ORNL-CF-70-3-2.txt

 

™

| B

 

DATE:

SUBJECT:

TO:

FROM:

OAK RIDGE NATIONAL LABORATORY

OPERATED BY
UNION CARBIDE CORPORATION
NUCLEAR DIVISION

UNION
CARBIDE

POST OFFICE BOX X
OAK RIDGE, TENNESSEE 37830

March 2, 1970

Calculation of Stresses During a Thermal
Transient in a MSBR Outlet Nozzle

Distribution

J. L. Spoormaker*

ABSTRACT

Internal Use Only

 

 

ORNL
CENTRAL FILES NUMBER

70~3-2

 

COPY NO. 41

Information is given about the thermal stresses devel-

oped in the outlet nozzles of a reactor vessel for a 1000

Mw(e) Molten-Salt Breeder Reactor for several step changes in

the salt temperature. Calculation of the temperature distri-

butions, as well as of the stresses, was carried out by finite

element computer programs. Step temperature changes of 1300
to 1400°F, 1300 to 1600°F, 1300 to 1800°F, 1300 to 1200°F,
and 1300 to 1100°F were considered. For each step change the

number of cycles to fallure was estimated and an estimation

of whether or not gross cyclic yielding would occur was made.

 

*¥On assignment to ORNL from Delft Technological University,
The Netherlands, under a fellowship program sponsored by the

Dutch Government.

NOTICE This document contains information of a preliminary nature
and was prepared primarily for internal use at the Oak Ridge
National Laboratory. It is subject to revision or correction and
therefore does not represent a final report. The information is
only for official use and no release to the public shall be made
without the approval of the Legal and Information Control Depart-

ment of Union Carbide Corporation, Nuclear Division.

 

 
 

 

1.
2.

O 0 I O

INTRODUCTION

3

CONTENTS

LIST OF FIGURES
NOMENC LATURE

DESCRIPTION OF CONFIGURATION AND FINITE

ELEMENT IDEALIZATTION

2.1, Configuration .....ceeevevereneerecnecenescacocnans
2.2. Finite Flement MeSh .. ¢veeeeeecececsocecaocacsancs
TEMPERATURE DISTRIBUTION CAICULATIONS ¢vvevececccosceoocens

STRESS ANALYSTS

4.1,
4.2,

5.1.
5.2.
5.3.
5.4.
5.5.
5.6.

CONCLUSIONS

REFERENCES
ACKNOWLEDGEMENTS .

General Remarks

Evaluation of Stresses
RESULTS OF STRESS COMPUTATIONS ....
Steady-State Condition ...

Step Change 1300
Step Change 1300
Step Change 1300
Step Change 1300
Step Change 1300

— 1400°F
— 1600°F

@ @ 0 0 0 0 0 ¢ 0 & 0 0 0 0 0 0 &6 0 0 0 0 0 9
e 0 @ 0 0 0 0 0 ¢ 0 06 0 0 0 0 0 O ¢ 0 ¢ 0 0 ¢
OOOOOOOOOOOOOOOOOOOOOOO
000000000000000000000000
000000000000000000000000
000000000000000000000000
OOOOOOOOOOOOOOOOOOOOOOOO
........................
OOOOOOOOOOOOOOOOOOOOOOOO
o . o 06 6 06 ¢ o 0 o o . e . .
o0 [ 2 ® o e o e o o

11

12
12
12
13
14
14
14
17
17
17
18
18
19
20
20
21

22
23

 
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

O ¢ I O bt A W N

-
O

'_.l
'_.l

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22 .

23.

24

LIST OF FIGURES

MSBR Reactor Vessel Flow Schematic.
MSBR Reactor Vessel Simplified Outlet Configuration.
MSBR Reactor Vessel Simplified Outlet Nozzle Detail.
Plot of the Outline of the Configuration.

Subplot of the
Subplot of the
Subplot of the
Subplot of the
Design Fatigue

Various Criteria for the

for INOR-8.

Temperature
Condition.

Temperature
Condition.

Temperature
Condition.

Temperature
Condition.

Temperature
Condition.

Temperature
Condition.

Distribution

Distribution

Distribution

Distribution

Distribution

Distribution

Element Idealization
Element Idealization
Element Idealization

Element Idealization

(Pipe Region).
(Intersection Region).
(Nozzle Wall Region).
(Flat Plate).
Strength, Sa’ for Ni-Mo—Cr Alloy.

Determination of the Design Stresses

Across Section A-A in the Steady-State

Across Section

Across Section

Across Section

Across Section

Across Section

Stress Distribution Across Section A-A

Condition.

Stress Distribution Across Section B-B

Condition.

Stress Distribution Across Section C=C

Condition.

Stress Distribution Across Section D-D

Condition.

Stress Distribution Across Section E-E

Condition.

B-B in the Steady-State

C-C in the Steady-State

D-D in the Steady=State

E-E in the Steady-State

F-F in the Steady-State

in

in

in

in

in

the Steady-State

the Steady-State

the Steady-State

the Steady-State

the Steady-State

Temperature Distribution Across Section A-A After the Step
Change 1300 — 1400°F.

Temperature Distribution Across Section B-B After the Step
Change 1300 — 1400°F.

Temperature Distribution Across §ection C-C After the Step
Change 1300 — 1400°F.

 
Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

25.

26.

27 .

28.

29.

30.

31.

32.

33.

34,

35.

36.

37.

38.

39.

40.

41,

42.

43,

4ts

45,

Temperature Distribution Across Section D-D After the
Change 1300 — 1400°F.

Temperature Distribution Across Section E-E After the

Change

Stress
1300 —

Stress
1300 -

Stress
1300 —

Stress
1300 —

Stress

Temperature
Change 1300

Temperature
Change 1300

Temperature
Change 1300

Temperature
Change 1300

Temperature
Change 1300

Stress Distribution Across Section
1300 — 1600°

1300 — 1400°F

Distribution Across
1400°F.

Distribution Across
1400°F.

Distribution Across Section C-C After the Step
1400°

Distribution Across Section D-D After the Step
1400°F.

Distribution Across
1300 — 1400°

F.

F.

Distribution Across
- 1600 oFc

Distribution Across
— 1600°F.

Distribution Across
— 1600°F.

Distribution Across
— 1600°F,

Distribution Across
- 1600 °F| o

F.

Section A-A After the Step

Section B-B After the Step

section E-E After the Step

Section A-A After the

Section B-B After the
section C-C After the
Section D-D After the
section E-E After the

A-A After the Step

Stress Distribution Across Section B-B After the Step
1300 — 1600°F.

Stress Distribution Across

1300 — 1600°F.

otress Distribution Across

1300 — 1600°F.

Stress Distribution Across
1300 — 1600°

Temperature
Change 1300

Temperature
Change 1300

Temperature
Change 1300

Temperature
Change 1300

F.

Distribution Across
— 1800°F.

Distribution Across
— 1800°F.

Distribution Across
— 1800°F.

Distribution Across
— 1800°F.

Section

Section

C-C After the Step

Section D-D After the Step

E-E After the Step

Section A-A After the

Section B-B After the

ocection C-C After the

oection D-D After the

Step

Step

Change

Change

Change

Change

Change

Step

Step

Step

Step

Step

Change

Change

Change

Change

Change

Step

Step

Step

Step
s

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

46,

47,

48,

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

6l.

62.

63.

64 .

65.

66.

Temperature Distribution Across Section E-E After the

Change 1300

Stress Distribution Across

— 1800°F.

1300 — 1800°F.

Stress Distribution Across

1300 — 1800°F.

Stress Distribution Across
1300 — 1800°F.

Stress Distribution Across

1300 — 1800°F.

Stress Distribution Across
1300 — 1800°

Temperature
Change 1300

Temperature
Change 1300

Temperature
Change 1300

Temperature
Change 1300

Temperature
Change 1300

Stress Distribution Across
1300 — 1200°

Stress Distribution Across

F.

Distribution Across
— 1200°F.

Distribution Across
— 1200°F.

Distribution Across
— 1200°F.

Distribution Across
— 1200°F,

Distribution Across
— 1200°F.

F.

1300 — 1200°F.

Stress Distribution Across
1300 — 1200°

Stress Distribution Across
1300 — 1200°

F.

F.

Section

Section

Section

Section

Section

Section A-A After the

Section A-A After the

Section B-B After the

A-A After

B-B After

C-C After

D-D After

E-E After

Section B-B After the

Section C-C After the

Section D-D After the

Stress Distribution Across Section E-E After the

1300 — 1200°

Temperature
Change 1300

Temperature
Change 1300

Temperature
Change 1300

Temperature
Change 1300

Temperature
Change 1300

F.

Distribution Across Section

— 1100°F.

DiStribution Across Section

— 1100°F.

Distribution Across Section

— 1100°F.

Distribution Across Section

— 1100°F.

Distribution Across Section

— 1100°F.

A-A After

B-B After

C-C After

D-D After

E-E After

otep

Step

Section C-C After the Step
Section D-D After the Step

Section E-E After the Step

the

the

the

the

the

otep

Step

Step

otep

Step

the

the

the

the

the

Step

Change

Change

Change

Change

Change

otep

Step

Step

Step

Step

Change

Change

Change

Change

Change

Step

Step

Step

Step

Step

 
Fig.

Fig.

Fig.

Fig.

Fig.

67 .

68.

69.

70.

71.

Stress Distribution
1300 — 1100°F.

Across

Section

Stress Distribution Across Section

1300 — 1100°F.

Stress Distribution
1300 — 1100°F.

Stress Distribution
1300 - 1100°F.

Stress Distribution
1300 — 1100°F.

Across

Across

Across

Section

Section

Section

A-A After the Step Change
B-B After the Step Change
C-C After the Step Change
D-D After the Step Change

E-E After the Step Change
0 T ™ =
Q

alt

ES @ chn

N ch HQ <

Q Q Q
ks
N

min

Q

max

Q

NOMENCLATURE

Modulus of elasticity

Biot's number

Allowable elastically calculated stress amplitude
Amplitude of stress fluctuation
Uniaxial yield strength
Coefficient of thermal expansion
Temperature

Temperature difference

Poisson's ratio

Radial stress

Circumferential stress

Axial stress

Shear stress

Minimum stress in meridional plane
Maximum stress in meridional plane

Surface stress
11

1. INTRODUCTION

In a MSBR of 1000 Mw(e) the salt enters at a temperature of 1050°F
and will rise about 250°F as it passes the core. Under normal conditions
it is assumed that the salt temperature in and around the outlet nozzle
will be at 1300°F.

There are, however, circumstances in which the salt from the core
changes rapidly in temperature. Shortly after such a change, high tem-
perature gradients, and hence high thermal stresses, will occur near the
inner surface of the outlet nozzle and the connected pipe. Because the
heat dissipates through the structure, discontinuity stresses are ailso
produced at the intersection of the pipe and the nozzle since the nozzle
is relatively thick in comparison with the pipe.

Information about the structural damage produced by rapid changes in
salt temperature is needed for the design of a MSBR. Consequently, the
thermal stresses were computed after five different step changes in salt

temperature. The step changes were:

Downward Upward
1300 — 1200°F 1300 — 1400°F
1300 — 1100°F 1300 — 1600°F

1300 — 1800°F

It was assumed that these transients would not last longer than 10
seconds, since measures could be taken in that amount of time to bring
the salt temperature back to normal. The time at which the highest sur-
face and discontinuity stresses would occur was determined by a number
of stress computations at different time points for the step change
1300 — 1600°F. From the results of these computations at 1, 3, 5, 7, and
9 seconds, it was learned that the highest surface stresses in the pipe
occur at about 1 second, and in the nozzle wall they occur at about 9
seconds. The highest discontinuity stresses occur at about 9 seconds.
Since the temperature distributions were similar for all step changes,
and since the differences between the stresses produced at 1 and 3 seconds
and at 7 and 9 seconds were not large, computations were carried out only

at 1 and 9 seconds for the remaining step changes.

 
12

With the results obtained from the stress computations, estimates
were made of the number of cycles to failure for each condition. A
judgement was also made regarding the likelihood of gross cyclic yielding

at the intersection between the pipe and the nozzle.

2. DESCRIPTION OF CONFIGURATION AND
FINITE ELEMENT IDEALIZATION

2.1. Configuration

 

The outlet nozzles are attached to a cylindrical vessel about 22 ft
in diameter. The diameter of the outlet nozzles at the connection is
23 in. (Fig. 1). Most of the salt flows directly from the inlet through
the core to the outlet nozzles, but some salt from the inlet‘flows through
the gap between the cylindrical wall and the reflector (see Fig. 2).

oince the highest stresses expected are due to thermal loading, the
nozzles were considered to be attached to a flat plate rather than to a
cylindrical shell. With this simplification it was possible to consider
an axisymmetric problem for the thermal loading. Since the vessel
diameter to nozzle diameter ratio is about 12:1, the results were ex-
pected to be reasonably accurate.

The configuration, as shown in Fig. 3, was extended as far as possible
in order to approximate the real situation. The flat plate was taken suf-
ficlently large for the degree of restraint against thermal expansion to
closely approximate that of the cylindrical wall. The criterion for the
length of the connected pipevwas that the discontinuity stresses should

be damped out to 10% at the end of the pipe.

2.2. Finite Element Mesh

The configuration shown in Fig. 3 was divided into a number of tri-
angular ring elements. A fine mesh was taken in regions where high
sStresses were expected. Although for the calculation of the temperature
distribution the mesh in some regions was finer than necessary, the same

mesh was used as for the stress analysis.

Plots and subplots of the mesh are given in Figs. 4 through 8.
\»

13

3. TEMPERATURE DISTRIBUTION CALCULATIONS

The determination of the temperature distribution was carried out by

a finite element computer program.l

The program calculates the tempera-
ture of the nodal points situated at the vertices of the elements into
which the body has been divided. The temperature of the centroid of an
element is obtained by taking the average of the temperatures of the nodal
points. The difference of the centroid temperature and a reference tem-
perature 1s multiplied by the coefficient of thermal expansion, and the
resulting numbers are the input data for the SAFE-PCRS stress analysis
program. %’ 3 |

The following simplifications were made for these calculations:

1. The problem is axisymmetric.

2. Under normal conditions, the salt temperature is at 1300°F.

3. The temperature of the salt in the gap between the wall and the
reflector does not change.

4. Except along boundaries where the configuration is in contact
with the salt, 1t was assumed to be insulated.

5. The material properties are temperature independent.

- The material properties used are:

Conductivity coefficient: 12.7 Btu/hr-ft-F

Heat capacity: 75.8 Btu-ft3-F
The film coefficients are:

In the nozzle: 1600 Btu/hr-ft2-F

In the gap: 150 Btu/hr-ftz-F

The heat source strengths due to gamma radiation are:

Perpendicular to nozzle wall: 27.4 exp (—0.818x) Btu/hr-in.°>
Perpendicular to vessel wall: 30.2 exp (—0.818x) Btu/hr-in.3 ,

where x 1s the distance, in inches, from the wall. Although the intensity
of the gamma radiation changes during a transient, this effect was not
taken into account, since the time considered was relatively short.

The steady-state temperature distribution was first calculated be-

cause it was not uniform due to the internal heat generation.

 
14

4. STRESS ANALYSIS

4.1. General Remarks

The stress computations were carried out by a stress analysis finite
element computer program which determines the elastic stresses in an axi-
symmetric body. Where the value of the "stress'" exceeds the yield strength,
the results from these computations must be interpreted as strain times
Young's modulus. Further discussion will be in terms of stress, since
the fatigue curves and Section III of the ASME Boiler and Pressure Vessel
Code are based on these elastically calculated stresses.

As already mentioned, in the first 10 seconds after the step change
in the salt temperature, high local surface stresses and high bending
stresses will occur. The surface stresses are high in the pipe and the
nozzle wall, while the bending stresses are dominant in the intersection
between the pipe and the nozzle. The stresses in these regions develop
as follows:

l. The Pipe. This rather thin and flexible part of the structure

 

changes rapidly in temperature. The highest surface stresses occur here
in the first seconds after the step change. These stresses quickly de-
crease because of the dissipation of heat.

2. The Nozzle Wall. This is a relatively thick and stiff part of

 

the structure and thus does not change as rapidly in temperature as does
the pipe. At 9 seconds after the step change, a region only 0.5 in. deep
is at a significantly different temperature from that in the steady-state
condition. The highest surface stresses occur at this time.

3. The Intersection. Due to the difference in thermal expansion be-

 

tween the pipe and the nozzle wall, high bending stresses occur here.
These stresses are classified as discontinuity stresses and can cause
cyclic yielding. The stresses produced by the pressure loading are also

of interest here.

4.2. Evaluation of Stresses

 

The stresses obtained by the finite element calculations were ..

o o o o . and o in each element. T
7> %9 9%y Opin? max hese stresses are assumed

o
15

to be constant within each element. Especially where steep thermal
gradients occur, the actual stresses vary significantly across an element
and the type of element (constant stress) which was used will not give
very accurate results unless a very fine mesh is employed. Higher order
elements or a finer mesh near the inside surface of the nozzle would im-
prove the results. For practical reasons these solutions were not applied.
According to Zienkiewicz (page 35, Ref. 4) the calculated stresses should
be assigned to the centroids of the elements.

For a section consisting of a row of elements, it is then possible to
plot the stress components at the centroids against the radius of these
centroids. The curve through these plotted points then gives a reasonable
approximation of the stress distribution through the wall in that section.

An approximation expression given by Manson’ enables us to check the
highest surface stress in the pipe and the nozzle wall. This expression,

which takes the Biot number into account, has the form

G:me{ 1
s 1-=v 1.35 4+ 3fi25'—

 

3
0.5 e'lé/B]

and gives the maximum surface stress due to a step change in fluid tem-
perature on one side of a thin restrained flat plate. This case is essen-
tially the same as a thin, infinitely long, cylindrical shell. Generally,
there was good agreement when the stresses in the steady-state condition
at the surface were taken into account.

For the evaluation of the stresses it was necessary to use a strength
theory since a triaxial stress condition existed. Because of its accepted
use in Section IIT of the ASME Code, the maximum shear theory was used.
The stress intensity was thus determined by taking the largest algebraic
difference between any of the two principal stresses at a point. ©Since
the thickness of the pipe and the nozzle wall was small in comparison
with the diameter of the nozzle, G, was expected to beASmall. From the
results of the stress computations it was found that C, was small through-
out the wall. Since o, is equal to zero at the surface, it was set equal
to zero everywhere. With this simplification the stress intensity was

just the highest stress component in absolute value.

 
16

The high local surface stresses were considered to be peak stresses
which could damage the surface by fatigue cracking. For the evaluation
of these stresses the amplitude of the stress fluctuation must be deter-
mined. This amplitude was found by taking the algebraic difference be-
tween the highest occurring surface stress in the structure and the sur-
face stress in the steady-state condition for the same spot. The amplitude
of the stress fluctuation was then half the difference of the stresses.
The mean stress and hold-time effects were not taken into account because
they were of no significance for the cases considered. The number of
cycles to failure for each step change was determined from the fatigue
curves in Fig. 9.

The evaluation of the bending stresses in the intersection between
the pipe and the nozzle was more complicated. In addition to the thermal
loading, the pressure loading should be taken into account. The internal
pressure in the nozzle was, however, low (14 psig), and hence the effect
of this loading was not expected to be significant. In order to deter-
mine the order of magnitude of the stresses produced by the pressure load-
ing, a simplified calculation was carried out. For this calculation it
was assumed that the pressure in the pipe was 30 psig and that the radial
stress at the edge of the plate was equal to the circumferential stress
in the vessel wall for the same internal pressure. A higher pressure
than 14 psig was taken since no end plate (causing an axial membrane
stress in the nozzle) was added to the configuration. The end plate was
neglected since the relatively thin flat plate behaves differently from
a cylindrical shell. It was found, from this calculation, that the stress
intensity in nearly the entire intersection was lower than 1 ksi. The
error in the determination of the thermal stresses was several times larger
than this, and hence the stresses produced by the pressure loading were
neglected.

In order to estimate whether or not serious cyclic yielding would
occur in the intersection, it was determined over what percentage of the
section a higher stress intensity than ZSy occurs, where Sy is the yleld

strength and is given in Fig. 10 as a function of temperature.

4
17
5. RESULTS OF STRESS COMPUTATIONS

In this chapter the results of the stress computations for different
conditions are presented. From these results estimates of the number of
cycles to failure have been made, and also it has been determined, for
each condition, whether or not gross cyclic yielding might occur.

The temperature distributions presented have been obtained by plotting
the nodal point values against the distance from the centerline. The
procedure by which the stress distributions were obtained was described
in Chapter 4. The stress component presented for each section is the
highest component occurring there, and since C. has been set equal to

zero this stress component is also the stress intensity.

5.1. Steady-State Condition

 

The temperature distributions through the wall at sections A-A, B-B,
C-C, D-D, E-E, and F-TF are presented in Figs. 11 through 16, respectively.
The stress distributions through the wall in the first five sectlons are
shown in Figs. 17 through Z21.

These stress distributions are necessary to determine the amplitude

of the stress fluctuation for the other conditions.

5.2. Step Change 1300 — 1400°F

 

The temperature distributions through the wall at sections A-A, B-B,
C-C, D-D, and E-E are presented in Figs. 22 through 26, respectively.
The stress distributions in the same sections are shown in Figs. 27
through 31.

The surface stress that gives the highest amplitude of stress fluctu-

ation occurs in section D-D, and at this spot we have:

The circumferential stress: 21 ksi
The surface temperature: 1380°F
The circumferential stress in the 7 ksi

steady-state condition:
The amplitude of the stress fluctuation: 14 ksi

From the fatigue curves in Fig. 9 we find that fatigue cracking is unlikely

for this condition.

 
18

For section B-B, where the highest discontinuity stresses occur, we
have at 9 seconds after the step change:

The average temperature: 1350°F
The yield strength at 1350°F: 20 ksi

From the stress distribution in Fig. 28 we find that no yielding will

occur.

5.3. Step Change 1300 — 1600°F

 

The temperature distributions throfigh the wall in sections A-A, B-B,
C-C, D-D, and E-E are presented in Figs. 32 through 36, respectively.
The stress distributions in the same sections are shown in Figs. 37 through
41. |

The surface stress that gives the highest amplitude of the stress

fluctuation occurs in section D-D, and at this spot we have:

The circumferential stress: 70 ksi
The surface temperature: 1540°F
The circumferential stress in the 7 ksi

steady-state condition: :
The amplitude of the stress fluctuation: 38.5 ksi

From the fatigue curves in Fig. 9 we find that the number of cycles to
failure might be as low as 90.

For section B-B, where the highest discontinuity stresses occur, we
have, at 9 seconds after the step change:

The average temperature: 1450 °F
The yield strength at 1450°F: 20 ksi

From the stress distribution in Fig. 38 we find that the stress intensity
is higher than ZSy in about 30% of this section. It can thus be suspected

that gross cyclic yielding might occur in this section.

5.4. Step Change 1300 — 1800°F

 

The temperature distributiens through the wall in sections A-A, B-B,
C-C, D-D, and E-E are presented in Figs. 42 through 46, reSpectively.
The stress distributions in the same sections are shown in Figs. 47 through
51.

The surface stress that gives the highest amplitude of the stress

fluctuation occurs in section D-D, and at this spot we have:
19

The circumferential stress: —-118 ksi
The surface temperature. 1700°F
The circumferential stress in the "7 ksi

- steady-state condition: | |
The amplitude of the stress fluctuation: 62.5 ksi

There are presently no fatigue data available for 1700°F, but since
Saltis very high it is estimated that cracking might occur after only one
or two cycles.

For section B-B, where the highest discontinuity stresses occur, we
have, at 9 seconds after the step change:

The average temperature: | 1550°F
The yield strength at 1550°F: 20 ksi

From the stress distribution in Fig. 48 we find that the stress intensity
is higher than 2Sy in about 55% of this section. It can be concluded that

gross cyclic yielding will occur for this condition.

5.5. Step Change 1300 — 1200°F

 

The temperature distributions through the Wall:in sections A-A, B-B,
C-C, D-D, and E-E are presented in Figs. 52 through 56, respectively. |
The stress distributions in the same sections are shown in Figs. 57 through
6l.

The surface stress that gives the highest amplitude of the stress

fluctuation occurs in section D-D, and at this spot we have:

The circumferential stress: 34 ksi
The surface temperature: 1225°F
The circumferential stress in the 7 ksi

steady-state condition:
The amplitude of the stress fluctuation: 13.5 ksi

From the fatigue curves in Fig. 9 we find that fatigue cracking is unlikely
for this condition.

For section B-B, where the highest discontinuity stresses occur, we
have, at 9 seconds after the step changei

The average temperature: 1250°F
The yield strength at 1250°F: 20 ksi

From the stress distribution in Fig. 58 we find that no yielding will occur

at the intersection.

 
20

5.6. Step Change 1300 — 1100°F

The temperature distribution through the wall in sections A-A, B-B,
C-C, D-D, and E-E are presented in Figs. 62 through 66, respectively.
The stress distributions in the same sections are shown in Figs. 67 through
71.

The surface stress that gives the highest amplitude of the stress

fluctuation occurs in section D-D, and at this spot we have:

The circumferential stress: | 58 ksi
The surface temperature: 1145°F
The circumferential stress in the 7 ksi

steady-state condition:
The amplitude of the stress fluctuation: 25.5 ksi

From the fatigue curves in Fig. 9 we find that the number of cycles to
failure might be as low as 2 X 10°.

For section B-B, where the highest discontinuity stresses occur, we
have, at 9 seconds after the step change:

The average temperature: 1220°F
The yield strength at 1220°F: 20 ksi

From the stress distribution in Fig. 68 we find that the stress intensity
is higher than ZSy in about 10% of this section. It can be concluded that

no gross cyclic yilelding will occur for this condition.

6. CONCLUSIONS

From the results of the stress calculations it was found that:

1. A step change of 100°F in the salt temperature upward or downward
will not cause any damage to the configuration.

2. The step change 1300 — 1100°F might possibly cause fatigue crack-
ing after a large number of cycles, but no gross cyclic yielding would
occur.

3. A step change from 1300 — 1600°F would cause fatigue cracking
after about 90 cycles and gross cyclic yielding might occur in the inter-
section between the pipe and the nozzle.

4. The step change 1300 — 1800°F is likely to cause cracks after
a very few cycles and gross cyclic yielding will occur in the intersection

between the nozzle and the pipe.

"
21

7. REFERENCES

J. L. Spoormaker, "Application of the Finite Element Method to the
Computation of Temperature Distributions in Axisymmetric Bodies,"
USAEC Report ORNL-TM-2894, Oak Ridge National Laboratory (to be
published).

Y. R. Rashid, "Finite Element Analysis of Axisymmetric Composite
Structures," USAEC Report GA-6303, General Atomic, June 4, 1965.

D. C. Cornell, "SAFE-PCRS — A Computer Program for the Stress Analysis
of Composite Bodies of Revolution, Input Instructions,' USAEC Report
GA-6588, General Atomic, August 1, 1965.

0. C. Zienkiewicz, The Finite Element Method in Structural and Con-

 

tinuum Mechanics, McGraw-Hill, 1967.

 

D. J. Lewis, E. J. Chubb, and H. A. Money, "Factors Affecting Thermal
Stress in a Power Plant," International Conference on Thermal Stresses
and Thermal Fatigue, Berkeley Nuclear Laboratories, September 23-26,
1969.

 
22
8. ACKNOWLEDGEMENTS

The author wishes to express his appreciation to R. B. Briggs of
the Director's Division for his overall direction and guidance. Members
of the Reactor Division Design Department, including J. R. McWherter,

C. W. Collins, W. K. Furlong, and H. A. McLain, supplied the necessary
MSBR information and made helpful suggestions. Finally, the author
acknowledges the help of J. M. Corum of the Reactor Division Applied
Mechanics Section in performing the stress analyses and evaluating the
results, and of W. G. Dodge of the Applied Mechanics Section in writing

the heat conduction computer programn.
 

23

9. FIGURES

 
25

ORNL-DWG 70-2354

+— w22 FT DIA. —»

 

 

*

 

Fig.

 

 

INLET
1050° F.

1.

OUTLET (4)
0 1300° F

MSBR Reactor Vessel Flow Schematic.
26

ORNL-DWG 70-2355

 

  

20 IN. DIA.

~—

 

 

 

  

 
 

“

 

19 IN. DIA.

  

 

1
_JL_ /4 IN. CLEARANCE

MSBR Reactor Vessel Simplified Outlet Configuration.

Fig. 2.
 

27

ORNL-DWG 70-2356

2 IN.-=| |=5 IN*

 

 

 

 

 

 

 

 

Yo S
/5 R
19 IN. 1. D.
20 IN. O. D.
! J ~

Fig.

 

 

 

30° _ ’

3. MSBR Reactor Vessel Simplified Outlet Nozzle Detail.
28

ORNL-DWG. 70-2357

MSBR OUTLET NOZZLE (SIMPLIFIED VEWSION
1

 

 

 

 

 

 

 

 

 

 

 

 

 

30.
25 F
s
£ E
—
= 20. b b
&
5
&
5* = c
2 15. B B
&
8
4 10,
A 4+ A
S.
0. - _
10. 1S. 20.

Radius (inches)

Fig. 4. Plot of the Outline of the Configuration.

 
29

ORVL-DWG 70-2358

MSBR OUTLET NOZZLE (SIMPLIFIED VEWSIOM
1)

 

 

 

 

 

 

. |
13.

w12,

<

&

B

S

e llo

&

5

&

3

T
9.
8.

1 G

7.

 

 

Radius (inches)

Fig. 5. Subplot of the Element Idealization (Pipe Region).

 
30

ORNL-DWG 70-2359

MSBR OUTLET NOZZLE (SIMPLIFIED VEWSIOW
1 |

 

 

 

 

 

 

 

 

 

 

 

 

 

1S.8 |
15.6
{
15.4
~ 15.2
2
E
4 15.0
=
: ]
£ 14.8
3
14.6
4.4 ‘
14.2
14.0 -

9.6 9.8 10.0 10.2 10.4 10.6

Radius (inches)

Fig. 6. Subplot of the Element Idealization (Intersection Region).

 

 
31

ORNL-DWG 70-2360

MSOR MTLFT NOZZLE (SIMPLIFIED VERSIOW

 

 

 

 

 

23.[
22.
2l.
£ 0. '
& <
qg* 4
7 19. fi
g fi
& (
§ (
5 18, «
A {
17. {
J
q
Y T -
16.
1S. -
10. 1. 12.

Radius (inches)

Fig. 7. Subplot of the Element Idealization (Nozzle Wall Region).

 
Distance from end of pipe (inches)

X

;g

.
»

22.

10.

 

Fig. 8.

ORNL-DWG 70-2361

MSBR OUTLET NOZZLE (SIMPLIFIED VERSION)

 

 

12. 13. . 18. 19.

Radius (inches)

Subplot of the Element Idealization (Flat Plate).

43
 

1/2€ (E)

Values of S;, psi (Sa

108

108

104

10

W 5 U ONDO-

ORNL-DWG 70-3301

1 2 3 4 567891 2 3 4 567891 2 3 4 567891 3 4 567891 2 3 4 567891

W P U OO NNOOO L\ W S U ONOD-

n

N

 

10 102 10° 104 10° 108
Number of Cycles

Fig. 9. Design Fatigue Strength, Sa, for Ni-Mo—Cr Alloy.

€€
3k

ORNL-LR-DWG 46316

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

30,000 | | ’ ‘ ‘
tx ULTIMATE TENSILE STRENGTH
25,000 ———— | -
T
~ 2 xYIEm
‘QLSTRENGTH |
20,000 . T(0\2% OFFSET) <
.U—, §\§\\§§~
B DESIGN STRESS— "Q"\\ \
0 15,000 FOR 316 STAINLESS 2 ~
L) STEEL \fli‘\" {5
& | {\\» STRESS FOR
10,000 | . RUPTURE IN —
STRESS FOR 1% CREEP IN—— =X\ 4 100,000hr
100,000hr \
| | %
2000 STRESS FOR 10° % /hr M.C. R————/ N
.
L]
0 400 800 1200 1600

TEMPERATURE (°F)

Various Criteria for the Determination of the
Design Stresses for INOR-8.

Fig. 10. Various Criteria for the Determination of the Design
Stresses for INOR-8.

v
35

ORNL-DWG 70-2363

 

 

 

 

 

 

 

 

 

 

 

TEMPERATURE 0O0I1STRiIBDVTIOM
L THRoOVOGHN THE WALL I M |
:' Sgcriony A -AR :" .
Fig. 11. Temperature Distribution
« A3 . Across Section A-A in the Steady-State
- 3 Condition.
N
< <
% N
by Y
s Q
T &
w W
" 4300 ~
q.5 10

DISTANCE FROWNM
CENTERLINE, INCHES

Fig. 12.

Condition.

ORNL-DWG  70-2364

 

TEMPERATVUVRE DISTRIBUT joN
THROVGH THE WwWALL I NV

 

 

 

 

 

 

 

 

 

 

 

Secrio¥vN B-B8B
1350
Temperature Distribution
Across Section B-B in the Steady-State
1300
95 §0.

*r

TEMPERATVRE

DISTANCE FROM
CENTERL |NE, |NCHES

ORNL-DWG. 70-2365

 

TEMPERATYRE D I1STRIBUTION

1350 p— THROVGHN THE wWALL N sSEcTiow C-C

 

fih

 

"

 

 

 

 

 

 

1300 ——
4.5 10

 

 

 

 

DISTANCE FROM CENTERLINE

Fig. 13. Temperature Distribution Across
Section C-C in the Steady-State Condition.

 
°c

TEMPERAT VR E

36

ORNL-DWG 70-2366

 

 

 

 

 

.l TEMPEBERATURE ODISTR IBVTION
. THROIVON THE WALL I~V SECTioN D-D
§q35 :
513 0
~
<
«
U
a /"——_——7
w
-
1300

 

 

 

 

 

 

 

 

 

 

a5
DISTANCE FRON ceEwvTERLINE

Fig. 1l4. Temperature Distribution Across Section D-D in the Steady-
State Condition.

ORNL-DWG. 70-2367

e

v

 

 

T TEMPERATURE DISTRIBUT/o N
THROVGH THNE WALL IN SECTION E -E
1350

 

 

 

/

 

 

 

 

 

 

 

 

 

 

 

 

 

_—
ff’ffd
1300

 

 

9.5 10 n
DISTANCE FROM CENTERLINE, /incHES

Fig. 15. Temperature Distribution Across Section E-E in the Steady-
State Condition.

ORNL-DWG 70-2368

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

@ TEMPERATVRE DISTR | BVT I8N THROUOG N
° TNE WALL |~ SEcTrionv F - F
w
X |
D 4350 4+
~ . i
( x—r
« // { r
: — |
t
W
= ‘ i | ; o
4300 : + -
0

DISTANCE FROnNM FRomMm S VRF ALE IN CO NTACT
WITH SALT INCHES

Fig. 16. Temperature Distribution Across Section F-F in the Steady-
State Condition.
37

ORNL-DWG 70-2369

 

 

_ CIRCUOMFERENT/IAL

STRESS OLISTR I8 vTrow
TwROyCw THE wALL /N

 

 

 

YT secriom A-A
N
“ \
*.
.
@ of——N
Q s
=
v \

 

 

 

| DISTANCE FRroNMm

 

CEVNTEORLINVE, I WCNES

-1 l | L

 

 

 

 

 

 

 

Fig. 17. Stress Distribution Across Section A-A in the Steady-State
Condition.

ORNL-DWG 70-2370

 

 

AXIAL STRESS DISTRIBUVUTION THRODUGH
THE WALL 1 S6criow B-RB

 

 

10

 

\\

o .
q.5 \\. 10.
DISTANCE FRom CENTERLINE \

 

 

 

 

 

 

 

STRESSs , KkKsS I

 

 

 

 

 

 

 

 

 

 

 

-10

Fig. 18. Stress Distribution Across Section B-B in the Steady-State
Condition.

 
38

ORNL-DWG 70-2371

 

 

 

 

 

 

 

 

 

 

 

 

CIRCUNFERENTIAL STRESS D!STRIB8VT/ON
,L_ THROUG ™ Tw€ WALL ' SECTIioN (C -C

: 2 Fig. 19. Stress Distribution
X Across Section C-C in the Steady-
. NN 30 State Condition.
w o -~ " \
“
W 4.5 \\
«
~ -2 —
A

DISTANCE FRom CO”T‘!LINE‘ INCHwES

-5 | | | | i |

 

 

 

 

ORNL-DWG 70-2372

 

CIRLUMPERENTIAL STRESS DISTRIBVYTION
THROUGN THNHE WALL |N SECTION D-D

 

 

 

 

 

 

 

 

10 +——o

-
o o o o v \
Fig. 20. Stress Distribution «x ‘\

Across Section D-D in the Steady- “ ~——_

State Condition. “ T
. 45 1o. 1.
" DISTANCE FRONM CENTERLINE INCHES

- 10

 

 

 

 

 

 

 

 

 

 

 

ORNL-DWG 70-2373

 

CIRCUMFERENT,AL STRES S OI1STRI)BVTIOWN
— THNROVGHW THE WwWALL IN SECTIiON E -E

 

 

 

 

 

 

-

~

 

 

 

 

 

 

T~

5 10. :
DISTANCE P ROM CENTERLINE , INcHES

 

— 11 2

 

 

 

\©

STRESS KSI
>

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 21. Stress Distribution Across Section E-E in the Steady-State Condition.
ORNL-DWG 70-2374

39

 

 

 

 

 

 

 

 

 

 

 

TEMPERATURE DISTRIBVTIoN

4
W TRovenw WwALL )~ sectiov R-AR
® 1400 i :
W ?

- «
3
~
<
« ;
: |
e i
t
w1300 ;

45 Y
DISTANCE FROr
CENTERLINE, INCHES

Fig. 22.

Temperature Distribu-

tion Across Section A-A After the
Step Change 1300 — 1L400°F.

ORNL-DWG 70-2375

 

TEMPERATURE
THROUGH THE WALL

DISTRIBUTION

IN SecTion B-B

 

1400
Fig. 23. Temperature
Distribution Across Section
B-B After the Step Change
1300 — 1L00°F.
4300

9.5
DRSTANCE FROM

CENTERLINE INCHES

 

1s

|

9¢

 

\\-

 

 

 

 

 

 

 

 

10

ORNL-DWG 70-2376

 

l

4400

\.

|
|

|
1
{

1

[

I

|

TEMPERATURE DISTRIBVTION

|

i

|

i

|

" THROUGCH THE wALL In SEcTion C~-C

4
!
;
|
!

e sm— e sovann]

 

 

\gs

15

1

=

 

 

 

 

1300

E

 

 

 

45

 

10.5

DISTANCE FROM CENTERL/INE,

INCHES

Fig. 24. Temperature Distribution Across
* Section C-C After the Step Change 1300 — 1L400Q°F.

 

 
°F

TEMPERATVRE

Lo

ORNL-DWG 70-2377

TEMNPERATVRE ODISTR I BUOTION

 

:L THRovVGH THNE WALL 1N~ SECTION D-D
« _
X
d
~
¢ 1400
Y
g
Q
X
W
W~

1300

g5 10. 11,

DISTANCE FROM CENTERLINE ,INCHES

Fig. 25. Temperature Distribution Across Section D-D After the Step
Change 1300 — 1L400°F.

ORNL-DWG 70-2378

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TEMPERATURE DISTRIBVYUT!ION !
THROUGH THE WALL IN SECTION E-E
e -]
1400
1300
9s 10 11 42

DISTANCE FRON CENTERLINE INCHES

Fig. 26. Temperature Distribution Across Section E-E After the Step :
Change 1300 — 1L400°F.

 

 

 
KSI

STRESS,

 

ORNL-DWG 70-2380

 

T T

AXIAL STRESS DISTRIBUVTION

 

THROVeW THE WALL I1N SEcTion B-8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tn

 

 

 

 

 

 

 

 

 

 

 

 

 

ORNL-DWG 70-2379
20
CIRCUMFERENTIAL STRESS DISTRIBVTION |
THROUGH YHE WALL IN SECTIiON A-R /
SV
10 10 /
9s ; -
X /
o y
A /-_ A
‘ P
)}f; “ ‘///” T
0 € o , .
('

9.5 10 . g / o
DISTANCE FROM ‘ 1s DISTANCE FROM CENTERLINE K INCNES
CENTERLINE, INCHES ,‘ //

-10 -0 ////
-10& -2.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 27. Stress Distribution Across Section Fig. 28. Stress Distribution Across Section B-B After
A-A After the Step Change 1300 — 1L00°F. the Step Change 1300 — 1400°F.
57R£Sses.i<$I

ORNL-DWG 70-2381

 

]

~ T HROUGH THE wnhAll

o

L

IN SECTION

|

CIRCUMFERENTIAL S TRESS DISTRI BUTION,

¢-C

 

10

«20

9s

 

_
<

 

\\

10.5

 

 

 

T

OISTANCE

FRor CENTERLINE , INCHE

11

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 29.

Stress Distribution Across Section
C-C After the Sept Change 1300 — 1400°F.

o

STRESSEs , KSI

 

ORNL-DWG 70-2382

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

D-D After the Step Change 1300 — 1L400°F.

CIRCUMFERENTINAL STRESS DPISTRIBVTION
THROVGH THE WALL IN SEcTien D-D
| |
( | ; ;
; ? z !
| 5 i !
: ! ) ‘
; ? é }
T
0 — — s
q.5 10 | | "
DISTANCE FROM CENTERLINE , INCHES
| | %
Tf ; ?
i :
i : é |
=10 | | | !
? 5 ? |
| |
| !
e i —
; |
1 1 |
Fig. 30. Stress Distribution Across Section

of
L3

ORNL-DWG 70-2383

 

T

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

] CIRCUMFBRENTIAL STRESS DISTRIBUT(ON
THROVGEH THE wAallt i1~ secTI10n# E-E
1¢
“ N g _
m‘ / \ \
w . . ‘ ,
n
- 10 11
W
« DISTANCE FROM CENTERL(NE.INCHES
- e b e —
"
-20

 

 

 

 

 

 

 

Fig. 31. Stress Distribution Across Section E-E After the Step
Change 1300 — 1L00°F.

 
Lh

ORNL-DWG 70-2384

 

600 t—m—

*F

TEMPERATURE

1500

TEMPERRATVRAE DISTRIBUTION
THROVUGH THE wALlL 1N

SEcTIioNn AR-A

 

1400

gs-

 

5s
1s

 

1300

N

 

 

 

 

g.5

10

DISTANCE FROM CENTERLINE , INCHES

Fig. 32.

Temperature Distribution

Across Sectlon A-A After the Step Change
1300 - 1600°F.

TEMPERAT vRE °F

ORNL-DWG 70-2386

 

V4boot——

1500 \

SECTiIoN C-C

TEMPERATURE DISTRIBUTION

THROUGH THE wAall 1~

 

 

 

 

 

 

 

1400 9ds
5s
1s é—-
{300
q.5 10 10.5

DISTANCE FROM LENTERLINE ,INCHES

ORNL-DWG 70-2385

 

1600 b= e HMPERATURE DISTRIBUTION

TROUGH THE WALL IN

SEcTion B-8B

 

 

 

 

 

 

 

i
1500 \
W 9s
e
W
: 1400
e
c
«
Y Ss
T
w
b~
1s
1 300
q.5 40

DISTANCE FROM CENTERL/NE

Fig. 33. Temperature Dis-
tribution Across Section B-B After
the Step Change 1300 — 1600°F.

Fig. 3L4. Temperature Dis-
tribution Across Section C-C After
the Step Change 1300 — 1600°F.
oL

TE/MMPERATVRE

°F

TEMPERATURE

TENPERATURE DISTRIBUTION
1600 L—-—
THROVGH THE WALL I SECTION D-D
1500
1400
5s
14300
9.5 10 11

L5

ORNL-IWG '70-2387

 

 

 

 

 

 

 

 

 

 

 

 

DISTANCE

Fig. 35.

FRolM cENVNTERLINE K TNCHES

D-D After the Step Change 1300 — 1600°F.

1.8

Temperature Distribution Across Section

ORNL-DWG 70-2388

 

1600F———

1500

/00

TEMPERATURE DISTR

THAODUVGHN THE WALL

)BvTION

 

IN SEcTion [F-E

 

 

 

 

 

 

 

 

 

 

 

9s
5s
1300
q.s 10 41 [y
DISTANCE FROM THE CENTERLINE , 1\NCHES

E-E After the Step Change 1300 — 1600°F.

Fig. 36. Temperature Distribution Across Section

 

 
L6

ORNL-DWG 70-2389

CIRCUMFERENTIAL STRESS DISTRIBUTION
THRoUGHM THE WALL IN SeEcTion R-A
40

 

30

 

 

LY

 

 

STRESS, KST

-10

 

-20

 

 

~30

 

\\‘?

Ss

as

 

-50

 

 

 

-n|

 

 

 

 

Fig. 37. Stress Distribution Across Section A-A After the
Step Change 1300 — 1600°F.
b7

ORNL-DWG 70-2390

 

R¥lAaL STRESS DISTRIBUTION
THROVGH THE wWAHll IN SECTION B-B

 

70

6o

 

40

 

/.
w A
., /
a T

 

 

 

 

 

 

 

 

 

 

-
w - -
X g5 10
W 1s _ DISTANCE FROM CENTERLINE ,LINCHES.
v
w -40 £
o
F / //
N
-20 /
Ss /
9s
- 40
- éo
.70

 

 

 

 

 

 

 

 

Fig. 38. Stress Distribution Across Section B-B After the Step
Change 1300 — 1600°F.
L8
ORNL-DWG 70-2391

CIRCUMFERENTIAL STRESS DISTRIBUTION
T HROUgH THE WALL IN SEcTioN C-C

 

 

 

 

 

 

 

 

 

 

 

 

 

20 gs
A 5¢ \
S/ .
| s
.\
\
\
q.5 10.5
DISTANCE FROM CENTERLINE, INCHES
H -
0
X
o« 10
n
W
«
-
Vi
1] 55
-20
// 9s
-30 /
-40
-50
-60

 

 

 

 

 

 

 

 

Fig. 39. ©Stress Distribution Across Section C-C After the Step
Change 1300 — 1600°F
49
ORNL-DWG 70-2392

Circumferential Stress Distribution
Through the Wall in Section D-D

 

10

 

 

R

g5 | 10.5 T~

\ DISTANCE FROM CENTER LINE ,INCHES
s

 

 

 

 

STReEss KkKSI
le]

 

 

- 30

 

-40

 

 

-50

 

-60

 

 

 

 

 

 

 

- 70

 

Fig. 40. ©Stress Distribution Across Section D-D After the Step
Change 1300 — 1600°F.

 
>0

ORNL-DWG 70-2393

 

CIRCUMFERENTIAL STRESS DISTRV'BUTION
20

 

 

THROUGH THE WALL IN SeEcTion E-F

10

 

\1

e ————————

 

 

 

 

 

 

 

10 1 12 2.8

DISTANCE FROM CENTERLINE, INCHES

sTress , KS I

-10

 

 

 

-40

 

 

-60

 

%7
]
//
|

 

 

 

 

 

 

 

 

 

 

Fig. 41. Stress Distribution Across Section E-E After the Step
Change 1300 — 1600°F.
°f

TEMPERATURE

tribution Across Section A-A After
the Step Change 1300 — 1800°F.

°g

TEMPERATURE

ol

ORNL-DWG 70-23%

 

ORNL-DWG 70-2395

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TEMPERATUYURE DISTRIBUTION TEMPERATUVURE DISTRIB UTION
THROUVUGC i THE WALL I'N THROUVGHKH THE WALL I N
sgcrTion A-A SEcT)oNn B-B
1800 1800
1700 1700
w \
o
w
4 o
>
< 500
1500 g :‘ 95
s s
Q.
p Y
1400 w 1400 :
-
12\\\\~__ :>\\\\-
1300 + 1300 -
95 10. 45 10.
DISTANCE FRoN DISTANCE FRort
CENTERLINE INCHES CENTERLINE ,INCHES
Fig. 42. Temperature Dis- Fig. 43. Temperature Distribution

1800

1700

ORNL-DWG 70-2396

 

TEMPERATUVRE DISTRIBVTION

THROUGH THE wWALL IN

SECTIOoN T -C

VS,

 

 

1500

 

O\
\

 

 

 

 

 

 

1300
9

 

N

.3 10
DISTANCE FROM CENTERLINE INCHES

Across Section B-B After the Step Change
1300 — 1800°F.

Fig. L4h. Temperature Dis-
tribution Across Section C-C After
the Step Change 1300 — 1800°F.

 
TEMPERARTURE °F

TEMPERATUVRE °F

52

ORNL-DWG 70-2397

 

 

 

 

 

 

 

 

 

 

TEMPERATURE DI1ISTRIBVTION
18004

THROUGH THE WALL IN

section D-D
1700 e
1500
9

< ¥

1300

 

q.5 10. A4.

DISTANCE FRONM CENTERLINE ,INCHES

Fig. 45. Temperature Distribution Across
Section D-D After the Step Change 1300 — 1800°F.

ORNL-DWG 70-2398

 

TEMPERATURE DISTRIBUVUTION
THROVGHM THE WwWALL IN
SEcTioN E-E

 

 

1500 ;

 

x

 

 

 

 

 

 

 

 

 

1300
a5 10. 11 2

DiISTANCE FROM CENTERLINE A LNCHES

Fig. 46. Temperature Distribution Across Section E-E After
the Step Change 1300 — 1800°F.
STRESS, KSI

>3

ORNL-DWG 70-2399

CIRCUMFERENTIAL STRESS OISTRIBUTION
THROUGHN THE WALL IN &SEgcTioN A-A

 

9s

20

 

 

 

 

/]

o

 

10
DISTANCE FROM CENTERLINE ,INCNES

P
)

-20

 

- &0

 

-60

 

-80

 

 

 

 

 

 

 

 

 

Fig. 47. Stress Distribution Across Section A-A After the
Step Change 1300 — 1800°F.

 
54

ORNL-DWG 70-2400

 

 

 

 

 

STRESS, KS1

 

 

 

 

 

 

AXIAL STRESS DISTRIBUVTION THROVENW
THE WALL 18 SEcTiON B-B
400 -
I
4°~L A
e
0 ,
///' 10
101 DISTANCE FRopmM CENTERLINE INCHES
201} |
501
/
100 %

 

 

 

 

 

 

 

Fig. 48. Stress Distribution Across Section B-B After the
Step Change 1300 — 1800°F.
55

ORNL-DWG 70-2401

 

CIRCUMFERENT |AL S TRESS DISTRiIBVTION
yol- THRoven TwE WALL I~ SEcTion C-C

oI

0 4 ; : .
95 1o 10.5

DISTANCE FRonm CENTERL/INE

—p—————arel

0

 

 

 

 

 

STRESS,6KS1

-20

 

- 40

 

- bo

 

 

- 80

 

-Qo

 

 

 

 

 

 

Fig. 49. Stress Distribution Across Section C-C After the
Step Change 1300 — 1800°F.

 
56

ORNL-DWG 70-2402

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CIRCUMFERENTIAL STRESS DISTRIBVTION
THROUGH THE WALL '~ sEcTtionNnv D-D
20
X 0o j .
. 11
. 95 /
“ DISTANCE FRoOM CENTERLINE, K INCNHES
W
<
.
“ s
-20
-40
-60
- 80
~-100
-410
L

 

Fig. 50. Stress Distribution Across Section D-D Atfter the Step
Change 1300 — 1800°F.

 
 

 

o7

 ORNL-DWG 70-2403

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

90 1 — CIRCUMFERENTIAL STRESS OISTRIBVTIDON
THROUGH THE WALL AT SEcCTIioN E-E
10
9¢
/ -
o ‘ \ , — X
4.5 10 11 12,
DISTANCE FROM CENTERLINE ZLNCHES

= _ 20
@ 2
X
v
“
«l
oL
-
“"/0

~ 60

~-80 ]

~100

- (20

 

 

 

 

 

 

 

 

 

Fig. 51. Stress Distribution Across Section E-E After the Step
Change 1300 — 1800°F.

 
58

ORNL-DWG 70-2404

TEMPERATVRE DISTRIBYUTION

 

 

u THROUGH THE WALL I1~¥# SECTIion A-A
. °
g 1300 i Fig. 52. Temperature Dis-
§ 1 tribution Across Section A-A After
% the Step Change 1300 — 1200°F.
. - 3
QY
qQ
v
W
* 4200 —
9.5 10.

DISTANCE FROM
CENTERLINE , INCHES

ORNL-DWG 70-2405

TEMPERATUVRE DISTRIBUTION
THROUGM THE wWALL W&
SeEcTtiov B-8B
Fig. 53. Temperature Distribution
Across Section B-B After the Step Change | 1s
1300 — 1200°F.

 

1200 —
9.5 10

DI STANCE FROM

 

CENTERLINVE , INCHES

ORNL-DWG 70-2406

 

TEMPERATURE DISTRIBUTION

 

 

:L THROUGH THE WALL IN SECTIDN C-C
w _ | Fig. 54. Temperature Dis-
©  Lapo P . tribution Across Section C-C After
2 the Step Change 1300 — 1200°F.
1 i
o |
Ww
Q.
r
w
40.5
= j200—n ; -

 

 

 

 

 

 

DISTANCE PROM CENTERLINE ,INCHES

9.5

 
°F

TEMPERAT URE

59

ORNL-DWG 70-2407

 

°f

1300

| T EMNMPERATURE DISTRIBVUT joN

THROUGHW THME WALL |1~ sE&cTioN~¥ D-D

 

s _— | —

 

 

1200

TEMPERATUVRE
w
] w

 

 

 

 

 

45

10 14.

DisTANCE FROMT CENTERLINE, INCHES

Fig. 55. Temperature Distribution Across Section
D-D After the Step Change 1300 — 1200°F.

ORNL-DWG 70-2408

 

 

1300

TEMPERATUVURE DISTRIBvTionNn

THROVE N

 

TNE WALL 1~ SEcrionNn E -F

 

 

 

1200

/4

 

 

 

 

 

 

9.5

10.

14 12

DiSTANCE FRomMm CENTERLINEG, K |NCKHES

Fig. 56.

Temperature Distribution Across Section E-E After the

Step Change 1300 — 1200°F.

 

 
60

ORNL-DWG 70-2409

 

CIRCUMFERENTIAL STRESS DISTRIBUT ION
THROUGH THE wALL IN Secrion A-ARA

 

 

 

 

 

20
10
~
v
X
wn
A
9
X 1s 9s
=~
0 ’ -
v\
sis 10
-10 T_. DISTANCE FRO M
CENTERL INE ,INCHES

 

 

 

 

 

Fig. 57. Stress Distribution Across Section A-A
After the Step Change 1300 — 1200°F.
61

ORNL-DWG 70-2410

 

10\

ARXIAL STRESS DISTRIBUTION
30— THROUGH THE WALL

IN S ECTiIOWN

 

 

’ N\

 

 

OISTANCE PROM CENTERLINE,

 

 

INCHWHES

 

STRESS  KS 1

-10

1s

A

W

10

 

-10

\

 

-3

 

 

 

 

 

 

 

 

Fig. 58. Stress Distribution Across Section B-B After the

. Step Change 1300 — 1200°F.

 

 
ORNL-DWG 70-2411

 

CIRCLUMFERENTIAL STRESS DISTRIBVTION
THROUGH THE wALL N SeEcTiov C-C

20

 

10

 

 

 

 

10.5

 

 

STRESS ,KSIT

0 N — ’ .
a5 \Dlsrnwcf FROM CENTERLINE LWNCHES
P \ .
\__
- 10 1s

 

 

 

 

 

 

 

Fig. 59. Stress Distribution Across Section C-C
After the Step Change 1300 — 1200°F.

ORNL-DWG 70-2412

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o C
CIRCUMFERENTIAL STRESS DISTRIBUT O N
THROVUGHN THE WALL 1N Sgction D-D

30

20

i

17,

X 10

w

v

. ¢

« 1s

-

"

{
) ' ! ’
9.5 10 — |
|
DISTANCE FROM CENTEHERLINE |, INCHES
- 10

 

 

 

 

 

 

 

 

Fig. 60.

Stress Distribution Across Section D-D

After the Step Change 1300 — 1200°F.

¢9
k SI

STRES S ,

 

63

ORNL-DWG 70-2413

CIRCUMPERAENTIAL S5TRESS DISTRiIBVTION
THROUGN THE wnl.'l. ‘N S ECTIon E-E

10.

DISTANCE FROM CENTERLINE | INCHES

Fig. 6l1. Stress Distribution Across Section E-E After the
Step Change 1300 — 1200°F.

 
ORNL-DWG 70-2414

 

 

 

 

 

 

 

 

 

TEMPERATVRE DISTR)BvT/ N
rHROUGH THE wall I1n
SeEcTion A-R
1s
uw
o
W 9s
o
>
o
<
L 4
w
a
C
w
-
1100
95 10.
DISTANCE FROM CENTERLINE,
INCH ES
Fig. 62. Temperature Dis-

tribution Across Section A-A After

the Step Change 1300 — 1100°F.

TEMPERATURE °F

6k

ORNL-DWG 70-2415

 

|

TEMPERATVRE DISTRIBUT!(ON

 

 

 

 

 

 

 

 

THROUEHN THE WALL )~ SECTtonv B-8
n
1300 Ts ]
W
°
w
o 9s
>
-
<
. /
w
a
L
w
-
1100
95 10.

OISTANCE FRo»Mm

CENTER.L /VE , /INCHES

Fig. 63.
Across Section B-B After the Step Change
1300 — 1100°F.

Temperature Distribution

 

 

 

 

 

 

 

 

 

 

ORNL-DWG 70-2416
| T T
TEMPERATURE DISTRIBVTION
THROUGH THNE WALL IN SECTIoN C-C
00 — —
13 1s ~
9s
1100
95 10.5

DISTANCE FROM

Fig. 64.

CENTERL 1wg

INCHES

>

C-C After the Step Change 1300 — 1100°F.

Temperature Distribution Across Section

v
°F

TEMPERATURE

. I
K
°
9s
O
Y,
d
~
<
[
Q
Q
r
w
-
1100 . + ,
4.5 10. 11.

65

ORNL-DWG 70-2417

 

TEMPERATURE DISTRIBuUTId®N
THROUGH THE WALL IN SEcT/iON D-D

 

 

 

 

 

 

 

 

 

 

Fig. 65. Temperature Distribution Across Section D-D After the
Step Change 1300 — 1100°F.

ORNL-DWG 70-2418

 

TEMPERATURE DISTRIBVTION
THROvVEN THE WALL IN SEcTiON E-E

—
1300 {-1s /

 

 

9s

 

 

1100

 

 

 

 

 

 

9.5

DISTANCE

Fig.

10 | 11 12
FROM CENTERLINE, INCHES

66. Temperature Distribution Across Section E-E After the

Step Change 1300 — 1100°F.

 

 

 
66

ORNL-DWG 70-2419
I | |

 

01— CIRCUMFBRENTIAL STARESS DISTRIBVUTION  _
THMROUGH THE WALL 1N SEcTioN A-R

 

30

 

ol

 

 

 

 

 

 

 

 

-4
"
X 10
‘.
A
w
«
-
" DISTANCE FROM CENTERLINE, INCHES
OTas \ )
is
-10 !
9
-20

 

 

 

 

 

 

 

 

Fig. 67. ©Stress Distribution Across Section A-A After the Step
Change 1300 — 1100°F.

€
67

ORNL-DWG 70-2420

 

 

) . l ' l

40 AXIRL STRESS DISTAIBUTION
THROUGN THE WALL IN SECTION B-B

30

 

20 \

9¢
1s
10 :

 

 

 

 

 

 

Tl
Y
X
"
: \ DISTANCE FROM CENTERLINE (INCHES
o A
« 5
. 9 \ 10
"
&
'10 \
A
-20

 

-30

 

-40

 

 

 

 

 

 

 

 

 

Fig. 68. Stress Distribution Across Section B-B After the Step
Change 1300 — 1100°F.

 
68

ORNL-DWG T0-2421

 

 

 

 

 

 

 

 

50
CIRCUMFERENTIAL STRESS DISTRIBUTION
0| THROUGM THE waLL IN SEcTioN (-C
30
20

 

 

 

 

 

 

10
9s
ODISTANCE FRon CENTERLINE, i1NCHES
0 \ . _
9.5 \ 10.5
/L—/
- ls

o \

N —

STRESS,  KSI

 

 

-20

 

 

 

 

 

 

 

Fig. 69. Stress Distribution Across Section C-C After the Step
Change 1300 — 1100°F.

<
69

ORNL-DWG 70-2422

 

 

 

 

 

 

 

 

 

 

 

 

 

 

!
| | I
401 ———  CIRCUMPERENTIAL STRESS DISTRIBUTION
THROUG THE WALL 18 seEcTioNn D-D
50
40
9s
30
20
1s
10 \
-4
wn
x
w
w
w
a
~
“ .5
___..—-————_'4
DISTANCE FROM CENTERLINE, INCHES
10

 

 

 

 

 

 

 

 

Fig. T70. Stress Distribution Across Section D-D After the Step
Change 1300 — 1100°F.

 
sTReEss, KSI

T0

ORNL-DWG 70-2423

 

 

 

 

 

 

 

 

 

 

 

 

 

50| CIRCYMFERENT IAL STRESS DISTRIBVUTION
THROVEM THE wall IN section E-E

40

9¢
30
20
1
10
DISTANCE FRoM CENTERLINE, INCHES

. ) . | ) ' .$

095 \ \ e

-10

 

 

 

 

 

 

 

 

 

Fig. 71l. ©Stress Distribution Across Section E-E After
Step Change 1300 — 1100°F.

the