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ORNL-TM-2029.txt
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ORNL-TM-2029.txt
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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.
|
|
.E‘( f
) (‘ )
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\/\.,‘_\\
\"
\
)
)
‘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
)
)
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
~
-
)
¥
£
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)