ML19296D385
| ML19296D385 | |
| Person / Time | |
|---|---|
| Site: | Davis Besse, Arkansas Nuclear, Crystal River, Midland  |
| Issue date: | 02/01/1980 |
| From: | BABCOCK & WILCOX CO. |
| To: | |
| Shared Package | |
| ML19296D379 | List: |
| References | |
| BAW-1610, BAW-1610-01, BAW-1610-1, NUDOCS 8003040498 | |
| Download: ML19296D385 (31) | |
Text
1 STRUCTURAL EFFECTS CF A"4S OVERPRESSURE TRANSIENTS Di BYRON JACKSCN PRIMARY PCMPS BABCCCK & WILCOX CO.
NPGD FEBRUARY 1,1980 8003040 1
s CCNT" LITS PAGE S L%'4ARY -----------
==--------------------------------------- 1 INTRC D UCT I C N -------------------------------------------- -- ----- 2
2 S cop e ----- -
Al lowab le S tr e s s -------------------- - ------ -- --- --------- -- 2 Irradi ation E f f e c t s ---------------------------------------- 3 ATWS Transien t -------- = = - -- - = = = -
3 PUMP DESCRIPTICN -- -
=------------------------------------- 3 MATHEMATICAL MC DE L ---------------------- --------------------- - 4
= ------ 8 pcp Case -
=-------9 Case Closure ---- -
- - - - - - - - - - - - - - - - - - - - - - =
STRESS EVALUATION --- -- = = -
12
---21 P CMP CASE DISTORTION ----------------- -
STRUCTURAL 1MTEGRITY -----------= = - - - = = ------------------------ 2 7 9-
i
_S Q"iARY The effect of an ATWS transient on the structural integrity of primary pu=ps manufactured by Byron Jackson for Babcock & Wilcox nuclear reactor is evaluated in this report. The pr Mary effect of the transient on the pump structure is.to cause a pressure surge that peaks at less than 3750 psi. -
The effect of the transient is evaluated by examining stresses caused by a static pressure of 3750 psi.
Also, a quantitive estimate of the deformation is made to determine the potential for interference with rotation of the impeller.
It was found that stress in the flanges, the closure, and those portions of the pump in which the bearings are mounted are within allowable stresses in accordance with ASME Nuclear Pressure Vessel Code for Level C incidents.
Stress,in' portions of the volute and the diffuser vanes do exceed allowable stressforLeve5Cincidents. The location and magnithde of these stresses are presented in this report. These stress levels are well below material rupture strength, and closure bolts are within allowable stress limits; therefore, it is concluded that the structural pressure boundary will not be violated.
An evaluation of deformation resulting from these stresses shows that displacements which could affect the rotating impeller are small compared to available clearances.
This provides assurance the structural integrity of the primary pump will be retained, and the post-ATWS function of the primary pumps will not be i= paired by an ATWS pressure pulse, which was determined in accordance with current NRC guidelines.
t III"'RCCUC"'ICN SCCPE This document addresses the effect of an ATWS pressure transient on the structural integrity of the primary reactor coolant pu=ps built for the reactors liste_d in Table 1.
TAB'l 1 REACTORS USING P fRCN JAC"<SCN PDGS CTILI" Y REACTOR Consumers Power Midland 1 Co.
Midland 2 Arkansas ANO-1 Power & Light Co.
Florida Power Corp.
Crystal River 3 Toledo Edison Co.
Davis Besse 1 A description of the pt p and its stress analysis is included.
A co=parison of stress in the pressure bo m w/ caused by the worst A'IWS transient is made with allowable stress for Level C incidents.
A quantitative estimate of distortien is included to determine poten~dal effects on impeller clearances. Flange seal capabili* des are also evaluated.
Earlier evaluation of the pump is included in topical report BAW 10099. That report determined the pressure at which stress reached allowable values for e=ergency conditions. The re-evaluation herein is based on current revised guidelines from NRC for ATWS evaluation.
ASME Allowable Stress Allowable stress for Level C service li=its are given in subsection NB of Section III, Division 1 of the ASME Pressure Vessel codes. The 4
limiting requirements for this application requires that primary =erbrane stress not exceed 1.2 S, and that primary =ertrane plus primary bending m
stress not exceed 1.8 S m
The pu=p is made frem u u:
..ic stainless steel casting per the requirements of ASTM A-351 Grade CF8M.
The value of S for this m
o material at 680 7 is 16,400 psi. Therefore:
Primary =ertrane allewable stress = 19700 psi Primary me=3rane + primary bending allcwable stress = 29500 psi Irradiation Effects The pri=ary pu=ps are sufficiently distant from the reactor to =ake irradiation effects negligible, therefore material properties of structural components in the pu=p do not include any = edification for irradiation effects.
ATWS Transient The pressure transient resulting from an ATWS event har been determined using the NRC guidelines of Alternate Nu=ber 3 specified in Volume 3 of NUPIG 0460. The results of this study are included in a letter report bearing the title " Analysis of S&W NSS Response to ATWS Events",
January 1900.
The above report shows the pressure transient peaks at a pressure less than 3750 psi, and that the coolant te=perature does not exceed 660 F.
The pu=p stresses are evaluated at 3750 psi, and the allowable stress for the pu=p =aterials is based on a te=perature of 680 F.
PUMP DESCRIPTICN The Byron Jackson pu=ps are vertical, single stage, single bottom suction, horizontal discharge, centrifugal dif fuser casing units with con-trolled leakage mechanical seals. They are driven by squirrel cage, vertical t
AC induction motors.
Some of the design features of this pu=p are listed below.
TABLE 2 - PUMP CESIGN P ARA >'ETERS Design Pressure 2,500 psig Design Temperature 650 F Operating Pressure 2,250 psig Rated Flow - 4 Pumps Cperating 86,000 gpm Maxi =um Flow 130,000 gpm Developed Head - 4 Pu=ps Cperating 327 feet Suction No::le Irner Diameter 28 inches Discharge NO: le Inner Dia=eter 28 inches Power Source 6,600 volts, 3 Phase, 60 H:
Motor Horsepower at Cperating Te=p.
6,090 HP acta &.g Speed 1,185 rp=
The pu=p asse=bly censists of the motor, the driver mount, the rotating ele:nent (ccupli.g, i=peller, and shaf t), the heat exchanger, the seal cartridge (and =echanical seals), the cover plate, and the case.
Each reactor contains four of these pu=p assemblies for the puGose of recirculating primary reactor coolant. The pu=ps are installed in the cold leg of the piping system between the steam generator and the reactor vessel.
The general arrangement of the pu=ps and sket:bes showing pertinent details of the pu=p are shown in Figures 1, 2 and...
GENEPAL CESCRI?*ICN CF MATHEMATICAL MCCEL The pu: p is =odeled in two parts: pu=p case and case closure. The purp case model is a three-dimensional finite ele: tent model. This model uses solid elements for the flanges and diffuser vanes. Shell ele =ents are used for the rolute, and for suction and discharge nozzles.
5 N
M h
m
.D I Z.08
~
w
=
M n8/I 9 i24 c.
ID y
) ll d
(y;-------------
Jl@L
("t
- M q
g W* :
W
.0 iP2 M
f/
- z W
N in T
a m
e y
N
- d I
b ao
-- G m
/
d 1
M NY 0
Age 2
x
'I d
g J
d o
. 0.8 0.IE l0i6 h
E, I
?.
') a,!
I r
a e
~s eo
!Ck k
a*
-W
- I C
RI c
M g
kM W
W x c.
EB B
i
- c. a.
[
8/9 9 i92
.iUI F.0E 2E/62 8 i9 L
Q I l]
~
a
~
m L
y-s
~
f}
b
- J
\\
ho M
U g"
3 i
(
+-
a En y s
L ll' G
9 A
Q %.
./ (N in U y N.
N) )
[h_
u u8/L 6.E m
0.12
2H LP C
I C
R R
T E
E 4
G ME R
E A
I i
Ot l
A C
6R S
9 A I
0E D
g
. C L
L 0
A I
R T
O N
F EG
+
L R N
I E A
A W T
~
a T O E P N
8 D
O
/
f
,' 2 S
S L R K
I A E C
m 4
N M A
R U J
y E S A
4 N
I t
N 0 O
I C R
Y v /N B
2 x
E I
LG I
F
~
s D
T N
d A Y
T R
F SA S A
L T I G
S S
0 s.
A LD T E N
T T
t I
R R
U E O R R H
S A
A O
S Bl O U f
A S
P P
D E P S T
EP P O C
E t
L G
'E F RI L
L 2
A A
N l
A U S C I
V N
I L
H S 4 U
R T
S S O/ R L3 O P
E A
S C
T T
T E
4 O N
O R
M I
R P
)
6 l
, i%/
f 1
yy j
y b ~'*
RO F
L g
I A
R Nm
,/
3g T
E E
W 9
g "8
D O
2 P
L S v
pg E A RE A A A N S DO g
R N I D j
T K O L N R L O I A F T
'%'E 3
r C
I R
T FAE z
IE Dt A 6R 9A 0E
. L 0C
o I
4+A y#
r I
\\
\\
k, 3
BY D JACKSCN PUMP CASING 7
8.
The case closure is a sy==etric structure.
It is modeled using axisym=e-tric two-dimensional finite element techniques. Each =cdel includes portions of the other structure.
Pump Case Model The pump case model is a three-dimensional mathematical representa-tion of the pump casing. The model also includes the cover plate but does not include the cover plate to pump case bolting.
Instead, the cover plate is joined rigidly to the upper flange of the pump case. The model's geometry is developed in three phases: The first phase censists of drawing a series of vertical cross sections through the pump case.
In the second phase, points (referred to as nodes) are defined en each local coordinate system which for= a grid over the gecmetry of that section. Elements are defined in the last phase of model construction.
Two types are used; shells (triangles or quadrilaterals), and solids (wedges or bricks). Triangular shell elements are defined from three nodes while four nodes are required to define the quadrilateral.
Four computer programs, referred to as preprocessors, are used.
The preprocessors check the data for undefined nodes, negative nodal areas or volumes (which indicate either duplicated nodes or badly skewed corners), misdefined material codes, and unspecified thicknesses (shell element nodes only).
Element Cefinitions The pump case portion of the nodal is built from 746 shell elements and 1,814 solid elements. The cover plate portion consists of 578 solid elements. Shell elements are connected to solid elements by means of 116 constraint sets.
A portion of the pu=p case model is shown in Figure 6.
i Method of Analysis (Pump Case)
The *hree-dimensional finite element method is used to calculate stress levels throughout the pump case. Two computer programs perform the required calculations using as input a three-dimensional mathe-matical model of the pump case to which specified boundary conditions are applied.
Highly Strer-
'reas Structurally, the pu=p case is a pressure vessel.
As such, volute wall thicknesses and diffuser vane cross sectional areas are for the most part determined by the design pressure. The high stress areas of the pump case for pressure leading (that is, for primary stress levels) are diffuser vanes seven thru nine, the volute wall at hydraulic sections seven thru nine, the junction of the suction no==le with the lower flange, and the junction of the discharge nozzle with the volute and the flanges.
Closure Model The finite element model for the closure is an axisy= metric mathematical representation of the components used to close the pressure boundary of the pt7 casing.
The components included in the model are the driver mount lower flange, the heat exchanger, the seal flange, the lower pressure breakdown device, the third seal backup flange, the driver count to case bolting, and the heat exchanger to driver mount bolting.
The case closure portion of the model consists of 323 axisy==etric ring elements (quadrilaterals or triangles) which are defined by 369 nodal points.
The driver mount consists of 174 elements, the case upper flange consists of 40 elements, and the stud and nut consists of 76 elements as shown in Figures 4 and 5.
Method of Analysis - Case Closure An axisy= metric finite element computer program is employed to
_g.
s e
4 x
\\,
/-
\\e s7 9
4
/ N
\\s1 Y
\\T x
~
N N
\\
C
/
fy 1.
r
-rm N
y FIGURE 4 FINITE ELEMENT MODEL TUN O -
T DU TT NS LOE MSA R C EVP I h R U OP
\\
(
/
LED l
OM ER E
U L
S O
O H
L D
C
/
U E
l T
S S
A F
C O
F D
O N
W 1
E E
1 I
V D
d' E
E L
D O
C
/
H LP
/
D
\\
X U
AV E
TS p
5
/
<\\
E
/
sR
\\
UG I
F T
\\
4 NY 1
GN IDDALC
evaluate the stresses throughout the case closure for internal pressure and bolt preloading. The solution consists of nodal deflections and element coordinate stresses calculated at the element centroid.
Conditions Analyzed Several conditions are evaluated. These are referred to as Basic Conditions. They include a bolt preload condicion, a design pressure condition and a normal operation pressure condition.
STRESS EVALUATICN The Byron Jackson pump evaluated in this report is used in several of the B&W Reactors.
A listing of these reactors is given in the Introduction to this report. The peak pressure during an ATWS transient for these reactors has been determined to be slightly less than 3750 psi (see page 3 ).
The allowable stress intensity for ATWS transients are based on ASME Section III rules for Level C conditiens, (previously " emergency conditions").
Primary membrane stress is compared to 1.2 S (19700 psi at 680 F).
Primary membrane plus bending is, compared to 1.8 5 (29500 psi ~at 680 F).
(For additional discussion of allowable stress, see page 2.)
Stress resulting from a pressure of 3750 psi has been compared to allowable values. Calculated stress intensities which exceed allowable values are summarized in Table 3.
The 'urber of elements whose stress exceed the allowable are tabulated as a percentage of the elements in the pump case.
The stress values are those at the centroid of each element, and may be used as a conservative evaluaticn of primary membrane stress.
(Con-servative, because true membrane stress for vanes is the average stress across the section. No attempt was made to remove this conservatism, because stress intensities which include 6 ccmponents of stress cannot be averaged directly.)
The location of these elements are presented in Figures 6 through 11.
The highest stress intensities occur in the root sections of vane Number 8, which is adjacent to the crotch.
(Vane 9 is an extension of the crotch.)
-17.
CENTROID STRESS INTENSITIES VANES - PLANE A FIGURE 6 7%
[/
/
/
W g
x
/A\\,</X\\,
s v
5 1 2 Sy'
% Et.EMENTS PLANE A l
F<>
100-110 62 s
(
7 Q
110-120 03, s
g
~120-130 03 g
130-140 02
~ '
E iso-ISO 2
3 '
3 I
VANE 4 SECTION A-A VANE 5 k
VANE 3 i '
VANE 6 x
/
\\
t-g
~
(
- 7 4
^
Y'
~
'7 VANE 2 i
/
J
~
- c.,
/
J
\\
VANE 1 w
1 i
^
V~
6f n
VANE 7 VANE 8 VANE 9 a
CENTROID STRESS INTENSITIES r
VANES - PLANE 8 FIGURE 7 p
N 8 A\\
PLANE B 7
\\
" 1 2 Sy
- f. ELENExis too-iio
- o. s 5
.E lio-i2o a.s E
120-130 c.5
<=
4
/
l P
VANE 4 SECTICN A-A VANE 5 VANE.3 N
VANE 6
/
i 1
k e,+
1
.,.s VANE 2 7
.aYf \\
4 d
g 3"
/
(
. il N VANE 1
,f i
q"h ; K. '-.
h%' A VME 7 VANE 8 VANE 9 CENTROID STRESS INTENSITIES VANES - PLANE C FIGURE 8
/
2q f/
m' N
N
//
// \\\\
Q'['5\\4\\
% 1 2 Sy
% ELEMENTS PLANE C I
g 100-110 03 g
lio-120 o.s 120-130 a.4 P
E iso-ino
- o. 4 J
n
?
g o
VANE 4 SECTION A-A VANE 5 VANE 3 VANE 6
)
1-N
'N A
g 4
L A
f j
in g
\\'ti
/
VANE 1
'-,n jd}%{
m
^
VANE 7 VANE 8 VANE 9 CENTRDID STRESS INTENSITIES VANES - PLANE D FIGURE 9 8 n\\
2q De h
,\\
PLANE D
%l2SM
% ELEMENTS a
O 100-110 ag E
p 110-120 e,2 120-130 02 y
y E
in-iso a.2
-c N >t
}
I f
f ANE 4 SECTION A-1, I
GE' V'.NE 5 ~
l VANE 3 N
NE 6
/
N A
.g VANE 2 3
/
/
A If F-J l
,I
?
\\{
VANE 1 x
Q VANE 7 I
VANE 8 VANE 9
-e S
T e
N E
g M
o, a.
r E
a e L
3 f
E hl c z s z i o 0N 4
s" 0
0 1
2 1
i 1
0 0
s 0
1 3
1 b$I
~
h.1 r
~
\\
7 1
,>y'?'% y.-
// #
l z
01 1
i.
~
0 S
e0
~
s' E
g1 I
g
/
T E
I E S T r
> y,,
e N U e
E L t
g3wT T O u
j a.4M N V O
f 2
I
{
.4 F
m, S O
/
S
,e.j E F
,e*:.#
R L T A
.s S H g
.g D P I O O T N
, 7,7.f.
R O
T f'
spf?4wt f<
-, ~~
E:2:-
s
.$Y E
,f
- A i [-l $'. E,' s C
j
?yim$
}c3 L5.+.g
_ h'f s.
)4, $$. :,
0
<a 1
d, k?
1 ER e
U g%
G d
I E0 F
1 r1 e -
t 0 u0 O2
=
=
G zw W
Q @
- b..$
.= ~
W U N W N w
'r4 O Oz 2
m o
o
.=
~
a a
e
=
m
- r. g t
[ r'
( ',
(
e u%
m WO
. #,.e,>
T\\\\\\\\
e W
u~
.' ' 8.*
HW c) e H&
e.a O mD 3O ZJ O r-t
+ * **
WQ l \\ \\t
~
ZHk N
O t.n
\\
a -.. *.
1 mg WJ h?
~2'
~; ^W Ct <r og m
4.
OE ii.4 sg 8O
. ' +, -
' }-: '
yLD
. 5 W
4 y
[ D..
'[ f.<
q
'dh..w%fa"wy,4.5h"~d.p,ff d
d
'X y
- .a m
W
- g. m.; g g.gg, 7%,7.s -
3 zGi'"*) *'
q'yy
. ?
?
-N+
ec a f,
- . '. ' ~- >. cst ^*T m
LL.
': 'li T T-? '
c)
GV M WO c-#
W r=4 C) e 4.e Q 3O OM
Since the root has larger area than the vane, much of the increase ; ress in the root elements is believed to be stress which would be classim :
as peak stress (i.e., due to discontinuities).
The membrane stress intensities for the volute shell are less than 15% in excess of the allcwable stress.
Stress which exceeds allowable values occurs only in the volute shell and in the vanes which connect the inner edge of the volute.
The flanges, closure plate, and closure bolts which surround the rotating machinery are stressed below allewable values.
The ecmbination of primary membrane plus pricah bending stress was evaluated by ce= paring stress intensities at the surfaces of the elements with Level C allowable stress (i.e,, 1.8 S ).
It was found that less than m
1% of the elements had surface stresses which exceed this value, and that these were located at the rcot of the vanes.
It is bel.ieved that a detailed evaluation would shew that ecst of the stress which exceech allowable stress in these few elements (i.e., 25) is attributable to peak stress rather than primary bending.
TABLE 3 -
SUMMARY
- CUANTITY OF ELEMENTS IN PUMP CASE 'EdICH EXCEEO 1.2 SM
% 1.2 S
% of Elements m
100-110 7.9 110-120 4.1 120-130 1.3 130-140 0.8
'140-150 0.2 Closure Bolts Two factors are of interest for evaluation of closure bolts.
The bolts must be streng enough to withstand pressure and gasket loads, and the bolts should preload the gaskets to seat them for the
' evaluated pressure.
A.
Bolt Strcncth The bolts are made from AS.'E SA 540 Grade 323 Class 4 =sterial.
o The stress value S for this =aterial is 32100 psi at 650 F.
Taking a
the ratio of actual bolt area to the required bolt area for the design pressure of 2500 psi and applying the applicable allowable stress rates for bolt sizing and service condition; for the ATWS postulated pressure of 3750 psi, it is found that the resul-dng bolt stress is 39% of the allowable stress.
2
= 13E i' in e
x 3750 esi x
1S (100%)
= 39.g
~64.e 2500 psi 2S '"
=
It is concluded that the bolt has adequate strength to with-stand the postulated ATWS transient.
B.
Gasket Seatine The talts for pumps at different reactor sites are preloaded to different values. The minimu= prelcad is 25280 psi.
By ratioing the bolt stress to seat the gasket *at 2500 psi to the po<.tulated ATWS transien~..
3750 psi, it is found that a bolt stress of 25130 psi is required to seat the gasket. It is concluded that the bolts are sufficiently preloaded to seat the gasket, and that the closure will not leak during the transient. Additional =argin exists for long-term leakage because the ATWS transient pressure is of short duration.
Heat Exchancer and Seal closure Bolts A similar evaluation of these bolts was
=ade.
It was found that bolt sizing was adequate to =aintain stress below ASME allowable stress, and that sufficient preload is applied to maintain required gasket seating loads at the 3750 psi ATWS transient pressure.
- Determined usind Appendix E 1210(a) (i) of ASME Pressure Vessel Code, Sub-subsec t ion of Section III.
Pt:MP CASE DISTORTION The magnitude and distribution of the stress at 3750 psi pressure was given in the preceding section. A related censideration is whether the distortion associated with this stress field would affect the Ibility of the impeller to rotate. This effect has been found to reduce the clearance between the impeller and the casing by only 56 (5 mils in 96 mils). > t is concluded that impeller rotation will not be affected by this amount of pump case distortion. This evaluatien is discussed in detail belcw.
Methodolocv The clearance between the impeller and the pu=p casing is smallest at ths wear ring in the suction " flange".
The. nimum diametral clearance at :.his point is.096 inches as shown in Figure 2.
The pump flanges at the suction and at the pump closure are quite massive, and the stresses in this region are within allowable stress.
These therefore behave as two rigid disks, connected by the vanes. The average strain in the direction paralle?. to the pump centerline is determined for each vane. These values are given in Table 4 From this data, the change in slope between the two flanges is determined. This, in turn, permits the lateral motion of the *.eal ring to be calculated, assuming the suction flange rotates about a point within the plane of the vanes, causing a lateral displacement of the wear ring, which is below the
'" hinge point".
This value, which is based on the elastic analysis, is increased by an inelastic factor which is the ratio of a secant modulus to the elastic modulus.
The secant modulus is based on a stress-strain curve
.i which uses ASME minimum stress values.
It is assumed that all vanes i
have the reduced modulus determined for the highest stressed vane..
9 TABLE 4 - AVERAGE AXIAL STRAIN IN VANES Vane Average Strain
-4 1
5.4 x 10 2
5.6 x 10~
3 6.6 x 10" 4
7.3 x 10~
~
5 7.4 x 10 6
7.5 x 10~
8.3 x 10 8
8.7 x 10~
9 7.8 x 10~
Average strain, 9 Vanes
-4
-e = 6.7 x 10 in/in Determination of Secant Modulus Maximum equivalent stress, vane 8 EE = 24.9 x 10 (8.7 x 10-4) = 21,650 psi 6
c*
=
max Total strain at 2165 psi stress e
=.0053 (see Figure 12)
Secant Modulus E
- = 21650 = 4.1 x 10
= c S
es Inelastic ratio 6
24.9 x 10 = 6.1 E
=
E 4.1 x 10' S
YOUNGS MODULUS E
= 24.9X106 (ASTM) 25000 -
680*F MAX. EQUIVALENT AXIAL STRESS IN VANE 8 (21,650 PSI) 20000 -
i Sy(680 F) = 18300 PSI (ASTM) 5 c-15000 -
J h
SECANT MODULUS E s
10000 -
\\
i 50 %
f
)
I f
f I
t t
i 1
1 0
1
.001.002.003.004.005.006.007.008.009.010 STRAIN IN/IN FIGURE 12 CETERMINATION OF INELASTIC STRAIN RATIO Wear Rinc Calculation The effect of strain in the vanes en the shift of the suction flange
- .a xc ar :::. ; - a :- : - :,
1: i: ::si The tilt of the suction flange with respect to the closure flange
.is determined by *.rst dete r ining the axis wuch remains parallel to both flanger. This is calculated by summing the product of the difference between the overall average strain and the strain of each vane, by the coordinate Y fer each vane and setting this sum of moments to zero. Stated mathematically; 9
I (e - e) Y
=0 e = average strain in each vane ii = average strain in all 9 vanes o
where Y = R sin S ; S = a.-y ; a = 20 + 40 (i-1) i i
i 1
i This is solved by iteration, using the midpoint between vanes 1 and-9 as an arbitrary origin.
Several angles y are used as trial values until the summation converges to cero.
This angle was deter-mined to be 70.7 degrees. This is the axis ibout which the moments are balanced, and which does not ro tate.
In other words (see Figure 13),
the flanges near vanes 4 and 9 remain equidistant.
The maximum slope occurs perpendicular to this axis (i.e., frem vanes 7 to 2).
The value of the slepe is determined in a similar manner, except that the value of the slope is determined such that the product of strain differences and the coordinate X is equal to zero. S ta ted mathematically; 9 [(e - e) - ex ]
X. =0 I1 1
1 1
where X = R cos8 g
S, = a -yr (y = 70.7 )
a, = 20 + 40 (1-1) 4 3
6 7
01 c1 y
9 X+
ARBITRARY 1
ORIGIN I
f%
/
,r l[
\\
/
1Y a
.y e R -e-FIGURE 13 DISTCRTION MCCEL 5 = equivalent strain rate for slope 0 (i.e., increased strain from pump centerline to the vane)
E = average strain in each vane E = average strain in all 9 vanes By iterative trials for the differential strain rate 5, the
~
summation goes to zero at 5,=.045 x 10 per inch. The slope is then O=6 L
max = EL R
Where L = Vane Length, = 12 inches and 6
= 5R max Numerically 0 = 0.045 x 10' (12)'= 5.4 x 10~
radian and the displacement d = OH = 5.4 x 10~ (15)
.0008 inches
=
where H = distance from vanes to wear ring, 15 inches.
Applying the inelastic factor E = 6.1 (see page 22)
Es The wear ring displacement
~
inelastic elastic E.
\\ s/
d
=.0008 (6.1) =.005 inches (This also includes inelastic elastic recovery displacement)
This is small compared to the minimum diametral clearance of
.096 inches; therefore, it is concluded that distortion.of the vanes will not produce suction flange displacement which would cause inter-ference with the i=peller rotation.
- e. :
STFUC* URAL IN*EORI""I In the preceding evaluations, the distribution of stress which exceeds AS:E allcwable stress 'for Level C events has been presented for the pump case and the diffuser vanes. Stress in all closure bolts are within allowable stress, and gasket seating has been found to be sufficient to meet ASME requirements at the ATWS pressure. A quantitative estimate of the effect of pump case distertion indicated that impeller rotaticn will not be restrained.
Several of the most significant stress levels are presented on a stress-strain curve for the nurp material (see Figure 14 ). The purpose of this graphic di.
rj of stress values is to illustrate that the stress values are significantly lower than ulti= ate strength, and that the resulting strain is small cc= pared to the =sterial alongation capability.
The curve was constructed to pass through the ASME design allowable values at 680 F (e.g., yield strength at 0.2% offset, and the ulti= ate strength). Typical material values are expected to be. higher.
For the diffuser vanes, two stress values are shown on the curve.
The maximum stress in vane 8 exists at the base of the vane, and undoubtedly includes stress which is classed by the ASME as peak stress.
Gaak stress is not required to be included for Level C events.)
This value represents the upper bound for stress at the centroid of any element. The other value is the average equivalent axial stress for vane 8.
It is based on the axial strain components averaged across a horizontal plane, and represents the maximum equivalent membrane stress in the diffuser vanes (see also page 22).
The maxi =um stress in the volute is also shown. The combination of primary me=brane plus bending stress is within ASME allowable stress. The value shown is the primary me=brane stress, and is taken from the centroid stress for the shell-type elecents.
It is concluded that the structural integrity of the pump is adequate to maintain the pressure boundary intact for the 3750 psi pressure postulated for an A""d5 incident.
e O
O e
e e
O 6
100 YOUNGS MODULUS E 90 25X106 p31 80 Su)ASME 9 680*F 67000 PSI 70 j
60 g
=
x f
h 50
\\-
'e
\\
5 PEAK liTRESS-VANE 8 40 30 MAX STfIESS-VOLUTE AVERAGE EQUIVALENT AXIAL STRESS-VANE 8 f
20 10 1.2 S
= 19700 PSI m
O I
i e
i 0
10 20 30 40 50 60 STRAIN-%
FIGURE 14 STRESS COW ARED TO STRESS-STRAIN CURVE
.