thermal stress and strain fatigue analysis
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operated y
UN IO N CARBIDE CORPORATION
for the
U.S . ATOMIC ENERGY COMMISSION
5 i
ORNL TM 78
THERMAL STRE SS A N D STRAIN FATIGUE AN AL Y S S OF THE
MSRE
FUEL AN D CO OLA NT PUMP TANK S
C .
G
abbard
NOTICE
Th is document contai ns information of a prel iminary na ture and was prepared
pr imar i ly fo r in te rna l use a t the Oak R idge Nat iona l Labora tory . I t i s sub jec t
to re vis io n or correct ion and therefore does no t represent a f inal report . The
in format ion i s no t to be abst rac ted repr in ted or o therw ise g iven pu b l ic d is -
seminat ion with out the approval of the ORNL pate nt branch Lega l and Infor-
mation Control Deportment.
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L E G A L N O T IC E
T h i s r epo r t w as prepared as
n
occount o f Government sponsored work . Nei ther the Uni ted S tates ,
nor the Commissio n, nor mny parson oct in g o behal f o f the Commiss ion:
A . Mokes any warronty or representat ion, expressed or impl ied, w i th res pect to the accuracy ,
completeness , or usefu lness o f the in formot ion conta ined in th i s repor t , or t ho t t he u s e o f
ony in format ion, opporotus , method, or process d isc lo sed in th i s repor t may not in f r ing e
pr i vate ly owned r ights ; or
B
Assumes
any l i a b i l i t i es w i th respect to the use of , or for damages
r e s u l t n g f ro m t h e u s e o f
ony in tormot ion, opporatus , method, or process d isc los ed in th i s repor t .
A s
used in the above, person ac t ing on behal f o f the Commiss ion inc lude s any employee or
cont rac tor
of the Commiss ion, or employee of such cont ractor , to the ex tent thot suc h employee
or cont rac tor o f the Commiss ion, or employee of such cont roc tor prepares , d isseminmtes , or
prov ides access to , any in format ion pursuant to h is employment
or
c on t rac t w i t h t he C om m i s si on ,
or h is employment w i t h such cont roc tor .
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Contract No. W-7405-eng-26
Reactor Div is ion
THERMAL-STRESS AND STRAIN-FATIGUE ANALYSES OF THE
MSR FUEL
ND
COOLANT
PUMP
TANKS
C
H Gabbard
DATE
ISSUED
OAK RIDGE NATIONAL LABORATORY
Oak Ridge Tennessee
opera ted by
UNION CARBIDE CORPORATION
f o r t h e
U
S. ATOMIC
ENERGY
COMMISSION
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CONTENTS
bstract
In t roduc t ion
Calc ula t i onal Procedures
t ra in Cycles
emperature Di s t r ibu t io ns
em perature D i s t ri b u ti o n C w e F i t t i n g
Thermal Stress Ana lysis
train Cycle Analysis
es u l t s
Temperature Di s t r ibu t io ns
hermal Stresses
t ra in Cycles
ressure and Mechanical St re ss es
ecommendations
Conclusions
References
Appendix
Distr ibution of Fiss ion Product Gas
Beta Energy
nergy Fl ux a t Pump Tank Outer Surf ace
Energy Flu x a t t h e Volute Support Cylinder Outer Surface
Energy F lux a t the Volute Support Cyl inder Inne r s ur fac e
Appendix
Estimation of Outer Surface Temperatures and
eat Transfer Coeff i c ien ts
Appendix C
Derivation of Boundary and Compatibility
quat ions f o r Thermal S t re ss Calcula t io ns
Appendix D
Explana tion of Procedure Used t o Evaluate
h e E f f e ct s o f C y cl i c S t r a i n s i n t h e MSRE Pumps
omenclature
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THERMAL-STRESS AND STRAIN-FATIGUE ANALYSES OF THE
MSRE FUEL AND COOLANT
PUMP TANKS
C H. Gabbard
Abstract
Thermal-s t ress and s t r a i n-f at igu e ana lyses of the MSR E
f u e l and coo lan t pump tan ks were completed f o r determining
the quan t i ty of coo l ing
i r
r e qu i re d t o o b t a i n t h e maximum
l i f e o f the pump tanks and t o de te rmine th e a cc ep tab i l i ty of
the pump tanks fo r the in tended service of 100 heat in g cyc les
from room tempe rature t o 1200°F and 500 r e a c to r power-change
cyc le s from zero t o 10 Mw.
A
coo l ing -air f low ra te of 200 cfm f o r the fu e l pump tank
was found t o be an optimum val ue t h a t pro vide d an ample margin
of sa fe ty . The cool ant pump tan k was found t o be capa ble of
the requ i red se rv ice withou t a i r cool ing .
I n t r o d u c t i o n
The f u e l pump fo r th e Molten S al t Reactor ~xp er im ent '
M S R E )
i s
sump-type
c e n tr if u g a l pump composed of a st a ti o n a ry pump ta nk and vo lu te
and
ro t a t i ng assembly ( see F ig. 1 ) .
The pump ta nk and vo lu te , which
i s co n st r uc t ed of
INOR-8
(72
N i
1 6 Mo, 7
C r
5 F e) ,
i s
a pa r t o f the
primary containment system, and th er ef or e th e high est degree of r e l i -
a b i l i t y
i s
r equ ir ed . The pump
i s
s imi la r t o o ther h igh- tempera tu re
mo lte n-s alt and liq ui d- me ta l pumps th a t have accumulated many thousands
of hours i n nonnuclear t e s t - loop service 2
Although these nonnuclear
pumps have been hi gh ly s ucc essf ul, th ey have no t been
s u b jec ted t o t h e
degree of therm al cy cl ing which
may
occur in a nuc lear p lan t .
t t h e r e -
fo re cannot be assumed from the ope rati ng record s t h a t pumps of t h i s type
w i l l be ad eq ua te f o r t h e MEBE.
S tr e ss c alc ula tio ns* were completed i n accordance wi th t h e ASME
Boiler and Pressure Vessel Code for determining the
w a l l
thicknesses and
nozz le r e in fo rcements r equ i red t o sa fe ly wi ths tand an in te rn a l p res sure
*Performed by L . V. Wilson.
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UNCLASSlF lED
ORNL R W G 5 6 0 4 3 A
S H F T W T ER
C OU P L IN G\ C OOLE D
S H F T S E L
LE K DETECTOR
L U B E O I L I N
L U B E O I L B R E T H E R
S H FT S E L
L U B E O I L O U T
LE K DETECTOR
SHIELDING PLUG
B U B B L E R T Y P E
L E V E L I N D IC T O R
X E N ON S TR IP
BUOY NCY
L E V E L
INDIC TOR
Fig 1 MSRE Fuel Pump G e n e r a l A s s e m b l y Dr a wi n g
P E R
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Ca lcu lat ion al Procedure s
Strain Cycles
Since thermal str es se s ar e considered t o be t ra ns ie nt and i n some
cases subjec t t o re l ie f by s t re s s re laxa t ion a t opera t ing tempera tu res,
they must be evaluated on a st ra in -fa ti gu e bas is, a s required by the Navy
Code. Two ty pe s of s t r a i n cy cl es
w i l l
occur during normal operation of
t h e pump:
1
hea tin g and cooling when th e re ac to r system i s heated from room tem-
peratu re t o operat ing temperature and returned t o room temperature,
and
2. power-change cyc les when the re ac to r power i s ra is ed from zero t o 10
Mw and returned t o zero.
The change i n s t r a i n must a ls o be considered f o r a loss-of-c ooling
a i r incident i n which the operating conditions would change from ( 1) r e-
ac to r power operation a t 10
Mw
w ith d e sign a i r flo w to (2 ) o p erat io n a t
10 Mw with no a i r f low t o (3) zero power operation with no a i r f low.
Temperature D i s t r i b u t io n s
The i n i t i a l s tep in the the rmal - s tre ss and s t ra in - fa t i gue ana lyses
was t o determine the temperature dis tri bu tio ns i n the pump tank f o r various
operating conditions based on the ef fe ct s of i nt er na l heat generation,
conductive heat f low, convective and radi ati ve heat t ra ns fe r with the
s a l t , and cooli ng of th e sh ie ld in g plug and upper pump tank s urf ace .
The
generalized heat conduction code4
GHT
Code) was used t o o bt ai n th e tem-
perature dist rib uti on s. During reaot or power operation, the fu el pump
tank w i l l be he ated by gamma, ra di at io n from bot h t he re ac to r ve ss el and
t h e f u e l s a l t
i n the pump tank and by be ta rad iat ion from the fi ss io n-
product gases. The maximum gamma heat -gen erat io n r a t e du ring r e ac to r
opera t ion a t 10
w
was calculated* t o be 18 .70 ~ t u / h r - i n . a t the inner
sur fac e of the upper port ion of t he pump tank, giv ing an average heati ng
ra te through the 1/2-in. - thick pump tank wall of 16.23 ~ t u / h r - i n . The
g a m heat-generation ra te i n the shielding plug above the pump tank
alcul.ated by B W Kinyon and H
J
Westsik.
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was cal cul ate d a t increments of 1/2 i n. based on an expone ntial decrease
i n t he he a t ing r a t e .
The be ta h eating, which va ri ed from 4.80 t o 22.22
~ t u / h r .n .2 was es t imated by dis t r ib ut in g the t o t a l be ta energy emit ted
i n th e pump tank over t h e pump-tank surf ace exposed t o th e f issio n-p rod uct
gase s (s ee Appendix A .
Preliminary ca lc ula t ions with the GHT Code indica ted tha t control led
coo ling of t h e upper pump tank sur fac e was necessary , no t onl y t o lower
the tnaximum temperature,
but a ls o t o reduce the tempera ture gradient i n
the sph erica l port ion of the pump tank near i t s
junction with the volu te
support cyl ind er i n order t o achieve acceptable thermal str es se s These
calcu la t io ns a l so predic ted excess ive ly high temperatures i n the volu te
sup por t cy li nd er between th e pump ta nk and the pump vo lu te. These hig h
temperatures were caused by a se ri es of po rts i n th e volu te support cyl in-
de r wa l l fo r dra in ing the sha f t l abyr in th l eakage back in to the pu p tank.
The dra in po r ts were or ig in a l ly loca ted
t
th e bottom of t he c ylin der
and r e s t r i c te d the conduction of heat downward i n t o th e s a l t . The maxi-
mum tempera tures were reduced t o n acceptable l ev e l by center ing th e
dr ai n po rt s between t h e pump tank and the pump vol ut e so th a t h eat con-
duct ion would be unres t r ic ted i n the both dire c t ion s . Fin a l tempera ture
di st r i bu ti on s f o r zero power op eration a t 1200°F, zero power operation
a t 1300°F, and 10-Mw ope ra ti on a t 1225°F were obtained f o r vario us coolin g-
a i r f low ra t e s by varying the e f fec t ive oute r -sur face hea t t r ans fe r coef -
fi ci en t. Temperature dis tr ib ut io ns were al so calcul ated f o r 10-Mw opera-
ti o n a t 1225 F,
zero power op era tio n
a t
1200°F, zero power oper ati on a t
1300°F, and zero power op erati on a t 1025°F without ex te rn al co oling.
The
method of obta ining the effe c t i ve outer-surface hea t t ra ns fer co eff ic i ent s
fo r th e va r ious condi t ions
i s
de scr ibe d i n Appendix B.
The pump tank and
volute support cyli nder geometry considered i n thes e calcu lat ion s i s
shown i n F ig. 2.
Temperature Distr ibution Curve Fitt ing
Before the
meridio nal and axial tempera ture dis t r ibut ions of the
pump
tank can be used i n the thermal st re ss equations, they must be ex-
pressed a s equations of th e following form (see p. 66 for nomenclature):
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U N C L A S S I F I E 0
ORNL LR DWG 6 9 R
T O P F L A N G E
OLUTE SUPPORT
CYLINDER
PUMP TANK
S P H E R IC A L
S H E L L
C Y L I N D E R [
L l Q U l D
L E V E L
L I Q U I D
L E V E L
Fig 2 Pump Tank and Volute Support Cylinder Geometry
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In te rn al Volute Support Cylinder A
Pump Tank
Spher ica l Shel l
For the in te rn a l cy l inde r and the
sphe r ica l she l l , the GHT tempera-
tur e d i s t r ib u t i on da ta were f i t t e d to the equat ion by the use of a l ea s t -
squares curve-fitting program.5
For the e xte rna l cylinder, manually
i t
equations containing only th e exponential terms were found ko f i t ex-
cept iona l ly we l l t o wi th in about 2 .5 in . of t h e top flange , where exces-
sive er ro rs were encountered. On th e othe r hand, t he least -sq uar es- fi t
e quat ions con ta in ing a l l t he t er ms f i t ve ry w e l l i n t he v i c in i t y o f t he
top f lange but devia ted near the cyl inder- to-shel l junction.
A
comparison
of the da ta obtained with the two f i t t i n g methods and th e HT d a t a f o r
the extern a l cyl inder i s shown i n Fig. 3 Since the cy l inde r - to- she l l
junct ion i s conside red t o be t he most c r i t i ca l a rea because of i t s h igh
oper atin g temperature, th e manually i t equation s were used f o r th e ex-
t e r n a l c y l inde r .
The po in ts on Fi gs . and
5
show the f i t obtained f o r
t yp i c a l s e t s o f GHT tempera ture-dis t r ibut ion da ta .
Thermal-Stress Analvsis
I n o r de r t o c a l c u l a t e t he t he rm al s t r e s s e s ,
the pump tank and volute
suppo rt c yl in de r were con sidered t o be composed of t h e foll owi ng members,
a s shown i n Fig. 2:
1
an int ern a l cyl ind er extending from the v olute t o the junction with
the sphe r ica l she l l , cy l inde r A,
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Fig 3
Comparison of Hand-Fit and Least -Sq uare-F it Tempera-
tu re Data wi th GHT Data f o r Cylinder B.
UNCLASSIFIED
ORNL-LR-DWG
6449 R
VOL UT E
-----
0 0 0
A
F U E L P UM P 1 0 - M w PO W ER 2 0 0 - c f m
FUE L AND COOLANT
PUMP
ZERO
POWER NO EXTER NAL COOLING
COOLING AIR FLOW
0 2
4
6 0 12
1 4
AXIAL POSITION :In.
Fig. 4 Axial Temperature Distribution of Volute Support Cylinder
a t Various Operating Conditions.
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UNCLASSIFIED
ORNL- -4-DWG 6 93R
2 0 0 0
I
i I
AND INDICAT E T EMPERAT U RES PREDICT ED BY T HE
T EMPERAT URE EQUAT IONS F OR T HE 0 A N D t o - M w
POWER CGSES WIT H 2 0 0 - c f m COOL ING A IR F L OW
I
I
C Y L I N D E R
I
J UNC T ION F UEL PUMP q O-Mw POWER NO EXT E RNAL COOL ING
6 0 0
0
2
4 6 8
1 0 1 2
4
16
M E R O I G N A L P O S I T I O N
(in.)
Fig. 5. Meridional Temperature D is t r i but i ons of the Tor isph er ic al
She l l a t Var ious Operat ing Condi t ions .
2
an ex te rna l cy l inde r ex tend ing from the junc t ion wi th the spher ica l
s h e l l t o t h e t o p f l an g e , cy l in d e r B, I and
3
th e pump tank sph eri ca l sh el l .
An Oracle program* was used t o obta in th e pre ssure s t re ss es , th e
s t r es s es from the a x i a l load on the cy l inder , the thermal s t r e s se s r e -
su l t in g from temperature g rad ien ts i n e i th er o r bo th cy l inders , and any
combination of these loadings.
The Program assumes th a t t he sphere i s
continuous i . e. , has no boundary oth er than th e cylind er junc tion) and
i s
a t
zero temperature.
The zero-temperature assumption req uir ed that
the temperature funct io ns of t he c yl in ders be adjus ted t o provide the
proper temperature re la ti on sh ip between t he th re e members.
The boundary
condi t ions fo r the ends of the two cyl inders spec if ie d tha t the s lope of
the cylinder walls was zero and that the radial displacements would be
Vh e Oracle program fo r ana lys i s of symmetrical ly loaded, ra di al ly
joined, cyl ind er-t o-sp her e attach men ts was developed by M E . Laverne and
F. J W i t t of ORNL.
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equal to the fr ee thermal expansion of the members a t t h e ir p ar t ic ul ar
temperatures. t was recognized a t th e beginning t h a t
some degree of
er ro r i n the thermal-stre ss calc ulat i ons would be introduced by th e ab-
sence of a thermal gradient on the sphere; but i n the cases where a i r
cooling was used t o l i m i t the gradient ,
the re su l ts were bel ieved t o be
reasonably acc urat e. Lat er ca lc ul at io ns showed, however, t h a t th e
stre ss es were very sen si t ive t o th e temperature gradient on the sphere,
and the refo re th e Oracle code was used only t o ev aluate the pressu re
st re sse s and the s t res ses from axi al loads.
In order t o calculate the thermal s t res ses , including the ef fe ct s
of the thermal gradient on the sphere, i t was necessary t o su bs t i tu te a
conical sh el l f or th e sphere. The angle of in te rs ec ti on between th e cone
and cy lind ers was made equal t o the equiva lent angle of in te rs ec tio n on
the ac tu al s tru ctu re. This su bs tit ut io n was required because moment,
displacement, slope, and forc e equations were not av ail ab le f o r thermal-
st re ss ana lysis of s pherical s he lls with meridional thermal gradients .
Thermal s tr es se s i n the two cy linde rs and the cone were calc ulate d
by th e use of the equations and procedures o utlin ed i n re fs . 6-9.
I n
order t o evaluate the four in tegra t ion co nstants required fo r each of
the three members, i t was necessary t o solve th e 1 2 simultaneous equa-
tions which described the following boundary and compatibility conditions
of the structure:
Cylinder
A
a t Volute Attachment. The slope of c yli nd er
A
was
taken as zero and the def lect ion as d l .
Cylinder B a t Top Flange.
The slope of cylinder B was taken as
zero and the deflect ion as
d l .
Cone a t Outside Edge. The slope of the cone was take n as zero
nd
the meridional fo rce was taken a s zero.
Junc tion of Cylinder A, Cylinder
B,
and Cone. The sunmation of
moments was taken a s ze ro; th e summation of r a d i a l fo rc es was take n a s
zero; th e slope s of cylinde r
A,
cyl inder
B,
and the cone were taken
t o be equal; and the de fle cti on s of cy lind er
A,
cyl inder B, and the
cone were taken t o be equa l.
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The following 12 equa tion s
which re more completely derived i n
Appendix C describe th e boundary and compat ibil i ty c ond ition s given
above
where
aB
Bc
W a n J ncWAc 1484.65Ta2
na n
tc
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Equations 1) hrough 12) are arranged so th a t the l e f t s ide con-
ta in in g the unknown in teg rat ion constan ts i s dependent only on the spe cif ic
pump tank configu ration, while the ri g ht side co ntaining th e thermal-
gradient terms
w i l l
vaxy for each case.
Afte r obtaining the four i nt eg ra tio n con stan ts fo r each member, the
bending and membrane s tr e s se s can be c al cu la te d using t he foll owi ng equa-
t ions for ei ther cyl inder or the cone:
For the pr inc ipa l meridional and circumferen tial s t res ses the applicable
equations are:
For cylinder A,
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N = O
For cylinder
B,
For the cone
M9
M
K
1.3J2 2.3J3P1 2.2J4P3
n c y n 1 2
I n
order t o fa c i l i t a te the so lu t ion of seve ra l cases and t o reduce
the amount of t ime involved i n calcu lati ng complete s t re ss dis tr i bu tio ns
an
I M
7090 program was wr it te n f o r t he
MSRE
pump configuration.
The
program ca lc ul at es th e temperature-dependent con stan ts of t he 12 simul-
taneous equat ions solves th e equat ions fo r the 12 inte gra t ion constants
and c al cu la t es th e bending membrane
and principal. s tresses
a t
65 loca-
t i ons .
Up
t o 25 cas es can be solved and th e number of ca ses t o be
solved and the constants i n the temperature dis t r i bu t io n equat ions are
inc luded as input da ta .
A
se t of gene ra l input da ta i s a l so required
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that contains the left-hand members of the simultaneous equations and the
pos i tion func tions t abu la t ed i n re fs .
7
and
9.
A spec ia l t e s t case with
a
uniform-temperature co nic al s h e l l was
prepared f or the I M 7090 program t o check the v a li d it y of
subs t i t u t i ng
the conica l she l l fo r th e spher i ca l sh e l l and t o ob ta in an over-all com-
parison between t he r es ul ts of the
IBM
and Oracle programs.
The compara-
t i ve re su l t s ar e shown i n Table 1 f o r the junction of th e th re e members.
As may be seen, the cone st re ss es agreed sa ti sf a c to r il y a t the junction
where they were a m a x i m u m Deviations between the results of the two
programs a t oth er meridional pos ition s were not considered important f o r
the cases of in t e r es t .
Table 1 Comparat ive Resu l ts f o r Conical and Sp her ic al Repres entat ion
Axia l o r Merid ional P r inc ipa l Ci r cumferen t ia l P r inc ipa l
S t r e s s ( p s i )
S t r e s s ( p s i )
I M 7090 programa Or ac le programb
I M 7090 Program Or ac le Program
Cylinder
A 3
276 -3 374
3
047 3 351
Cyl inder B 091
7
365 - 018 -4
548
Cone or sp here 25 196 -25
703 3
572
3
967
%or cyl inder-to-cone Junct ion.
b ~ o r yl inder- to-sphere junct ion.
Thermal-stress calc ulat ion s were completed fo r th e va rious operat ing
condi tions l i s t ed previously i n the sect ion on temperature d is t r i but i ons .
Strain-Cycle Analysis
I n order t o determine th e optimum cooling-air flow ra te and the l i f e
of th e pump tank ,
i t
was necessa ry t o determine t h e allow able number of
each type of ope rationa l cycle ( heating and power change) f o r each of
sever al cool ing-ai r f low ra tes .
I f pl, p2, pn ar e th e an tic ipa ted
values for the various operat ional cycles
and N
1
*2
.
.
N
a re t he
n
allowable number of cycles determined from the thermal-stress and strain-
fat igue data ,
the usage fac tor i s defined as
A des i gn a i r
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flow can then be s elec ted t o minimize th e usage f ac to r and give t he maxi
mum
pump-tank li f e .
The per mis sib le number of each type of o pe ra tio na l cy cle
i s
de t e r -
mined by comparing t he maximum s t r e s s amplitude f o r each typ e of cy cle
with th e design fa tig ue cu rves. The maximum st r e s s amplitude incl ude s
th e thermal st re ss es caused by meridional thermal gradie nts, the thermal
stresses caused by t ransv erse thermal gradie nts, and the pressure s tre ss es
caused by the 50-psi in te rn al pressure.
A discu ssion of th e variou s typ es of st re ss es primary, secondary,
lo ca l, and thermal) and th e ef f e c t s of each on th e design of th e pump
tanks i s given i n Appendix D A discus sion of the procedure used i n
determining the allowable number of cycles i s presented, and th e design
fa ti gue curves of INOR-8 a r e included .
Result s
Temperature Distributions
The re su lt s of th e
GHT
temperature dis t r ibut ion calculat ions for
pe rti ne nt opera ting conditio ns ar e shown i n Figs. and 5 f o r th e f u e l
and coola nt pumps. The sp he ric al sh e l l rneridional temperature di st ri bu -
t io ns f or the fu el pump a t various cool ing a i r f low ra te s and reac tor
power leve ls of zero and 10 Mw a r e shown i n Fig s. and 7.
Thermal Stresses
Typical therma l-stress pr of il es of the f u e l pump at a cooling-air
flow r a te of 200 cfm with th e re ac to r power a t
zero and 10
w
a r e shown
i n Figs. and 9; si mi la r pr o f il es of th e coola nt pwrrp ar e shown i n Figs.
10 and 11
The re lat ive ly high s t re sse s a t the top f lange ar e believed
t o be caused by the poor f i t of the temperature equations i n tha t area,
a s shown i n Fig.
3
The st re ss a t th e top f lange was calculated t o be
1 5 000 ps i when th e le as t- sq ua re s- fi t tem-perature equ ation was used.
I t
was found, however, th at t h i s equation introduced st re ss er ro rs a t th e
cone-to-cylinder junction. Therefore, the ac tua l s tr es s pr of i le s along
the e nt ir e length of the exte rna l cyl inde r would probably be be t t e r
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U N C L A S S I F I E D
O R NL L R D WG 6 4 4 9 4 R
2 6 8 1 0 2 4 6
MERlDlONAL POSITION
O n . )
Fig. 6. Meridional Temperature Distributions of the Torispherical
Sh el l a t a Reactor Power of 10 w and Various Cooling Air Flow Rates.
U N C L A S S I F I E D
O R N L L R DW G 6 4 4 9 5 R
i4 I
C Y L I N D E R
I
2 4 6
4
4 16
MERlD lONA i POSITION ~ n . )
Fig. 7. Meridional Temperature Di str ibu tio ns of the Tori spher ical
Sh e ll a t Zero React or Power and Various Cooling Air Flow
Rates.
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UNCL SSIFIED
O R N L - L R - D W G 64496R
3 0 0 0 0
6
4 2 4
AXIAL POSITION ( i n . )
Fig. 8.
Fuel Pump Pri nc ip al Thermal St re ss es a t Cylinders A and
B
f o r Ope ration a t Zero Power and
t
10
Ivfw with
a Cooling Air Flow Rate
of 200 cfm.
UNCLASSIFIED
ORNL LR DWG
6 97
1 2 0 0 0
0 2
3 4 5 6
MERIDIONAL POSITION in.)
Fig.
9.
uel Pump
Princi pal Thermal Stre sses a t Spher ica l Shel l
f o r Operation a t Zero Power
and
a t 10
w
with a Cooling Air Flow Rate of
200 cfm.
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UNCLASSIFIED
ORNL-LR-DWG
64498
and
V OLUT E
20, 000
301000
-
V
a
-
10 Mw,NO EXT ERN AL COOLING
i
W 0 1
j I
I I I
/ I0 Mw, NO E X T E RNA LCOOLI NG
ZERO POWER,NO EXTERN AL
- 3 0 , 0 0 0
.
- 6 -4 2 0 2 4 6
8
A X I A L P OS IT I ON
h n
)
Fig 10 Coolant Pump Pr in ci pa l Thermal St re ss es t Cylind
B
for Operation a t Zero Power and a t 10 Mw
UNCLASSIFIEO
O R N L - L R - D W G
6 99R
M E R l D l O N A L P O S I T I O N (in.)
Fig
11 Coolant Pump Pr in ci pa l Thermal St re ss es a t Spher ica l She l l
for Operation
a t
Zero Power and a t 1 0 Mw
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represented by a composite of the two s t re ss pro f i l es ; th at i s , t would
be bes t t o use the s t r e s s p ro f i l es f rom the manually f i t t emperature func-
t io ns near the junct ion and from th e leas t -squares funct ions near the to p
f lange.
Since the cone-to-cyl inder junct ion i s the more cr i t i c a l are a
and s ince the s t r ess es a t the to p flange do not l i m i t the number of per-
miss ible s t r a i n cycles , the s t r ess es from the manual ly i t equa tions were
used in comple ting the s t r a in -cyc le ana lys i s . The cy l inder i s su f f i c i e n t ly
long tha t the t emperature e r ro r a t the top f lange has a r e l a t ive ly smal l
e f f e c t on the s t r es ses a t the cy l inder - to -she l l junc tion .
Str a in Cycles
The r es u l t s of the s t r a in - f a t ig ue ana lyses a re p resen ted i n Tab les
2, 3, and 4
predicted usage fact or of 0 .8 or le ss indi cate s a safe
Table 2.
Fue l Pump S tr ai n Data f o r Heating Cycle
i r
Max imum
S t r e s s
Cycle Cycle
S t r e s s
Flow Arnpli tu de
Allowable Fract ion Fract io n i n
cfm>
I n t e n s i t y
p s i
Cycle s Per 100 Cycles,
p s i Cycle P, /N
Heating Cycle t o 1200°F
Heating Cycle t o 1300°F
Loss-of-Cooling-Air Accident
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Table
3.
Fuel Pump S t r a in Data f o r Power-Change
Cycle from Zero t o 10
w
St r e s s
Cycle Cycle To ta l
Air s t r es s Allowable Frac t ion Frac t ion i n Usage
Range Amplitude
cycles
cfm) psi
Pe r 500 Cycles, Fact or,
p s i
c
yc l e
P2/N.2 P ~ / N ~
Table 4.
Coolant Pump S tr ai n Data f o r Heating
and Power-C hange Cycle s
Heating Cycles Power Change
from Zero
To 1200°F To 1300°F t o 10 w
Maximum s t r e s s int en si ty , p si
Str ess ampli tude, ps i
Allowable cycles
Tota l re laxat ion
P a r t i a l r e la x a ti o n
Cycle f ra c t i on per cycle
Tota l r e laxa t ion
P a r t i a l r e la x a ti o n
Cycle fraction in 100 cycles
Tota l re laxat ion
Pa r t i a l r e l a xa t i on
Cycle f rac t io n i n 500 cycles
Tot al usage facto ra
Tota l r e laxa t ion
Pa r t i a l r e l a xa t i on
?For 100 heating cyc les t o 1200°F and 500 power cyc les from zero t o
10
Mw
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ope ratin g co ndi tion f o r th e d es ire d number of hea ting and power-change
cycles. The re su lt s are based on th e assumption of t o t a l s tr e ss relaxa-
t i on a t each operat ing condit ion and are therefore conservative. The
loca tion of maximum s tr es s in te ns i t y during the heating cycle i s not
nec ess arily the same a s the lo ca tio n of m ximum st re ss range during the
power-change cycle. This al so provides conservative re su lt s, since th e
m x i m u m
s tr a in s fo r each type of cycle were added t o determine the
usage
fac tor , and the to ta l
s tr ai n a t t he ac tu al po int of maximum s tr a i n would
be l e s s than th e s t ra in value used. Since th e pump tank
w i l l
safely en-
dure th e de sir ed number of he atin g and power cyc les with t h i s co nserva tive
approach, i t was not considered necessary t o lo ca te and determine th e
ac tua l maximum t o t a l s t r a in . The coola nt pump w i l l operate a t a lower
temperature than t he f u el pump, so th e s t re s s relax ation during each
cycle w i l l probably be incomplete and th er ef or e a la rg e r number of c yc les
w i l l be permissible.
As shown i n Table 4, th e assumption of p a r t i a l r e-
laxa tion ra th er th an t o t a l relax ati on permits more than twice th e number
of heating cycles . For th e f u e l pump, th erm al-s tress and pl as ti c- st ra in
calc ulat i ons were al so made fo r the short 36-in.-diam cylinder ~ o n n ec t-
in the two to ris ph er ic al heads. The permissible number of cy cles a t
t h i s lo catio n was found t o be g reat er than those shown i n Tab le 2, and,
therefore, the cycles i n the cyl inder do not
l i m i t
t he l i f e of t he
tank.
Pressure and Mechanical Stresses
The res ul ts of the pressure st re ss c alcu lat io ns made with the Oracle
program ar e shown i n Fig s. 12 and 13. The s tr es se s, which include both
primary and discon tinuity stres ses , ar e fo r a pressure
of 1.0 psi and are
di re ct ly propor t ional t o pressure.
The maximum s t r e s s from t he a x i a l
l oad ex i s t s a t t he
suction nozzle at tachment and i s equal t o 1.766 t imes
th e load i n pounds.
Recommendations
The
strain-cycle data of Tables 2,
3, and 4 indi ca te th t the de-
sired number of st ra in cycles on the fu el pm p can be safe ly tol era ted
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UNCLASSIFIED
ORNL- LR DWG 645 00
I00
.
N TER N AL PR ESSU R E
=
1.0
ps i
STR ESS AT 'P PR ESSU RE
=
D,=MERIDIONAL STRESS
D e=C I R C U MFER EN TI AL STR ESS
6 0
=INSIDE
= O U T S I D E
-f
I
S P H E R l c A L S H E L L J U NC T IO N
1 0 0
6
4 - 2 0 2 4
6
8
A X I A L P O S I T I O N
( i n )
Fig 12
Fuel and Coolant Pump Pres sur e S tre ss es a t Cylin ders A
and
B
UNCLASSIFIED
ORNL-LR-DWG 64501
I N TER N AL PR ESSU R E=1.0 ps i
STRESS A T ' ~ P R E S S U R E P X S TR E SS
T j.0
ps
I
w-- - - -d - - - - .+ - - - ----- ---
----
u+=MERIDIONAL STRESS
ug=C I R C U MFER EN TI AL STR ESS]
= INSIDE
C Y L I N D E R
JU N C TI ON
=OUTSIDE
0 I I
I
0
I 2 3 4 5
6
7
8 9
MER lD lON AL POSI TI ON
( i n )
Fig 13
Fuel and Coolant Pump Pressure St re ss es a t S phe rical
She l l
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when any cool ing a i r flow between 100 and 300 cfm i s used; and there -
for e th e a i r cooling can be contro lled manually by a remotely operated
cont rol valve.
coo lin g-a ir flow r a t e of approximately 200 cfm i s recom-
mended f o r th e following reasons:
1
The pred ict ed usage fa c to r i s reasonably near th e minimum value.
2 . There i s a wide range of acceptable f low ra te s on e i th er s ide
of t h i s des ign a i r f low ra te .
3.
t a i r flow ra te s gre ate r than 200 cfm th e maximum st re s s in -
te ns i t y during zero power operat ion increas es re la t i ve ly rapi dly and de-
cre as es the permis sible number of hea ting cy cles .
S in ce t h e r e i s a p o s s i b i l i t y o f e r r o r i n t h e temp er at ur e d i s t r i b u -
t i on ca lcu la t ions because o f unc er t a in t i es in the hea t generat ion r a t e s
and hea t t r ansfe r coef f i c i en t s
it i s
recomm.ended t h a t t h e tem pera ture
grad ient on the sp he ric al s h e l l be monitored by using two thermocouples
spaced 6 in . apa rt ra di al ly . This give s the maximum temperature d i f-
ference between the two thermocouples and therefore reduces the effect
of any thermocouple er ro r . Since th e thermal grad ient of th e sp her ica l
sh e l l n ea r t h e junction i s of primary importance i n determining the t he r-
m a l
st re sses the d i f fe re nt ia l temperature measurements and the d ata of
Figs. 6 and 7 can be used to se t the ac tua l cool ing-ai r f low ra te on the
pump. This method has the disadvantage of r eq uir ing se ve ral adjustments
a s the temperature and power le ve l ar e ra ise d t o the operat ing point .
f
d i r e c t measurement of th e flow r a t e were po ss ibl e minor adjustme nts
could be made a f t e r the system reached opera ting condi tion s. Since no
co oli ng -ai r flow measuring equipment i s planned f o r th e f u e l pump a t t h e
present t ime a preoperat ional ca l ib rat ion of the cool ing-ai r f low ra te
versus valve po sit ion should be made t o permit th e approximate a i r f low
ra te t o be se t p r io r t o high-tempera tu re operat ion.
The design temperature di ffe ren ce between th e two thermocouples f o r
monitoring the thermal gradient
i s
100°F a t a power l ev e l of 10
w
and
a
thermocouple spa cing of
6
i n .
The maximum allo wab le t emp era ture d i f -
ference
i s
200°F f o r 10-Mw operation . Af ter the coo lin g-a ir flow r a t e
has been s e t f o r 10-Mw ope rati on
a readjustment of the flow should be
made
i f necessary a t zero power operat ion t o prevent
a
negative thermal
gra die nt on th e sphere. This ad jus ted cool ing -ai r flow should the n become
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t he ope ra t i ng value .
During the p re cr i t c a l t e s t in g and power opera t ion
of t he reac to r t should be kept i n mind th at any sig ni fi ca nt change i n
th e fu e l pump coo l ing- air f low ra te w i l l c ons t i t u t e a s t r a i n c yc le and
w i l l
repr esen t a decrease i n the usable l i f e of the pump tank. Therefore
an ef fo r t should be made t o keep the number of coo l in g-a ir f low r a te ad-
justm ents t o a minimum.
The e ff ec t of hea t ing t he sys tem t o 1300°F i s a l so shown i n Tables
2 3 and 4 The f u e l and co olan t pumps can sa fe ly endure o nly about
half a s many heat ing cyc les t o 1300°F as t o 1200°F. For the co olant
pump 100 heat in g cyc les t o 1300°F would e ss en t i al ly consume th e l i f e of
the pump tank.
A t 1300°F the a ssumpt ion of t o t a l s t r e s s re l axa t ion i s
re a l i s t i c and no addi t ion a l conserva t ism should be claimed by i t s use .
Therefore
t
i s recommended th a t th e system not be h eated t o 1300°F on
a r ou t i ne ba s i s
Since t h e f u e l and cool ant pump tan ks a r e prim ary containment mem-
be rs th e maximum valu e of t h e usage fa c t o r must no t exceed 0.8 which
i s t he accep tabl e upper
l i m i t
To avoid exceeding t h i s l i m i t an accu-
r a t e and up-to-date record should be maintained of th e usage fa c to r and
the complete s t ra in cyc le hi s tor y of both the f u e l and the coolant pumps.
I n ca lcu la t in g the usage fac tor p a r t ia l power-change cyc les i n which
rea c to r power i s increased only a f r ac t ion of th e t o t a l power should be
considered as complete power cy cles u nles s the number of p a r t i a l c ycles
i s a la r ge f r ac t i on of the t o t a l when a pump tank has passed through the
permi t ted number of cyc les . I n t h i s case ad di t i on a l thermal s t re ss
ca lc ula t ion s should be made t o determine the proper e ff ec t of the p ar t i a l
cyc les .
Although the s t ra in -cyc le da ta ind ica te th a t th e coolant pump i s
accep tab le f o r t he spec i f i ed number of s t ra in cycl e s t he s t r e s s i n t en s i t y
i s uncomfortably high. These st re ss es can be reduced by lowering the
thermal gradient on the sph er ica l sh e l l by using a reduced thickness of
in su la ti on on the upper surfa ce of th e pump tan k.
Since nuc lear hea t ing
i s not involved in th e coolant pump the proper amount of i ns ul at i on can
be s t be determined on th e Fue l Pump Prototyp e Test Fa ci li ty which i s
pres ent ly under const ruc t ion.
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Conclusions
The s t r a in -cy c le ana ly s i s ind ica tes th a t the fu e l pump w i l l b e s a t i s -
fac to ry f o r th e in tended l i f e of 100 heat i ng c ycles and 500 power-change
c yc l es i f t s a i r c oo le d. No s p e c i a l c o ol in g
w l l
b e r equ i red f o r t h e
coo lan t pump. conse rvati ve des ign s provided by th e use of s tandard
s a f e ty f a c t o r s i n t h e s t r a i n - f a t i g u e d a t a and i n t h e u sage f a c t o r .
Ad-
d i t i o n a l conservatism of an unknown magnitude i s provided by th e assump-
t i o n of t o t a l s t r e s s r e l ax a t i o n a t e ach o p er a ti n g co n d i ti o n and by t h e
fa c t th a t th e ac tu a l maximum s t ra in shou ld be l e s s than the ca lcu la ted
maximum s t a i n .
I n a dd it io n t o t h e safe ty f a c t o r s ou t l in ed above the fu e l and coo l-
an t p u p t an k s a r e c apabl e of exceeding t h e i r r eq u ir ed s e r v i ce l i f e by
f ac to r s o f 2.2 and 1.4 re sp ec tiv el y bef ore th e maximum per mis sib le usage
f ac to r i s ex ceed ed.
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References
1. Molten-Salt Reactor Program Qua rt er ly Progress Report f o r Period End-
ing Ju ly 31, 1960, ORNL-3014.
2 A. G.
Grinde l l ,
W .
F. Boudreau, and
H. W .
Savage, ~evelopmentof
Cen trifu gal Pumps fo r Operation with Liquid Metals and Molten Sa lt s
a t 140C-1500 F, Nuclear Sci . and Eng. 7( 1 ), 83 (19 60).
3.
Ten ta t ive S t r uc t u ra l Design Bas i s fo r Reac tor P res sure Vesse l s and
Dire c t ly Associa ted Components ( ~ r e surized, Water-Cooled Systems
esp. p. 31, PB 151987 ( ~ e c .1 1958) , U. S. Dept. of Commerce, Office
of Technical Services .
T .
B .
Fowler, Gen eral ize d Heat Conduction Code f o r th e IBM 704 Com-
pute r, ORNL-2734 ( 0 c t . 14, 1 95 9) , and supplement ORNL CF 61-2-33
P.
B .
Wood, NLLS:
A
704 Program f o r Fi t t i n g Non-Linear Curves by
Least Squares, K-1440
a an
28, 19 60 ), Oak Ridge Gaseous Pl an t;
SHARE D i s t r ib u t i o n No. 8371838.
F. J . W i t t Thermal St re ss Analysis of C yl in dr ic al Sh el ls , ORNL
CF 59-1-33
Mar.
26, 1959).
F.
J .
Stanek, S t re s s Analys is o f C y l ind r ica l She l l s ,
ORNL
CF 58-9-2
( ~ u l y2, 1959).
F.
J .
W i t t Thermal Analysis of Conical Shells, ORNL CF 61-5-80
(J ul y 7, 1961).
F.
J .
Stanek, St re ss Analysis of Conical She lls ,
ORNL
CF 58-6-52
( ~ u g . 8, 1 95 8) .
C . W . Nes tor, Re ac tor Phy sic s Ca lc ul at io ns f o r t h e MSRE, ORNL
CF 60-7-96
( J U ~ Y
26, 1960).
T .
Rockwell ( ed .) , Re ac to r Sh ie ld in g Design Manual, p 392, McGraw-
H i l l
New York, 19 56 .
M. Jakob, Heat Tra nsf er, Vol.
I
p 168, Wiley, 1949.
A. I. Brown and S. M . Marco, Int rod uct ion t o Heat Transfe r, p 64,
McGraw-Hill, New York, 1942.
Ib id , p 91.
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15.
B F.
Lange, Design Values f o r Thermal St re ss i n Du cti le Ma ter ia ls ,
Welding Jou rnal Re se ar ch Supplement, 411 (1958).
16.
S. S. Manson, Cyc lic L if e of D uc ti le M at er ia ls , Machine Design 732
13% ( ~ u l ~
,
1960).
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APPENDIX
Di st ri bu ti on of Fission-Product-Gas Beta Energy
The to t a l energy tha t
w i l l
be relea sed i n the fu e l pump tank by the
fission-product gases has been reporte dlo by Nestor t o be 1 5
kw
This
energy
w i l l
not be uniformly deposited on the
surface a rea exposed t o
gas, however,
so
t
was neces sary t o determine
i t s
d i s t r ib u t i on over the
su rf ac es of t he pump tank.
The pump tan k was assumed t o be of s t r a i g h t
cy li nd ri ca l geometry, a s shown i n Fig.
A.1
and the d i s t r ibu t ion o f the
energy f lux a t t he cy l ind r i ca l wa l l s was ca lcu la t ed a s ou t l ined i n the
following sect ions. The dis tr ib ut io n of energy t o the upper surface was
approximated by assuming a d i s t r ib ut ion s imi l ar t o th at fo r the outs ide
wal l .
Energy Flux a t Pump Tank Oute r Surf ace
t was assumed
that
th er e was no s el f- sh ie ld in g o r shi elding from
th e volute support cylinder , and the l i ne source (dy,dx) was integrat ed
over th e enclose d volume (se e Fig .
~ . 2 ) l
o obta in the energy f l ux
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UNCLAS S IF IE D
O RNL LR DWG 6899
6
in .
D I A
5 in. D l A
Fig
A 1
Assumed Pump Tank Geometry
U N C L A S S I F I E D
O R N L L R D W G
68994
Fig A 2
Diagram f o r Determining Energy Fl ux a t Pump Tank O uter
Surface
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square ratio of the center-of-gravity distance:
The values of at Pl Pa and P; were evaluated as functions of
%
and h by the Numerical Analysis Section of ORGDP.
The beta-energy dis-
tribution is shown in Fig. A 4
Fig.
A 3
Diagram for Determining Energy
Flux
at Outer and Inner
Surf
ces of the Volute Support Cylinder
UNCLASSIFIED
O RNL- LR- DW G 645 ZR
4 0 0 0 p
I
I
I
TORISPHERICAL SHELL . INSIDE
I.
XIAL POSIT ION OF CYL INDER A
IS MEASURED FROM SPHERE-TO-
CYLINDER JUNCTION
5 0 0 0
'I *-\\{+
2. RADIAL POSIT IONS OF SHIELDING
VOLUTE SUPPORT CYLINDER'K,INSIDE
PLUG FACE AND TORISPHERICAL
S H E L L A R E M E A S U R E D F R O M
P U M P C E N T E R L I N E
0
I
I
I I
I
0
2
4 6 8 ( 0 I 2 14 16 18
P O S I T I O N in )
Fig. A 4
Beta-Energy Distribution of Fuel Pump Tank Volute Sup-
port Cylinder and Shielding Plug.
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Estimation of Outer Surface Temperatures and
Heat Transfer Coeff ic ients
The GHT Code fo r ca lcu la t in g the comple te temperature di s t r i bu t io n
of th e pump tank could not con sider th e ef f ec ts of th e flowing a i r s t ream
on th e temperature d is tr ib u ti o n of th e pump tan k because of t he tempera-
tu r e r i se o f t he cooling a i r
a long th e pwnp tank surface . I n order t o
obta in t he t empera ture d i s t r i bu t ion ,
i t
was nec ess ary t o coup le t he pump
tank su rface wi th the surroundings
by
use of an e f fe c t i v e heat t r a ns fe r
co ef fic ien t hce) and th e ambient temperature.
t
was imprac t ica l t o
obta in
a n
e f fe c t i v e coe f f i c i en t a t each po in t a long the sur face, and
therefo re the va lue of hce was ca lc ula t ed a t the cyl in der - to- she l l junc-
ti o n, where th e therm al s tr e s s problem was most severe, and the n ap pl ied
over the e n ti r e upper surf ace of t he pump tank.
The air -co ol ed upper por tio n of th e f u e l pump tan k i s shown sche-
m a t i ca l l y i n F ig .
B 1
The pump tank
i s
s ub j e ct t o t he rm a l r a d i a t i on
and convect ion heat ing from the fuel
s a l t ,
f
i ss ion-product be ta hea t ing,
and gamma-radiat ion i n te rn al heat in g. This heat
i s
conducted t o the
UNCLASSIF IED
ORNL LR DWG 899
OOLING-AIR
SHROUD
INSUL AT IO N
\ P U M P T A N K W A L L
84 7 = h
8,-8,)
f
Fig. B 1
Schemat ic Diagram of Cooling-Air Shroud and Pump Tank
Wall.
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pump
tank surface where
i t
i s t r a n sf e r re d t o t h e c oo ling
i r by
two paths:
1) d ire c t forced convection t o th e cool ing a i r and
2)
r a d ia t i on t o t h e
coolin g shroud and forced convection t o th e same cooling a i r .
Heat i s
a lso conducted p ara l le l t o the
pu p
tank surface, but t h i s heat t ra nsf er
i s assumed t o be
zero in estim ating th e surface temperature and heat
t rans fe r coe f f ic ien ts .
The temperature di st ri b ut io n through the pump tank wal l can be cal cu-
lat ed12 a s ou tli ned below, assuming cons tant gamma heat-g enerati on r a t e
through the wall
A t
t h e i n t e r i o r
w a l l
where
x 0,
and the ref ore
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and f o r any place within t he w a l l
t h a t i s , x 0,
The temperature i s then
A t t h e i n t e r i o r
w a l l
x 0,
and therefore
and
f
t he hea t t r a ns fe r from the ou te r su r face i s expressed by an e f -
fec t ive coeff ic ient wi th respect t o the ambient temperature ra t he r than
th e act ua l forced-convection cooling system temperature, the ou te r sur-
face temperature can be ca lcu late d a s fol lows from Eq . ~ . 6 ) i th x t
where
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and
where 8 i s th e ef fe ct iv e ambient temperature, and
4e
Solving Eqs. (B.10) ( B . ) , and (B.12) s imultaneously f o r
e
y i e l d s t h e
fol lowing equat ion:
Solv ing Eq. ( ~ . 1 3 ) o r hce m d rea r ranging the t erms g ives
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The d i f f i cu l t y i n ca lcu la t ing th e oute r sur face temperature
9
from Eq. B.13) re su l t s from the fa c t tha t the hea t t ra ns fe r coe ff ic ien ts
hc e
and h
ar e hig hly temperature dependent, and
.Q3
must be known before
f
accura te coeff ic ients can
be
cal cul ate d. However, f o r a given se t of re -
ac tor opera t ing condi t ions , i t
i s
evident from the preceding equations
th a t the se lec t ion of
an
arb i t r a ry value of 8 w i l l r e s u lt i n a pa r t i c u l a r
va lue of the t o t a l hea t t ran sfe r across the ou ter surface, and a par t ic u-
l a r value of h i s r equ ir ed t o d i s s i pa t e t h i s qua n t i t y of he at t o t he
ce
surroundings.
Since the temperature drop across the pump tank wall
i s
small f o r th e cases of in te re st , 8 can be used t o compute the value of
3
the in t e rn a l sur face hea t t r an s fe r coe f f ic ien t h , and the value of
f
hc e
can then be
cal cul ate d by Eq. B . l 4 )
.
The following procedure was used t o estimate th e e ffe ct iv e outer
sur face hea t t r an s fe r coe f f ic ien t s fo r var ious cool ing-a i r f low ra te s :
1 Values of h versu s inn er surfa ce temperature 8 were calcu -
f 2
l a t e d by Eq. B.15), below, and pl ot te d on Fig . B ~ : I ~
4 4
D
F F el G 2
- r e a
hf -
+ 1.5
-
O2
2.
The to t a l hea t t r ans fe r red I + ) was ca lcu la ted versus the outer
su rf ace temperature 8 by Eq.
B.16), below, a f te r f i r s t ca lcu la t ing
UNCLASSI F I ED
ORNL-
L R -
OW 645 3
4
7
8 900 4000
100
4200 1300
4400
SURFACE TEMPERATURE IDF
Fig. B.2.
Pump
Tank Inner Surface Heat Transfer Coefficient Versus
Outer Surface Temperature.
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hce by Eq. B.14)
3.
The forced convection heat t ra ns fe r co eff ici ent s f o r the pump
tank o ute r sur face and th e cooling shroud were calc ula ted as a func t ion
of a i r flow by Eq. B.17) and p lo tt e d on Fig . B.3:14
4.
The heat t ransf er red t o the cool ing shroud by thermal radia t io n
was ca lcu lat ed versus shroud temperature f o r each of sev era l values of
Q3
and plotted on Fig. B.3.
A t equi l ibr ium condit ions , the heat radia ted t o th e shroud q3-
p l u s t h e h eat t r an sf e r r ed d i r ec t l y t o t h e co ol in g a i r q 3 5 must equal
-
t h e t o t a l h ea t t r a n sf e rr e d
q,),
and the he at tra nsf err ed from th e shroud
UNCL ASSIF IED
O R N L L R D W G 6 4 5 0 4
COOLING SHROUD TEMPERATURE OF)
4150 I 0 5 0 9 5 0 8 5 0 7 5 0 6 5 0 5 5 0 4 5 0 3 5 0
6 0 0 0
c
-
5 0 0 0
m
-
T
4 0 0 0
J
3 0 0 0
n
LT
LT
0 0 0
w
LT
F
4000
u
0 1 00 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0
COOLING AIR FLOW c tm )
Fig . B.3. Convective Heat Tra nsf er Co ef fi ci en t Versus A i r Flow and
Heat Tra nsfe rred t o Shroud Versus
Shroud Temperature.
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t o t h e co ol in g a i r ( q
must b e eq u a l t o t h e h ea t t r an s f e r r ed t o t h e
4-5
shroud from th e pump tan k. There fore, f o r each assumed valu e of th e
3
h eat t r an s f e r r ed t o t h e sh ro ud s ca l cu l a t ed v e r su s co o li n g a i r f l ow
ra te f rom the expres s ion
where
and
The pa r t ic ul ar shroud temperature required t o accept th e heat (q
3-4
from the pmp tank surface s obtained from Fig. B.3. The heat tr an sf er -
red f rom the shroud t o the coo l ing a i r s t h en ca l cu l a t ed :
q4-5 = hc(e4 0,)
.
For each value of
3 q3 43
and q4-5 ar e p lot ted ver sus cool ing -ai r f low
rate as shown on Fig. B.4 and the i n t er sec t io n of t he two curves de te r -
mines the coo l ing-a i r f low ra te tha t w i l l produce the pa r t i cu la r va lue
of e3. A plo t o f e versus c ool ing -ai r f low r a t e can the n be made a s
i n Fig . B.5, and the e f fe c t iv e su r face hea t t r a ns fe r c oe f f i c i en t s h
ce
f o r use i n t h e GJT Code can be ca lcu la ted f o r any a i r f low ra t e us ing
Eq. ( ~ . 1 4 ) .
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0 100 2 0 0 3 0 0 400 5 0 0 600
C O O L I N G A I R F L O W cfrn)
Fig
B 4
Shroud Heat T ra ns fe r Versus Cooling A i r Flow
UNCLASSIFIED
O R N L - L R - D W G 64506
--
0 1 0 0 2 0 0 300 400 5 0 0 600 7 0 0
A I R F L O W
c f r n
Fig B 5 Nominal Surface Temperature Versus Cooling A i r Flow
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assumpt ion requires that the s lope nd the shear forc e equat
f i e d by a sign change t o compensate f o r the reversed sig n o
cyl inders .
Derivations of the 12 simultaneous equations from the
boundary o r co mp at ibi lit y con diti ons ar e given below. The
ti o n s f o r moment displacement slope and she ar for ce were
r e f .
6
fo r the cyl inders and ref . 8 f o r th e cone. The coni
t ions differ somewhat from those presented in ref . 8 becaus
nary version of t he re port was used th a t did not include t
a thermal gradie nt through th e wall . l l the terms consid
f e c t s of in te rn a l pre ssu re and mechanical loading were omi
the cy l i ndr i ca l and con ica l sh e l l equa tions .
The following mat eria l constants geometric constants
s ta nts and auxi l ia ry funct ions are used in the boundary a
equations
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t
was necessary t o adj us t th e pump tank co nfigura tion sl ig ht ly so
that the boundaries of the separate members would coincide with tabulated
values f o r the cone and cylinders:
=
78 5 deg
cot = 0 2035
a
=
7 125 i n
a
Ycl
=
7 271
s in
Yc = 18 0 in
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The values of Xcl and Xc were adjusted t o the near est value
i n r e f
9:
The cy li nd er mean rad ius was then co rre cte d:
La i
6 5 in
. 8 0 in
The values of y and y were adjusted t o the near est ta b ate d values
a i
i n r e f 7
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The following cylind er po sit i on funct ions were taken from ref .
7:
Volute, Junc tion, Top Flange,
Function
a
3.6
Y a b = O
yb 4.4
M
0.049 -2
O
0.007546
M2
-0.02418 0 -0.02337
M3
-65.64
2 O
-50.065
M4
32.39 0 155.02
The following cone pos iti on f unc tio ns were taken from re f . 9:
Function
Jun cti on , Cone Outer Surf ace,
Xcl
6.3
Xc 9.9
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Junction , Cone Outer Sur face,
Function Xcl 6.3 Xc2 9.9
61
10.1451 -54.918
62
4,47331 -108.588
63
-0.0014f44
-0.00008719
The cone aux il ia ry temperature fu nctio ns
were
obtained from the
following expressions
:
E t c a cot 72Tc5
2
4 rTc3 459.95Tc5 11.555Tcj
PC
-2Ftp cot
6
Tc4
-17. 183Tc4
3
PC
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The temperature d is t r i bu t i on s f o r the cy l in der s and cone were ex-
pressed i n th e fol lowing forms:
Cylinder A
Cylinder B
Cone
C
I t
T c l
=
2 3
Yc
Tc2 Tc3Yc Tc4yc Tc5Yc
A t
the pump volute (ya
=
3 .6 ) , the s lope o f cy l inder A
=
0,
and
dw
a
aB Y
=
C
w
dL E t
na n
A t
t h e pump vo lu te (ya
=
3.6) , the ra di a l d isplacement of A
= aC@
1
and
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and therefore
t t h e cone-c ylinde r jun ction, t h e summation of moments 0, t h a t i s ,
M a - + M c = 0
and
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A t th e cone-cylinder junction, the summation of ho riz on tal and v e rt i c a l
f o r c e s
=
0, and the re fo re , f o r the ve r t i c a l fo rces ,
Qc sin
+
Nc
cos
=
0
cos q
Qc = *c s n
For the hor izonta l forces ,
Qc
cos
9
+
Nc s i n
9 =
2
-N
OS
N~ s i n 9
=
N
s i n
9
-
sin
.
c s i n c
c0s2
For the summation of horizontal forces on both the cylinders and the
cone,
and
+ 6DaQTb4 Db y e
(
n b ~ n )aB na n
-
p
t an s in 9 - Y : c ~ ~ Q ~ ~
6 . 2 0 9 4 79 . 3 8 ~ ~ 3 . 0 ~ ~ )
b
344. 12
Ta4 Tb4)
229.41Tb5
. C . 4 )
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A t th e junction, th e slope of Cylinder A
=
slope of Cylinder B,
and
ta
C C W + C C W = - E -dy
na n n b n f ( T a 2 C T b 2 ) - q b y e
A t
the junction, th e s lope of Cylinder
A =
slope of the Cone llC,l and
a
B B E
2
C
c W
r a n C
cncwAc
=
na n
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A t th e junction, th e displacement of Cylinder
A =
the displacement of
Cylinder B, t h a t i s ,
and
A t
the junction, th e displacement
of
Cylinder A
=
the displacement of
the Cone, and
w =
u c o s
4 V
s i n
4 ,
a
naNn ma
=
cos
4
Et
2
- s n 4
cncvnc
JlK3 ~ loge pC
Etc
s i n
4
(Tcl Tc2Yc Tc3y
Tc4y:
Tc5y,)
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The f i n a l fo rms of t hese 1 2 equat ions a re a r ranged so t ha t t h e l e f t
hand si de co ntaining t he unknown in te gr at io n con stant s s dependent only
on the sp ec i f ic pmp tank conf igura t ion while the r ig ht s ide containing
the t empera ture d i s t r i bu t ion t erms w i l l va ry fo r each ope ra t i ng condi t i on .
The mat r ix of i ntegr a t ion constant coe ff i c ien ts f o r th e 12 equat ions s
shown i n Table l
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Table l Simultaneous Equation Matrix
oef fic ien ts of Unknown Int egr ati on Constants
na nb.
and
nc
Equation
Number
l a 2a 3a l b C2b 3b 4b Cl c C2c 3c C4c
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APPENDIX D
Explanation of Procedure Used to Evaluate t he Eff ect s of
Cyclic Str ain s i n t he MSRE Pumps
An e s s e n t i a l d i f f e r e n c e i n s t r u c t u r a l d e s i gn f o r h i gh - te m pe r at u re
operat ion a s compared with design fo r more modest cond ition s i s the need
to cons ide r c reep and re laxa t ion of the s t ruc tura l ma te r ia l . Many of the
methods and procedures pre sent ly s pec i f ied a s a s t ru c tur a l des ign bas is
in t he ASME Boi ler and Pressure Vessel Code Unfired Pressure Vessels
Sec t ion V I I I and i n th e prel imina ry des ign ba s is developed by th e ~ a v
become meaningless at hig h temperatures. Thus a revised design basi s
must be formulated when high-temperature cond itions a re consid ered. The
ope rati ng program of any component must be examined and the desi gn bas is
selec ted must be used to determine whether the number of o perati onal cycles
which can be sa fely to lera ted exceeds the number of the cycles which i s
desi red during the l i fe of the component. I f necessary the number of
operat ional cycle s of th e component must be lim ited t o the value which
can be safel y tol erat ed. As may be seen th e de ta il s of the operating
program ar e extremely important and must be sele cted with considerable
ca re .
The concept of s t r e ss i s used he re a s a convenience in d iscuss ing
t h e e f f e c t s o f c y c l i c s t r a i n s b e ca us e
t
i s t h e p r i n c i pa l v a r ia b l e i n
conventional problems of el as ti ci ty . Properly however the discu ssion
should be i n terms of s tra in s when dealin g with high temperatures and
e s p e c i a l l y i n d e s c r ib i n g t h e rm a l e f f e c t s i n s t r u c t u r e s . W it h t h e s e
fac to r s i n mind four gene ra l types of s t r e sses were cons ide red in e s-
t a b l i s h i n g a d e s i g n b a s i s f o r t h e
MSR
pumps which
w i l l
opera te a t tem-
pe ra tures wi th in the c reep and re laxa t ion r ange ; these a re pr imary
secondary lo ca l or peak and thermal. The primary st res ses are dir ect
or shear stre sse s developed by the imposed loading which ar e necessary
to sa t i s f y only the s imple laws of equi l ibr ium of ex te rna l and in te rn a l
forc es and moments. When primary st res ses exceed the y iel d str eng th of
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t he mate ri a l , y i e ld ing w i l l continue u n t i l th e member breaks, unle ss
s t r a in hardening o r r ed i s t r ibu t ion o f s t r e s ses l im i t s the de fo rmation .
Secondary s t resses are d i rec t or shear s t resses developed by the con-
s t r a in t of ad jacent pa r t s o r by se l f - cons t r a in t of the s t ruc tu re .
Sec-
ondary s t r ess es d i f f e r f rom primary s t r es ses i n th a t y i e ld ing o f the ma
t e r i a l r e su l t s i n r e l a x a t i o n of t h e s t r e s se s . Loc al o r peak s t r e s se s
ar e the highest st re ss es i n the region being studied. They do not cause
even noticeab le minor dis to r t io ns and ar e object iona ble on ly as a pos-
s ib le source of f a t igue c racks . Thermal s t r e ss es a r e in t e r na l s t r e ss es
produced by co ns tr ai nt of thermal expansion. Thermal st re s s es which in -
volve no general d i s t or t i on were considered t o be lo ca l s t res se s . Thermal
s t r es ses which cause gross d is tor t io n , such as those r esu l t i ng f rom the
temperature dif fer en ce between sh el ls a t a junction, were considered t o
be secondary stresses.
I n th e present examination, fou r sources of s tr es se s were considered.
P ressure d i f f e r ences ac ross the she l l s
w i l l
produce membrane pressure
st re ss es . These st re ss es a re primary membrane st re ss es . The pres sur e
d i f f e r e n c e s w i l l
al s o produce dis co nti nui ty st re ss es , which are secondary
bending st re ss es . Temperature grad ient s along th e she ll s w i l l produce
st r ess es which are due both t o th e temperature var i a t i on s and t o the d i f -
ferent ia l-expansion-induced d isc ont inu i t i es a t th e sh el l junctions . These
st re ss es ar e secondary bending str es se s. Temperature gra die nts acro ss
t h e w a l ls of t h e sh e l l s w i l l produce thermal s t re s s e s which ar e assumed
t o be l o c a l s t r e s s e s .
The ASME Code i s genera l ly accepted a s the b as i s f o r eva lua t ing p r i -
mary membrane st re ss es , and th e allowable s tr e s se s f o r INOR-8 a t th e op-
era t in g temperatures of the pumps were obtained from the c r i t e r i a s et
fo r t h in th e code, with one exception.
reduction fac to r of two-thirds
was appl ied t o the s t r es s t o produce a creep ra te of 0 .1 i n 10 000
r
i n o rder t o avoid poss ib le p rob lems assoc ia t ed wi th th e e f f ec t of i r r a d ia -
ti o n on t h e cree p rat e. * The maximum allowab le s t r e s s t 1300°F i s 2750
ps i, and th e primary membrane s tr e ss e s were li mi te d t o t h i s value. The
*Based on data from R . W Swindeman, ORNL.
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primary s tr es se s were not considered fur th er except f rom the standpoint
of exc essive deformations produced by primary plu s secondary s tr es se s.
I n o rde r t o eva luate the e f f e c t s of secondary and lo ca l s t r e sses ,
re pe ti ti ve lo adin g and temperature cy cle s must be considered because
fr ac tu re s produced by thes e t ypes of
s t r e s s a r e u sua l l y t h e r e su l t o f
s t r a in f a t igue . Data which g ive the cyc les - to - f a i lu re ve r sus the t o t a l
or p l as t i c s t r a i n range per cycle may be used f o r s tudying cycl i c
condi-
t i o n s . The t o t a l s t r a i n ra ng e p e r c y cl e i s d ef in ed a s t h e e l a s t i c p l u s
pl as t i c s t ra in range t o which th e member i s subjected dur ing each cycle .
The p la s t i c s t r a in r ange pe r cyc le i s t he p la s t i c component of the t o t a l
s tr a i n range pe r cyc le. The str ai n- cy cl in g i nfor mati on may be compared
with the c alcu late d cyc lic st ra in s in the member. Since most formulas
express
s t r e ss r a the r than s t r a in a s a func t ion of loading o r tempera -
tu re d is t r ib ut i on , assuming e la s t ic behavior of the mater ia l , it i s con-
venient , a s s ta ted before , t o transform th e t e s t data f rom the form of
s t r a in ve r sus cyc les - to - f a i lu re t o the form of s t r e ss ve rsus cyc les - to -
f a i l u r e by mult ip ly ing the s t r a in va lues by the e l a s t i c modulus o f the
mate r ial . The re su lt in g values have th e dimensions of st re ss but , sinc e
the t e s t s were made in the p la s t ic range, they do not represent ac tu al
s t r e s se s .
When the a nal ysi s of st re ss es i n a member reve als a b ia xi al or t r i -
a x i a l s t r e s s c on di ti on , it i s necessary t o make some assumption regarding
th e fa i l ur e cr i t er io n t o be used. I n the p l as t i c range, where most of
th e s ign i f i can t secondary and lo ca l s t r e sse s l i e , t he re i s no experim.enta1
evidence t o indi cate which theory of fa i l ur e i s most accurate .
There-
fore , it has been recommended15 t h a t t h e maximum sh ea r th eo ry be used,
s ince
it i s
a l i t t l e more conservative and re s ul ts i n simpler mathemati-
c a l expressions. The fol lowing ste ps used i n developing th e procedure
were taken from ref.
3:
1
C a lc u la t e t h e t h r e e p r i n c i p a l s t r e s se s a l, a2 a3 a t a g iv en
point .
2
Determine t he maximum shear s tr e s s which i s th e l ar ge s t of t he
t h r e e q u a n t i t i e s
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3.
blu ltip ly t h e maximum she ar s t r e s s by two t o gi ve t h e maximum
in te ns i t y of combined str ess .
4
Compare t h i s qu ant i ty with the
E
AE
values obtained from uni-
a x i a l s t r a i n -c y c l in g t e s t s .
S t a t ed more simply , t he procedure i s t o use t h e s t re s s i n t en s i t y
represent ing t he la rg es t a lgebr a ic di f fe r ence between any two of the th ree
p r i n c i p a l s t r e s s e s
The procedure ou t l ined above fo r eva lua t ing the e ff ec ts of cyc l ic
loadings and cyc l ic thermal s t r ai n s was used t o examine th e cy cl ic se c-
ondary and local
s t re ss es which w i l l be produced i n p or ti on s of t h e MSRE
pumps. The procedure i s ess en t i al ly th at sp eci fie d by th e Navy Code;
however, th e Navy Code was developed pr im ar il y f o r ap pl ic at io n s
i n which
the maximum temperatures would be below those necessary for creep and re-
laxa t ion of the mater ia l . Thus, sever a l of the s t ep s out l in ed in the
Navy Code were
m.odi fied f o r th e p resent eva lua t ion.
The assumption was made th a t th e temper atures were s u f fi c ie n tl y high
and th a t the t imes a t these tempera tures were su ff ic ie nt ly long fo r com-
p l e t e s t r e s s r e l a xa t ion t o oc cu r. Thus t he s t r a i n s which t he e l a s t i c a l l y
ca l cu l a t ed s t re s se s repre sen t ed were t aken a s en t i r e ly p l a s t i c . On t h i s
b a si s , s t r a i n c yc li ng d a ta i n th e form of p l a s t i c r a t h e r t h an t o t a l s t r a i n
range per cycle versus cycl es- to- fai lu re were used.
Figures D l and D.2,
which giv e s t r a i n fa ti gu e da ta f o r INOR-8 a t 1200 and 1300°F, were ob-
tain ed from a l im ite d number of st ra in- cyc l ing t e s t s performed by th e
ORNL Metall urgy Div isio n.
The dashed curv es were ob tained from th e pl as -
t i c
s t ra in range per cyc le curves and repr esent a conserva t ive es t imate
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Fig D 1
S t ra in F a t igue Curves fo r INOR 8 a t 1200°F
UNCLASSIFIED
ORNL-LR-DWG 64509
10~
5
. o - '
-
W
>
W
a2
2
k
0-3
5
o - ~
10-I 100 5 10' 102 {o 3 2 5
lo4
lo5 2 lo6
N
CYCLES TO FAILURE
Fi g D 2
S t r a in F a t igue Curves fo r
INOR 8 a t 1300°F
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of the to t a l s t r a in range pe r cyc le .
t
was assumed t h a t t he m ate r ia l
exh i b i t s pe r f ec t p l a s t i c i t y above the p ropor tiona l l i m i t no s t r a i n
hardening) , and the e l a s t i c s t r a i n a t t he p ropor t iona l l m t was added
t o t h e p l a s t i c s t r a i n r ange
a t
each po in t. The dashed curv es were used
t o obta in an es t imate of the cycle s- to- fa i lure , assuming th a t no re laxa-
t i on o r s t r ain -ha rdening occurs .
St ra in hardening would dis plac e t h e
dashed curves upward.
Fig ure s D.3 and D.4, which give th e s t r e s s amplitude ve rsu s number
of cy cle s f o r INOR-8 a t 1200 and 1300°F wit h complete rel ax at io n, were
derived from the so l i d cu rves fo r F igs.
D l
and D.2 by mul tipl ying th e
p l a s t i c s t r a i n r an ge by E t o o b ta i n a pseudo
st re ss range and then d i -
v i di n g by 2 t o o b t a i n t h e a l t e r n a t i n g s t r e s s .
The dashed curves i n Figs .
D.3 and D.4 re pres ent th e re su lt s of th i s operat ion . The sol id curves
represent th e a l lowable values of a l te rna t in g s t re ss and were const ructed
by placing
a
f ac to r o f sa f e ty of a t l ea s t 10 on cyc les and a f ac t o r o f
sa fe ty o f a t l ea s t 1 . 5 based on s t r ess . The sa f e ty f ac to r of 10 on cyc les
i s b ased on u n c e r t a i n t ie s i n t h e c a lc u l a ti o n s , s c a t t e r of t e s t d at a , s i z e
ef f ec ts , sur face f in ish , a tmosphere, e t c . These reduct ion fa ct or s ar e
l e s s co nservativ e than tho se spe cif ied by the Navy Code.
However, they
have been used i n high-temperature design fo r se ver al years
a t ORNL, and
the cur rent fee l in g of one of th e or i g in ato rs of the Navy Code i s th at
th e reduct ion fa ct or s s peci f ied i n tha t document a re over -conservative
and w i l l be reduced t o those used i n t h i s invest igat ion . * Figures D.5
and D.6 were o bta ine d i n th e manner a s Fig s. D.3 and D.4 bu t were based
on t o t a l s t r a i n r a the r than p l as t i c s t r a i n . They r ep resen t a l lowable
va lues of a l t e rna t ing s t r e ss i f no r e l axa t ion occur s.
The l i f e of a component undergoing cy c li c s t r a i n depends on mean
st ra in as wel l a s cycl ic s t ra in ; however, fo r most app l ica t ions i n which
the loading i s a lmost e nt i r e l y due t o thermal cycling and no severe
st ra in-conc ent ra t ions ex is t , the ef fe ct of mean s t ra in can be expected
t o be secondary t o tha t o f cyc l i c s t r a in .
For these app l ica t ions , cyc l i c
l i f e can be determined d i r ec t l y from st ra in range computat ions 16
The
*Personal communications between B F. Langer of Westinghouse Electric
Corp., B et t i s Plan t , and
B
L. Gr eenstreet , ORNL.
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UNCLASSIFIED
O R NL L R D WG 6 4 5 1 0
0
m
10
W
LT L L O WA B L E S T R E S S
z
2 2
W
4
10
5
lo3
404
4 5
lo6
N. N U M B E R O F C Y C L E S
Fig
D .3 .
S t r e s s Amplitude Versus Number of Cy cles f o r INOR 8 a t
1200°F with Complete Stress Relaxation
Fig D 4
S t r e s s Amplitude Versu s Number of Cy cles f o r INOR 8 a t
1300°F wi th Complete S tr e s s Relax ation
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U N C L n S S l F l E D
O RN L L R D W G 6 4 3 2
Fig
D 5
S tr e s s Amplitude Versus Number of Cycles f o r
IN O R 8 t
1200°F wi th No Relaxatio n
U N C L n S S l F l E D
O R N L L R D W G 6 4 5 1 3
2
{ 0 5 2
lo6
N NUMBER O F C Y C L E S
Fig
D 6
S t r e s s Amplitude Versus Number of Cycles f o r
IN O R 8 t
1300°F with No Relaxat ion
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ef fe ct of mean s t ra in i s fu r t he r reduced when gross rela xat ion tak es place
during each cycle, a s i s expec ted i n th e p resen t case .
Thus f o r the
MSRE
pump s tr e ss evaluatio n, th e mean st ra in was assumed i n a l l case s t o be
zero, and the e f f ec t of cycl ic s t re ss es was determined d i re ct ly from th e
pl ot s of t h e a llowable a l ter nat ing s t re ss versus the number of cycles .
Each of t h e components examined w i l l be subjected t o se vera l opera-
t in g cond it ions .
S i n c e s t r a i n s w i l l occur th a t a r e beyond the e l as t i c
l i m i t t he s t r uc t u ra l eva lua tion was based on a f i n i t e l i f e , and the
damaging ef fe ct of a l l s ig ni f ica nt s t ra in s was considered.
Suppose, f o r example,
th at th e s t re ss es produced by n d i f fe re nt op-
erat ing condit ions have been determined and that
it
has been found
that
t h e se s t r e s se s w i l l produce val ue s of Salt which can be desi gn ate d a s
Sl, S2, .. S .
t i s a l s o known t h a t Sl i s repeated p t imes during th e
n
l i f e of t h e component, and S i s repeated p t imes, e tc . From Figs . D . 3
2 2
and D 4
it
i s found that
N1 N2
N
are t he a l lowable cycles f o r each
n
of the ca lcu la t ed s t r e sses .
The values
P1/~l, P ~ / N ~ , p n / ~ , a r e c a l l e d
cyc le r a t io s because they r ep resen t th e f r ac t io n of the t o t a l l i f e which
i s u sed a t e ac h s t r e s s v al ue .
A s a f i r s t approximation , an appl ica t i on
might be considered sa t i s fac tor y i f
Fatigue t e s t s have shown, however, t h a t f a i lu re can occur a t cumulative
cycle rat io summations different f rom unity.
I f t h e l ow er s t r e s s v a lu e s
a re app li ed f i r s t and fo llowed by the h igher s t r e ss va lues, t he cyc le
r a t i o summation a t fai lu re can be coaxed a s high a s 5.
On th e ot he r
hand,
i f t h e most damaging s t r e s se s a r e a l l a pp l ie d f i r s t , f a i l u r e c an
occur a t cyc le r a t i o summations a s low a s 0.6, or even lower.
These are
extreme co ndit ions and ar e based on low-temperature fa ti gu e da ta which
may or may not be repr es ent ati ve of behavior under s t r a i n cycling .
For
random combinations, cy cl e- ra tio summations us ual ly aver age -clo se t o
uni ty .
Therefore, 0.8 was used i n the prese nt evaluation a s a conserva-
t i ve a llowable l imi t .
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t
should be no ted th a t i n cor rec t ly app ly ing any des ign c r i t e r i a ,
a point-by-point an al ys is must be made. That i s , t he complete opera ting
h is to ry f o r each sing le poi nt must be examined.
Sh or t c u t s may sometimes
be taken, bu t they must necessa r i ly l ead t o over ly conserva t ive res u l t s .
I n swnmary, t h e permi ssib le c yc le s of each type were determined f o r
th e MSRE f u e l and co ola nt pumps by combining th e secondary and lo c a l
s t re ss es a t each poi nt . Poi nts were then found which gave maximum va lues
fo r th e maximum in te ns it y of combined st re ss . These l a t t e r value s were
divided by 2 t o obtain the a l t er na t i ng s t r es s . The al lowable number of
cyc les fo r each a l te rna t in g s t r es s were ob tained from F igs . D.3 o r D . 4
assuming complete rel ax at ion . The cycle ra t i o s were then obtai ned t h a t
were based on the expected number of times each stress w i l l be repeated,
and var iou s combinations of t he cycle r a t i o s were summed a t a pa rt ic u la r
point and compared with the 0.8
l i m i t
To in v es t i g a t e t h e i n c r ea s e i n
l i f e i f n o r e l ax a t i o n o ccu rr ed , Fi gs . D.5 and D.6 were used i n plac e of
Figs. D.3 and
D 4
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NOMENCLATURE
Volute support cylinder mean radius
Exponential constant i n cylind er
B tempera-
ture equat ion
In tegra t ion cons tan t s
In tegra t ion cons tan t s fo r cy l inder
A
(n
= 1
2, 3,
4
Integ rat io n cons tants fo r cyl inder B
(n
= 1 ... 4
Inte grat i on cons tants f o r cone (n = 1
... 4
Flexura l r ig id i t y o f cy l inder
Dimensionless temperature parameter
Modulus of elast ici ty
Geometric cons tants f o r radiat ion heat t ra ns fe r
Forced convect ion heat t ransfer coef f ic ient
Effec tive heat tr an sf er co eff ici en t of pump
tank outer surface
Heat tr a n sf e r co ef fi ci en t of pump tank inn er
surface
Auxil iary temperature functions f o r cone
(n
= 1 ... 4
Thermal conductivity of INOR-8
Auxil ia ry s t r e s s func t ions fo r con ical s he l l s
(n
=
1
... 4
Axial cylinder posit ion from cone-to-cylinder
junction
Bending moment
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Constants in cylinder
B
temperature equation
n 1 ... 5 )
Constants in cone temperature equation n 1
...
5 )
Wall thickness of cylinder
tc
Wall thickness of cone
t
Thickness of cooling air gap
g
Displacement of cone perpendicular to surface
Meridional displacement of cone
Displacement functions for cone n
1 ... 4 )
Radial displacement
W Displacement functions for cone n 1 . 4
n
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