Thermal stress and strain fatigue analysis

8/20/2019 Thermal stress and strain fatigue analysis

1/78

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.


2/78

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

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B

Assumes

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r e s u l t n g f ro m t h e u s e o f

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A s

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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

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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 .


3/78

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


4/78


5/78

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


6/78


7/78

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.


8/78

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


9/78


10/78

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.


11/78

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):


12/78

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


13/78

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,


14/78

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.


15/78

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.


16/78

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.


17/78

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


18/78


19/78

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,


20/78

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


21/78

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


22/78

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


23/78

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.


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.


24/78

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.


25/78

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


26/78

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


27/78

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


28/78

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


29/78

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


30/78

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


31/78

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.


32/78

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.


33/78

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.


34/78

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).


35/78

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


36/78

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


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


37/78


38/78

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.


39/78

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.


40/78

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


41/78

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


42/78

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


43/78

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.


44/78

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.


45/78

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 ) .


46/78

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


47/78


48/78

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


49/78

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


50/78

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


51/78

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


52/78

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


53/78

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


54/78

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


55/78

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 )


56/78

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


57/78

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,)


58/78


59/78


60/78

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


61/78

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


62/78

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


63/78

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.


64/78

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


65/78

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


66/78

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


67/78

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


69/78

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 .


71/78

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


72/78

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

Documents

Thermal stress and strain fatigue analysis