ML20235Z093
| ML20235Z093 | |
| Person / Time | |
|---|---|
| Site: | San Onofre  |
| Issue date: | 02/28/1989 |
| From: | Flanders H, Green D, Watson T WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML13303B064 | List: |
| References | |
| WNEP-8909, WNEP-8909-R, WNEP-8909-R00, NUDOCS 8903150133 | |
| Download: ML20235Z093 (58) | |
Text
_ _ . . . .
WESTINGHOUSE CLASS 3 8
SAN ONOFRE UNITS 2 & 3 FUEL RACK SEISMIC ANALYSIS METHODS AND PARAMETERS NOTh"E The use of the words flaw and/or defect. and failure andfor fracture as may be contained herein is derived directly from the ASME Code and used for that purpose only.
February 1989 Revision 0 Author:
H. E. F anders Advanced Engineering Analys.is Verified by: hdb T. C. Watson Advanced Engineering Analys.is Approved by: i. D5k Io[$T
, J. reen, Man .
van ed Engineering Analysis WESTINGHOUSE ELECTRIC CORPORATION Nuclear Components Division 8301 Scenic Highway Pensacola, FL 32514-7810 8903150133 890310 PDR ADOCK 05000361 P PDC
TADLE OF CONTENTS Section Title Page List of Tables III List of Figures IV Ef fectiye Struetura1 Propertles . . .. ..... ..... . . ..... . .. I 1
]* Properties... ..... .. I 1.1 Cell to Cell Connection [
]* Performance Study...... ..... 3 1.2 Cell to Cell l 1.3 Fuel Rack Base Plate [.
... 4
]*................. ..
1.4 Base Plate / Support Pad [ ]* Properties 6 8
1.5 [ ]* Structural Model Verification. . .. ... . .
Cell Wall Impaet Stif f ness .......--------- 10 2 .
Hydrodynamic Mass . .. .. ... .... .. .... . I2 '
3 ....
Rack to Pool Hydrodynamic Mass. . .... . 12 3.1 3.2 N-S Rack to Pool Wall Hydrodynamic Mass 26
( lI'E...................-..
Fuel Assembly to Cell Hydrodynamic Mass....... 29 3.3 36 4 San Onofre Seismic Resu1ts .. . . .. . .. ......
Rack Absolute Displacements..... .. 36 4.I _.. . .
4.1.1 Absolute Displacement Results... . ... . 36 4.1.2 Absolute Displacement vs [
]*......,....._.. 36 4.1.3 Absolute Displacement vs [.
37
]*_.........-......._--...~.
Rack ReIatiye Displacements... .. ........... .. .. ....... 38 4.2 Rack Displacement Characteristics . _.......-... 38 4.3 5 I l' - - ~~~- "
6 References -. . .-- - ---- -- ~ " """- """ ""~" * "~""
11
TABLE OF TABLES Title Page Table 39 41 San Onofte Rack Displacement Summary .- . .----.--.-- -
4:2 Maximum [ ]* Displacements . . .-- - - -.--- -- .. 40 g-
]* Displacements - - - - ~ ~ ~ ~ - ~ - - 4I 4-3 Maximum [ .
E E
+
k s
i iii
me TABLE OF FIGURES Title Page Figure
}* S t u d y .. ..- ~.~.-.. - --..- .- - - 9 1-1 Ce11 [ .
Ce11 Wa11 impaet Stif f ness 1I 21 . -. .------.-.~.----~~-
N-S Hydrodynamic Mass Modal Study . 31 31 . .. ..---- .
l'
.]*
l la la N S Hydrodynamic Mass .... 32 32 [ ]* Displacement. [
}* N-S Hydrodynamic Mass ... 33 33 [ }* Displacement [:
ja N-S Hydrodynamic Mass . 34 1 34 [ ]* Displacement, [
ja Displacement,[ Lumped]* N S Hydrodynamic Mass . . 35 35 [
}* Displacement Plots . 42 41 Maximum ( . . - . .... ,.. . .
Support Pad Tine History Displacements .. . . . 43 -
4-2 Region 1 Standard Fuel N-S Direction
[~ ]*
44 43 Support Pad Time History Displac,ments -. .-..- ---~~--
Region 1 Standard Fuel N-S Direction
[. l'
.]* S t u d y .. .... . . . 45 4-4 [ ]* Displacement (.
Region i Standard [ }* N S Displacement ! .)* Study . -. . 46 45 [ Region]*1 Standard [- .]* E-W 47 4-6 Region 1 Raek Module Displacement Study .- . - -.-.- -. ...
-]* Displacement Plots - . - . .. 48 4-7 Maximum [
49 48 [ - )* Vs Sliding Motion ..
50 49 Region 1 [' ]* Characteristics . .. ..
- ---- -- --- -. . 52 51 [ ]* Seismic Model iV
~
i 1.0 [ ]* Structural Properties .
The basis of the calculation for the [ .]* structural properties, which represent ~
~
]* in the the [
[ ]* structural model, is presented in thi. section.
1.1 Cell to Cell Connection [ ]* Properties .
The properties of the cell to cell connection in the [ ]* model are [ .
]* These values are the ratio of (
.]* This is calculated as follows.
).. .
~
. b,e The [ ]* moment in the cell is obtained from the structural model by [
The [ ]* rotation of the cell at the cell to cell connection is then needed. [
1 .
1 1
ob
) . ..
4
~
- b,c
\
W 1
The [. ]* of the cell at the cell to cell connection is obtained from the structural model by adding the [ ]* st the relevant point on each of the cells and dividing by the number of cells. The method used to calculate the [
]* is explained in Section 1.3.
The rotational stiffness of the cell to cell connection is as shown below.
- s.<
~
_ b,c An example of this calculation is given below. This example is for the cell to cell connection si 29.4 inches above the rack base plate on the Region 11 rack.
l l
l 2
t
\
J U.
I 1
l l
I l
i L2 Cell to Cell [~ '.]* Performance Study To address the performance of the fuel rack [ .]* structural connections, in lieu of load-deflection tests, a sensitivity study was performed. It is noted that since there is a
[. ]* of welds, the racks are not expected to have missing or inef fective
[ ]* -However, to perform the sensitivity study on the rack's dynamic response, the number of [ ]* connections was conservatively reduced by 10% in the seismic model. This produced a [ ]* change in the primary frequency of the fuel rack.
Since the [ ]* performance study was based upon n ['
,)* the results of the N-S hydrodynamic mass distribution ' study (Section 3.2) will be used as shown in the following calculation to quantify the displacement results of the [- )* performance study. Since the horizontal response spectra is relatively flat in the frequency range of these studies, the change in frequency for small frequency ranges is a reasonable measure of the change in seismic response.
\
3 l
l
Frequency Ratio of Hydrodynamic Mass Study (Section 3.2)
[ ]*
Displacement Ratio of Hydrodynamic Mass Study (Section 3.2)
I ]*
Frequency Ratio of [ ]* Performance Study I ]b Displacement Ratio of [, ]* Performance Study
( )...
Thus the study r. hows that the 10% reduction of welds produces an increase of [ ]* in
.the rack displacement results. [
]*,c 1.3 Fuel Rack Base Plate [ ]*
The overall base plate rotational stiffness for the [ ]* structural model is calculated
]* The
[
rotation of the rack base is calculated by [
]*
- n.e W
4 l
s.
i
~~ lb,c fi.
t then
- n.
- b,c The total moment applied to the rack base is the [-
P An example calculation is given below. This example is for the Region 11 rack. Rather than list the data for all the cells, the data for only two representative cells will be listed
- the corner cell and the cell diagonally ad.incent to the corner.
5
_ ___ _j
~
a UZ d j i
b b I
2 I _
~
~ b,c 1.4 Base Plate / Support Pad [ ]* Properties The nonlinear model uses a combination of rigid beams and vertical spring elements on the ends to represent the [
]* The vertical stiffness of the effective corner pads is calculated by [.
.]* The formula is derived as follows:
6
where e- - rotation of the base L -- distance between support pads n..
where 6 - deflection of support pad F - verticalload on support pad ky - vertical stiffness of support pad .
" b.c where M - moment on the rack base -
s..
An example calculation is shown below. This example calculation is for the Region 11 rack.
7 L _ __u_____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
- *D.,
g )...
1.5 [ ]* Structural Model Verification A finite element model of the effective structural model is compiled and run to obtain
[ ]* These frequencies are compared with those of the structural model to insure that the effective structural model is an adequate dynamic representation of this fuel rack structure. The comparison of the [.' .)*
which is up to [' ]b shows that the first mode frequency matched within [ ]b and the modes up to the [ ]b Thus it was concluded that the effective structural model is an adequate dynamic representation of the fuel rack structure.
An additional study of [ ,)* was performed to show that the effective structural model has the capability to produce the [
.]* The effective model has nodal connectivity at [ .)b points along the length of the cell. [
la The results of this study, shown in Figure 11, are the mode shapes and frequencies of the cells and fuel assemblies. This study shows that the effective structural model (and the nonlinear seismic model which uses the effective structural properties as a basis) has sufficient finite element details to produce the higher cell modes of response associated with the fuel assembly impacting.
8
I e
f 9
i i U
l 4
m 9
1
~
I I -
l
\
j l
2.0 Cell Wall Impact Stiffness The impact stiffness between the fuel assembly and cell is based upon the series combination of the fuel grid impact stiffness and the local stiffness of the cell wall. The impact stiffness of the fuel grid is supplied by the fuel vendor. The stiffness of the cell wall during impact with the fuel assembly grids is based upon [.
]* classical methods in " Theory of Plates and Shells" second edition, by S. P. Timoshenko, [
]* are used to calculate local atiffness in the cell wall.
10
)
6
.i l
i l
FIGURE 2-1. CELL WALL IMPACT STIFFNESS 11
3.0 Hydrodynamic Mass 3.1 Rack to Pool Wall Hydrodynamic Mass The value of hydrodynamic mass for the fuel rack cell is based upon [
]* As shown in the following calculation, the hydrodynamic masses for flow [
.]* The effects of different rack to rack gaps and rack to wall gaps are included.
The pool size, rack sizes, rack to rack gaps, and rack to wall gaps are specified in the following table. l l
l The detailed calculations for the N S direction are presented as a sample calculation of the method which is applicable to both directions.
The equivalent pool and rack dimensions are obtained from the pool layout as shown in the following calculation.
l l
l 4
l l
12
Actual Pool / Rack Dimentions - Full Pool
~ ~
Rack Height La in b ,
Length Pool Wall E-W Axis Law in ;
Length Pool Wall N S Axis LsN in Rack / Wall Flow Gap
- East Wall Gz in Rack / Wall Flow Gap
- West Wall Gw in Rack / Wall Flow Gap' North Wall Gy in Rack / Wall Flow Gap
- South Wall Gs in Floor to Base Plate Height Fo in Typical Cell Width Wc in Number Cells in E-W Directions NCEW Number Cells in N-S Directions N CNs -
Ennivelent Pool /Reck Dimentinn N.S Full Pool Acceleration a BL in b FL in EGx in EGs in SCg in SCw in _
m a
13
i I
i 11 L A
~
The hydrodynamic mass associr.ted with flow through the side channels can be calculated I l'
- _R from continuity V.A. = VrAt where A - frontal area of the solid
.. substituting produces
- .. s
~
14 I
, 2 ,
i
- c j l:,. -j l
Substituting; t
- where a
~
. Hydrodynamic Mass per Side Channel Full Peet b
Blockage Width Flow Length BL~ in Rack Height FL in Side Channel Gap 1 SCt = SC LH in Side Channel Gap 2 SC =.SC, SCs in Side 1 Mass SC, in Mao. Ib Side 2 Mas:
Maob lb Combined Flow Channel Mass i
Mao Ib M
M 15
I
-(
Infinite End Conditions (Case 2 of Ref,1)
! '[ p a,b Hydrodynamic Mass (Front 'or Back)
Wall Effect - '
(Case 13 of Ref.1)
= am M
a
- M M
.[ . ).
Q 16
. _ _ _ _ . _ _ _ _ _ _ _ . - _ . . _ . _ . - _ _ _ _ _ . _ _ _ . _ _ _ _ _ _ _ _ _ - _ _ _ . _ _ _ _ _ _ . _ _ _ _ _ . _ _ _ M
u ..
l
~
- h. Full Pool NS Man Ib [ _]b l k
)*
For[
The gap between the bottom of the rack and the pool floor is relatively small so the The
)*
hydrodynamic mass is calculated (
distance from the top of the rack to the water surface is very large (essentially infinite
]*
for water flow purposes) so the racks are [
Since the water will take the path of least resistance the elevation at which the flow will split, with water above that elevation going over the top of the rack and water below that point going under the rack, will be (-
.)* This elevation was found to be [.
.)*A
.]* of the racks The hydrodynamic mass for [
- will be calcolated [
.)*
The rack height for flow ( )*is:
I 16 The rack height for flow [ }* is:
I 16 17
- t. .._.;.
1
.h
-.. I' Priam Effect (Ini'Inite Medium)
' (Case 3 of Ref.1)-
[; ja,b 1'
[ )b 8,b
(
up 8,b 4
i,
.I L
9 18 I
1 - - - - - - _ ._ __ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
i End Effect (Infini;c Medium)
(Case 2 of Ref.1)
[ ja b
- a,b M
WWul 8,b 6
emm '
W e
19
l d N' ,_,j , ..
I: s . ,
I l'
Wall Effect (Case 13 of Ref.' 1)
.. s E
8,b m
M 8,b i:
M M
w W
a,b M
[
Pb l
20 i
1
a f
ja, L~
The hydrodynamic mast associated with ( )* can be calculated on the basis of the kinetic energy of the fluid as shown in Reference 2. The procedure is the same as for the [ }* mass calculation.
~
~ a,b m
.- I a.D l l
l l
i 21
4
~1 q .
/ Infinite End Canditions r.
- (Case 2'of Ref.1) .
- [- ja,b .
8,b 1
~
enum N
'V', 8,b
~ :
-l l
22 4
(
l
.1 fi 1
H.
- - 4, b .
Wall Effect
^
l-(Case 13 of, Ref.' 1) _
[ )*,b -
[.. _
1,b ennu '
M i..
.i 8,b i
e M'
meuru j..b
[
23
(.:: : - '
F J.
.j.
j i
b '
s Full Pool N-S -
Mavs Ib ~ [ lb l'
Full Pool N S.
]* May Ib ( lb
[-
I lE Full Pool NS
- ng M
- a b.
Ma Ib Mg Ib Ms- Ib Imp
~24
I Full Pool NS a
b N
Mit Ib
~
Mas Ib Maa Ib I
- It is noted that the actual number of storage locations in the pool is [ jb rather than
}b However, the value of [ ]b is based on the idealized pool configuration of
[
[ }b storage locations in the east west direction and [ l storage locations in the b
north south direction which is the basis for the calculated total pool hydrodynamic mass.
[
.]*
25
t 4
b 3.2 N-S Rack to Pool Wall Hydrodynamic Mass [ 3]*
The fuel rack and spent fuel pool configuration in the N-S direction is [
.]b The gaps between the racks and pool wall on the
- t. North and South ends are approximately~ equal, and the gaps between the rack modules are approximately equal. This layout configuration is such that the response of the racks can be obtained from a model which uses hydrodynamic mass thet ['
]* The following paragraphs present discussions on hydrodynamic mass distribution, the hydrodynamic mass [ ,]* and a comparison of fuel rack seismic results of both methods to show that the row of [
fuel racks in the N-S direction can be adequately modeled with two fuel racks using the
..7 ,
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i-(
l k
I
,)s,b f
i ,I
,f
'; e le.;
. 4 s.
l $b bl I
--, .; ' 26
, r,s
![
- 4
., .* , j '
i .
ct,b '
h M
i '
a l
l 1
I t 9
27
S ,
as 9
is NS EW '
Direction Direction -
D
[ }m Hydrodynamic Mnen Results Frequency of Primary R.ack Mode (N-S) f Hz
]* Displacement 6mi in.
Msximum Rack [ c
]* Displacement 6,i in.
Maximum Rack [
[ }* Hydrodynamic Mats Results Frequency of Primary Rack Mode (N 5) fs Hz
]* Displacement one in.
Maximum Rack [
)* Displacement 6, in.
. Maximum Rack [
[ l'
. . Rg -
j.
~
. . RA ja
. Rr ~
- ~~
4 am b a
k e i
l 28 9
3.3 Fuel Assembly to Cell Hydrodynamic Mass In addition to the hydrodynamic mass between the cell and pool wall, there is a hydrodynamic mass effect between the fuel assembly and the cell wall. [
)* Using [ }*the ;
)* will be calculated as shown below.
l' hydrodynamic mass due [
15
[
m *$
d puses 29 a
r=
Cell Height H in ~b Cell Width, ID W in Fuel Bundle '
Rod / Rod Pitch P in Rod OD D in Fuel Asseeably Length _g L in
} ~
Lg in BW in A, in8 Ag in8 ,
6 Ma Ib 3
Mg Ib M lb Mgg Ib .
Mg lb Man Ib _ _
M M
l l
' 1 l 30 -
2
Figure 3-1 N-S }tdrodyrmic Moss liodal Sttdy _
q l
1W 31
4 -
I 4
9 k*
l l
l l
l r
32 ,
t 1
A is %
/
/
4 I
J G
d l
l l
l l
33 g , .
E ,
G I i
.e G
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34
.x i .
57 I I
I 4
35 \
x s
e ,
a o
j- 4.0 San Onofre Seismic Results A summary of the seismic displacement results from the bounding cases of the seismic analysis is presented i:. Table 4-1. These bounding cases are the combinations of parameters (such as fluid coupling, coefficient of friction, structural characteristics of Region 1 and Region 2, and fuel loading which vary within the spent fuel pool) that produce the bounding values of fuel rack responses.
4.1 Rack Absolute Displacements 4.1.1 Absolute Displacement Results The maximum absolute displacements for both a Region 1 rack module and a Region 2 rack module are listed in Table 4-2. [:
]* Additional absolute displacement results are provided in Figure 4-1 which graphically presents the rack absolute displacements throughout the [ .]* It should be noted that the plots reflect the maximum absolute values of the rack displacements [
.]a,b 4.1.2 Absolute Displacement Vs. [ }*
Figures 4 4 and 4-5 show the results of a study to evaluate the effects of the [
.}* The study was performed for the Region
}a,b It can be I racks and included the use of [
seen from a review of the data that rack displacements for the mean value [.
}.,b The following I
36 "D
calculation shows that the displacements [
lb
~
a,b L .-
4.1.3 Absolute Displacement Vs. ( l' Figure 4-6 shows the results of a study to evaluate the absolute displacement of a single rack module as a function of [. ' ]* This study was performed to obtain the
- ~ ]* which will produce the combination of racks to be used in the [
maximum relative displacement between racks. The results of rack displacement for (.
.) *.
1 37
s 7
4.2 Rack Relative Dispiscements
[
1sb Additional displacement results are provided i Figure 4-7 which graphically presents the rack relative and absolute displacements L throughout the [ ]* It should be noted that the plots reflect the maximum absolute values of the rack displacements during the [
l' 4.3 Rack Displacement Characteristics t Figures 4-8 and 4-9 provide additional plots of rack module displacement data which .
illustrate the difference in rack behavior between [ .
4 7
3 14 M
IA 38
d
~
p.. .
Y
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e i .
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u w
.N D .
=
k 8 . .
/
m l
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I "
I 39
,4 -
TABLE 4-2 4
MAXIMUM [ [ DISPLACEMENTS UNITS (IN.)
. ion Region 1 Region 2 ficient Standard Fuel Standard Fuel 2xStandard Fuel
[ ]"
N-S E-W N-S E-W N-S E-W
_b 4
304 40
TABLE 4-3 a
MAXIMUM -
[ DISPLACEMENTS UNITS (IN.)
! Region i Renion 2 Piction I Standard Fuel Standard Fuel 2xStandard Fuel sefficient i ]" '
- N-S l E-W N-S I E-W N-S E-W \
I
_bj .
_t ;
_ Q.
s' AEA-88-304 41 .
W
\ A e
-6 l l s F-O J
D.
H Z
k LU a
. d I i i 1 X
I I
42
FIGURE 4-2 5UPPORT PAD TIME HISTORY DISPLACEMENTS REGION 1 STANDARD FUEL N-5 DIRECTION A,b
]
~
.{
\
e N
l l
43 ,
k
^
FIGURE 4-3 SUPPORT PAD TIME HISTORY DISPLACEMENTS REGIO _N 1 STANDARD FUEL N-5 DIRECTION
_w WE e
/
mamm 44 s
t O
d r I
e i e
}
(PI u ..
ll d i
M e.
M llm-10 1
s U
o a
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45 .-
I
4 D_
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B 8 y n
I t
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46
~
FIGURE 4-6 ..
REGION I RACK MODULE DISPLACEMENT STUDY ~
b C VARIOUS FUEL LOACING CONDITIONSk,b
]
[
a.
47
4 d
1 m
I-O
._J O_
l--
Z LU Z
UJ U
C
__J O_
W w
W I I t -
e 1 I I
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C Z .
48 e'
s
e FIGURE 4-8
_ _ a
. VS SLIDING MOTION e
4
(
(d ammma 49
f D.
c I
I (n b U
b W
~
LU F-U E
tr E
I
-,0 -
F-Z LU I
LU U
=
E
- _J
! Q.
3 W e -
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1 I t l l .
I , ..
1 .
1 50 s-
er f
5.0 I
=
m 0
51
4 ENE (PLN4 VIEW)
__ a,b 52
.s . ..
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6.0 References . ..
p ..
' ~
7-
1.
R. J, Fritz, "The Effects of Liquids on the Dynamic Motions of Immersed Solids", '
Journal of Engineering for Industry,Trans.of the ASME, February 1972, pp 167-172.
- 2. D. F. DeSanto, "Added Mass and Hydrodynamic Damping of Perforated Plates Vibrating in Water", Journal of Pressure Vessel Technology, Trans. of the ASME) "
May 1981, Vol.103, pp 175-182.
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