card 18.
AMU4(1), M 4 ( 2 ) ,
..., AMU4(8).
The same as Card 3 except
f o r t h e f o u r t h region of t h e w a l l ( t h e second gamma s h i e l d ) . Card 19.
..., ALPW4(8).
ALPHA4(1), ALPHA4(2),
The same as Card 4
except f o r t h e f o u r t h region of t h e w a l l ( t h e second gamma s h i e l d ) . Card 20.
BETA4(1),
BETA4(2),
...,
BETA4(8).
The same as Card 5
except f o r t h e f o u r t h region of t h e w a l l ( t h e second gamma s h i e l d ) .
..., A4(8). The same as Card 6 except f o r t h e f o u r t h region o f t h e w a l l ( t h e second gamma s h i e l d ) . Card 22. EMU5(1), EMU5(2), ..., EMU5(8). The same as Card 2 except f o r t h e f i f t h region o f t h e w a l l ( t h e b i o l o g i c a l s h i e l d ) . Card 23. AMU5(1), AMU5(2), ..., AMU5(8). The same as Card 3 except t
Card 21.
A4(1), A4(2),
f o r t h e f i f t h region of t h e w a l l ( t h e b i o l o g i c a l s h i e l d ) . Card 24.
ALPHAs(1); ALPHA5(2),
..., ALPHAs(8).
The same as Card 4
except f o r t h e f i f t h region o f t h e w a l l ( t h e b i o l o g i c a l s h i e l d ) . Card 25.
BETAS(l),
BETAS@),
..., BETAS(8).
The same as Card 5
except f o r t h e f i f t h region o f t h e w a l l ( t h e b i o l o g i c a l s h i e l d ) . Card 26.
A5(1), A5(2),
..., A5(8).
The same as Card 6 except f o r
t h e f i f t h region o f t h e w a l l ( t h e b i o l o g i c a l s h i e l d ) . The format statement f o r a l l o f t h e above c a r d s i s 8F9.0.
Since
only t h e f i r s t 72 spaces on each d a t a card are used, t h e l a s t e i g h t may be used f o r i d e n t i f i c a t i o n purposes.
I f fewer than e i g h t energy groups
are used, t h e unused d a t a f i e l d s may e i t h e r be punched w i t h a z e r o or l e f t blank.
I n e i t h e r case, t h e energy-summing DO loops s u b s c r i p t e d
J, K, L, and N must be changed t o correspond t o t h e number of energy
groups used; t h a t is, i f t h e r e are s i x energy groups, DO 100 I = 1,6; and K, L, and N a r e a l s o 1,6.
I f t h e DO loops are not changed t o c o r r e s -
pond t o t h e number of energy groups used, d i v i s i o n by zero w i l l occur.
51
*
The next s e t of d a t a entered i s energy'independent and i s assumed t o be c o n s t a n t over t h e range of temperatures covered i n t h e program. This information should be given on t h e two following c a r d s . Card 27.
CON1, CON2, CON3, CON4, CONS, TO, HT, and HF.
The thermal
c o n d u c t i v i t i e s (Btu/hr*ft*OF) of t h e m a t e r i a l s i n each of t h e f i v e r e g i o n s The temperature on t h e
should be e n t e r e d i n the f i r s t f i v e d a t a f i e l d s . i n s i d e s u r f a c e o f t h e r e a c t o r room wall, TO i n
OR,
the height of the
r e a c t o r room, HT i n f t , and t h e f i l m c o e f f i c i e n t on t h e s i d e s of t h e a i r channel, HF i n B t u / h t * f e o o F , should be e n t e r e d i n d a t a f i e l d s s i x through eight.
The format f o r t h i s card i s t h e same as t h a t f o r t h e previous
26 c a r d s (8F9.0). Card 28,
TA, EPSIL, VEL, ACHAN, CP, RHO, and SIGMA a r e r e s p e c t i v e l y
t h e i n l e t a i r temperature,
0
R, t h e e m i s s i v i t y o f t h e s u r f a c e o f t h e a i r
channel (dimensionless and assumed t o be equal f o r both s i d e s o f t h e a i r channel), t h e v e l o c i t y of t h e a i r , f t / s e c , ft?, t h e s p e c i f i c h e a t of a i r , Btu/lb-OF,
t h e width o f t h e a i r channel, t h e d e n s i t y of air, lb/ft?,
t h e Stefan-Boltzmann c o n s t a n t (Btu/hr-ft? *OP), e n t e r e d according t o format 6F9.0,
F18.0.
and
These v a l u e s must be
Again, t h e l a s t e i g h t spaces
can be used f o r i d e n t i f i c a t i o n .
P r e p a r a t i o n o f Case Data
Once t h e i n p u t d a t a have been supplied, one card must be prepared f o r each c a s e t o be run. and T6.
EL1 through EL5
be used f o r each of t h e f
t o t h e material t h i c k n e s s e s ( f t ) t o
s i n t h e w a l l , and T6 i s t h e tempera-
t u r e of the external surf
concrete biological shield i n
The format 8F9.0 allows n
f o r each d a t a f i e l d and t h e last e i g h t
spaces f o r i d e n t i f i c a t i o n quired.
OR.
cases, the c a r d s could be numbered
Numbering
t h e u s e r ' s convenience and i s n o t re-
The firstSDO loo
rogram must always be changed t o DO
29 through 44.
w
This c a r d c o n t a i n s EL1, EL2, EL3, EL4, EL5,
5000 I = l , N where N is t h e number o f c a s e s t o be run.
A l l c a s e s must
have t h e same a i r temperature, TA, and t h e statement immediately
1
-
52
following DO 5000 I = 1 , N must be w r i t t e n to correspond t o t h e a i r temperature used.
ELS(I),
The DIMENSION statement c o n t a i n i n g ELl(1) through
T6(I), BOP(I), and BAM(1) must be checked t o see t h a t a s u f f i c i e n t
dimension size i s given t o allow a l l o f t h e c a s e s t o be run.
BOP(1) and
BAM(1) are dummy v a r i a b l e s and may be l e f t blank.
Typical Computer Sheets
The assembly o f t h e c o n t r o l cards, deck, i n p u t d a t a , and case d a t a c a r d s f o r t h e TSS computer program i s i l l u s t r a t e d i n Fig. D.l.
Typical
d a t a f o r 32 cases t o be run w i t h one energy group a r e given i n Table D.1.
The o u t p u t d a t a a t t h e bottom o f t h e a i r channel f o r one case are given i n Table D.2,
and t h e o u t p u t d a t a a t t h e top o f t h e a i r channel f o r t h e
case are given i n Table D.3.
53 t
ks L
c
I
Fig. D . l .
Assembly of Data Cards for TSS Computer Program.
54
55
1
56
3 0 0 2 UP1
3003 V i ? !
n
h d I
57
I
J'
I N A T l d Y THICUNFSSES (FEET)
.
.
- ...
.
.
-.
.-.-
-.
_.
..
..
.
..
..
.. .-
60
Appendix E NOMENCLATURE
A = dimensionless c o n s t a n t used i n t h e Taylor buildup equation
4
= u n i t a r e a o f reactor room wall, f t a
= s p e c i f i c h e a t a t c o n s t a n t pressure, Btu/lb*'F P E = energy o f i n c i d e n t gamma c u r r e n t , MeV H = v e r t i c a l l e n g t h o f a i r channel, f t
C
h = convective h e a t t r a n s f e r c o e f f i c i e n t , Btu/hr*ft? *OF '
-
k = thermal conductivity, Btu/hr*ft*'F
= e q u i v a l e n t c o n d u c t i v i t y where t h e s u b s c r i p t s a and b r e f e r t o
ka-b
any two a d j a c e n t materials
L
5:
t h i c k n e s s o f a material lamination
Lch = width of a i r channel ( d i s t a n c e between a d j a c e n t surfaces of
f i r s t and second s t e e l gamma s h i e l d s ) , f t
MWL = h e a t conduction rate o u t of t h e reactor room t o t h e a i r channel, Mw Q = volumetric gamma h e a t i n g rate, Btu/hr-f$ q* = h e a t conduction rate o u t o f t h e reactor room t
t h e a i r channel,
Btu/hr= ft? q i = rate a t which t h e gamma h e a t generated i n t h e c o n c r e t e i s con-
ducted back toward t h e a i r channel, B t u / h r * f t ?
QR = rate o f r a d i a n t h e a t t r a n s f e r between t h e w a l l s o f t h e a i r channel, Btu/hr* f t?
T = temperature, OF Ua = bulk v e l o c i t y o f c o o l a n t air, f t / s e c x = d i s t a n c e perpendicular t o t h e s u r f a c e o f t h e r e a c t o r room w a l l ,
ft
a
and ~3= dimensionless c o n s t a n t s used i n t h e Taylor builkup equation E = s u r f a c e e m i s s i v i t y of walls o f a i r channel
0 = t i m e , hours p = t o t a l gamma a t t e n u a t i o n c o e f f i c i e n t , ft-1
%
= gamma energy a t t e n u a t i o n c o e f f i c i e n t , f t - l
-<
w
61
p = density, lb/ft? (J
= Stefan-Boltzmann constant
go = incident gamma current, photons/c# â&#x20AC;&#x2DC;sec
Subscripts Used With Terms
0 through 6 = numbers denoting a lamination interface as illustrated in Fig. 2 and usually associated with temperature, T a = air
c = concrete I = insulation i = energy group j = lamination
s = skin lamination on reactor side of wall
FS = first steel gamma shield SS = second steel gamma field T = total
-C
U
63 ORNL TM-2029 Internal 1.
2. 3. 4. 5. 6-7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. , 21. 22. 23. 24. 25.
M. C, E. E. R. W. F. S.
Bender E. Bettis S. Bettis G. Bohlmann B. Briggs K. Crowley L. Culler J. Ditto
H. D. D. W. F. C.
G. A. E. F. C. l-l.
Duggan Dyslin Ferguson Ferguson Fitzpatrick Gabbard
W. W. A. 'P. H. P. R. G. R. H.
R. R. G. N. W. R. J. H. E. E.
Gall Grimes Grindell Haubenreich Hoffman Kasten Kedl Llewellyn MacPherson McCoy
Distribution 26. 27.
R. L. Moore H. A. Nelms
28. 29. 30.
E. L. Nicholson L. C. Oakes A. M. Perry T. W. Pickel J. R. Rose M. W. Rosenthal Dunlap Scott W. C. Stoddart
31. 32-33. 34-35. 36. 37.
External
38. 39. 40. 41. 42. 43. 44. 45-46.
D. R. H. J. M.
A. E. K. R. E.
Sunberg Thoma Walker Weir Whatley
47. 48. 49-58. 59. 60.
Document Reference Section GE Division Library Laboratory Records Department Laboratory Records, ORNL R. C. ORNL Patent Office
J. C. White W. R. Winsbro Central Research Library
Distribution
61.
P. F. Pasqua, Nuclear Engineering Tennessee, Knoxville, Tennessee
62.
L. R. Shobe, Engineering Mechanics Department, Tennessee, Knoxville, Tennessee '
63-77. 78. .
Department,
University
Division of Technical Information Extension Laboratory and University Division, USAEC, OR0
University
of of
&ii