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O A K RIDGE N A T I O N A L LABORATORY operated by U N I O N CARBIDE CORPORATION for the U.S. A T O M I C ENERGY C O M M I S S I O N

ORNL- TM- 78

THERMAL-STRE SS AND STRAIN-FATIGUE ANALYSES OF THE MSRE FUEL AND COOLANT PUMP TANKS

C. G. Gabbard

NOTICE This document contains information of a preliminary nature and was prepared primarily for internal use at the Oak Ridge National Laboratory. It i s subject to revision or correction and therefore does not represent a final report. The information i s not t o be abstracted, reprinted or otherwise given public dissemination without the approval of the ORNL patent branch, Legal and Information Control Department.

HELP

LEGAL NOTICE T h i s report was prepared as an account o f Government sponsored work.

Neither the United States,

nor the Commission, nor any person acting on behalf of the Commission:

Makes

nny warranty or representation, expressed or implied, w i t h respect t o t h e accuracy,

completeness, any

or usefulness of the information contained i n t h i s report, or that the use of

information,

apparatus,

method, or process disclosed

i n t h i s report may not infringe

p r i v a t e l y awned rights; ar

Assumes any l i a b i l i t i e s w i t h r e s p c t t o the use of, or far damages resulting from the use of

any information, apparatus, method, or process disclosed in t h i s report. A s used i n the above, "person acting on behalf of the Commission" includes any employee or contractor of the Commission, or employee of such contractor, to the extent that such employee or

contractw

of the Commission,

or employee o f such contractor

prepares,

disseminates,

provides occess to, any information pursuant +a h i s employment or contract w i t h the Commission, or h i s employment w i t h such controctor.

Contract No. W-7405-eng-26

Reactor Division

* IrC 8

THERMAL-STRESS AND STRAIN-FATIGUE ANALYSES OF THE MSRE FUEL AND COOLANT PUMP TANKS

C H. Gabbard

DATE ISSUED

oCT

- 3 1962

OAK RIDGE NATION& LABORATORY Oak Ridge, Tennessee operated by UNION CARBIDE CORPORATION for the U. S. ATOMIC ENEBGY COMMISSION

iii

CONTENTS Abstract

.......................................................

................................................... Calculational Procedures ....................................... Strain Cycles ...............................................

Introduction

................................... Temperature Distribution Curve Fitting ...................... Thermal-Stress Analysis ..................................... Strain-Cycle Analysis ....................................... Results ........................................................ Temperature Distributions ................................... Thermal Stresses ............................................ Strain Cycles ............................................... Pressure and Mechanical Stresses ............................ Recommendations ................................................ Conclusions .................................................... References ..................................................... Appendix A . Distribution of Fission-Product-Gas Beta Energy ................................................... Energy Flux at Pump Tank Outer Surface ......................

4 4 4

Temperature Distributions

Ehergy Flux at the Volute Support Cylinder Outer Surface Energy Flux at the Volute Support Cylinder Inner Surface Appendix B

7 15 16 16 16 20 22 22

27 29 29

....

....................................

Appendix C Derivation of Boundary and Compatibility Equations f o r Thermal Stress Calculations

..................... Appendix D . Explanation of Procedure Used to Evaluate the Effects of Cyclic Strains in the MSRF: Pumps ............... Nomenclature ................................................... I

Estimation of Outer Surface Temperatures and

Heat Transfer Coefficients

41 56 66

THERMAL-STRESS AND STRAIN-FATIGUE ANALYSES OF THE MSRE FUEL AND COOLANT PUMP TANKS

C. H. Gabbard Abstract Thermal-stress and s t r a i n - f a t i g u e analyses of the MSRE f u e l and coolant pump tanks were completed f o r determining t h e quantity of cooling a i r required t o obtain the maximum l i f e of the pump tanks and t o determine t h e a c c e p t a b i l i t y of t h e pump tanks f o r t h e intended service of 100 heating cycles from room temperature t o 1200째F and 500 r e a c t o r power-change cycles from zero t o 10 Mw.

A cooling-air flow r a t e of 200 cfm f o r the f u e l pump tank was found t o be an optimum value t h a t provided an ample margin of s a f e t y . The coolant pump tank was found t o be capable of t h e required service without a i r cooling. Introduction The f u e l pump f o r t h e Molten S a l t Reactor Experiment'

(MSRE) i s a

sump-type c e n t r i f u g a l pump composed of a s t a t i o n a r y pump tank and volute and a r o t a t i n g assembly (see Fig. 1). The pump tank and volute, which i s constructed of INOR-8 (72% N i , 16% Mo, '7% C r , 5%Fe), i s a p a r t of t h e primary containment system, and t h e r e f o r e t h e highest degree of r e l i The pump i s similar t o other high-temperature

a b i l i t y i s required.

molten-salt and liquid-metal pumps that have accumulated many thousands of hours i n nonnuclear t e s t - l o o p service.

Although these nonnuclear

pumps have been highly successful, they have not been subjected t o t h e degree of thermal cycling which may occur i n a nuclear p l a n t .

It t h e r e -

f o r e cannot be assumed from the operating records t h a t pwnps of t h i s type

w i l l be adequate f o r t h e MSRE. S t r e s s calculations* were completed i n accordance with t h e ASME B o i l e r and Pressure Vessel Code f o r determining t h e w a l l thicknesses and nozzle reinforcements required t o s a f e l y withstand am i n t e r n a l pressure ~~~~~

*Performed by L. V. Wilson.

UNCLASSIFIED ORNL- LR- D W G - 5 6 0 4 3 - A

SHAFT C O U P L l NG,

WATER COOLED

SHAFT SEAL

LEAK

DETECTOR

L U B E O I L IN L U B E OIL BREATHER SHAFT SEAL

LUBE O I L OUT

LEAK

DETECTOR

SHIELDING PLUG

BUBBLER TYPE L E V E L INDICATOR

XENON

S T R I F'PER 4

BUOYAN CY LEVEL INDICATOR

Fig. 1. MSRE Fuel Pump G e n e r a l Assembly D r a w i n g . U

. W

3 of 50 p s i .

I n addition t o t h e s e pressure s t r e s s e s , t h e f u e l pump tank

w i l l be subjected t o r e l a t i v e l y high thermal s t r e s s e s because of t h e high thermal gradients which w i l l be imposed by nuclear heating and t h e l a r g e temperature d i f f e r e n c e between t h e t o p flange, which will be a t 250 t o

300째F, and t h e pool of molten salt i n t h e tank, which w i l l be a t 1225째F. Although t h e coolant pump will not be subjected t o nuclear heating, t h e r e

w i l l be a l a r g e temperature d i f f e r e n c e between t h e t o p flange and the molten salt i n the pump tank. Since t h e ASME Pressure Vessel Code and Code Case I n t e r p r e t a t i o n s do not adequately cover t h e design of a v e s s e l a t creep range temperat u r e s under r e l a t i v e l y high c y c l i c thermal s t r e s s , t h e thermal s t r e s s evaluation w a s conducted under t h e r u l e s of t h e Navy Code.3 Code covers t h e design of pressurized-water r e a c t o r systems.

The Navy The problems

of design i n t h e creep range a r e not e x p l i c i t l y covered, but design c r i t e r i a a r e e s t a b l i s h e d f o r v e s s e l s subjected t o thermal s t r e s s and c y c l i c

plastic strain.

Thermal s t r e s s e s a r e considered as t r a n s i e n t i n the Navy

Code and must be evaluated on a f a t i g u e b a s i s using the estimated maximum numbers of various operational cycles and Miner's accumulative damage theorem as t h e design

rite ria.^

Automatic flow c o n t r o l of t h e cooling a i r t o t h e upper pump tank surface was i n i t i a l l y proposed so t h a t t h e temperature gradient on t h e s p h e r i c a l s h e l l would remain r e l a t i v e l y constant a t various operating conditions.

The complexity and possible lack of r e l i a b i l i t y of the auto-

matic c o n t r o l system made it desirable, however, t o determine whether a f i x e d a i r flow could be used f o r a l l t h e operating conditions of t h e pump. Calculations were t h e r e f o r e made f o r e s t a b l i s h i n g the temperature d i s t r i b u t i o n s , thermal s t r e s s e s , pressure s t r e s s e s , and permissible number of operational cycles f o r various modes of operation and various

cooling a i r flow r a t e s .

From t h i s information, it w a s possible t o s e l e c t

operating conditions t h a t would permit t h e maximum number of operational cycles and provide an ample f a c t o r of s a f e t y above t h e 100 heating and

500 power-change cycles a n t i c i p a t e d f o r t h e MSRE.

4 Calculational Procedures S t r a i n Cycles Since thermal s t r e s s e s a r e considered t o be t r a n s i e n t and i n some cases subject t o r e l i e f by s t r e s s r e l a x a t i o n a t operating temperatures, they must be evaluated on a s t r a i n - f a t i g u e b a s i s , a s required by t h e Navy Code.

Two types of s t r a i n cycles will occur during normal operation of

t h e pump:

I. heating and cooling when t h e r e a c t o r system i s heated from room temperature t o operating temperature and returned t o room temperature, and 2.

power-change cycles when t h e r e a c t o r power i s r a i s e d from zero t o 10

Mw and returned t o zero. The change i n s t r a i n must a l s o be considered f o r a loss-of-cooling a i r incident i n which the operating conditions would change from (1)r e -

a c t o r power operation a t 10 Mw with design a i r flow t o ( 2 ) operation a t

10 Mw with no a i r flow t o (3) zero power operation with no a i r flow. Temperature D i s t r i b u t i o n s The i n i t i a l s t e p i n t h e thermal-stress and s t r a i n - f a t i g u e analyses

w a s t o determine t h e temperature d i s t r i b u t i o n s i n t h e pump tank f o r various operating conditions based on t h e e f f e c t s of i n t e r n a l heat generation, conductive heat f l o w , convective and r a d i a t i v e heat t r a n s f e r with t h e

salt, and cooling of t h e shielding plug and upper pump tank surface.

The

generalized heat conduction code': (GHT Code) w a s used t o obtain t h e temperature d i s t r i b u t i o n s .

During r e a o t o r power operation, t h e f u e l pump

tank will be heated by g a m r a d i a t i o n from both t h e r e a c t o r v e s s e l and t h e f u e l s a l t i n the pwrrp tank and by b e t a r a d i a t i o n from the f i s s i o n product gases.

The maximum gamma heat-generation r a t e during r e a c t o r

operation a t 10 Mw was calculated* t o be 18.70 Btu/hr-in.3 a t t h e inner surface of t h e upper portion of t h e pump tank, giving an average heating r a t e through t h e 1/2-in. -thick pump tank w a l l of 16.23 Btu/hr*in. 3 . g a m heat-generation r a t e i n t h e shielding plug above t h e pump tank W a l c u l a t e d by B. W . Kinyon and H. J. Westsik.

The

5 w a s c a l c u l a t e d a t increments of 1/2 i n . based on an exponential decrease i n t h e heating r a t e .

The b e t a heating, which varied from 4.80 t o 22.22

Btu/hr-in.2, was estimated by d i s t r i b u t i n g t h e t o t a l b e t a energy emitted i n t h e pump tank over t h e pump-tank surface exposed t o t h e fission-product gases ( s e e Appendix A ) . Preliminary c a l c u l a t i o n s with t h e GIEC Code indicated that c o n t r o l l e d cooling of t h e upper pump tank surface w a s necessary, not only t o lower t h e maximum temperature, but a l s o t o reduce t h e temperature gradient i n t h e s p h e r i c a l portion of t h e pump tank near i t s junction with t h e volute support c y l i n d e r i n order t o achieve acceptable thermal s t r e s s e s .

These

c a l c u l a t i o n s a l s o predicted excessively high temperatures i n t h e volute support cylinder between t h e pump tank and t h e pump volute.

These high

temperatures were caused by a s e r i e s of p o r t s i n t h e volute support c y l i n d e r w a l l f o r draining t h e shaft l a b y r i n t h leakage back i n t o t h e ~umptank. The d r a i n p o r t s were o r i g i n a l l y located at t h e bottom of t h e cylinder and r e s t r i c t e d the conduction of heat downward i n t o the s a l t .

The m a x i -

mum temperatures were reduced t o an acceptable l e v e l by centering t h e d r a i n p o r t s between t h e punrp tank and t h e pump volute so that heat conduction would be u n r e s t r i c t e d i n t h e both d i r e c t i o n s .

F i n a l temperature

d i s t r i b u t i o n s f o r zero power operation a t 1200"F, zero power operation a t 1300"F, and 10-Mw operation a t 1225째F were obtained f o r various cooling-

a i r flow r a t e s by varying the e f f e c t i v e outer-surface heat t r a n s f e r coefficient.

Temperature d i s t r i b u t i o n s were a l s o calculated f o r 10-Mw opera-

t i o n a t 1225"F, zero power operation a t 1200"F, zero power operation a t 1300째F, and zero power operation a t 1025째F without e x t e r n a l cooling.

The

method of obtaining t h e e f f e c t i v e outer-surface heat t r a n s f e r c o e f f i c i e n t s f o r t h e various conditions i s described i n Appendix B.

The p u q tank and

volute support c y l i n d e r geometry considered i n these c a l c u l a t i o n s i s shown i n Fig. 2. Temperature D i s t r i b u t i o n Curve F i t t i n g Before t h e meridional and axial temperature d i s t r i b u t i o n s of t h e pump tank can be used i n t h e thermal s t r e s s equations, they must be expressed as equations of t h e following form (see p. 66 f o r nomenclature):

6 J

UNCLASSIFIED ORNL-LR-DWG 64491 R

'LlQU I D L E V E L Fig. 2.

P u p Tank and Volute Support Cylinder Geometry.

I n t e r n a l Volute Support Cylinder "A"

Ta2L + T

L2 + Ta4L 3

, a3

External Volute S u m o r t Cvlinder "B" 0 = T b bl

T L b2

T L2 b3

+ Tb4L 3 + Tb5e -bL

Pump T a n k Spherical S h e l l

= -T c l

Tc2

Tc 3Yc + Tc4Yc2

Tc5Yc3

For t h e i n t e r n a l cylinder and t h e s p h e r i c a l s h e l l , t h e GHT temperat u r e d i s t r i b u t i o n d a t a were f i t t e d t o the equation by t h e use of a l e a s t squares c u r v e - f i t t i n g p r ~ g r a m . ~For t h e e x t e r n a l cylinder, manually f i t equations containing only t h e exponential terms were found %o f i t exc e p t i o n a l l y w e l l t o within about 2.5 i n . of t h e t o p flange, where excess i v e e r r o r s were encountered.

On t h e o t h e r hand, t h e l e a s t - s q u a r e s - f i t

equations containing a l l t h e terms f i t very well i n the v i c i n i t y of t h e t o p flange but deviated near t h e c y l i n d e r - t o - s h e l l junction.

A comparison

of t h e d a t a obtained with t h e two f i t t i n g methods and t h e GHT d a t a f o r the e x t e r n a l cylinder i s shown i n Fig. 3.

Since t h e c y l i n d e r - t o - s h e l l

junction i s considered t o be t h e most c r i t i c a l a r e a because of i t s high operating temperature, t h e manually f i t equations were used f o r t h e ext e r n a l cylinder.

The p o i n t s on Figs. 4 and 5 show t h e " f i t " obtained f o r

t y p i c a l sets of GHT temperature-distribution d a t a . Therma1-S t r e s s Analvsi s

I n order t o c a l c u l a t e t h e thermal s t r e s s e s , t h e pump tank and volute support c y l i n d e r were considered t o be composed of t h e following members,

as shown i n Fig. 2: 1. an i n t e r n a l cylinder extending from t h e volute t o the junction with

t h e s p h e r i c a l s h e l l , cylinder "A, Y

8 4

4000

UNCLASSIFIED ORNL-LR-DWG 64490 I

800 POINTS PREDICTED BY "HAND FIT" EQUATION

o \

POINTS PREDICTED BY "LEAST SQUARES"

EQUATIONS

600

t-4

n W a 400 I

200

0 0

A X I A L POSITION

5 (in.)

Fig. 3. Comparison of "Hand-Fit" and "Least-Square-Fit" Temperat u r e Data with GIEC Data for Cylinder "B."

UNCLASSIFIED ORNL-LR-DWG 6449 R

4400

4200

4000 I

lL L

cc W

800

w X 0

600

coc

200 0

0x14: P C S l i l 3 N ( n.)

Fig. 4. Axial Temperature D i s t r i b u t i o n of Volute Support Cylinder a t Various Operating Conditions.

9 .)

.INCLASSIFIED O R N L - L R - D W G 64493R

2000

AND INDICATE TEMPERATURES PREDICTED BY THE TEMPERATURE EQUATIONS FOR THE 0 A N 0 f O - M W POWER CASES WITH 2 0 0 - c t m COOLING AIR FLOW

1800

YLINDER IUNCTION

FUEL PUMP, IO-Mw POfiER, NO EXTERNAL COOLING

7600

-ar LL

1400

1200

roo0

800

i 600

6 0 10 MERIDIONAL POSITION ( I n )

Fig. 5. Meridional Temperature D i s t r i b u t i o n s of t h e Torispherical S h e l l a t Various Operating Conditions. 2.

an e x t e r n a l cylinder extending from t h e junction with t h e s p h e r i c a l s h e l l t o t h e t o p flange, cylinder "B,"

and

t h e pump tank s p h e r i c a l shell. A n Oracle program* w a s used t o obtain t h e pressure s t r e s s e s , t h e

s t r e s s e s from t h e a x i a l load on t h e cylinder, t h e thermal s t r e s s e s r e I

s u l t i n g from temperature gradients i n e i t h e r o r both cylinders, and any combination of these loadings. continuous ( i . e . ,

The Program assumes that t h e sphere i s

has no boundary o t h e r than t h e cylinder junction) and

i s a t zero temperature.

The zero-temperature assumption required that

t h e temperature functions of the cylinders be adjusted t o provide t h e proper temperature r e l a t i o n s h i p between t h e t h r e e members.

The boundary

conditions f o r t h e ends of t h e two cylinders s p e c i f i e d t h a t t h e slope of t h e cylinder w a l l s was zero and that t h e r a d i a l displacements would be

q h e Oracle program f o r a n a l y s i s of symmetrically loaded, r a d i a l l y joined, cylinder-to-sphere attachments was developed by M. E. LaVerne and F. J. W i t t of ORNL.

10 equal t o t h e f r e e thermal expansion of t h e members a t t h e i r p a r t i c u l a r temperatures.

It w a s recognized a t t h e beginning t h a t some degree of

e r r o r i n t h e thermal-stress c a l c u l a t i o n s would be introduced by t h e absence of a thermal gradient on the sphere; but i n t h e cases where a i r cooling w a s used t o l i m i t t h e gradient, t h e r e s u l t s were believed t o be reasonably accurate,

Later c a l c u l a t i o n s showed, however, t h a t t h e

s t r e s s e s were very s e n s i t i v e t o t h e temperature gradient on t h e sphere, and t h e r e f o r e t h e Oracle code was used only t o evaluate t h e pressure s t r e s s e s and t h e s t r e s s e s from axial loads. I n order t o c a l c u l a t e t h e thermal s t r e s s e s , including t h e e f f e c t s of t h e thermal gradient on t h e sphere, it was necessary t o s u b s t i t u t e a conical s h e l l f o r t h e sphere.

The angle of i n t e r s e c t i o n between t h e cone

and cylinders w a s made equal t o t h e equivalent angle of i n t e r s e c t i o n on the actual structure.

This s u b s t i t u t i o n was required because moment,

displacement, slope, and force equations were not a v a i l a b l e f o r thermals t r e s s a n a l y s i s of spherical s h e l l s with meridional thermal gradients. Thermal s t r e s s e s i n t h e two cylinders and t h e cone were calculated by t h e use of t h e equations and procedures outlined i n r e f s . &9.

order t o evaluate the f o u r i n t e g r a t i o n constants required f o r each of the t h r e e members, it was necessary t o solve t h e 12 simultaneous equat i o n s which described t h e following boundary and compatibility conditions of t h e s t r u c t u r e : Cylinder "A" a t Volute Attachment. taken as zero and t h e d e f l e c t i o n a s Cylinder "B" a t Top Flange. zero and t h e d e f l e c t i o n a s

The slope of c y l i n d e r "A" was

-al.

The slope of cylinder "B" w a s taken as

-mi.

Cone a t Outside Edge.

The slope of the cone w a s taken a s zero and

t h e meridional force was taken a s zero. Junction of Cylinder "A," Cylinder "B," and Cone.

The summation of

moments w a s taken a s zero; t h e summation of r a d i a l f o r c e s w a s taken as zero; t h e slopes of cylinder "A," cylinder "B," and t h e cone were taken t o be equal; and the d e f l e c t i o n s of cylinder "A," cone were taken t o be equal.

cylinder "B," and t h e

The following 12 equations, which are more completely derived i n

Appendix C, describe t h e boundary and compatibility conditions given above :

na n

- 0.00711J1-

c l aw/ + c 2aw'2 + c3aw; + c4aw:, 1

1.3J2

- 122.82J3 - 324.9J4 -

;

229.41Tb5

b2 F

;

(3)

4aB

C naQn +

+ 3.0J3)

= 6.2094(79.38J4

3U.12(Ta4 + Tb4)

+ 229.41Tb5 F b3

; (4)

aB Z t v

W' na n

na n

CnbW[

= 279.04(Ta2 + Tb2 )

- 1116.2Tb5 bF

;

(5)

1 2 Bc t a n 2

64.983(9.9225J2

nc nc

= 1484.65Ta2

- lO.lOlJ, +

98.456J3 + 976.93J4)

;

(6)

CnaNn

= 154.05(Tal

CnbNn

Tb5

- Tbl) - 616.21 -

GncW'nc = 0.0408J1

-12895.8J4

- 200.68J3

- 24.503J2 - 600.37J3 - 14?10.6J4

CncQnc = 196.02J4 + 3J3

;

W' = 279.04(Tb2 + 15.94Tb3 + 190.56Tb4)

nb n

;

(9)

;

(10)

- 1116.2Tb5 bF

;

(11)

4 - F1 CnbN,

154.05Tb5

F2 I n these equations,

F1 edY

J1 = 20.9cl

, ,

J2 = 459.95Tc5 - ll.555Tc3 J3

17.183Tc4

J4 = 19.165Tc5

. W

Equations (1)through (12) a r e arranged so that t h e l e f t side cont a i n i n g the unknown i n t e g r a t i o n constants i s dependent only on t h e specif i c pump tank configuration, while t h e r i g h t s i d e containing t h e thermalgradient terms will vary f o r each case. A f t e r obtaining t h e f o u r i n t e g r a t i o n constants f o r each member, t h e bending and membrane s t r e s s e s can be calculated using t h e following equat i o n s f o r e i t h e r cylinder o r t h e cone:

u In*

For t h e p r i n c i p a l meridional and c i r c w n f e r e n t i a l s t r e s s e s t h e applicable equations are:

For cylinder â&#x20AC;&#x153;A,â&#x20AC;?

14 N e = - C C naNn

’

N+=O

For c y l i n d e r ”B,”

CnbMn

c,~N, - E

2D-

(Tb3 + 3Tb4

~e -dy ~

N+=O

5”) - D b2y

-dy >

For t h e cone,

M+ =

C CncMyn

JlK2

+ ~1.35 22 +

2.3J3P1

+ 2.2J4P3

+ 1.352 + 1.6J 3P 1 + 1.2667J4P3

. I n order t o f a c i l i t a t e t h e s o l u t i o n of s e v e r a l cases and t o reduce t h e amount of time involved i n c a l c u l a t i n g complete s t r e s s d i s t r i b u t i o n s , an IBM 7090 program was w r i t t e n f o r t h e MSRE pump configuration.

The

program c a l c u l a t e s the temperature-dependent c o n s t a n t s of the 12 s i m u l taneous equations, solves t h e equations f o r t h e 12 i n t e g r a t i o n constants, and c a l c u l a t e s t h e bending, membrane, and p r i n c i p a l stresses a t 65 locations.

Up t o 25 cases can be solved, and t h e number of c a s e s t o be

solved and t h e constants i n t h e temperature d i s t r i b u t i o n equations a r e included as input d a t a .

A s e t of general input d a t a i s a l s o required I

15 that contains t h e left-hand members of t h e simultaneous equations and t h e

p o s i t i o n functions tabulated i n r e f s . 7 and 9. A s p e c i a l t e s t case with a uniform-temperature conical s h e l l w a s

prepared f o r t h e IBM 7090 program t o check t h e v a l i d i t y of s u b s t i t u t i n g t h e conical s h e l l f o r t h e s p h e r i c a l s h e l l and t o obtain an o v e r - a l l comparison between t h e r e s u l t s of t h e IBM and Oracle programs.

The compara-

t i v e r e s u l t s a r e shown i n Table 1 f o r t h e junction of t h e t h r e e members. A s may be seen, t h e cone s t r e s s e s agreed s a t i s f a c t o r i l y a t t h e junction

where they were a maximum.

Deviations between t h e r e s u l t s of t h e two

programs a t other meridional p o s i t i o n s were not considered important f o r t h e cases of i n t e r e s t .

Table 1. Comparative Results for Conical and Spherical Representation -~ ~~

Axial or Meridional Principal Stress (psi)

IBM 7090 Programa

Circumferential Principal Stress (psi)

Oracle Programb

IBM 7090 Program

Oracle Program

Cylinder "A"

-3 276

-3 374

-3 047

-3 351

Cylinder "B"

7 091

7 365

-4 018

-4 548

-25 196

-25 703

-3 572

-3 967

Cone or sphere

?For cylinder-to-cone junction.

bFor cylinder-to-sphere junction.

Thermal-stress c a l c u l a t i o n s were completed f o r the various operating conditions l i s t e d previously i n t h e section on temperature d i s t r i b u t i o n s . Strain-Cvcle Analvsis I n order t o determine t h e optimum cooling-air flow r a t e and the l i f e of t h e purrrp tank, it w a s necessary t o determine t h e allowable number of each type of operational cycle (heating and power change) f o r each of

..., pn a r e t h e a n t i c i p a t e d values f o r t h e various operational cycles and N1, N2, ..., Nn a r e t h e s e v e r a l cooling-air flow r a t e s .

If pl,

p2,

allowable number of cycles determined from the thermal-stress and s t r a i n f a t i g u e data, the "usage f a c t o r " i s defined a s V

(pi/Ni).

A design a i r

16 flow can then be selected t o minimize t h e usage f a c t o r and give t h e maxi-

mum punrp-tank l i f e . The permissible number of each type of operational cycle i s d e t e r mined by comparing the maximum s t r e s s amplitude f o r each type of cycle with t h e design f a t i g u e curves.

The maximum s t r e s s amplitude includes

the thermal s t r e s s e s caused by meridional thermal gradients, the thermal s t r e s s e s caused by transverse thermal gradients, and t h e pressure s t r e s s e s caused by t h e 50-psi i n t e r n a l pressure. A discussion of t h e various types of s t r e s s e s (primary, secondary,

l o c a l , and thermal) and t h e e f f e c t s of each on t h e design of t h e pump tanks i s given i n Appendix D.

A discussion of t h e procedure used i n

determining t h e allowable number of cycles i s presented, and t h e design f a t i g u e curves of INOR-8 a r e included. Result s Temperature D i s t r i b u t i o n s The r e s u l t s of t h e GHT temperature d i s t r i b u t i o n c a l c u l a t i o n s f o r p e r t i n e n t operating conditions a r e shown i n Figs. 4 and 5 f o r the f u e l and coolant pumps.

The spherical s h e l l meridional temperature d i s t r i b u -

t i o n s f o r t h e f u e l pump a t various cooling a i r flow r a t e s and r e a c t o r power l e v e l s of zero and 10 Mw a r e shown i n Figs. 6 and 7. Thermal S t r e s s e s Typical thermal-stress p r o f i l e s of t h e f u e l pump a t a cooling-air flow r a t e of 200 cfm with t h e r e a c t o r power a t zero and 10 Mw a r e shown i n F i g s , 8 and 9; s i m i l a r p r o f i l e s of t h e coolant purrrp a r e shown i n Figs.

10 and 11. The r e l a t i v e l y high s t r e s s e s a t the t o p flange a r e believed t o be caused by t h e poor f i t of the temperature equations i n that area, as shown i n Fig. 3.

The s t r e s s a t t h e t o p flange w a s calculated t o be

1 5 000 p s i when t h e l e a s t - s q u a r e s - f i t temperature equation w a s used.

w a s found, however, that t h i s equation introduced s t r e s s e r r o r s a t t h e cone-to-cylinder junction.

Therefore, t h e a c t u a l s t r e s s p r o f i l e s along

t h e e n t i r e length of t h e e x t e r n a l cylinder would probably be b e t t e r

. I

UNCLASSIFIED ORNL-LR-DWG 64494R

4800

4600

4400

cc 3

z W (L

4200

+ W

4000

800

F i g , 6. Meridional Temperature D i s t r i b u t i o n s of t h e Torispherical S h e l l a t a Reactor Power of 10 Mw and Various Cooling-Air Flow Rates.

UNCLASSIFIED O R N L - L R - O W G 6449 R

4 400

CY LI N D ER

,.-

4 200

W [L

$ 4000 [L

a W 2 W I800

600

JUNCTION

6 8 10 MERIDIONAL POSITION (in.)

Fig. '7. Meridional Temperature D i s t r i b u t i o n s of t h e Torispherical S h e l l a t Zero Reactor Power and Various Cooling-Air Flow Rates.

. UNCLASSIFIED ORNL-LR-DWG 64496R

30,000

20,000

40,000

-a

a Lo

c n

K v) k

-?O,OOO

-20.000

-6

-2

-4

A X i A L POSITION ( i n . )

Fig. 8. Fuel P m p P r i n c i p a l Thermal S t r e s s e s a t Cylinders "A" and "B" for Operation a t Zero Power and a t 10 Mw w i t h a Cooling-Air Flow Rate of 200 c f m . UNCLASSIFIED ORNL-LR-DWG 64497

4000

2000

ZERO POWER, 2 0 0 - c f m COOLING AlF I I

0 C Y L l N DER JUNCTION

__ - -2000

\i &

I I

--*

0 v)

-4000 w

Lz I-

-/ + t \ I 1 ' ~ O M W .200-cfm COOLING AIR

-6000

- 8000 -10,000

-12.000

I 0

MERIDIONAL

POSITION (in.)

Fig. 9. Fuel Pump P r i n c i p a l Thermal S t r e s s e s a t S p h e r i c a l S h e l l f o r Operation a t Zero Power and a t 10 Mw with a Cooling-Air Flow Rate of 200 c f m .

19 UNCLASSIFIED ORNL-LR-DWG 64498

30,000

20,000

- 10.000

-20.000

-30,000 -4

-6

-2

A X I A L POSITION ( i n . )

Fig. 10. Coolant Pump P r i n c i p a l Thermal S t r e s s e s a t Cylinders "A" and "B" f o r Operation a t Zero Power and a t 10 Mw.

UNCLASSIFIED ORNL-LR-DWG 64499R

! -

-.-

In a 0 0

-9 0

n c ln

- 20 0

MERIDIONAL POSITION (in.)

Fig. 11. Coolant Pump P r i n c i p a l Thermal S t r e s s e s a t Spherical S h e l l

for Operation a t Zero Power and a t 10 Mw.

represented by a composite of the two s t r e s s p r o f i l e s ; that is, it would

be b e s t t o use the s t r e s s p r o f i l e s from the manually f i t temperature funct i o n s near t h e junction and from t h e least-squares functions near t h e t o p flange.

Since the cone-to-cylinder junction i s the more c r i t i c a l area

and since the s t r e s s e s a t t h e t o p flange do not l i m i t the number of permissible s t r a i n cycles, t h e s t r e s s e s from t h e manually f i t equations were used i n completing t h e s t r a i n - c y c l e a n a l y s i s .

The c y l i n d e r i s s u f f i c i e n t l y

long that the temperature e r r o r a t t h e t o p flange has a r e l a t i v e l y small e f f e c t on t h e s t r e s s e s a t t h e c y l i n d e r - t o - s h e l l junction. S t r a i n Cycles The r e s u l t s of t h e s t r a i n - f a t i g u e analyses a r e presented i n Tables 2, 3, and 4.

A predicted usage f a c t o r of 0.8 o r l e s s i n d i c a t e s a safe

Table 2 .

Air ( C f d

Maximum Stress Intensity (Psi1

Fuel Pump S t r a i n D a t a for Heating Cycle

Stress Amplitude (Psi1

Allowable Cycle s

Cycle Fraction Per Cycle

Cycle Fraction i n 100 Cycles, p, /N,

0.00143 0.00040 0.00040 0.00047 0.00077 0.00114

0.143 0.040 0.040 0.047 0.077 0.114

0.00156 0.00076 0.00086

0.156 0.076 0.086

Heating Cycle t o 1200째F 50

100 150 200 2 50 300

31 14 14 16 21 26

124 400 143 095 760 955

15 7 7 8

562 200 072 048 10 880 13 477

2 2 2 1

700 500 500 100 300 880

Heating Cycle t o 1300째F 50

100 150 200 2 50 300

28 19 20 23 30 36

966 104 590 811 895 099

14 483 9 552 10 295 11 905 15 447 18 049

640 1 300 1 150 900 550 420

0.00111

0.111

0.00181 0.00238

0.181 0.238

Loss-of-Cooling-Air Accident 200

94 885

47 443

0.012

1.2

Fuel Pump S t r a i n Data for Power-Change Cycle from Zero t o 10 Mw

Table 3 .

Maximum Range (Psi1 50

100 150 200 250 300

37 971 24 763 1 8 930 1%814 1 8 775 1 8 639

Stress Amplitude (Psi1 18 12 9 9 9 9

Table 4.

985 382 465 407 388 320

Allowable Cycles

Cycle Cycle Total Fraction Fraction i n Usage 500 Cycles, Factor, Per Cycle Z Pi/Ni

P2/N2

520 1 000 1 600 1 600 1 600 1 600

0.00192

0,001 0.000625 0.000625 0.000625 0.000625

0.961 0 . SO0 0.312 0.312 0.312 0.312

1.10 0.54 0.352 0.359 0.389 0.426

Coolant Pump S t r a i n Data f o r Heating and Power-Change Cycles Heating Cycles To 1200째F

To 1300째F

Power Change from Zero t o 10 Mw

Maximum stress i n t e n s i t y , p s i

63 650

69 100

10 160

S t r e s s amplitude, p s i

31 825

34 550

5 080

Allowable c y c l e s Total relaxation P a r t i a l relaxation

4 400 220 520

140 290

0.00454

0.00714

0.00192

0.00344

0.454 0.192

0.7l4 0.344

Cycle f r a c t i o n p e r cycle Total relaxation P a r t i a l relaxation

0.00227

Cycle f r a c t i o n i n 100 c y c l e s Total relaxation P a r t i a l relaxation Cycle f r a c t i o n i n 500 c y c l e s

0.114

T o t a l usage f a c t o r " Total relaxation P a r t i a l relaxation

0.568 0.306

?For 100 heating c y c l e s t o 1200째F and 500 power cycles from zero t o 10 Mw.

operating condition f o r t h e d e s i r e d number of heating and power-change cycles.

The r e s u l t s a r e based on t h e assumption of t o t a l s t r e s s relaxa-

t i o n a t each operating condition and a r e t h e r e f o r e conservative.

The

l o c a t i o n of maximum s t r e s s i n t e n s i t y during t h e heating cycle i s not n e c e s s a r i l y the same as the l o c a t i o n of m a x i m u m stress range during t h e power-change cycle.

This a l s o provides Conservative r e s u l t s , since t h e

maximum s t r a i n s for each type of cycle were added t o determine t h e usage f a c t o r , and t h e t o t a l s t r a i n a t the a c t u a l point of maximum s t r a i n would Since t h e pump tank will s a f e l y en-

be l e s s than t h e s t r a i n value used.

dure the d e s i r e d number of heating and power c y c l e s w i t h t h i s conservative approach, it w a s not considered necessary t o l o c a t e and determine t h e actual maximum t o t a l strain.

The coolant pump w i l l operate a t a lower

temperature than t h e f u e l pump, so t h e stress r e l a x a t i o n during each c y c l e will probably be incomplete and t h e r e f o r e a l a r g e r number of c y c l e s

w i l l be permissible.

A s shown i n Table 4, t h e assumption of p a r t i a l re-

l a x a t i o n rather than t o t a l r e l a x a t i o n permits more than twice the number

of heating cycles.

For t h e f u e l pump, thermal-stress and p l a s t i c - s t r a i n

c a l c u l a t i o n s w e r e a l s o made f o r t h e s h o r t 36-in.-diam c y l i n d e r connecting t h e two t o r i s p h e r i c a l heads.

The permissible number of c y c l e s a t

t h i s l o c a t i o n w a s found t o be g r e a t e r than those shown i n Table 2, and,

t h e r e f o r e , t h e cycles i n t h e c y l i n d e r do not l i m i t t h e l i f e of t h e pump tank.

Pressure and Mechanical S t r e s s e s The r e s u l t s of t h e pressure stress c a l c u l a t i o n s made w i t h t h e Oracle program a r e shown i n Figs. 1 2 and 13.

The s t r e s s e s , which include both

primary and d i s c o n t i n u i t y s t r e s s e s , are f o r a pressure of 1.0 p s i and are d i r e c t l y proportional t o pressure.

The maximum stress from t h e a x i a l

load e x i s t s a t t h e suction nozzle attachment and i s equal t o 1.766 times t h e load i n pounds.

Re c ommendat ions T h e s t r a i n - c y c l e data of Tables 2, 3, and 4 i n d i c a t e t h a t t h e de-

s i r e d number of s t r a i n cycles on t h e f u e l pump can be s a f e l y t o l e r a t e d

INTERNAL PRESSURE = I O psi STRESS A T ' b " PRESSU x STRESS AT I 0 P S I

__i_

u) W) u

%-r %-r

9-0

5-0

u) t-

- 20

- 60

_ _ ~

SPHERICAL

-100

SHELL

JUNCTION

-6

-2

-4

A X I A L POSITION (in

Fig. 12. and "B I'

Fuel and Coolant Pump Pressure S t r e s s e s a t Cylinders "A"

UNCLASSIFIED ORNL-LR-DWG 64501

-2 40 ffl

W m [L

tffl

uo=CIRCUMFERENTIAL STRESS

r =INSIDE 0 =OUTSIDE 0 0

MERIDIONAL POSITION (in )

Fig. 13. Shell.

Fuel and Coolant Pump Pressure S t r e s s e s a t Spherical

24 when any cooling a i r flow between 100 and 300 cfm i s used; and, t h e r e -

f o r e , t h e a i r cooling can be c o n t r o l l e d manually by a remotely operated c o n t r o l valve.

A cooling-air flow r a t e of approximately 200 cfm i s recom-

mended f o r t h e following reasons: 1. The predicted usage f a c t o r i s reasonably near t h e minimum value.

There i s a wide range of acceptable flow rates on e i t h e r s i d e

of t h i s design a i r flow r a t e . 3.

A t a i r flow r a t e s g r e a t e r than 200 cfm, t h e maximum s t r e s s i n -

t e n s i t y during zero power operation i n c r e a s e s r e l a t i v e l y r a p i d l y and dec r e a s e s t h e permissible number of heating cycles. Since t h e r e i s a p o s s i b i l i t y of e r r o r i n the temperature d i s t r i b u t i o n c a l c u l a t i o n s because of u n c e r t a i n t i e s i n t h e heat generation rates and heat t r a n s f e r c o e f f i c i e n t s , it i s recommended t h a t the temperature gradient on t h e s p h e r i c a l s h e l l be monitored by using two thermocouples spaced 6 i n . a p a r t r a d i a l l y .

T h i s gives t h e maximum temperature d i f -

ference between t h e two thermocouples and t h e r e f o r e reduces t h e e f f e c t of any thermocouple e r r o r .

Since t h e thermal g r a d i e n t of t h e s p h e r i c a l

s h e l l near t h e junction i s of primary importance i n determining t h e t h e r m a l s t r e s s e s , t h e d i f f e r e n t i a l temperature measurements and the data of

F i g s , 6 and 7 can be used t o set t h e a c t u a l cooling-air flow r a t e on t h e pump.

T h i s method has the disadvantage of r e q u i r i n g s e v e r a l adjustments

as t h e temperature and power l e v e l are r a i s e d t o t h e operating p o i n t . I f d i r e c t measurement of t h e flow r a t e were p o s s i b l e minor adjustments

could be made a f t e r t h e system reached operating conditions.

Since no

c o o l i n g - a i r flow measuring equipment i s planned f o r the f u e l pump a t t h e present t i m e , a preoperational c a l i b r a t i o n of t h e c o o l i n g - a i r flow r a t e versus valve p o s i t i o n should be made t o permit the approximate a i r flow r a t e t o be s e t p r i o r t o high-temperature operation. The design temperature d i f f e r e n c e between the two t h e r m c o u p l e s f o r monitoring t h e thermal gradient i s 100째F a t a power l e v e l of 10 Mw and a thermocouple spacing of 6 i n .

The maximum allowable temperature d i f -

ference i s 200째F f o r 10-Mw operation.

A f t e r t h e c o o l i n g - a i r flow r a t e

has been s e t f o r 10-Mw operation, a readjustment of t h e flow should be made, i f necessary, a t zero power operation t o prevent a negative thermal gradient on t h e sphere.

This adjusted c o o l i n g - a i r flow should then become

25 t h e operating value.

During t h e p r e c r i t i c a l t e s t i n g and power operation

of t h e r e a c t o r it should be kept i n mind t h a t any s i g n i f i c a n t change i n t h e f u e l pump c o o l i n g - a i r flow r a t e will c o n s t i t u t e a s t r a i n cycle and

will r e p r e s e n t a decrease i n t h e usable l i f e of t h e pump tank.

Therefore,

an e f f o r t should be made t o keep t h e number of c o o l i n g - a i r flow r a t e adjustments t o a minimum. The e f f e c t of heating t h e system t o 1300°F i s a l s o shown i n Tables

2, 3, and 4.

The f u e l and coolant pumps can s a f e l y endure only about

h a l f as many heating cycles t o 1300°F as t o 1200°F.

For the coolant

pump, 100 heating cycles t o 1300°F would e s s e n t i a l l y consume t h e l i f e of t h e pump tank.

A t 1300°F the assumption of t o t a l stress r e l a x a t i o n i s

r e a l i s t i c , and no a d d i t i o n a l conservatism should be claimed by i t s use. Therefore, it i s recomnended t h a t t h e system not be heated t o 1300°F on a r o u t i n e basis.

Since t h e f u e l and coolant pump tanks a r e primary containment members, t h e maximum value of t h e usage f a c t o r must not exceed 0.8, which i s t h e acceptable 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 t h e usage f a c t o r and t h e complete s t r a i n cycle h i s t o r y of both t h e f u e l and t h e coolant pumps. I n c a l c u l a t i n g t h e usage f a c t o r , p a r t i a l power-change cycles i n which r e a c t o r power i s increased only a f r a c t i o n of t h e t o t a l power should be considered as complete power cycles u n l e s s t h e number of p a r t i a l c y c l e s i s a l a r g e f r a c t i o n of t h e t o t a l when a pump tank has passed through t h e permitted number of cycles.

I n t h i s case, a d d i t i o n a l thermal s t r e s s

c a l c u l a t i o n s should be made t o determine t h e proper e f f e c t of t h e p a r t i a l cycles. Although t h e s t r a i n - c y c l e data i n d i c a t e t h a t t h e coolant pump i s acceptable f o r t h e s p e c i f i e d number of s t r a i n cycles, t h e stress i n t e n s i t y i s uncomfortably high.

These s t r e s s e s can be reduced by lowering t h e

thermal gradient on t h e s p h e r i c a l s h e l l by using a reduced thickness of i n s u l a t i o n on t h e upper surface of t h e pump tank.

Since nuclear heating

i s not involved i n t h e coolant pump, t h e proper amount of i n s u l a t i o n can

b e s t be determined on t h e Fuel Pump Prototype Test F a c i l i t y , which i s p r e s e n t l y under construction.

Conclusions The s t r a i n - c y c l e a n a l y s i s i n d i c a t e s t h a t t h e fue, pump w i

be satis-

f a c t o r y f o r t h e intended l i f e of 100 heating cycles and 500 power-change cycles i f it i s a i r cooled. coolant pump.

No s p e c i a l cooling will be required f o r t h e

A conservative design i s provided by t h e use of standard

s a f e t y 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 data and i n t h e usage f a c t o r .

Ad-

d i t i o n a l conservatism of an w h o m magnitude i s provided by t h e assumpt i o n of t o t a l s t r e s s r e l a x a t i o n a t each operating condition and by the f a c t t h a t t h e a c t u a l maximum s t r a i n should be less than t h e c a l c u l a t e d maximum s t r a i n . I n a d d i t i o n t o t h e s a f e t y f a c t o r s o u t l i n e d above, t h e f u e l and coolant pwnp tanks a r e capable of exceeding t h e i r required s e r v i c e l i f e by f a c t o r s of 2.2 and 1.4, respectively, before the maximum permissible usage f a c t o r i s exceeded.

27 References

1. Molten-Salt Reactor Program Q u a r t e r l y Progress Report f o r Period Ending J u l y 31, 1960, Om-3014.

2. A. G. Grindell, W. F. Boudreau, and H. W. Savage, "Development of Centrifugal Pumps f o r Operation with Liquid Metals and Molten S a l t s

a t 1400-1500 F," Nuclear Sci. and Eng. 7(1), 83 (1960).

3. Tentative S t r u c t u r a l Design Basis f o r Reactor Pressure Vessels and D i r e c t l y Associated Components (Pressurized, Water -Cooled Systems )

esp. p. 31, PB 151987 (Dec. 1, 1958), U. S. Dept. of Commerce, Office of Technical Services.

T. B. Fowler, Generalized Heat Conduction Code f o r t h e IBM 704 Com-

puter, ORNL-2734 (Oct. 14, 1959), and supplement ORNL CF 61-2-33 (Feb. 9, 1961).

P. B. Wood, NL;LS:

A 704 Program f o r F i t t i n g Non-Linear Curves by

Least Squares, K-1440 (Jan. 28, 1960), Oak Ridge Gaseous P l a n t ; SHARE D i s t r i b u t i o n No. 8371838.

6. F. J. W i t t , Thermal S t r e s s Analysis of C y l i n d r i c a l Shells, ORNL CF 59-1-33(Mar. 26, 1959). 7. F. J. Stanek, S t r e s s Analysis of C y l i n d r i c a l Shells, ORNL CF 58-9-2 ( J u l y 22, 1959).

8. F. J. W i t t , Thermal Analysis of Conical Shells, ORNL CF 61-5-80 ( J u l y 7, 1961). 9. F. J. Stanek, S t r e s s Analysis of Conical Shells, ORNL CF 58-6-52 ( A u g . 28, 1958).

10. C . W. Nestor, Reactor Physics Calculations f o r t h e MSRE, ORNL CF 60-7-96( J u l y 26, 1960). 11. T . Rockwell (ed.), Reactor Shielding Design Manual, p 392, McGrawH i l l , New York, 1956.

12. M. Jakob, Heat Transfer, Vol. I, p 168, Wiley, 1949. 13. A. I. Brown and S. M. Marco, Introduction t o Heat Transfer, p 64, McGraw-Hill, New York, 1942.

14. I b i d , p 31.

15. B. F. Lange, "Design Values f o r Thermal S t r e s s i n Ductile Materials," Welding Journal Research Supplement, 411 (1958).

16. S. S. Manson, "Cyclic L i f e of Ductile Materials," Machine Design 32, 13-

( J u l y 7, 1960).

29 APPENDIX A

D i s t r i b u t i o n of Fission-Product-Gas Beta Enernv The t o t a l energy t h a t w i l l be r e l e a s e d i n t h e f u e l pump tank by t h e fission-product gases has been reported"

by Nestor t o be 15 kw.

This

energy w i l l not be uniformly deposited on t h e surface area exposed t o gas, however, so it w a s necessary t o determine i t s d i s t r i b u t i o n over t h e surfaces of t h e pump tank.

The pump tank w a s assumed t o be of s t r a i g h t

c y l i n d r i c a l geometry, as shown i n Fig. A . l ,

and t h e d i s t r i b u t i o n of t h e

energy f l u x a t t h e c y l i n d r i c a l w a l l s w a s c a l c u l a t e d as o u t l i n e d i n t h e following s e c t i o n s .

The d i s t r i b u t i o n of energy t o t h e upper surface was

approximated by assuming a d i s t r i b u t i o n s i m i l a r t o t h a t f o r t h e o u t s i d e

wall. Energy Flux a t Pwnp Tank Outer Surface

It w a s assumed that t h e r e w a s no s e l f - s h i e l d i n g or shi'elding from t h e v o l u t e support cylinder, and t h e l i n e source (dy,dx) w a s i n t e g r a t e d over t h e enclosed volume (see Fig. A.2)11 t o o b t a i n t h e energy f l u x a t Pl:

dy dx a sec2 8 de

4 7 0

[Jyl 4 T O

"1 J 0

dy dx de

+ y2 ) -1/2

a2 sec2

30 UNCLASS1 FlED ORNL-LR-DWG 68993

36 i n . 15 in. DID,

1 --

h, = 8 in.

Fig. A . l .

. _

Assumed Pump Tank Geometry.

UNCLASSIFIED ORNL-LR-DWG 68994

i d z = u sec2 8 de

+ . T t

\ \ L-

y+-

_\_

I4 I I I I

I I I

Fig. A.2. Surface.

Diagram f o r Determining Energy Flux a t Pmp Tank Outer

31 where

x1 = f ( 2yR0 -1

= tan

-1

82 = t a n S

- y2 ) 112

2 -112 + y )

2 2 -112 h2(x + y )

hl(x

= energy source per u n i t volume

Energy Flux a t t h e Volute Support Cylinder Outer Surface Figure A . 3 and t h e following equation were used f o r determining t h e energy f l u x a t t h e o u t e r surface, P2, of t h e volute support cylinder:

where Y1 = Ro - R 1

x1 =

81 = t a n

f [R:

tan

-1 -1

hl(x

]112

- Rl)2

2 4

+y )

2 2 -112 h2(x + y )

Energy Flux a t t h e Volute Support Cylinder I n n e r Surface The energy f l u x a t P3, as shown on Fig. A.3,

w a s approximted by

c a l c u l a t i n g t h e f l u x a t P$ using equation A.2 and t h e appropriate values of R1 and R

visible t o P

. 3

This value w a s then corrected for t h e a d d i t i o n a l volume by t h e d i r e c t cross-section a r e a r a t i o and t h e inverse

square ratio of the center-of-gravitydistance:

$(at P3) = 1.26 $(at P;)

The values of $ at P1, P2, and P; were evaluated as functions of hl and h by the Numerical Analysis Section of ORGDP. The beta-energy dis2 tribution is shown in Fig. A.4.

UNCLASSIFIED 68995 ORNL-LR-DWG

VOLUTE SUPPORT CYLINDER

PUMP TANK OUTER SURFACE

Fig. A.3. Diagram for Determining Energy Flux at Outer and Inner Surfaces of the Volute Support Cylinder.

TORISPHERICAL SHELL. INSIDE

-l

7 3000

f z 2

2000

1 AXIAL POSITION OF CYLINDER A

IS MEASURED FROM SPHERE-TOCYLINDER JUNCTION

1000

i SUPPORT CYLINDER &,INSIDE ~

2 RADIAL POSITIONS OF SHIELDING PLUG FACE AND TORlSPHERlCAL SHELL ARE MEASURED FROM PUMP CENTER LINE I

POSITION (in )

Fig. A.4. Beta-Energy Distribution of Fuel Pump Tank, Volute Support Cylinder, and Shielding Plug.

APPENDIX B Estimation of Outer Surface TemDeratures and Heat Transfer Coefficients The GHT Code f o r c a l c u l a t i n g t h e complete temperature d i s t r i b u t i o n of t h e pump tank could not consider t h e e f f e c t s of t h e flowing a i r stream on t h e temperature d i s t r i b u t i o n of t h e pump tank because of t h e temperat u r e rise of t h e cooling a i r along t h e pump tank surface.

I n order t o

obtain t h e temperature d i s t r i b u t i o n , it w a s necessary t o couple t h e pump tank surface with t h e surroundings by use of an e f f e c t i v e heat t r a n s f e r c o e f f i c i e n t ( h ) and t h e ambient temperature. It w a s impractical t o ce obtain an e f f e c t i v e c o e f f i c i e n t a t each point along t h e surface, and w a s calculated a t t h e c y l i n d e r - t o - s h e l l juncce t i o n , where t h e thermal stress problem w a s most severe, and then applied

t h e r e f o r e t h e value of h

over t h e e n t i r e upper surface of t h e pump tank. The air-cooled upper portion of t h e f u e l pump tank i s shown schematically i n Fig. B.l. I

The pump tank i s subject t o thermal r a d i a t i o n

and convection heating from t h e f u e l salt, fission-product b e t a heating,

and gamma-radiation i n t e r n a l heating.

This heat i s conducted t o t h e

UNCLASSIFIED ORNL- LR-DWG 68996

COOLING-AIR FLOW

COOLING-AIR SHROUD

43-4

1 *or Fig. B.l. Wall.

\PUMP

TANK W A L L

q =hf (8,-8,) f

Schematic Diagram of Cooling-Air Shroud and Pump Tank

34 pump tank surface where it i s t r a n s f e r r e d t o the cooling a i r by two paths: (1)d i r e c t forced convection t o the cooling a i r and ( 2 ) r a d i a t i o n t o t h e

cooling shroud and forced convection t o t h e same cooling a i r .

Heat i s

a l s o conducted p a r a l l e l t o t h e pump tank surface, but t h i s heat t r a n s f e r i s assumed t o be zero i n estimating t h e surface temperature and heat

transfer coefficients. The temperature d i s t r i b u t i o n through the pump tank w a l l can be calcu-

lated12 as o u t l i n e d below, assuming a constant gamma heat-generation r a t e through the w a l l

d20

- -- - ax

k q y x + c1 â&#x20AC;&#x2122;

=--+dx

A t t h e i n t e r i o r w a l l , where x = 0,

and t h e r e f o r e

and f o r any place within t h e w a l l , t h a t is, x # 0,

The temperature i s then

A t the i n t e r i o r w a l l x = 0, and t h e r e f o r e

e = c2 = e 2 and

If t h e heat t r a n s f e r f r o m t h e o u t e r surface i s expressed by an e f -

f e c t i v e c o e f f i c i e n t w i t h r e s p e c t t o t h e ambient temperature rather than the a c t u a l forced-convection cooling system temperature, t h e o u t e r sur-

f a c e temperature can be c a l c u l a t e d as follows from Eq. (B.6) w i t h x = t :

where

I '

and

gt -+2

e3 t

g t = h 8 - h 8 ce 3 ce 4e where 8

(B.lO)

(B. 11)

i s t h e e f f e c t i v e ambient temperature, and

gt Solving Eqs. (B.10),

= hfel

(B.ll)J

- hfQ2 + QYt+

(B.12)

and (B.12) simultaneously for 8 3 y i e l d s t h e

following equation :

hcehft

hcek

hcehft + k(hce

hf)

hfk hcehft + k(hce + h f )

hcehft + k(hce + h f ) t ( h f t + 2k)

hcehft + k(h,,

9/ + hf)

(B.13)

Solving Eq. (B.13) f o r hce and rearranging the terms gives hfk(O1

- 6,) + kgs

+ t ( h f t + 2k) 3

(B.14)

The d i f f i c u l t y i n c a l c u l a t i n g t h e o u t e r surface temperature (0,)

from Eq. (B.13) r e s u l t s from t h e f a c t t h a t t h e heat t r a n s f e r c o e f f i c i e n t s hce and h

a r e highly temperature dependent, and

accurate c o e f f i c i e n t s can be c a l c u l a t e d .

must be known before

However, f o r a given s e t of r e -

a c t o r operating conditions, it i s evident from t h e preceding equations t h a t t h e s e l e c t i o n of an a r b i t r a r y value of

w i l l result i n a particular

value of t h e t o t a l heat t r a n s f e r a c r o s s t h e o u t e r surface, and a p a r t i c u -

l a r value of h

i s required t o d i s s i p a t e t h i s q u a n t i t y of heat t o t h e ce surroundings. Since t h e temperature drop a c r o s s t h e pump tank w a l l i s

small f o r the cases of i n t e r e s t , â&#x201A;ŹJ3 can be used to compute t h e value of t h e i n t e r n a l surface heat t r a n s f e r c o e f f i c i e n t (h ), and t h e value of f

can then be c a l c u l a t e d by Eq. (B.14). The following procedure was used t o estimate t h e e f f e c t i v e o u t e r

surface heat t r a n s f e r c o e f f i c i e n t s for various c o o l i n g - a i r flow r a t e s : 1. Values of h versus inner surface temperature ( 0 ) were calcuf 2 lated by Eq. (B.15), below, and p l o t t e d on Fig. B.2:I3

4 - 0,) 4

u F F (0,

r e a

The t o t a l heat t r a n s f e r r e d

(%)

(B.15)

i1.5

- 02

w a s c a l c u l a t e d versus t h e o u t e r

surface temperature ( 6 ) by Eq. (B.16), below, a f t e r f i r s t c a l c u l a t i n g 3

UNCLASSIFIED ORNL-LR-DWG

600

700

800

900 4000 4100 SURFACE TEMPERATURE ("F)

4 200

4300

64503

4400

Fig. B.2. Pump Tank Inner Surface Heat Transfer C o e f f i c i e n t Versus Outer Surface Temperature.

hce

by Eq. (B.14):

gt 3.

= hce(03

- e4e)

(B.16)

The forced convection heat t r a n s f e r c o e f f i c i e n t s f o r the pump

tank o u t e r surface and t h e cooling shroud were c a l c u l a t e d as a function of a i r flow by Eq. (B.17) and p l o t t e d on Fig. B.3:14

hc = 0.0225

0.4 (Pr) (Re)'"

(B. 17)

Q The heat t r a n s f e r r e d t o t h e cooling shroud by thermal r a d i a t i o n

was calculated versus shroud temperature f o r each of several values of O3 and p l o t t e d on Fig. B.3. A t equilibrium conditions, t h e heat radiated t o t h e shroud (q3 4 )

) must equal plus t h e heat t r a n s f e r r e d d i r e c t l y t o the cooling a i r ( q 3-5 t h e t o t a l heat t r a n s f e r r e d (%), and t h e heat t r a n s f e r r e d from t h e shroud

UNCLASSIFIED ORNL-LR-DWG 64504

COOLING SHROUD TEMPERATURE ("F)

1450

1050

950

850

100

200

300 400 500 COOLING AIR FLOW (cfm)

750

650

550

450

350

-- 6 0 0 0

+ L

f 2

5000

-m

n 3

5 4000 W

z1 0

3000

n W

f 2000 0

z a

+ n I-

a 1000 w I

d m

0 0

600

700

800

Fig. B.3. Convective Heat Transfer Coefficient Versus A i r Flow and Heat Transferred t o Shroud Versus Shroud Temperature.

) must be equal t o t h e heat t r a n s f e r r e d t o t h e t o t h e cooling a i r (q 4-5 shroud from t h e pump tank. Therefore, f o r each assumed value of G3, t h e heat t r a n s f e r r e d t o t h e shroud i s c a l c u l a t e d versus cooling a i r flow r a t e from t h e expression

where

and

q3-5

= hc(B3

- e5)

The p a r t i c u l a r shroud temperature required t o accept t h e heat (q3-4 )

from t h e pump tank surface i s obtained from Fig. B.3.

The heat t r a n s f e r -

red from t h e shroud t o t h e cooling a i r i s then c a l c u l a t e d :

and q4-5 a r e p l o t t e d versus c o o l i n g - a i r flow 3â&#x20AC;&#x2122; q3-4, r a t e as shown on Fig. B.4, and t h e i n t e r s e c t i o n of t h e two curves d e t e r -

For each value of 8

mines the c o o l i n g - a i r flow rate t h a t w i l l produce the p a r t i c u l a r value

e3.

versus c o o l i n g - a i r flow r a t e can then be made as 3 i n F i g . B.5, and the e f f e c t i v e surface heat t r a n s f e r c o e f f i c i e n t s h ce f o r use i n t h e GIfl7 Code can be c a l c u l a t e d f o r any a i r flow r a t e using of

A p l o t of 8

Eq. ( B . 1 4 ) .

40 UNCLASSIFIED

ORNL-LR-DWG

6000

6450

5000

5 -m +

4000

I w 0 E

LL W

3000

z a

+ rn I

2 2000

z a

0 I

p” t 000

0 COOLING AIR FLOW l c f r n l

Fig. B.4.

Shroud Heat Transfer Versus Cooling Air Flow.

1200

L LL W 3

n + a

E (000 a

5I-

u 0

800

m _1 a z n 0 z 600

I 400

, 1

AIR FLOW ( c f m )

Fig. B.5.

Nominal Surface Temperature Versus Cooling Air Flow.

APPENDIX C

Derivation of Boundary and Compatibility Equations f o r Thermal S t r e s s Calculations The procedures f o r c a l c u l a t i n g thermal s t r e s s e s i n c y l i n d e r s and cones are f u l l y described i n r e f s . 6 through 9.

The g e n e r a l layout of

t h e pump tank s t r u c t u r e and t h e s i g n convention used i n t h e stress a n a l y s i s are shown i n Fig. C . l . t o be r i g i d .

The cone-to-cylinder j o i n t i s assumed

It i s necessary t o evaluate f o u r i n t e g r a t i o n c o n s t a n t s for

each of t h e t h r e e members by solving 12 simultaneous equations d e s c r i b i n g the boundary conditions of the s t r u c t u r e and t h e c o m p a t i b i l i t y conditions

which i n t e r r e l a t e t h e t h r e e members a t t h e i r junction.

Since t h e posi-

t i o n f u n c t i o n s for c y l i n d e r s a r e t a b u l a t e d i n ref. 8 only for p o s i t i v e 1

values of L, t h e cone-to-cylinder junction i s made t h e o r i g i n and t h e c y l i n d e r axis i s assumed t o be p o s i t i v e i n e i t h e r d i r e c t i o n .

This

UNCLASSIFIED ORNL-LR-DWG 64507

Fb= 4.4

CYL.

TOPFLANGE

X = 6.3

CYL. P

VOLUTE

Fig. C . l . ture.

Schematic Diagram and Sign Convention of Pump T a n k Struc-

42 assumption r e q u i r e s that t h e slope and t h e shear f o r c e equations be modif i e d by a sign change t o compensate f o r the reversed sign on one of t h e cylinders. Derivations of t h e 12 simultaneous equations from the s p e c i f i c boundary or compatibility conditions a r e given below.

The basic equa-

t i o n s f o r moment, displacement, slope, and shear f o r c e were obtained from r e f . 6 f o r the cylinders and r e f . 8 f o r t h e cone.

The conical s h e l l equa-

t i o n s d i f f e r somewhat from those presented i n r e f . 8 because a preliminary version of t h e report w a s used t h a t d i d not include t h e e f f e c t s of a thermal gradient through t h e w a l l .

All t h e terms considering t h e e f -

f e c t s of i n t e r n a l pressure and mechanical loading were omitted from both t h e c y l i n d r i c a l and conical s h e l l equations. The following material constants, geometric constants, p o s i t i o n cons t a n t s , and auxiliary functions a r e used i n t h e boundary and compatibility equations:

= 26.3 X

t = 0.75

Et3

D =

12(1

- p")

4mb5 d4

7.81 x

p = 0.3

Y =

6 10

6 ,

= 1.016 X 10

43 L

F1=d

4 + 4 ,

F2 = F1 edY

It w a s necessary t o a d j u s t t h e pump tank configuration s l i g h t l y so that t h e boundaries of the separate members would coincide with t a b u l a t e d

values f o r t h e cone and c y l i n d e r s :

pc2

3.3045

â&#x20AC;&#x2122;

---

1.349

pc = 1.1598 t

cot

= 0.5

= 78.5 deg

= 0.2035

xc xCl

xc2 a

Ycl

, ,

= 2 @ , c l = 6.254%

= 2pcdYc2 = 9.844

= 7.125 i n .

I =

sin

5 2

= 18.0 i n .

7.271

, ,

44 The values of Xcl

and Xc2 were adjusted t o t h e n e a r e s t values t a b u l a t e d

i n ref. 9: Xcl

= 6.30

ycl =

xc2

(zp

= 7.376

= 9.90

The c y l i n d e r mean r a d i u s "artw a s then corrected: a = Y

sin

1.6523 at

Ybi

1*6523 = 0.30479 7.228 x 0.75

= BLai

= 3.588

= @\i

4.416

= 6.5 i n .

i j i = 8.0 i n .

Lai

The values of yai and y

@ = 0.55207

'ai

= 7.228

were adjusted t o t h e n e a r e s t t a b u l a t e d values

i n r e f . 7. a'

= 3.6

, ,

La = 6.521

4.4

43 = 7.970 .

The following cylinder p o s i t i o n functions were taken from r e f . 7:

Function

Volute, ya = 3.6

Junction, Y a b = O

0.049

-2.0

-0.02418

Top Flange, yb = 4.4

M2 M3

M4 Ql

&2 Q3

&4 N1 N2 N3

-0,. 02337

-65.64

+2.0

-50.065

32.39

155.02

0.07319

-2.0

0.03091

0.02482

-2.0

-0.01582

33.25

-2.0

-104.95

-98.03

+2.0

-205.08

-0.01209 -0.02450 -16.19 -32.82

-0.01241

w; w;

0.03659

wc:

0.007546

0 +1.0 0 +1.0 1.0 -1.0

-0.01168 -0.00377 -77.51 -25.03 0.00791 0.01546

-49 02

1.0

-102.54

-16.62

1.0

52.48

The following cone p o s i t i o n functions were taken from r e f . 9:

Function M Yl M Y2 M Y3

Junction, Xcl = 6.3

Cone Outer Surface, xc2 = 9.9

3.3798 -1.0712 -0.000601

M Y4

-0.0013052

Qcl

-0.45082

4.4317

1.0224

-2.2413

&c2 Qc3 Qc4

-0.0004356 -0.00014553

0.000010179 -0.000003558

46 Junction, Xcl = 6.3

Function

Cone Outer Surface, xc2 = 9.9 -54.918

10.1451

Wdl

-108.588

4.47331

Wd2 w;3

-0.001444

-0.00008719

0.004322

-0.0002494

Wd4

(vc - Well (vc - W c l 2 (vc - wc l3

-13.313 -27,449 -0.01553

(vc - wc)4

0.0051

0.10078

0.04081

0.007l098

0.0011659

2.2948

3.1988

1.9948

2 . $988

9.9225

24.5025

K2 K3

K4 p1

p2 p3

19.845

49.005

147.684

900.559

19.691

120.074

The cone a u x i l i a r y temperature functions were obtained from t h e following expressions: cot

J1 = -(EtcQ:

Etca cot

= -20.9Tcl

Tcl

(r 72Tc5

- Tc3)

= 459.95Tc5 - 11.555Tc3

-2Etca J3

cot

4 = -17.183Tc4

T c 5 = -19.165Tc5

*c4

6 @C

-3Etca J

cot

4? The temperature d i s t r i b u t i o n s for t h e c y l i n d e r s and cone were expressed i n t h e following forms: Cylinder "A"

8 a = T a1 + T a2 xB + T

tr B

+ Ta4(g7

Cylinder "B"

Tcl Yn L

Tc2

A t t h e pump v o l u t e (ya = 3.6)'

dwa - dL

+ T c 3Y c + Tc4yc2

Tc5Yc3

t h e slope of c y l i n d e r "A" = 0, and

o=Et

c c w ' = - Eta CnaWA

= 279.04(Ta2 + 13.04

A t t h e pump volute (ya = 3.6)'

and

t h e radial displacement of "A" =

a 'I

and t h e r e f o r e

CnaNn

= 0

(c.2)

A t the cone-cylinder junction, t h e s u m a t i o n of moments = 0, t h a t is,

Ma-M,,+Mc=O,

and

2DaaTb3 + D b y e -dy

CncMp

+ J1K2

+ 1.352 + 2.35 3P1 + 2.2J4P3 1 - c C 4aB2

= 0

M na n

--4ap2

M + C C M = nb n nc Yn

- Tb3) - J1K 2 +

2Dm(Ta3

1.3J2 + 2.35 P + 3 1

+ 2.2J4P3

114.7(Ta3

- Tb3) - 0.00711J1 -

1.3J2

- D b2y e -ay

- 122.82J3 - 324.9J4 - 229.41Tb5

F b2 1

(c.3)

A t t h e cone-cylinder junction, the summation of h o r i z o n t a l and v e r t i c a l

f o r c e s = 0, and t h e r e f o r e , f o r t h e v e r t i c a l forces, sin

4 +

Ne cos

= 0

or cos

Qc =

For t h e h o r i z o n t a l forces, Qc cos

4 +

Ne s i n

2 cos

4 +

sin

= N~

(

sin

6P pfm)

For t h e summation of h o r i z o n t a l forces on both t h e c y l i n d e r s and the cone,

Qa +

&b - Ne

and

1 4aB

na n

+ 6DaaTa4 + 1 4aB

E cnbQn

(-E

6.2094(79.38J4 + 3.0J3)

- 344.12(Ta4

CneQne + 8J4Pl +

+ Tb4) + 229.41Tb5 F D 1

(c.4)

A t t h e junction, t h e slope of Cylinder "A" =

slope of Cylinder "B,"

and dw

- -a

= - s c C W'+mTb2-bye Et nb n

na n

dw b

---

+ Tb2)

na n

CnaWA

W' = 279.04(Ta2 + Tb2) nb n

- E2t by

-dY

e -dY

b - 1116.2Tb5 F

(C.5)

A t t h e junction, t h e slope of Cylinder "A" = slope of t h e Cone 'IC,''

dYc

2p3 W/ - J K + J P +(J3 ncnc 11 2 1 3

a@ - C C

2 Bc 2 naWn ' - r t a n

and

4 c cncw'nc

~4P1)

(J3

~4P1)

aB t

cnaW'n - -%

tan2

64.983(9.9225J2

nc nc

= 1484.65Ta2

- lO.lOlJ,

+ 98.456J3 + 976.93J4)

(C-6)

51 b

A t t h e junction, t h e displacement of Cylinder "A" = t h e displacement of

Cylinder "B," t h a t is,

and

5 Et

- ~mal N =~

2 CnaNn CnaNn

cnbNn - mbl - 7

CnbNn = Eta(Tal

CnbNn

= 154.05(Tal

Et - Tbl) - a y

-dY

e-dy

Tb5 - Tbl) - 616.21 -

(c.7)

A t the junction, t h e displacement of Cylinder "A" = the displacement of

t h e Cone, and

= u cos 4 - V

J1 log,

cncw'n -

"E t C C naNn - m a l = c o s $

- J1K 3 +

sin

p, + (3J2 + 2J3P1 + J4P3)

=3 +

Cgcl

-a

sin

pc2 +

Cncvnc

- JlK3 +

+ Tc2Yc + Tc3Yc2 + Tc4y,'

(Tcl

J1 loge

Tc5yc) 4

CnaNn

sin2

E cnc(vnc - w

tc cos 4

Eaal

-m

’

sin2 - tc cos 4 sin

) =

(13.654P1 + 2.1J3)P1

4 ( T + ~T ~Y

+ T

c2 c

E;a s i n

4 (Tcl +

Tc2Yc

... + Tc5Y4c )

Y2 c3 c

sin

~T ~ Y4 ~ ~Y ~ )

= Ernal

t h e r e f ore a

nc sin2

4 (13.6J4P1 + 2.1J3)P1

and a

-t

CnaNn

2 sin 4 tc cos 4

cnc(vnc - wnc 1

-12895.8J4

- 200.68J3

A t t h e o u t e r surface of t h e cone,, t h e slope = 0, and n

ncW’nc

- K1J1 +

PlJ2

+ 2P, 1 +3 (J3 + P1J49 = 0 3

W’ = 0.0408J1 nc nc

- 24.503J2 - 600.37J3 - 14710.6J4

(C.9)

A t t h e cone o u t e r surface, t h e meridional membrane f o r c e = 0, and

CncQnc

= 8P J

1 4

+ 3J3

= 196.02J4

A t t h e t o p flange, t h e slope of Cylinder

C W’ = 279.04(T%2 + 15.94Tb3 nb n

+ 3J3

(c .lo>

“B” = 0, and

+ 190.56Tb4) -

- 1116.2Tb5 bF

2 A t t h e t o p flange, t h e displacement of Cylinder ”B” = -6

w = “ C C b

N nb n

+ Tb4 (.)‘]-Ye B

“E t C C nbNn = y e-dY - mb5

-dY

I’ and

(c.11)

4 CnbNn

- F1 (C .12)

154.05Tb5 F2

The f i n a l forms of t h e s e 12 equations are arranged so t h a t t h e l e f t hand s i d e containing the unknown i n t e g r a t i o n constants i s dependent only on t h e s p e c i f i c pump tank configuration, while t h e r i g h t s i d e containing t h e temperature d i s t r i b u t i o n terms w i l l vary f o r each operating condition.

The matrix of i n t e g r a t i o n constant c o e f f i c i e n t s f o r the 1 2 equations i s

shown i n Table C .1.

Table C .l. Simultaneous Equation Matrix ~

~~~~~

Coefficients of Unknown I n t e g r a t i o n Constants Cna,

Crib,

and Cnc

E quat ion Nwnbe r

‘4-a

-0.01241

-0.03659

-49.02

-16.62

-0.01209

-0.0245

-16.19

-32.82

-0.22696

-0.1253

0 -0.1253

‘3a

0.22696 -0.1253

0 0.1253

c2b

c3b

c413

0.22696

3.3798

-1.0712

-2.7993

6.3485

-0.1253

-0.22696

-0.1253

0.1253

-1.0

1.0

clc

c2c

1.0

-1.0

1.0

5.3205

-5 3205

5.3205

1.0

9.637

128.212

-264.36

-54.918

-108,588

0 0 0

7.91 x

1.546

-1.168 x

-3.77 x

-1.0

-919.2 0

4.4317

-290.69 0

-2.2413

c3c

c4c

-6.01 x

-1.3052

-2.705

-9.03 x

0.009384 U

-0.14957 -8.719 x 10-5

1.018 x

0 -0.28086 0

4.912 x -2494 x -3.558 x

-102.54

52.48

-77.51

-25.03

56 APPENDIX D

Explanation of Procedure Used t o Evaluate the Effects of Cyclic Strains i n the MSRE Pumps J. M. Corm

A n e s s e n t i a l difference i n s t r u c t u r a l design f o r high-temperature

operation a s compared with design f o r more modest conditions i s the need t o consider creep and relaxation of the s t r u c t u r a l material.

Many of the

methods and procedures presently specified a s a s t r u c t u r a l design b a s i s i n t h e ASME Boiler and Pressure Vessel Code, Unfired Pressure Vessels, Section V I I I , and i n the preliminary design b a s i s developed by t h e Navy3 Thus a revised design b a s i s

become meaningless a t high temperatures.

must be formulated when high-temperature conditions a r e considered.

The

operating program of any component must be examined, and t h e design b a s i s selected must be used t o determine whether the number of operational cycles which can be s a f e l y t o l e r a t e d exceeds the number of the cycles which i s desired during the l i f e of the component.

I f necessary, the number of

operational cycles of the component must be limited t o t h e value which can be s a f e l y t o l e r a t e d .

A s may be seen, t h e d e t a i l s of the operating

program a r e extremely important and must be selected w i t h considerable care. The concept of s t r e s s i s used here as a convenience i n discussing t h e e f f e c t s of c y c l i c s t r a i n s because it i s the principal variable i n

conventional problems of e l a s t i c i t y .

Properly, however, the discussion

should be i n terms of s t r a i n s when dealing with high temperatures and, especially, i n describing thermal e f f e c t s i n structures.

With these

f a c t o r s i n mind, four general types of s t r e s s e s were considered i n est a b l i s h i n g a design basis f o r the MSRE pumps which w i l l operate a t temperatures within t h e creep and relaxation range; these a r e primary, secondary, l o c a l o r peak, and thermal.

The primary s t r e s s e s are d i r e c t

o r shear s t r e s s e s , developed by the imposed loading, which a r e necessary t o s a t i s f y only t h e simple laws of equilibrium of external and i n t e r n a l forces and moments.

When primary s t r e s s e s exceed the y i e l d strength of

t h e material, y i e l d i n g w i l l continue u n t i l t h e member breaks, unless ,

s t r a i n hardening or r e d i s t r i b u t i o n of s t r e s s e s l i m i t s t h e deformation. Secondary s t r e s s e s a r e d i r e c t or shear stresses developed by t h e cons t r a i n t of adjacent p a r t s or by s e l f - c o n s t r a i n t of the s t r u c t u r e .

Sec-

ondary s t r e s s e s d i f f e r from primary s t r e s s e s i n t h a t y i e l d i n g of t h e m a t e r i a l results i n r e l a x a t i o n of t h e s t r e s s e s .

Local or peak s t r e s s e s

a r e the highest s t r e s s e s i n t h e region being studied.

They do not cause

even n o t i c e a b l e minor d i s t o r t i o n s and a r e objectionable only as a poss i b l e source of f a t i g u e cracks.

Thermal s t r e s s e s a r e i n t e r n a l s t r e s s e s

produced by c o n s t r a i n t of thermal expansion.

T h e m 1 s t r e s s e s which i n -

volve no general d i s t o r t i o n were considered t o be l o c a l s t r e s s e s .

Thermal

s t r e s s e s which cause gross d i s t o r t i o n , such as those r e s u l t i n g from t h e temperature d i f f e r e n c e between s h e l l s a t a junction, were considered t o be secondary s t r e s s e s . I n t h e present examination, f o u r sources of s t r e s s e s were considered. Pressure d i f f e r e n c e s a c r o s s the shells w i l l produce membrane pressure

stresses.

These s t r e s s e s a r e primary membrane s t r e s s e s .

The pressure

d i f f e r e n c e s w i l l a l s o produce d i s c o n t i n u i t y s t r e s s e s , which a r e secondary bending s t r e s s e s .

Temperature g r a d i e n t s along t h e s h e l l s w i l l produce

s t r e s s e s which a r e due b o t h t o t h e temperature v a r i a t i o n s and t o t h e d i f ferential-expansion-induced d i s c o n t i n u i t i e s a t t h e s h e l l junctions. s t r e s s e s are secondary bending stresses.

These

Temperature g r a d i e n t s a c r o s s

the w a l l s of the s h e l l s will produce thermal s t r e s s e s which are assumed

t o be l o c a l stresses. The ASME Code i s g e n e r a l l y accepted as t h e b a s i s f o r evaluating p r i mary membrane stresses, and t h e allowable s t r e s s e s for INOR-8 a t t h e ope r a t i n g temperatures of t h e pumps were obtained from t h e c r i t e r i a s e t f o r t h i n t h e code, with one exception.

A reduction f a c t o r of two-thirds

w a s applied t o t h e stress t o produce a creep r a t e of 0.1% i n 10 000 hr i n order t o avoid p o s s i b l e problems a s s o c i a t e d with t h e e f f e c t of i r r a d i a t i o n on t h e creep rate.*

The maximum allowable s t r e s s a t 1300째F i s 2750

p s i , and t h e primary membrane s t r e s s e s were l i m i t e d t o t h i s value.

*Based on data from R . W . Swindeman, ORNL. 'v

The

primary s t r e s s e s were not considered f u r t h e r except from t h e standpoint of excessive deformations produced by primary p l u s secondary s t r e s s e s . I n order t o evaluate the e f f e c t s of secondary and l o c a l s t r e s s e s , r e p e t i t i v e loading and temperature cycles must be considered because f r a c t u r e s produced by t h e s e types of stress a r e u s u a l l y t h e r e s u l t of s t r a i n fatigue.

Data which give the c y c l e s - t o - f a i l u r e versus t h e t o t a l

or p l a s t i c s t r a i n range p e r cycle may be used f o r studying c y c l i c conditions.

The t o t a l s t r a i n range per cycle i s defined as t h e e l a s t i c p l u s

p l a s t i c s t r a i n range t o which t h e member i s subjected during each cycle. The p l a s t i c s t r a i n range p e r cycle i s t h e p l a s t i c component of the t o t a l

s t r a i n range per cycle.

The s t r a i n - c y c l i n g information may be compared

with t h e c a l c u l a t e d c y c l i c s t r a i n s i n the m e m b e r .

Since most formulas

express stress r a t h e r than s t r a i n as a function of loading o r tempera-

ture d i s t r i b u t i o n , assuming e l a s t i c behavior of t h e material, it i s convenient, as s t a t e d before, t o transform t h e t e s t data from t h e form of s t r a i n versus c y c l e s - t o - f a i l u r e t o t h e form of stress versus cycles-tof a i l u r e by multiplying t h e s t r a i n values by t h e e l a s t i c modulus of t h e material.

The r e s u l t i n g values have t h e dimensions of stress but, since

t h e t e s t s were made i n t h e p l a s t i c range, t h e y do not r e p r e s e n t a c t u a l stresses. When t h e a n a l y s i s of s t r e s s e s i n a member r e v e a l s a b i a x i a l or tri-

a x i a l s t r e s s condition, it i s necessary t o make some assumption regarding the f a i l u r e c r i t e r i o n t o be used.

I n t h e p l a s t i c range, where most of

t h e s i g n i f i c a n t secondary and l o c a l s t r e s s e s l i e , t h e r e i s no experimental

evidence t o i n d i c a t e which theory of f a i l u r e i s most accurate.

There-

f o r e , it has been recomended15 t h a t the m a x i m u m shear t h e o r y be used, since it i s a l i t t l e more conservative and results i n simpler mathematic a l expressions.

The following s t e p s used i n developing t h e procedure

were taken from r e f . 3:

1. Calculate t h e t h r e e p r i n c i p a l s t r e s s e s

(ul, u2, u3)

a t a given

point. 2.

Determine t h e m a x i m u m shear stress which i s t h e l a r g e s t of the

three quantities

Multiply t h e maximum shear s t r e s s by two t o give t h e "maximum

i n t e n s i t y of combined s t r e s s

Compare t h i s q u a n t i t y w i t h t h e E AE values obtained from uni-

a x i a l strain-cycling t e s t s . S t a t e d more simply, t h e procedure i s t o use t h e s t r e s s i n t e n s i t y representing t h e l a r g e s t a l g e b r a i c d i f f e r e n c e between any two of t h e t h r e e principal stresses. The procedure o u t l i n e d above f o r evaluating t h e e f f e c t s of c y c l i c loadings and c y c l i c thermal s t r a i n s w a s used t o examine t h e c y c l i c secondary and l o c a l s t r e s s e s which will be produced i n p o r t i o n s of t h e MSRE pumps. The procedure i s 5 s s e n t i a l l y t h a t s p e c i f i e d by t h e Navy Code; however, t h e Navy Code w a s developed p r i m a r i l y f o r a p p l i c a t i o n s i n which t h e maximum temperatures would be below those necessary f o r creep and r e l a x a t i o n of t h e material.

Thus,

s e v e r a l of the s t e p s o u t l i n e d i n t h e

N a v y Code were modified f o r t h e present evaluation.

The assumption w a s made t h a t t h e temperatures were s u f f i c i e n t l y high and t h a t t h e times a t t h e s e temperatures were s u f f i c i e n t l y long f o r comp l e t e stress r e l a x a t i o n t o occur.

Thus t h e s t r a i n s which t h e e l a s t i c a l l y

c a l c u l a t e d stresses represented were taken as e n t i r e l y p l a s t i c .

On t h i s

basis, s t r a i n cycling data i n t h e form of p l a s t i c r a t h e r than t o t a l s t r a i n

range p e r cycle versus c y c l e s - t o - f a i l u r e were used.

Figures D . l and D.2,

which give s t r a i n f a t i g u e data f o r INOR-8 a t 1200 and 1300째F, were obt a i n e d from a l i m i t e d number of s t r a i n - c y c l i n g t e s t s performed by t h e ORNL Metallurgy Division.

The dashed curves were obtained from t h e p l a s -

t i c s t r a i n range per cycle curves and represent a conservative estimate

UNCLASSIFIED ORNL-LR-DWG64508

IO0 5 2 I

i 10.' I

, " 2 L 10-' W 0

b $

lo-'

IO"

IO'

loz

103 2

104 2

105 2

lo6

N, CYCLES TO FAILURE

Fig. D.l.

S t r a i n Fatigue Curves for INOR-8 a t 1200'F.

UNCLASSIFIED ORNL-LR-DWG 6 4 5 0 9

to-' 2

Fig. D.2.

loo 2

to1 2

5 lo3 2 M, CYCLES TO FAILURE

IO' 2

lo4

105

106

S t r a i n Fatigue Curves for INOR-8 a t 1300째F.

* w

of t h e t o t a l s t r a i n range per cycle.

It w a s assumed t h a t t h e m a t e r i a l

e x h i b i t s p e r f e c t p l a s t i c i t y above the proportional l i m i t (no s t r a i n hardening), and t h e e l a s t i c s t r a i n a t t h e proportional l i m i t w a s added t o t h e p l a s t i c s t r a i n range a t each p o i n t ,

The dashed curves were used

t o obtain an estimate of t h e cycles-to-failure, t i o n o r strain-hardening occurs.

assuming that no relaxa-

S t r a i n hardening would displace t h e

dashed curves upward. Figures D . 3 and D.4,

which give t h e s t r e s s amplitude versus number

of cycles f o r INOR-8 a t 1200 and 1300째F w i t h complete relaxation, were derived from t h e s o l i d curves f o r Figs. D . l and D.2 by multiplying t h e p l a s t i c s t r a i n range by E t o obtain a pseudo s t r e s s range and then d i viding by 2 t o obtain 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 represent t h e r e s u l t s of this operation.

The s o l i d curves

represent t h e allowable values of a l t e r n a t i n g s t r e s s and were constructed by placing a f a c t o r of s a f e t y of a t l e a s t 10 on cycles and a f a c t o r of s a f e t y of a t l e a s t 1.5 based on s t r e s s .

The s a f e t y f a c t o r of 10 on cycles

i s based on u n c e r t a i n t i e s i n the calculations, s c a t t e r of test data, s i z e e f f e c t s , surface f i n i s h , atmosphere, e t c .

These reduction f a c t o r s a r e

l e s s conservative than those s p e c i f i e d by t h e Navy Code.

However, they

have been used i n high-temperature design for several years a t ORNL, and t h e current f e e l i n g of one of t h e o r i g i n a t o r s of t h e Navy Code i s that t h e reduction f a c t o r s s p e c i f i e d i n t h a t document a r e over-conservative and w i l l be reduced t o those used i n t h i s investigation.*

Figures D . 5

and D . 6 were obtained i n t h e manner a s F i g s , D . 3 and D . 4 but were based on t o t a l s t r a i n r a t h e r than p l a s t i c s t r a i n .

They represent allowable

values of a l t e r n a t i n g s t r e s s i f no r e l a x a t i o n occurs. The l i f e of a component undergoing c y c l i c s t r a i n depends on mean s t r a i n as w e l l as c y c l i c s t r a i n ; however, f o r most a p p l i c a t i o n s i n which t h e loading i s almost e n t i r e l y due t o thermal cycling and no severe strain-concentrations e x i s t , t h e e f f e c t of mean s t r a i n can be expected t o be secondary t o t h a t of c y c l i c s t r a i n .

For t h e s e applications, c y c l i c

l i f e can be determined d i r e c t l y from s t r a i n range computations.16

Corp.,

The

*Personal communications between B. F. Langer of Westinghouse E l e c t r i c B e t t i s Plant, and B. L. Greenstreet, O m .

UNCLASSIFIED

N, NUMBER OF CYCLES

S t r e s s Amplitude Versus Number of Cycles for INOR-8 a t Fig. D . 3 . 1200째F w i t h Complete S t r e s s Relaxation.

UNCLASSIFIED ORNL-LR-DWG 64511

RAIN CYCLING DATA)

N, NUMBER OF CYCLES

Fig. D.4. Stress Amplitude Versus Number of Cycles for INOR-8 a t 1300째F w i t h Complete Stress Relaxation.

UNCLASSIFIED ORNL-LR-DWG 64542

10'

lo2

to3

lo4

lo5

lo6

N , N U M B E R OF CYCLES

Stress Amplitude Versus Number of Cycles for INOR-8 at Fig. D . 5 . 1200째F with No Relaxation.

UNCLASSIFIED ORNL-LR-DWG 64513

Stress Amplitude Versus Number of Cycles f o r INOR-8 at Fig. D . 6 . 1300째F with No Relaxation.

. 64 e f f e c t of mean s t r a i n i s f u r t h e r reduced when g r o s s r e l a x a t i o n t a k e s place Thus f o r t h e MSRE

during each cycle, as i s expected i n t h e present case.

pump s t r e s s evaluation, the mean s t r a i n w a s assumed i n a l l cases t o be zero, and t h e e f f e c t of c y c l i c s t r e s s e s w a s determined d i r e c t l y from t h e p l o t s of t h e allowable a l t e r n a t i n g stress versus t h e number of cycles. Each of t h e components examined will be subjected t o s e v e r a l operat i n g conditions.

Since s t r a i n s will occur t h a t a r e beyond t h e e l a s t i c

l i m i t , t h e s t r u c t u r a l evaluation w a s based on a f i n i t e l i f e , and t h e

damaging e f f e c t of a l l s i g n i f i c a n t s t r a i n s w a s considered. Suppose, for example, t h a t the s t r e s s e s produced by n d i f f e r e n t ope r a t i n g conditions have been determined and t h a t it has been found t h a t t h e s e s t r e s s e s w i l l produce values of Salt

Sl, S2,

... Sn .

which can be designated as

It i s a l s o known t h a t S1 i s repeated p1 times during t h e

l i f e of t h e component, and S i s repeated p times, e t c . From Figs. D.3 2 2 N a r e t h e allowable c y c l e s f o r each and D.4 it i s found t h a t N 1' N2' n of t h e c a l c u l a t e d s t r e s s e s . The values pl/N1, pn/Nn are c a l l e d p2/N2,

...

cycle r a t i o s because they r e p r e s e n t t h e f r a c t i o n of t h e t o t a l l i f e which i s used a t each s t r e s s value.

A s a f i r s t approximation, an a p p l i c a t i o n

might be considered s a t i s f a c t o r y i f

i=n

i=1

-pi -< N Li

1.0

Fatigue t e s t s have shown, however, t h a t f a i l u r e can occur a t cumulative cycle r a t i o summations d i f f e r e n t from u n i t y .

If t h e lower s t r e s s values

are applied f i r s t and followed by t h e higher s t r e s s values, the cycle

r a t i o sumnation a t f a i l u r e can be "coaxed" as high as 5.

On t h e o t h e r

hand, i f the most damaging s t r e s s e s a r e a l l applied f i r s t , f a i l u r e can occur a t cycle r a t i o sumnations as low as 0.6, or even lower,

These a r e

extreme conditions and a r e based on low-temperature f a t i g u e data which may or may not be r e p r e s e n t a t i v e of behavior under s t r a i n cycling.

For

random combinations, c y c l e - r a t i o summations u s u a l l y average-close t o unity.

Therefore, 0.8 w a s used i n t h e present e v a l w t i o n as a conserva-

t i v e allowable l i m i t

It should be noted t h a t i n c o r r e c t l y applying any design c r i t e r i a , a point-by-point a n a l y s i s must be made.

That i s , t h e complete operating

h i s t o r y for each s i n g l e p o i n t must be examined.

Short c u t s may sometimes

be taken, but t h e y must n e c e s s a r i l y lead t o overly conservative r e s u l t s .

I n summary, t h e permissible cycles of each type were determined for t h e MSRE f u e l and coolant pumps by combining t h e secondary and l o c a l

s t r e s s e s a t each p o i n t .

P o i n t s were t h e n found which gave m a x i m u m values

f o r t h e "maximum i n t e n s i t y of combined s t r e s s . " divided by 2 t o o b t a i n the a l t e r n a t i n g stress.

These l a t t e r values were The allowable number of

cycles f o r each a l t e r n a t i n g stress were obtained from Figs. D.3 or D.4, assuming complete r e l a x a t i o n ,

The cycle r a t i o s were t h e n obtained t h a t

were based on t h e expected number of times each stress will be repeated, and various combinations of t h e cycle r a t i o s were summed at a p a r t i c u l a r p o i n t and compared with t h e 0.8 l i m i t .

To i n v e s t i g a t e t h e i n c r e a s e i n

l i f e i f no r e l a x a t i o n occurred, Figs. D . 5 and D.6 were used i n place of F i g s . D . 3 and D . 4 .

NOENCLATURE

Volute support c y l i n d e r mean r a d i u s

Exponential constant i n c y l i n d e r "B" temperature equation

5.' c2

I n t e g r a t i o n constants

I n t e g r a t i o n constants f o r c y l i n d e r "A" ( n = 1, 2, 3, 4 )

'nb

I n t e g r a t i o n constants f o r c y l i n d e r "B" ( n = 1, 4)

I n t e g r a t i o n constants for cone ( n = 1,

...,

D = ~ t ~ / [ 1 2( 1p2 ) I

..., 4 )

F l e x u r a l r i g i d i t y of c y l i n d e r

d = b/f3

Dimensionless temperature parameter

Modulus of e l a s t i c i t y

F1 = (b/9)4 + 4 F

= F ed Y 1

Fa' Fe hC

Geometric constants for r a d i a t i o n heat t r a n s f e r Forced convection heat t r a n s f e r c o e f f i c i e n t

hc e

E f f e c t i v e heat t r a n s f e r c o e f f i c i e n t of pump tank o u t e r surface

Heat t r a n s f e r c o e f f i c i e n t of p u p tank i n n e r surface

Auxiliary temperature f u n c t i o n s f o r cone 4) ( n = 1,

Thermal conductivity of INOR-8

A u x i l i a r y s t r e s s functions f o r conical s h e l l s 4) ( n = 1,

...,

Axial c y l i n d e r p o s i t i o n from cone-to-cylinder junction

Bending moment

Bending moment functions f o r c y l i n d e r ( n = 1,

..., 4 )

M yn

Bending moment f u n c t i o n s f o r meridional plane 4) of cone (n = 1,

Men

Bending moment f u n c t i o n s for c i r c u m f e r e n t i a l plane of cone ( n = 1, 4)

Membrane f o r c e

...,

Membrane f o r c e functions f o r c y l i n d e r ( n = 1,

..., 4 )

Membrane f o r c e functions f o r c i r c u m f e r e n t i a l plane of cone ( n = 1, 4)

...,

P n

Auxiliary s t r e s s f u n c t i o n s f o r c o n i c a l sh tlls 4) ( n = 1,

P r a n d t l number

Normal shear f o r c e

Qn 'nc

...,

Shear f o r c e f u n c t i o n s f o r c y l i n d e r ( n = 1

..., 4 )

Shear f o r c e f u n c t i o n s for cone ( n = 1,

..., 4 )

Heat t r a n s f e r r e d a c r o s s i n n e r pump tank surface

Heat t r a n s f e r r e d a c r o s s o u t e r pump tank surface

Heat input t o i n n e r pump tank surface by f i s s i o n product-gas beta r a d i a t i o n I n t e r n a l heat generation rate from gamma r a d i a tion

q3-4

Heat t r a n s f e r r e d from o u t e r pump tank surface t o cooling shroud

q3-5

Heat t r a n s f e r r e d from o u t e r pump tank surface t o cooling a i r

q4-5

Heat t r a n s f e r r e d from t h e cooling shroud t o the cooling a i r

Reynold s number

Tan

Constants i n c y l i n d e r "A" temperature equation ( n = 1, 4)

...,

Constants in cylinder "B" temperature equation 5) (n = 1,

...,

Tbn

Constants in cone temperature equation (n = 1,

..., 5 )

Wall thickness of cylinder

Wall thickness of cone

Thickness of cooling air gap

Displacement of cone perpendicular to surface

Meridional displacement of cone

' n c

Displacement functions for cone (n = 1,

g C

..., 4 )

Radial displacement

Displacement functions for cone (n = 1, Slope functions for cylinder (n = 1, Slope functions for cone (n = 1,

28c+c

Dimensionless coordinate of cone

Y = BL

Dimensionless coordinate of cylinder

Meridional position on cone from apex

Coefficient of thermal eqansion Characteristic length of cylinder

4aaTb5

Y ' 4

e *Z

+ 4 Temperature Local temperature

.,., 4 )

..., 4 )

Distance through pump tank wall

..., 4 )

One h a l f of cone v e r t e x angle

Poisson's r a t i o

Bending s t r e s s

Membrane stress

cr 8i'

P r i n c i p a l meridional s t r e s s e s i n s i d e and outside

P r i n c i p a l circumferential s t r e s s e s i n s i d e and out s i d e

Stefan-Boltzman constant Subscripts

Cylinder "A" ( i n t e r n a l volute support c y l i n d e r )

Cylinder "B" ( e x t e r n a l volute support cylinder )

Cone ( s u b s t i t u t e f o r pump tank s p h e r i c a l s h e l l i n thermal s t r e s s c a l c u l a t i o n s )

Meridional plane

Circumferential plane

ACKN0WL;EDGMEPIPIS

The author wishes t o acknowledge t h e work of J. M. Corm i n t h e preparation of Appendix D, "Procedure Used t o Evaluate t h e E f f e c t s of Cyclic S t r a i n s i n t h e M S R E Pumps."

The Oracle S t r e s s Analysis Program

used to determine stresses produced by pressure and a x i a l loads w a s prepared by M. E. Laverne.

The a s s i s t a n c e of F. J. W i t t i n regard t o

t h e thermal s t r e s s c a l c u l a t i o n s i s a l s o acknowledged.

Internal Distribution 1. G . 2. S. 3. M. 4. C . 5. E. 6. M. 7. E. 8. S. 9. C. 10. W. 11. C. 12. R. 13. S. 14. T. 15. J. 16. L. 17. J. 18. G . 19. J. 20. J. 21. D. 22. N. 23. J. 24. A.

25-39. C. 40. R.

41. B. 42. A. 43. R. 44.

45. P. 46. E. 47. E. 48. 49. 50. 51.

52. 53.

P. R. J. M. M. R.

M. Adamson E. Beall Bender E. B e t t i s S. B e t t i s Blander G. Bohlmann E. B o l t J. Borkowski F. Boudreau A. Brandon B. Briggs Cantor E. Cole A. Conlin T . Corbin M. Corm A. C r i s t y L. Crowley H. DeVan A. Douglas E. Dunwoody R. Engel P. Fraas H. Gabbard B. Gallaher L. Greenstreet G. Grindell H. Guymon H. Harley N. Haubenreich C. Hise E. Hoffman P. Holz J. Ked1 A. Lane E. LaVerne I. Lundin N. Lyon

54. H. G. MacPherson 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70.

71. 72. 73.

74. 75. 76.

77. 78. 79. 80. 81. 82. 83. 84. 85.

86. 87-88. 89-90. 91-93. 94-98. 99.

D. Manly B. McDonald K. McGlothlan C. M i l l e r C . Moyers E. Northup F. Parsly P. P a t r i a r c a H. R . Payne A. M. Perry R. C Robertson M. W . Rosenthal 11. W. Savage A. W. Savolainen R. Schneider D. Scott M. J. Skinner A. N. Smith P. G. Smith I. Spiewak B. Squires F. J. Stanek J. A. Swartout A. Taboada J. R . Tallackson D. B. Trauger W. C . Ulrich A. M. Weinberg J. H. Westsik F. J. W i t t L. V. Wilson H. C . Young Reactor Division Library Central Research Library Document Reference Section Laboratory Records Department Laboratory Records, ORNL-RC W. W. C. E. J. T. L.

External D i s t r i b u t i o n

100-101.

Reactor Division, AEC, OR0 102. Division of Research and Development, AEC, OR0 103. I?. P. Self, AEC, OR0 104. W. L. Smalley, AEC, OR0 105.

v '5

J. Wett, AEC, Washington

106-120. Division of Technical Information Extension