DCL-87-072, Applicant Exhibit A-6,consisting of Forwarding Nonproprietary Version of Addl Info on Rack-to Rack Interactions,

Applicant Exhibit A-6,consisting of Forwarding Nonproprietary Version of Addl Info on Rack-to Rack Interactions,

ML20237J253
Person / Time
Site:	Diablo Canyon
Issue date:	06/17/1987
From:	Shiffer J PACIFIC GAS & ELECTRIC CO.
To:	NRC OFFICE OF INFORMATION RESOURCES MANAGEMENT (IRM)
References
DCL-87-072, DCL-87-72, OLA-A-006, OLA-A-6, NUDOCS 8709030535
Download: ML20237J253 (111)

Text

b$ ~ 2 ? 3~

6/./ 7/f 7 PGandE $ h it No. 6

/} - b O FACIFIC gas AND E LE C T RIC 97 mc 26 p 7 79 C O M PANY

.r 9 384/3 l 77 BEALE STREET . S AN FR ANCISCO. CALIFORNI A 94106 .[(4.16)781 4211

• TW X 910 3 72 6 5 8 7 j

April 9, 1987

- . o. . ,4g .. .

seWCLEAA Powie GtmERAftON PGandE Letter No.: DCL-87-072 Nuclear Regulatory Commission ATTN: Document Control Desk Hashington D.C. 20555 Re: Docket No. 50-275, OL-DPR-80 Docket No. 50-323, OL-DPR-82 Diablo Canyon Units 1 and 2 Additional Information on Rack-to-Rack Interactions - Nonproprietary Report Submittal Gentlemen:

On April 7, 1987, PGandE submitted a proprietary report entitled " Additional Information on Rack-to-Rack Interactions" (" Report").

In the interest of providing the Report for Staff review in a timely manner, O only the proprietary version of the Report was submitted on April 7, 1987. In accordance with 10 CFR 2.790, this letter provides a nonproprietary version of the Report. Enclosure 1 includes the nonproprietary version of the Report.

Enclosure 2 includes a copy of the Report highlighting those portions of the text, tables, and figures which are considered proprietary. These enclosures are provided for Staff review of PGandE's application for withholding from public disclosure as discussed in the April 7, letter.

Kindly acknowledge receipt of this material on the enclosed copy of this letter and return it in the enclosed addressed envelope.

Sincerely,'

Enclosures cc: L. J. Chandler' J. B. Martin M. M. Hendonca P. P. Narbut B. Norton H. E. Schierling C. Trammell O cc w/o Enclosure 2:

CPUC 87o9o30535 e70617

$DR ADOCK 05000275 PDR Diablo Distribution Reracking Service List 1374S/0049K/MLM/1998

7 I

NUCLEAR REGULATORY COMESSION o,,,,,,, ,,,, ,,, g, 4 g Q .

Docket N 5~o-b $7- OL4 In the matter of b t6 (om m.g }

\ l

1. " IDENTiflID O APphcant Intervenor

/- REClWED y97yyy Cont's 0!rr Contractor gg7 &~{G_ Q 0*" mm Reporter WYTH  % yn (

\

• \

i f

I i

- - - - - - _ - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -- -- -- --- - - - - _ a

g DIABLO CANYON POWER PLANT UNITS 1 AND 2 ADDITIONAL INFORMATION ON RACK-TO-RACK INTERACTIONS (Nonproprietary Version)

O Pacific Gas and Electric Company April 7, 1987 O 1 1374S/0049K

TABLE OF CONTENTS i

1. INTRODUCTION

2. BACKGROUND OF DESIGN BASIS. ANALYSES

3. DESCRIPTION OF TWO-DIMENSIONAL OF PARAMETRIC STUDIES 3.1 Single-Rack Model 3.2 Multi-rack Model 3.3 Cases Studied

4. ANALYTICAL METHODOLOGY

5. HYDRODYNAMIC COUPLING I i 5.1 Development of External Coupling Terms 5.2 Parametric Studies for Equivalent Lateral Gap (ho) 5.3 Effects of Vertical Flow 5.4 Modeling of Fuel Assemblies 6 RESULTS OF ANALYSES 6.1 Single Rack 6.2 Multi-rack Interactions i 6.2.1 Interior Rack Array 6.2.2 Exterior Rack Array 6.2.3 Fabrication and Installation Tolerances' l

7. CONCLUSIONS l

8. REFERENCES l

l l

'l O ,

1374S/0049K j

- - _ _ - - _ . - _ . - _ = - _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ - - . _ - -

-_ q l

PGandE Letter No.: DCL-87-072 O -

ENCLOSURE 1 i

ADDITIONAL INFORMATION ON RACK-TO-RACK INTERACTIONS 1

(Nonproprietary Version)- l I

/

O 4 1

1 1

1 i

O 1374S/0049K l \

' j

1. INTRODUCTION In response to NRC Staff requests, PGandE submitted additional information.on spent fuel rack interaction parametric studies on February 6, 1987 (PGandE Letter No. DCL-87-022). On February 18, 1987, the Staff and PGandE met to discuss the parametric studies.- Following the meeting, the Staff requested additional information, which necessitated further investigations'(NRC Letter dated February 26,' 1987). These further parametric studies and their results were reviewed by the Staff on March 26, 1987. This report documents the description and results of the additional parametric studies that were presented to the Staff at the March 26 technical review meeting and alto responds to the Staff's information requests dated February 11 and 26, 1987.

I In response to these Staff requests, rocking, a lower coefficient of friction, fluid coupling effects, and variations in fabrication and installation tolerances were incorporated in.the parametric studies. As specified by the Staff, resultant fuel-to-rack, rack-to-rack, and rack-to-wall forces were compared for the single-rack and multi-rack models. Time-history data have been provided in this report.

l O

1374S/0049K l

2. BACKGROUND OF DESIGN BASIS ANALYSIS The analytical methodology used for obtaining rack interaction impact loads is described in the Reracking Report submitted by PGandE on September 19, 1985 (Reference 1). In generai, the methodology includes several conservative assumptions applied to a single rack model to obtain conservative impact loads which were used as the basis for rack-qualification. Some of these conservative assumptions are listed below:

a s

e Each adjacent' rack module was assumed to move in a manner equal and opposite (out .ijf phase) to the rack module being analyzed. This assumption was incorporated in the model by utilizing a reference-impact plane midway between adjacent racks.

• .The fluid coupling coefficients were based on the conservative assumption that adjacent rows of racks are an infinite distance away (the distance is measured perpendicular to the horizontti ground motion). This neglects the cross-coupling effect of the adjacent rows of racks and results in higher displacements and impact forces.

e The impact spring coefficients were set at a value significantly higher (oyer 10 times) than the calculated values to produce conservative impact forces.

O 1374S/0049K - 2'-

L

g

• All hydrodynamic coupling calculations were conservatively based on the initial gap. Parametric studies showed that progressive time-dependent vari: tion of gaps (nonlinear coupling), if considered, would further reduce rack responses.

The friction coefficients used were 0.2 and 0.8.

The racks and fuel were analyzed using an eight degree-of-freedom system to model their three-dimensional behavior during an earthquake.

It was PGandE's judgment that the above conservatism, when used in a single-rack analysis, provide an adequate design basis to accommodate -

multi-rack impact effects.

O The results of PGandE's design basis analysis, as reported in the Reracking Report, demonstrate conservative design margins between predicted and allowable loads.

Tables 2-1 and 2-2 summarize the maximum impact loads and the qualification basis of the racks, as reported in the Reracking Report, the Seismic Analysis Report (Reference 2), and other supporting documentation.

~

i O

1374S/0049K _ - _ _ - - - - _ _ _ _

3. DESCRIPTION OF THO-DIMENSIONAL PARAMETRIC STUDIES The objective of the parametric studies repo/ted herein is to show quantitatively that PGandE's methodology for tbtaining the design basis impact loads, reported in the Reracking Report, is conservative. These studies were performed by the same group of individuals who performed the original analysis. Additionally, all work was reviewed and accepted by PGandE to assure the accuracy and completeness of the evaluations.

3.1 SINGLE-RACK HODEL The single-rack model (Figure 3-1) was developed for a 10 x 10 rack .

module fully loaded with fuel. Consistent with the design basis model, 40 percent of the fuel mass was modeled as one lumped mass (Mass A) located near the top of the rack to simulate the rattling effect of the fuel assemblies. The balance of the fuel mass was located at the base of the rack. The mass of the rack was lumped at the centroid of the rack.

The rattling mass was assigned a transnational degree-of-freedom; the rack centroid was represented by three degrees-of-freedom (transnational, vertical, and rocking).

O 1374S/0049K __ __-_

Two cases were studied using the single rack-model. In the fir'st case, all model parameters were set at the same conservative values as those reported in the Reracking Report. This case was used to develop benchmark loads for comparison'with other cases, since it represented PGandE's conservative analysis input for a two-dimens'enal model.

In the second case the model parameters were revised to represent realistic input values as follows:

In calculating the fluid coupling coefficient, the presence of adjacent rows of racks was accounted for by considering them as vertical planes located at a lateral distance 7.5 inches on either.

side of the rack (versu~s the nominal 2.25-inch gap between two adjacent arrays). Analytical studies have shown that use of a 7.5-inch gap is conservative (see Section 5 of this report).

Both the rattling springs and the exterior impact springs were repre;ented by their calculated values scaled up (approximately 1-1/2 times) to account for strain rate and material variability.

( ,

3.2 HULTI-RACK H0 DEL Two rack arrays were studied. These arrays are identified as Sections AA  ;

i and BB in Figure 3-2. The array identified by Section AA was selects:1 to  ;

study the behavior of a typical interior row, whereas the second array (Section BB) was selected to study the behavior of a row of racks with a gap larger than 7.5 inches, which occurs along the periphery of the spent fuel pool.

1374S/0049K 1

, Figure 3-3 shows the two-dimensional dynamic model used in the analysis of the racks in Section AA. A similar model was developed for j SectionBB.[

] The parameters for the model were developed in a manner similar to that used for the single-rack model, except that more realistic assumptions were made tcs :ompute the fluid coupling coefficients and spring constants, as l follows:

1  :

In calculating the fluid crapling coefficients for Saction AA, the presence of adjacent rows of racks was accounted for b.y considering them as vertical planes located at a lateral distance of 7.5 inches I on either side of the rack array (versus the nominal 2.25-inch gap O e* as c * < c' o i ii>> ^ i>*ic i *#ei >* a ****

the 7.5-inch gap (h0) conservatively estimates the coupling effects of adjacent rack arrays (see Section S of this report).

For Section BB, fluid coupling coefficients were developed by conservatively assuming that the adj? cent wall is approximately 37 inches away from all racks in the array. This assumption of uniform channel width was made to simplify the analy31s, and it is conservative, as only one out of four racks is approximately 37 inches away from the wall and the other three are much closer to the wall.

i O

4 1374S/0049K '

L__ _ --_--- - .- - .- -

I

l Both the rattling springs and the exterior impact springs were represen'.ed by their calculated values scaled ep (approximately 1-1/2 times) to accour.t for strain rate and material variability.

The Hosgri east-west and vertical ground motions were applied simultaneously to the model. The east-west horizontal time-histories were applied since they represent the most conservative horizontal seismic input.

e i

The key model parameters are summarized in Tables 3-1 and 3-2.

3.3 CASES STUDIED .

Table 3-3 summarizes the description and objective of each ca n studied.

In general, these cases were selected to study the following:

l Conservatism in PGandE's design basis methodology using a l two-dimensional, single-rack model l

Comparison of multi-rack response with the single-rack response determined using PGandE's design basis methodology l

• Effects of full and empty vacks (11 assemblies) l l

Effectsoflargerlateralgaps[ ]on rack response l l

• Effects of manufacturing tolerances on rack response i

I 1374S/0049K i

4. ANALYTICAL METHODOLOGY v

The analytical methodology is similar to the one described by Levy and Hilkinson, (Reference 3). In general, the analysis includes the following steps:

Sten 1: The system kinetic energy was ce.lculated considering the combined effects of the following:

1 O

• 1 1

i Sten L After the system kinetic energy was developed, [

] equation of motion was used to solve for the fluid reaction force:

l j

l 1

i i

1374S/0049K  ;

l

.._-_---__--._--.m

O -

1 i

O Sten 3:

The equations of motion developed in Step 2 were solved using the computer code DYNAHIS, which employs a nonlinear, time-history analysis using a central difference integration i technique. Additional discussions of DYNAHIS were provided to the NRC during the review of the Reracking Report.

i 1

1374S/0049K g

5.- HYDRODYNAMIC COUPLING

, O-5.1 DEVELOPMENT OF EXTERNAL COUPLING.TEPMS 1

5 4 O

1 l

l l

O 13745/0049K - 10 -

.. u.

l 4

O -

l .

O

~

1 I

i 1

5.2 PARAMETRIC STUDIES FOR EQUIVALENT LATERAL GAP (h I 0

i i

I l

.1 I

O  !

l 1

-)

.1374$/0049K ,,

("%

V 1

e 1

I 5.3 EFFECTS OF VERTICAL FLOH J

j N

1 l

1

-l 13745/0049K -j2-  ;

a

O i

/

x /

n V

i j

1 1374S/oo49g ' ~ - - ~ - - - _ _ _ _ _ _

j

~

.l l

5.4 MODELING OF FUEL ASSEMBLIES I

The PWR fuel assemblies used in the Diablo Canyon Unit I and 2 reactors contain 264 fuel rods in a 17 x 17 array. The fuel. rods are 0.374 inches in diameter arranged in a square lattice with a pitch of 0.496 inches.

Therefore, the gap between 'the adjacent fuel rods is less than 1/8 inch (0.122 inches nominal). The cross-sectional dimension of the rod array is 8.404 inches square. Since the storage cell opening cross-sectional.

dimension is 8.85 inches, the net lateral spacing between the fuel assembly and the storage cell is 0.446 inches. The lateral movement of j

the fuel assembly in the storage cell causes the water to flow past the l assembly. Since the flow between these narrow channels formed by the array of rods involves repeated changes in the flow cross-section of width from 0.122 inches to 0.496 inches - a fourfold change in transverse flow area - the hydraulic pressure losses through these channels are an order of magnitude greater than what the fluid encounters flowing through the assembly / cell wall gap. The hydraulic pressure loss due to flow l

j through these narrow convergent / divergent channels is an important mechanism for energy loss from the vibrating rack system. However, in the conservative approach used to model fluid coupling, no such flow, and therefore, no such loss occurs; all the fluid is assumed to flow in the assembly / cell wall space.

i O  !

! l l

1374S/0049K a

( 6. RESULTS OF ANALYSES

.( -

6.1 SINGLE RACK Table 6-) summarizes the maximum impact loads for parametric Cases 1 l

and 2.

l l

l s

.O 1

Therefore, the results of Case 1 show that PGandE's design basis methodology is l

conservative. ,

Figures 6-1 through 6-4 provide time-history plots of the rack translation and wall impact forces as obtained fNm Case 1.

O l

l

, 1374S/0049K l

6.2 MULTI-RACK INTERACTIONS 6.2.1 Interior Rack Array Table 6-2 thows the results of the multi-rack analyses. Cases 3 and 4 represent analyses of the interior array identified by Section AA. These j cases were chosen to predict tack behavior under different loading j configurations. Case 3 represents an array of four fully loaded racks, and Case 4 represents three loaded racks and one empty rack (11 fuel l <

assemblies). The results show that for both cases the fuel-to-rack and rack-to-rack impact loads are enveloped by Case 1, which reflects the  ;

results based on the conservative design methodology employed by PGandE, Although rack-to-wall loads based on Csses 3 and 4 are greater than the corresponding loads obtained from Case 1, their magnitude is enveloped by the rack-to-rack load resulting from Case 1. l Figures 6-5 through 6-17 show typical time-history plots of rack translation and wall impact forces for Case 3.

l l

+

O  ;

i I

13745/0049K  !

l p 6.2.2 Exterior Rack Arrav V

1 Section BB was chosen for analysis to quantify the effects on rack l behavior in the few cases where scacing between the rack and the wall exceeds 7.5 inches.

.I c

The results of the analysis (Table 6-2) show that the fuel-to-rack and rack-to-rack impact forces are enveloped by Case 1.

O l

l l

6.2.3 Fabrication and Installation Tolerances Table 6-3 provides results of the multi-rack analyses which postulated variable gaps resulting from fabrication and installation tolerances.

The results show that the fuel-to-rack and rack-to-rack impact forces are )

enveloped by the corresponding loads obtained from Case 1, and that rack behavior is not sensitive to typical fabrication tolerances.

b'

/~

i

\

1 j 13745/0049K l

___-_ a

R g 7. CONCLUSIONS

\g)

In conclusion, the two-dimensional parametric studies demonstrate that the use of conservative springs and fluid coupling inputs in the j Reracking Report yield conservative rack and fuel assembly impact loads.

These studies provide a high level of confidence that the design basis model has predicted conservative rack qualification loads, which ensures compliance with all design criteria. Table 7-1 summarizes these loads.  ;

l .I l

i

! i i

I l

l l

a 1 f

I l

O i

1374S/0049K ,

_________________ _ D

8. REFERENCES 1

i 1. Reracking of Spent Fuel Pools, Diablo Canyon Units 1 and 2 Enclosure to PGandE Letter No. DCL-85-306, dated September 19, 1985.

2. Seismic ~ Analysis Report, " Seismic Analysis of High Density Fuel Racks for Pacific' Gas and Electric for Diablo Canyon Nuclear Power Station," Rev. 3, September 3, 1986, A. Soler, TM #779. '

3.- Levy, S., and Milkinson, J.P.D., The Comnonent Element Method in Dynamics with Annlications to Earthauake and Vehicle Enaineerino, McGraw-Hill, New York, 1976. .

4. Lamb, H., Hydroovnamics, Dover Publications, New Ycrk,1945.

5. Fritz, R. J., "The Effects of Liquids on the Dynamic Motions of Immersed Solids," Journal of Enuineerina for Industrv, Trans. of the ASME, February 1972, pp. 167-172.

O 1374S/0049K - _ _

]

I TABLE 2-1

'O .

Results of Desian Basis Analysis (Single Rack, 8 Degrees-of-Freedom)  :

Imoact Loads (Kies)(A)

Friction Frf Frr Frw l

f&ef fici ent _

p = 0.8 249 88 39(b) p = 0.2 242 105(b) 63(c) 1 O

l I

l l

a. Frf is the rack-to-fuel impact load; Frr is the rar.k-to-rack impact load; Frw is the rack-to-wall impact load. j 3

b. The maximum load resulted from an empty rack (11 fuel assemblies).

c. The value applies to rack "H" only.

)

1374S/0049K l

'l l

TABLE 2-2 Qualification Basis for Racks

.(Reracking Report)

Imoact location Allowable Lead (Kios)(a)

Fuel-to-rack 883 Rack-to-rack 175(b) s l Rack-to-wall 175 for rack (b)

) 80 for wall (c)

C\

U l

1

a. The allowable loads refer to a 10 x 11 rack. 1 i

b. The loads correspond to the allowables per spring. Both the girdle bars and baseplate are represented by two springs each.  ;

c. l The walls have been shown to be qua11 fled for substantially larger j

(=200 kips) Ioads. J

~

O l i

1374S/0049K E --_------ -- _-- -- --_------_ - j

.j

~

TABLE 3-1 L

Kev Model Parameters  !

(Single-rack Model)  !

A. SPRING CONSTANTS

1. Fuel-to-Rack

a. Springs 3, 4 l

2. Rack-to-Rack / Rack-to-Wall

a. Girdle bars: ,

Springs I and 2

b. Baseplate:

Springs 5 and 6 O

B. fi&P_1

1. Rack-to-Rack

2. Rack-to-Wall l

3. Fuel Assemblies to Cells  ;

I i

l l

O l 1374S/0049K E__--._______-___-=

- . _ _ _ _ _ _ _ _.-- j

TABLE 3-2 Kev Model Parameters (Multi-rack Model)

A. SPRING CONSTANTS

1. Fuel-to-Rack

2. Rack-to-Rack Girdle bars Baseplate

3. Rack-tf>-Hall Girdle bars Baseplate

8. fa&ES -

1. Rack-to-Rack

2. Rack-to-Mail

3. Fuel Assemblies to Cells l

l l

O 4

l 1374S/0049K i

l l

ll ll i

e e v

i t

c e

i-b O

s v d e

i d

u m3 t n S

i o

s t e n .

s i a r w 3 E

C s

c f e eLB A

T i

t o

n o

D 6 2

p i

r c

s e

D m

o d

e e

r F

f-o s

e e

r g

e D .

l -

e -

d o -

M -

e R

f o 0 N 0 e 1 2 3 4 5 s 6 '

a C

N t ll

"ASLE 9- l 6'JMMAJEf CF PARAMETRIC 6700156 fcR Equh/AIEidT LATERAL GA@

DESCRIPTION LATERAL GAP hASES ,

l l

{

l l

l I ) l l

l l

6 5S/0_049L

<______13_

TABLE 6-1 Summary of Sinale Rack Results Imoact Loads (Kios)(a)

Qig Description Frf Frr Fwr 1

2 O

a. Frf is the maximum rack-to-fuel impact load as represented by springs 3 and 4 (Figure 3-1); Frr is the maximum rack-to-rack impact load as represented by springs 2 and 6; Frw is the maximum rack-to-wall impact load as represented by springs 1 and S.

O 1374S/0049K TABLE 6-2 Summary of Multi-rack Results Analysis Imoact Loads (Kios)(a) rr Fm CAlt Description 3

1 4

O >

I i

l i

a. Frf is the maximum rack-to-fuel impact load as represented by springs 3 and 4 (Figure 3-2); Frr is the maximum rack-to-rack impact load as represented by' springs 2 and 6; Frw is the maximum rack-to-wall impact load as represented by springs I and 5. l

(

1374S/0049K .

L___________________________________--_________________

TABLE 6-3 O)

Summarv of Multirack Results (Effect of Tolerances)

Imoact Leads (Kios)(R)

Description Cases Frf Irr Frw i

6 i

/

1 7

O

a. Frf is the maximum rack-to-fuel impact load as represented by springs 3 and 4 (Figure 3-2); Frr is the maximum rack-to-rack impact load as represented by springs 2 and 6; Frw is the maximum rack-to-wall impact load as represented by springs 1 and 5.

b.

c.

O 1374S/0049K __--____ ____ _ N

eq TABLE 7-1 Q -

MAXIHUM LOADS Rack Impact Loads -

Quat Rack Model(a) Assumotion(b) g (c) g (d) {

Licensing Basis SR C l 249 105 1 SR C 2 SR R

\

3 , MR R 4 MR R 5 MR R l

6 MR R

~

7 MR R Allowables 883(') 175(r) 200(w) 1 l

l l'

(a) SR - Single Rack Analysis, MR - Multiple Rack Analysis l i

(b) C - Conservative Assumptions Used in Analysis (high spring constants and large hydrodynamic gaps) l i

R - Realistic' Assumptions Used in Analysis i (c) Maximum fuel impact load (rack-to-fus1), all loads in kips 1 (d) Maximum of rack-to-rack or rack-to-wall loads, all loads in kips (e) Allowabir, for 10 X 11 rack; Allowable for 10 X 10 rack is 803; (r) - rack f and (w) - wall O

1374S/0049K i

)

q l

l e

E.,

~

W .

a O I e.

s a

5 m

I i N l N  ;

b O .

l 1365S/0049K i - - - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _. _

,i

O -

10'- O"

~ '

. 15 R k%, g l

l l~

ur

" h j.

!",, _ g =o .p.

. Ret @Typr" , e e nie - 12 g "en I8I Op *p n i r n

4 Q

8x2 + 4k2 eD" O .I.

~

Plus 3 Region I -

Misc.J HO, *K" r 10 s . 1r 1

Cells 9x6 10 x S B g .

"G" "C" *D' 2 'A 2 -

=

8 x10 10 x10 9 x 10 Re(son i lI " '

A

• A 10 x 10 -

t.

k E "F* *J*

• D l*

• Ag*

fg'.' 8x9 los9t6 9 x 10 Region i oj J-iO a 10 4g

. 1 wrs

ERG iemag e

u-ii E U Eto' p o kkkhs@hkSM

/weg rd ,

yp y a h 4~

4 5 }

2'"

g94 i o. . . . ,.

+ i-O = 3s' .

F1gisM9K 3

3 _

O -

w 5

E 5

I 5

E E

a C; -

W

.L O E J

E E

.L N

m i

m 6

u. l O

13655/0049K -> 32 - l 1

_j

l I

O l

1

-l O

F i g. 5-1 T yp i ca l Four RocP. Arroy Used for Hydrodynamic Coupling O  :

1 1365S/0049K _ 33 ,

r O .

a O

1 1

i I

a YbbOMM gg -

I 1365S/0049K x

)

i s.

I J

Fig. 5-3 D istr ibut ion of F low Between i Fue l Assemb l ies and Ce l ls i See F o g b 2 f or uttec)

O l

1365S/0049K f

-- -- _o

O .

G 6J

.s

- . g <-

5 a

O 8

?

E e

.at e

aw Y

e ll:

O 1365S/0049K _ _ _ _ - _ _ _ _ - _ _ _ -

0 e

s 4

W w

0 w

e

.oe dm0 W

eme e

C W

ne I*

at u

a LJ ar.

N W

6m 3

he a

b i

i i

l I

i l

1 13655/0049K _ 37 i

- 1 1

l 1

l A

U l

i s s i B G

e E $

u q i

.G U j u

O lhe = e a

M WO pd U

W M

O ua s l

Y u

4 K

m 4

tC

(

G k l c

80 .

m '

$Rs I

O 1365S/0049K _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _

e e

O .

5 5 4

W 9

e 3

u Os

.i O u U

e

' 8u 5

N O

u I' s g

U

.a h

be 3

te we b

O 1365S/0049K -

39 - i

g u k=ammal R

GW-e W'

W k

O

+

w C

O

=

U

- S ese B

C S

w b

.he U e t 9

E e

e G.

h 3

he w

Ide d

13655/0049K W

4

' I 8 l

I

• l 1

i e M

W8 i e

a u

O se,n C

.Oe M

S m

E E

5 he b

.ht u

gt i CK e

W be D

80

.e b

,I i

13655/0049K

'i

-i i

. i e

O LJ M i i W

e S

(J b

C w

C 0

e

'M S

s=e

e. 1 C

S b

N

.at uwa e

E N

l

' W b

3 40 m

b i

l 1

1365S/0049K '

6 A*

i m

. W' 5

5 w

0 em C

C

-e M

W me O

E 5

w N

.at UG e

E e

t 40 G  !

w <

I 3

hD  !

w f l

. 1 l

i i

\

l I

i 13655/0049K 4AW*

O I

w M

W e

a u

l N

g, ,

O ,

sue S

. I

~. ,

l a

e

=

m a

E O

1 1365S/0049K  !

I

t . .

I a e n

O.

u O

w u

u o

l u

u e

n.

a m

em4 M

=

s oi i M

N

.u l

.a, i

w w

3

.=.e w

i 1

1 3

1 1365S/0049K l l

1

-____--_-_-_____ _ A

ie n.- .

e I l 4

l l 6

f*)

G vi 4

kJ.

b O

lo-G 6

6 U

e i Pa8 W

3 O

e,n and U

4 s 1 ese esub i l

G b

- j h

l k

i

. \

1365S/0049K - 46.-

ii i i l

O e

l t i M

W e

5  ;

b I

O >

E e

b

.as M

4 K

N as up i U

O ' i l

1355S/0049K -

l

I I

1 I

i i

• o a E O

G en

+ 4 4.J L

C w

e i

.E.

Y 4

m Y

C 4

b

>=

Js 4.4 4

E f9 m

I ga t I

8,  !

I I

l 1

l 1365S/0049K .

. . . . . . . . . . . . . . . . iti O

O i

U n

a u

$ r ,:

O i; e

.ht e

=

e.m U

.E 5.

2 13655/0049K _ 49 _

q.

E u> .

s O

n W

m 4

LJ b

O w

C O

u 4

a m W

C

.w U

9 m

m 4

4Jl3 y U u  ;

D i CD w

b O

1 1365S/0049K _ - - _ _ - - _ _ _ _ - _ _ _ _ -

WP

+

6 O

r,

+.

s m

e. -

Q t.

'W

.U w

- ~

O _

u.

2 h

e

" LJ 2

i W

-3 6

O 1365S/0049K M

4 l

s U n

W en 4

• l.2 L

O to.

W

. g O

6'

_I IMl8 P's S

3 o

so and U

hU m

I t

8.

O l

l I

4 l

i l

1365S/0049K  !

PGandE Letter No.: DCL-87-072 O .

ENCLOSURE 2 ADDITIONAL INFORMATION ON RACK-TO-RACK INTERACTIONS O

O 1374S/0049K

[.

PROPRiTARY DIABLO CANYON POWER PLANT UNITS 1 AND 2 ADDITIONAL INFORMATION ON RACK-TO-RACK INTERACTIONS O

Pacific Gas and Electric Company April 7, 1987 O

1374S/0049K

PROPRiTARY :

TABLE OF CONTENTS

1. INTRODUCTION

2. BACKGROUND OF DESIGN BASIS ANALYSES

3. DESCRIPTION OF THO-DIMENSIONAL OF PARAMETRIC STUDIES 3.1 Single-Rack Model 3.2 Multi-rack Model 3.3 Cases S,tudied

4. ANALYTICAL METHODOLOGY

5. HYDRODYNAMIC COUPLING 5.1 Development of External Coupling Terms 5.2 Parametric Studies for Equivalent Lateral Gap (ho) 5.3 Effects of Vertical Flow 5.4 Modeling of Fuel Assemblies l

6 RESULTS OF ANALYSES '

6.1 Single Rack 6.2 Multi-rack Interactions 6.2.1 Interior Rack Array 6.2.2 Exterior Rack Array i 6.2.3 Fabrication and Installation Tolerances

7. CONCLUSIONS j

8. REFERENCES O

1374S/0049K L_____________________________ _

PRO)RETARY p/

x_

1. INTRODUCTION In response to NRC Staff requests, PGandE submitted additional I information on spent fuel rack' interaction parametric studies on-February 6, 1987 (PGandE Letter No. DCL-87-022). On February 18, 1987, I the Staff and PGandE met to discuss the parametric studies. Following the meeting, the Staff requested additional information, which 4 necessitated further investigations (NRC Letter dated I 1

l February 26, 1987). These further parametric studies and their results were reviewed by the Staff on March 26, 1987. This report documents the description and results of the additional parametric studies that were presented to the Staff at the March 26 technical review meeting and alsro responds to the Staff's information requests dated February 11 and 26, 1987.

In response to these Staff requests, rocking, a lower coefficient of friction, fluid coupling effects, and variations in fabrication and i

installation tolerances were incorporated in the parametric studies. As specified by the Staff, resultant fuel-to-rack, rack-to-rack, and rack-to-wall forces were compared for the single-rack and multi-rack models. Time-history data have been provided in this report.

1 i

O 1374S/0049K - _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ - _ - _ _ - _

PROPRETARY

2. BACKGROUND OF DESIGN BASIS ANALYSIS The analytical methodology used for obtaining rack interaction impact loads is described in the Reracking Report submitted by PGandE on September 19,198S (Reference 1). In general, the methodology includes several conservative assumptions applied to a single rack model to obtain conservative impact loads which were used as the basis for rack

) qualification. Some of these conservative assumptions are listed below:

1 Each adjacent rack module was assumed to move in a manner equal and opposite (out of phase) to the rack module being analyzed. This assumption was incorporated in the model by utilizing a reference-impact plane midway between adjacent racks.

j

• The fluid coupling coefficients were based on the conservative assumption that adjacent rows of racks are an infinite distance away (the distance is measured perpendicular to the horizontal ground motion). This neglects the cross-coupling effect of the adjacent rows of racks and results in higher displacements and impact forces.

i i The impact spring coefficients were set at a value significantly i

higher (over 10 times) than the calculated values to produce 1 conservative impact forces.

O 1374S/0049K L

PROPRIETARY e

All hydrodynamic coupling calculations were conservatively based on V- kheinitialgap. Parametric studies showed that progressive time-dependent variation of gaps (nonlinear coupling), if considered, would further reduce rack responses, e

The friction coefficients used were 0.2 and 0.8.

The racks and fuel were analyzed using an eight degree-of-freedom system to model their three-dimensional behavior during an earthquake.

It was PGandE's judgment that the above conservatism, when used in a

)

single-rack analysis, provide an adequate design basis to accommodate . )

multi-rack impact effects.

O The results of PGandE's design basis analysis, as reported in the Reracking Report, demonstrate conservative design margins between predicted and allowable loads. Tables 2-1 and 2-2 summarize the maximum impact loads and the qualification basis of the racks, as reported in the Reracking Report, the Seismic Analysis Report (Reference 2), and other supporting documentation.

4 O

1374S/0049K .

_a

PROPRIETARYl

3. DESCRIPTION OF THO-DIMENSIONAL' PARAMETRIC STUDIIS The objective of the parametrh studies reported herein is to show quantitatively that PGandE's methodology for obtaining the design basis irpact loads,' reported in the Reracking Report is conservative. These studies were performed by the same group of individuals who performed the original analysis. Additionally, all work was reviewed and accepted by PGandE to assure the accuracy and completeness of the evaluations.

3.1 SINGLE-RACK MODEL The single-rack model (Figure 3-1) was developed for a 10 x 10 rack -

module fully loaded with fuel. Consistent with the design basis model, 40 percer.t of the fuel mass was modeled as one lumped mass (Mass A) located near the top of the rack to simulate the rattling effect of the fuel assemblies. The balance of the fuel mass was located at the base of l

the rack. The mass of the rack was lumped at the centroid of the rack.

The rattling mass was assigned a transnational degree-of-freedom;-the rack centroid was represented by three degrees-of-freedom (trar?slational, vertical, and rocking). Springs 1 and 2 represent the stiffness of the

~

girdle bars, and springs 5 and 6 simulate the stiffness of the rack baseplate. The rack feet are represented by springs 7 and 8. Each spring simulates the composite stiffness of the two corresponding springs shown in Figure 6.2.2 of thG Reracking Report. Consistent with the original model, springs 7 and 8 are connected with friction springs to simulate sliding.

u 1374S/0049K 1 J

J

PROPREIARY l Two cases were studied using the single rack-model. In the first case, all model parameters were set at the same conservative values as those reported in the Reracking Report. This case was used to develop benchmark loads for comparison'with other cases, since it represented PGandE's conservative analysis input for a two-dimensional model.

l In the second case the model parameters were revised to represent realistic input values as follows:

i e In calculating the fluid coupling coefficient, the presence of adjacent rows of racks was accounted for by considering them as vertical planes located at a lateral distance 7.5 inches on either-side of the rack (versus the nominal 2.25-inch gap between two adjacent arrays). Analytical studies have shown that use of a i 7.5-inch gap is conservative (see Section 5 of this report).

Both the rattling springs and the exterior impact springs were represented by their calculated values scaled up (approximately 1-1/2 times) to account for strain rate and material variability.

l 3.2 MULTI-RACK MODEL  !

l Two rack arrays were studied. These arrays are identified as Sections AA i

and 88 in Figure 3-2. The array identified by Section AA was selected to study the behavior of a typical interior row, whereas the second array (Section BB) was selected to study the behavior of a row of racks with a gap larger than 7.5 inches, which occurs along the periphery of the spent l fuel pool.

1374S/0049K 4

PRD)RiTARY Figure 3-3 shows the two-dimensional dynamic model used in the analysis of the racks in Section AA. A similar model was developed for Section BB. Each rack was represented by four degrees of freedom simulating fuel rattling, transla' ion, and rocking of the racks. The parameters for the model were developed in a manner similar to that used for the single-rack model, except that more realistic assumptions were made to compute the fluid coupling coefficients and spring constants, as follows:

1 In calculating the fluid coupling coefficients for Section AA, the presence of adjacent rows of racks was accounted for by considering l them as vertical planes located at a lateral distance of 7.5 inche's l

on either side of the rack array (versus the nominal 2.25-inch gap l between adjacent rack module walls). Analytical studies showed that the 7.5-inch gap (h0) conservatively estimates the coupling effects of adjacent rack arrays (see Section 5 of this report).

For Section BB, fluid coupling coefficients were de;aloped by conservatively assuming that tide adjacent wall is approximately 37 inches away from all racks in the array. This assumption of uniform channel width was made to simplify the analysis, and it is conservative, as only one out of four racks is approximately 37 inches away from the wall and the other three are much closer to the wall.

l 1374S/0049K - -___ _ _

PRO)RETARY l i

Both the rattling springs and the exterior impact springs were represented by their calculated values scaled up (approximately 1-1/2 times) to account for strain rate and material variability.

The Hosgri east-west and vertical ground motions were applied simultaneously to the model. The east-west horizontal time-histories I

{

were applied since they represev' the mort conservative horizontal s'eismic input.

i The key model parameters are summarized in Tables 3-1 and 3-2.

3.3 CASES STUDIED -

Table 3-3 summarizes the description and objective of each case studied.

In general, these cases were selected to study the following:

Conservatism in PGandE's design basis methodology using a two-dimensional, single-rack model l

Comparison of multi-rack response with the single-rack response j determined using PGandE's design basis methodology

• Effects of full and empty racks (11 assemblies)  !

l

• Effects of larger lateral gaps (h0 > 7.5 in. on rack response Effects of manufacturing tolerances on rack response 1374S/0049K '

PRO?RETARY___

4. ANALYTICAL METHODOLOGY The analytical methodology is similar to the one describad by Levy and Wilkinson, (Reference 3). In general, the analysis includes the following steps:

Sten 1: The system kinetic energy was calculated considering the combined effects of the following:

e K): Hass effects of the rattling fuel represented by Mass A (Figure 3-1). Mass A represents 40 percent of the total fuel mass.

• K:

2 Mass effects of the rack and nonrattling fuel (5) percent of fuel mass), considering both translation and roding.

• K:

3 Fluid effects due to fuel rattling, considering l coupling between the fuel assemblies and rack cells.

• K:

4 Fluid effects due to external hydrodynamics, considering the coupling between adjacent racks or walls.

K:

S Mass effects of water contained within the rack.

Sten 2: After the system kinetic energy was developed, the following Lagrange's equation of motion was used to solve for the fluid 1

reaction force:

.d /8K J 8K ,

gI d t' j 8x[ 8xg where K is the system kinetic energy,g x is the i th O absolute degree-of-freedom, and Qg is the generalized force 1374S/0049K l

PROPRIETARYl _

in the i th degree-of-freedom. A set of equations results from this step which can be written as follows:

{h) = [M3~I {Qg} + [M3-I {R) where {q) represents the matrix of accelerations in the generalized coordinate system defined relative to the fuel pool generalized coordinate; [M3 is the mass matrix containing both diagonal and off-diagonal terms, and includes terms for fluid l coupling, mass cf the rack, and fuel assemblies; {Qg} is the matrix of generalized forces, which includes the effect of external spring forces; and (R) is a vector containing pool wall and floor accelerations.

l Steo 3: The equations of motion developed in Step 2 were solved using the computer code DYNAHIS, which employs a nonlinear, time-history analysis using a central difference integration technique. Additional discussions of DYNAHIS were provided to the NRC during the review of the Reracking Report.

O 1374S/0049K PRO?RELUY l

5. HYDRODYNAMIC COUPLING 5.1 DEVELOPMENT OF EXTERNAL COUPLING TERHS In Section 4 of this report, each parameter used to compute the system kinetic energy was described. One of the key parameters that affect the behavior of racks is the external hydrodynamic effect, identified as K.4 As discussed by H. Lamb (Reference 4) and R. J. Fritz (Referenced),thekineticenergyinthetranslationofthei th rack due to external hydrodynamic effects can be written as:

. . .2 . .

K 4 9 - Bq ,j ,9 (q,_j )(qg )+ B g,. 9 (qg ) + By ,q,j (q, ) ( qq ,j )  !

where B is a hydrodynamic coupling coefficient, and qi is the

- I generalized translation velocity of the i th rack centroid. The i

coupling coefficients are: I 3

Bg ,j,g -(pHN /12)/hg ,j,g 3

Bg,9,j= -(pHH /12)/hg,g,j ,

2

=-

B g,g (Bj ,j,g +Bg,q,j) + ptW /2h 0 where h g ,j,9 is the inter-rack gap between the (1-1)th and i th gap, and h is the gap between the rack array and a hypothetical lateral 0

O 1374S/0049K PROPRE"ARY O

V boundary assumed to simulate the effects of an adjacent array of racks or wall (Figure 5-1).

Typically, the inter-rack gaps are 2-1/4 inches (the clear spacing between girdle bars is 1/4 inch). Unless noted otherwise, the rack-to-rack gap of 2-1/4 inches was used in the analysis. The rack-to-wall gap was conservatively selected as 3 inches. The lateral gap (h0 ) used in the analysis of an interior array was obtained by multiplying'the nominal inter-rack gap (2-1/4 inches) by a scaling factor (approximately 3.3) to allow for flow of fluid in the channels located between the racks in the adjacent arrays. Parametric studies reported in sections 5.2 and 5.3 show that this factor is conservative. For the rack array located near the periphery of the spent fuel pool, the largest

( nominal gap between the rack and wall was substituted for h without 0

any scaling factor since the walls provide a solid boundary.

5.2 PARAMETRIC STUDIES FOR EQUIVALENT LATERAL GAP (h }

0 l

In order to calculate a conservative value for the equivalent lateral gap h0, a number of cases involving different combinations of rack arrays were studied. These cases are listed below:

i

- l Case I: Six racks in three rows with one moving rack; the adjacent i

boundary is stationary.

O 1374S/0049K PROPRiTARY :

/ Case II: Five racks in one row with only the middle rack moving; the adjacent boundary is stationary.

Case III: Five racks in one row with the middle three racks moving in phase.

Case IV: Five racks in one row with the middle rack moving out of phase with the adjacent two racks.

The objective of the parametric gap studies was to equate the total system kinetic energy for each case to the kinetic energy produced-by an equivalent array of racks. This produces information on the equivalent lateral gap (h0) as a function of the actual gap (h). The results, f summarized in Tabic 5-1, show that a scaling factor of 1.36 is sufficient to describe the geometry of the lateral gap. PGar.dE's use of a large scaling factor of 3.33 (7.5/2.25 in.) is conservative, as it underestimates the fluid coupling effects of adjacent rack arrays, thereby producing the potential for greater displacements and impact loads.

5.3 EFFECTS OF VERTICAL FLOW The parametric gap studies described in Section 5.2 were based on a simplifying assumption that all fluid flow occurs in the horizontal '

plane. Due to the projection of girdle bars located near the top of the rack (and the lead-in edge of the rack), the upward flow of fluid 1374S/0049K _ _ _ - _ - _ - _ _ - _ _

PROPRETARY .

I between interior racks would be constricted. Therefore, the effect of O '

vertical flow of fluid between interior racks is negligible. However, the racks located near the periphery of the pool may have gaps larger than 2 inches. For these racks, the effect of vertical flow of" fluid on the equivalent lateral gap requires further investigation.

The following two cases were studied:

Case A: Flow between the racks Case B: Flow between fuel assemblies and rack cells I

Case A shows that the average value of the calculated horizontal flow is approximately 80 percent of the total flow if vertical flow is neglected. This study used a nominal valut of 2-1/4 inches for inter-rack pap and, for simplicity, neglected the effects of constriction at the elevation of the girdle bars. Figure 5-2 shows the variation of flow along the height of the rack. The study concluded that use of approximately 80 percent of the fluid roupling coefficients developed for

{

l planar flow assumptions is realistic 1or the peripheral rack channels.

However, no reduction of the coupling coefficients was necessary for the interior rack channels due to the consi'riction afforded by the girdle  ;

bars and the lead-in edges.  ;

l The results show that for Case B the flow is very close to horizontal except near the top 5 percent of the rack height. As shown in Figure 5-3, the average value of the calculated horizontal flow is O

1374S/0049K -

PRO?RETARY

( approximately 98 percent of the total flow if vertical flow is neglected. Therefore, no reduction of fluid coupling coefficients is necessary to account for vertical flow of fluid.

5.4 H0DELING OF FUEL ASSEMBLIES The PHR fuel assemblies used in the Diablo Canyon Unit I and 2 reactors contain 264 fuel rods in a 17 x 17 array. The fuel rods are 0.374 inches in diameter arranged in a square lattice with a pitch of 0.496 inches.

Therefore, the gap between the adjacent fuel rods is less than 1/8 inch (0.122 inches nominal). The cross-sectional dimension of the rod array

• s 8.404 inches square. Since the storage cell opening cross-sectional' dimension is 8.85 inches, the net lateral spacing between the fuel assembly and the storage cell is 0.446 inches. The lateral movement of the fuel assembly in the storage cell causes the water to flow past the assembly. Since the flow between these narrow channels formed by the array of rods involves repeated changes in the flow cross-section of width from 0.122 inches to 0.496 inches - a fourfold change in transverse flow area - the hydraulic pressure losses through these channels are an order of magnitude greater than what the fluid encounters flowing through the assembly / cell wall gap. The hydraulic pressure loss due to flow through these narrow convergent / divergent channels is an important l

mechanism for energy loss from the vibrating rack system. However, in l the conservative approach used to model fluid coupling, no such flow, and therefore, no such loss occurs; all the fluid is assumed to flow in the assembly / cell wall space.

O 1374S/0049K _

u

PROPRITARY . i

/

6. RESULTS OF ANALYSES 6.1 SINGLE RACK Table 6-1 summarizes the maximum impact loads for parametric Cases 1  ;

and 2. The table indicates that Case 1, which utilizes parameters and methodobgyequivalenttoPGandE'sdesignbasismethodology, predicted f

the highest fuel-to-rack impact load of 129 kips and a rack-to-rack impact load of 90 kips. Since Case 1 utilizes inputs identical to those used in the design basis model, Case 1 was used for comparison with the parametric multi-rack studies to quantify the conservatism in the licensing basis model. Due to the introduction of " softer" springs in' I Case 2, the rocking behavior of the rack is especially pronounced for higher friction coefficients, resulting in rack-to-rack and rack-to-wall impacts. However, these loads are still less than the maximum rack-to-rack load obtained from Case 1. Siellarly, although Case 2 shows the highest rack-to-wall impact loads, the magnitude is significantly lower than the rack-to-rack impact load predicted by Case 1. Since the racks were originally evaluated for the greater of the rack-to-rack and rack-to-wallimpactforces, Case 1isconservativE Therefore, the

~

resul's of Case 1 show that PGandE's design basis methodology is conservative..

Figures 6-1 through 6-4 provide time-history plots of the rack translation and wall impact forces as obtained from Case 1.

O 1374S/0049K PROPRETARY 6.2 MULTI-RACK INTERACTIONS 6.2.1 Interior Rack Arrav Table 6-2 shows the results of the multi-rack analyses. Cases 3 and 4 represent analyses of the interior array identified by Section AA. These cases were chosen to predict rack behavior under different loading configurations. Case 3 represents an array of four fuliy loaded racks, and Case 4 represents three loaded racks and one empty rack (11 fuel assemblies). The results show that for both cases the fuel-to-rack and rack-to-rack impact loads are enveloped by Case 1, which reflects the results based on the conservative design methodology employed by PGandE.

Although rack-to-wall loads based on Cases 3 and 4 are greater than the corresponding loads obtained from Case 1, their magnitude is enveloped by the rack-to-rack load resulting from Case 1. i Figures 6-5 through 6-17 show typical time-history plots of rack j translation and wall impact forces for Case 3.

l l

13745/0049K PROPRETARY 6.2.2 Exterior Rack Array Section 88 was chosen for analysis to quantify the effects on rack behavior in the few cases where spacing between the rack and the wall exceeds 7.5 inches. Case 5 contains two racks with spaces greater than 7.5 inches;onerackTRackK)hasa37-inchclearance,andtheother (Rack H) has a 13-inch clearance. This array was modeled assuming that all racks were separated from the wall by 37 inches in order to minimize the complexity of the analysis. The results of the analysis (Table 6-2) show that the fuel-to-rack and rack-to-rack impact forces are enveloped by Case 1. The rack-to-wall load of 51 kips for a coefficient of friction of 0.2 is enveloped by the rack-to-rack impact load of 90 kips reported for Case 1. For a coefficient of friction of 0.8, however, the O wall impact load of 107 kips is greater than the rack-to-wall load reported for Case 1. Nonetheless, given the conservative nature of the model, the higher wall impact load obtained from Case 5 is compatible i with the parametric study trends.

6.2.3 Fabrication and Installation Tolerances Table 6-3 provides results of the multi-rack analyses which postulated variable gaps.resulting from fabrication and installation tolerances.

The results show that the fuel-to-rack and rack-to-rack impact forces are enveloped by the corresponding loads obtained from Case 1 and that rack behavior is not sensitive to typical fabrication tolerances.

O 1374S/0049K ____ -

Pil0)RETARY .

7. CONCLUSIONS In conclusion, the two-dimensional parametric studies demonstrate that the use of conservative springs and fluid coupling inputs in the Reracking Report yield conservative rack and fuel assembly impact loads.

These studies provide a high level of confidence that the design basis model has predicted conservative rack qualification loads, which ensures compliance with all design criteria. Table 7-1 summarizes these loads.

O O

1374S10049K l

l PROPREURY -

.)

A 8. REFERENCES l V

1. Reracking of Spent Fuel Pools, Diablo Canyon Units 1 and 2 Enclosure to PGandE Letter No. DCL-85-306, dated September 19, 1985.

2. Seismic Analysis Report, " Seismic Analysis of High Density Fuel Racks for Pacific Gas and Electric for Diablo Canyon Nuclear Power Station," Rev. 3, September 3, 1986, A. Soler, TM #779.

i

3. Levy, S., and Hilkinson, J.P.D., The Comoonent Element Method in i

Dynamics with Aeolications to Earthauai? and Vehicle Enaineerina, McGraw-Hill, New York, 1976. -

4. Lamb. H., Hydrodynamics, Dover Publications, New York, 1945.

5. Fritz, R. J., "The Effects of Liquids on the Dynamic Motions of Immersed Solids " Journal of Enaineerina for Industry. Trans. of the ASME, February 1972, pp. 167-172.

1 I

l l

l I

l

. i v

1374S/0049K PROPRET/RY .

TABLE 2-1 Results of Desian Basis Analysis (Single Rack, 8 Degrees-of-Freedom)

Imoact Loads (Kios)(a)

Friction Frf Frr Frw Coefficient p = 0.8 249 88 39(b) p - 0.2 242 105(b) 63(c)

O

a. Frf is the rack-to-fuel impact load; Frr is the rack-to-rack impact load; Frw is the rack-to-wall impact load.

b. The maximum load resulted from an empty rack (11 fuel assemblies).

c. The value applies to rack "H" only.

1374S/0049K _ _ _ - _ _ - _ _ -

I l

PROPRETARY l TABLE 2-2 Qualification Basis for Racks  !

(Reracking Report)

I l Imoact Location Allowable load (Kios)(a)

Fuel-to-rack 883 l Rack-to-rack 175(b)

Rack-to-wall 175 for rack (b) 80 for wall (c)

O I

i

a. The allowable Toads refer to a 10 x 11 rack.

b. The loads correspond to the allowables per spring. Both the girdle bars and baseplate are represented by two springs each.

c. The walls have been shown to be qualified for substantially larger

(=200 kips) loads.

j J

v )

l l

1374S/0049K l

r l PROPRETARY !

f TABLE 3-1 Kev Model Parameters (Single-rack Model)

A. SPRING CONSTANTS

1. Fuel-to-Rack

a. Springs 3, 4 0.14x106 lb/in. (Case 1) 0.21x105 lb/in. (Case 2)

2. Rack-to-Rack / Rack-to-Hall

a. Girdle bars:

Springs 1 and 2 0.2x10{lb/in.(Case 0.1x10 lb/in. (Case 2)1)

b. Baseplate: -

Springs 5 and 6 0.2x107 lb/in. (Case 1) 0.2x10 lb/in. (Case 2)

B. GAP.1

1. Rack-to-Rack O.25 in.

2. Rack-to-Wall 2 in. (clear between girdle bar and wall)

3. Fuel Assemblies to Cells 0.151 in. (each side of fuel assemblies) l O

1374S/0049K - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ .

l PRO?RUARY O

• TABLE 3-2 Kev Model Parameters '

(Multi-rack Model)

A. SPRING CONSTANTS l l

1. Fuel-to-Rack 0.21x105 lb/in.

2. Rack-to-Rack Girdle bars 0.05x106 lb/in.

Baseplate 0.10x106 lb/in.

3. Rack-thWall Girdle bars 0.10x106 lb/in.

Baseplate 0.20x10 lblin.

B. G6P.1 ~

1. Rack-to-Rack 0.25 in.

2. Rack-to-Wall 2 in. (clear between girdle bar and wall)

3. Fuel Assemblies to Cells 0.151 in. (each side of fuel assemblies)

.e.

O 1374S/0049K )

ae aa an an r) t sd vo l p mi mi ov neei enh c m r l i if sw rat f 1 f o1 fa f e t en i od oc op op v ka rv mrospt kyw ca ne e m i

ar s sas sds so s t i nsl ars t a t na t c f c e

me ti eu a( rs rrt csC caC c t

c h s cn v e al ek e ey e i

b noy rykr i u f ch f sh fb . f t rs f at f pt f 1 f O ecg egc l o r. eri eai es es h b o soag ui r w gw ee p

sl o

nl rn oo mree en e ecs ec i

t os tl s t na o E' d l d o cder ol a nt r a t aat aaC t

aa enh wh gp ina aip usl l du url ur ur l eu l eh l vat ot nm t m aas at s al t al eGe DPm h eio Smsc bno voe vae voi vo Oac El r El r Et w Et

)

. y ys

_ n c t dw tk

?i i p iog pc sn

_ e s;s e dt m ul n ma d p

- s5 i s E g l fi er a;

_ a) t a ui n f r ,iu g)

_ hp = - a n h7 p-ll esi op en5l d ot 0t s fa e

nl r Oep ens ne7f s eo e d t l t

_ fh s o( n fhn o( at wr ns ihc o ew 3. w n bt

_ i d o o r;

n wti ;t1 o a ao sac it se r;t t

u n

t mc uu tss ul n r) a .

khi cct ews n i kb c 5a

, r) s

.n ib r

a

_ S o oi g oeo nn a s o)l as7 nno vn

_ i dn nc i rdi .a s t eei en  ; il ;ne r a p 8. ;i c 3

e s

o vmr o p vag ohn s 5. st dua sir d g1 ) 5g sO

_ - a i

r mds mci k

c7n el e df r k

c7; e

de;o7i m.n k c;

3 C c i r a=a a a3e al pt - r a s sue sdp r gt ow; rd obot 0p ro

. f e kl v kis hs l o) 0i l at ohs L o D cu

_ OE B

A T

n o

cfi a

rea t v t al c rfi t

d( n e

dsc al o yris l a l

rn t

n dhs d

e(

al en rt s yr l an i

l vinl t

.b(

.si c

d e

dn i

t ti r nne tws noi oeg l nn u

f ;7 t n 5. a oeha u i es ai o

p eis l ntt f;5 ni l erl ya nos n ni k s 5nl i

r c

cf n ano cra aae jnr yar l h p ec0n eaho lhno ec ea0 k22aa .h e l y

s jic d d l cs u

rr( c l coc rr(1 cr l e A A F h u h u

_ D T F T F m

o d

e e

r F

f o 4 4 6 6 6 6 6

- 1 1 1 1

_ s 1 e

e r

_ a e

_ D k k k k k c) c) c) c) c

_ k k a a a c

a c

a RM RM a8 R8 RM Ra l R R en en en en e d

e e e l

pi o l o pi l

pi o l o l pi pi o l l it it i t i t i M g g tc tc tc tc t n n l e l e l e l e l i i uS uS uS uS u S S M( M( M( M(

M(

.O

_ o

_ N e 1 2 3 4 5 6 7

_ s

_ a C

UJASES DESCRIPTION LATERA i ~ ' '

I . ', , dh kho

[  :

--4 k , ,j ho =

{'] {"'] e4uivAteNT AK#AT

& 4Ae:K6,cNe McMNdr

[] -

[ ^" ] d h ..

fho l-+ l -+l ho s O L'1 f@uivALENT De.K bl -

S pe:KG,cNE McMNot

['1

--kho l-+ l g g ih l-+ldh no l -l. I -+ 1 g ~q e uu.,ume.

su nm mvm m E'] >

O l +- l ,h 14-1 ?

E l4 i gl -t h lel l +- l

PRO)RETARY l TABLE 6-1 Summary of Sinole Rack Results Imoact Loads (Kios)(a)

Cng Description 1 Single rack; conservative spring constants; and ho = =

y = 0.8 129 0 0 y = 0.2 127 90 0 2 Single rack; realistic spring constants; and ho=7.5 in.

p = 0.8 65 78 44 y = 0.2 67 39 39 1

l l

a. Frf is the maximum rack-to-fuel impact load as represented by springs 3 and 4 (Figure 3-1); Frr is the maximum rack-to-rack impact load as represented by springs 2 and 6; Frw is t maximum rack-to-wall impact load as represented by springs I and 5. e two-dimensional rack-to-rack and rack-to-wall loads were distributed be equivalent to the licensing basis results where springs were modeled in each corner]

O '

1374S/0049K - ___- _____ __- _ _ _

PRO?R D RY l .

TABLE 6-2 Summarv of Multi-rack Results Analysis Imoact Loads (Kios)(a)

C111 Description 3 Multi-rack (Section AA);

fully loaded; realistic spring constants; ho-7.5 in.

p = 0.8 72 74 69 p = O.2 65 27 42 4 Hulti-rack (Section AA); one empty and three loaded racks; realistic spring constants; ho=7.5 in, p = 0.8 78 73 75 p = 0.2 65 17 38 p) q 5 Hulti-rack (Section BB);

fully loaded; realistic spring constants; ho=37 in.

on one side and no flow on the other p = 0.8 71 76 107 p = 0.2 62 29 51

a. Frf is the maximum rack-to-fuel impact load as represented by springs 3 and 4 (Figure 3-2); Frr is the maximum rack-to-rack impact load as represented by. springs 2 and 6; Frw is t maximum rack-to-wall impact load as represented by springs 1 and 5. The two-dimensional rack-to-rack and rack-to-wall loads were distributed be equivalent to the licensing basis results where springs were modeled in each corner]

O i

13745/0049K l

. l

7 PROPRETARY TABLE 6-3 Summary of Multirack Results (Effect of Tolerances)

Imoact Loads (Kins)(a)

Calgi Description Frf Frr frw 6 Hulti-rack (Section AA);

three fully loaded racks, one empty; realistic spring constants; ho=7.

variable gaps (b)5 in.;

y = 0.8 77 34 63 p = 0.2 63 33 37 7 Multi-rack (Section AA);

fully loaded; realistic spring constants; ho=7.5 in.;

variable gaps y = 0.8 75 80 74 y = 0.2 61 33 53

a. Frf is the maximum rack-to-fuel impact load as represented by springs 3 and 4 (Figure 3-2); Frr is the maximum rack-to-rack impact load as represented by springs 2 and 6; Frw is ths. maximum rack-to-wall impact load as represented by springs 1 and 5. LT_he two-dimensional rack-to-rack and rack-to-wall loads were distributed to be equivalent to the licensing basis results where springs were modeled in each corner,

b. Gaps between girdle bars (0.25 in. top; 1.875. 1.375, 1.25 in. bottom).

c. Gaps between girdle bars (0.25 in top; no gap at bottom).

O l 1

1 1374S/0049K I

PROPRETARY l TABLE 7-1 MAXIMUM LOADS Rack Impact Loads Gn.g Rack Mode 1(a) Assumotion(b) g (c) g (d)

Licensing Basis SR C 249 105 1 SR C 129 90 2 SR R 67 78 3  : MR R 72 74 4 MR R 70 75 5 MR R 71 107 6 MR R 77 63 7 MR R 75 SO A110wables 883(') 175(r) 200(w) l l

(a) SR = Single Rack Analysis, MR = Multiple Rack Analysis (b) C = Conservative Assumptions Used in Analysis (high spring constants and large hydrodynamic gaps)

R = Realistic Assumptions Used in Analysis (c) Maximum fuel impact load (rack-to-fuel), all loads in kips (d) Maximum of rack-to-rack or rack-to-wall loads, all loads in kips (e) Allowable for 10 X 11 rack; Allowable for 10 X 10 rack is 803; (r) = rack and (w) - wall O

1374S/0049K O

O- ..

liii :e f.

G C3C, l

e i

t 82= W t 2' S

m E

$ E E d B

, - --y- - b, i

w ,

@~C a Z_

E

. - -@ g a

g g g E

j N ,

. s .,

Mr g

O v = -

rq- ,

,s

@* m 4 g

b '

F g t .

-- A e @$* --

2 t _

I i TN NNNNNN .

L&.

G O

1365S/0049K r

1 PROPRliTAlY:

O .

~

j

.  : 5='

i R e

I e sdI W "o "N" Ref. Typ , E. 9x9 mico -l2 . b

!2 p *p h1 ,

1 6 Q p "B" h 8x2 + 4x2 a

- e p3 Region 1 Plus j , *K" N9 9x6 10 x 9 lf B el s 8 "G" "C" "D 2 "A 2

~

10 x 10 Region i V

• 8 x 10 9 x 10

• A A 10 x10 -

O h "

F" "J" " D g" "Ag" Ref Region I gg g. 8x9 10 x 9 t6 9 x 10 o pE 10 x10 *y g

. NP>=

I i

d  !:

. Y!h[If$ispa,iggN

L $ j "E" "L" "M" Y 6 mil 9x9 10 x 11

. w[CI N Pit. $is 9 l U

• 4.

eq l y u @4  ; * ,

- a b n Dga

" i 10' - 8" 9 g*

- -, +-

, g, 35' - 0" O ,

F1gg Typical Layout of Unit i Spent Fuel Pool 3 _ _

A T

E N N /

/

I R

/

P " -

O

?

i '

4 #. //

1 Hi a

R P

W t

s s

@// E

~

k / K A

U

/ Q gh /

/

H T

R A

E

$ b@//

I R

G S

/

ob/

O H

rs t

e .

vy Y il tb am t e ns I

$ @/// r e

n A

R R

A es _ i T sA e

/ L S E

rl pe eu e /

/

l P

o o

W T

S f@/

RF A

O h /

' E L

/ E

~

4 )* cf a i

/

D M

Wl e. G /

K C

s .

- / A R

e / I

- C

/ TA s

/ M c

' ik TR pc ya

- k k@'/

}

7

/

is 3

l l i R f@/ /

/

/

3 i

g a F W C /

t s /

E a

ef b/

y @)/

/

O

[hr

/

/

f /

_ /

gu gx

, p !j 'i/

- Il c, cL 1 ;j

e PRO?RETARY ! '

d Assumed Lateral Boundary

/ / / / / / / / / / / / / / / / //

l E '

/ j Rock i-l Rock i Rock i+1 /~

htign > ,,_ _ _ , , ,

e ,

_(,j_qq, ,o 5 yrrnet

/ '

V l r~? / /  !

O  !////////////////l L h-l,i h,i+1 i

i Fig. 5-1 Typical Four Rock Array Used for Hydrodynamic Coupling 1365S/0049K l

)

H!0MllETARY

(

l. --

.9

.8 AVERAGE -

.7 _ _

m .6 - -

.5 - -

• 4 .

.3 _ _

W = 108, L= 176.9

.2 __

l ~~

y/H j t i i i i f f I I I a I I i l I l i i i i i i

.I .2 .3 .4 .5 .6 .7 .8 .9 1.  !

t

.N O Ttf 9 .

1.

q3/qg = IFATio ol' FL.ow DETWEEN 6 PIMEN960$L. ANAL.Y%

AHp 2 PIMEN9 PHAL ANALT916 l

f. y/H = NON FIMENGloNAL 'TE*M Wi1H legefpur D Hif.idrHT. l 151di. 6 2 plGTmenuTio4 of Fl4W be.TNEEM rat #,(y O

1365S/0049K PRO?fuETRY ;

O<'

' .0

.9- -

\ l

.E _

n .I

\ .6 O

.5 w=10.0, L=l69 4

.3

.2

y/H l  !

.I .2 .3 .d .5 .6 .7 .E .9 f.0 l

Fig. 5-3 D i str ibut ion of F low Between Fuel Assembl ies and Ce l ls tSee F ec 5 2 for Notect 13655/0049K O 'f ~

_f k

l 0

2 m.

s

.I l o

' c.

s i

i 2

E o ",

c. f>

l 4

'l

- (

L \. o , es 0 a )

C 2 2

1 r

o =o O N oC f

n e o e d

) o.SE

'lo-i r t F a

l r E s o s M n

' I a .

l T r .

T r r o o k c n s.

k e.

o o

R 1

6 a j

's.

d 2 l

S i e

r u

g b - o E F -

o. S 4 A fa C R

O o F o

i. 2 S

I D

T O :o 36 E .i n,

o O

L P

= S .

3 Le.na .

G I

M5s 5M b*' F lllllf I1!

l l

O I 8

i N

3 l

==E: b .

4 ca 1 g Clll3 "

• Clllt:

ca d  ;,

l ,

te l P .

- I! '

---

_ .- Y I ,

O s t y 4 ein' d p o 1:

.g u c

• EW 3u w E

5 "g m 4 8

,8 .

=

i W =

t

$E*

8 W * $E e

i "l wl ,

I r

N >

8  ?

J * .e* i

< e ew i m '

L .E

, w m.

O m l 4

• l 1r o

, er C

L '

8 4 cv i

m O

8

• C

.J

$0'0 $0'0 00*0- E0'0- $0'0- 80'0

• A S0'0

'N!-dSIO .

13655/C049K 8 u.

. 0 0

0 2

Y a R

A c.

's 1 i E

I R

P o O c.

R s P

i

2. ~

=

o g o.

'4 l

2

(

1 e

s 4 3

S a o C o- E e 2 S c 1 A r C o F

h.

.R t6 _

c oC oE F O a .

po S mN

'lo- G I g

E kn M - ci I W ar Rp T F T S o o

o. O t {(

e L P k c

a R

o G o I _

F 3 _

's. 6 e

r u

g _

o i

o. F _

4 _

m o

c i.

o o.

? 8;O. o 8 - g R- 84= 8 8iT

.O e a>e !

0m 32N I '

~

o 0

0 0

2 Y

R A ' 0 0

T L

I

' 8 l

R P

O 0 0

k .

6 2

I '

1

=

y 0

0 et 4

'l e 2 s 1 a S C 0 r 0 E o f

2 S ) _

1 A e 2 C c r

.R o m O

F o 0 CO t d

e E F c e

0. S a r

'lO- Z p F m

E I f M -W o I k T FT c e 0

a e 0 O R r g

8 L o e P t D

( -

k c

. a 0 R 0 1 0

F

'6 4

6 e

0 r 0 u g

4 i F

0 0

'2 0

0 O o D b * ** 84 84*

.O-J oo4o' o.'mJeuoEou.

8 A" , oO N 0 W$s%8 v k e we 8 f  : \ll1I1 l\ 1

Y 0 R 0 A 8

'l T

E I

R P

O v 0 0

6 R

P )v 1 0

0 4

'l n

0 0

- # 2 1

- A 0C J 0E f OS

'l -

c E M

O

- a> 0 0

I T

- N' 8

/

0 fpt l 0

'6 0

0 j

4

- .u

- A 0

\

v 0

'2 f

v n 0 0

nnc e

4* a' ' 0 E'.

h r .- 'e

= e' O

gUbx '

O _

0 0

o 2

)'

~

o Y o.

R /

ht A b T

E I 0 R 0 P s O ' 1 R 2 P

bV o c.

'4 [

J

=

A i

~

0

( e 0 s ) _

h 2 a 6 Y 1 C

r o o s

. f d e

oC E n e o r L

c. S i F O [l V

'lO-E M

I t

l a

s n e f

o T a e r r 0 T g 0 e k D_

6 c (

f I R

a _

o 6

c. 6

's l

/ 2 e 1

r M u g

i J 0 E F 0 S I

4 A C

g R O

A 0 0

F V '2 f o b S V

I D

s 0 T O

f 0 L

o P n' n - 5? 5' -

3 :.

@rE O G I

F

a~80n im'

' l L

O 0

0 0

2 Y

R A

T E

k h v

o c.

s

'l P

R

\l v 0 0

O 6 1

R P - y :2 o

o. .

4

'l 4

(

0 0 e.

]o t

J c Y, 2 1

, m o o r d e

0 . e 0 o r i r o

O V

'l e.

i..

e e

r o

p-,' , t 0 1 se

[

h 0 s

xc p

s u

N 3 0 7

\ 0 e

'6 2 e 1 r M e

' s i

] t 0 E v 0 S f 4 A C

y R O

n F v

0 0

'2 O

l n S v 0 I

D T

n 0 O L

E n a  :

i R A'o P E4 0:

iro O I G

F

=a$0^ .p l I <

9 6

8 '

> (y g s 8

[ i P

~

- ~

rm 8 .:

~ -

.4 Y

" ~s GV

.t 8

• s 2 0

u O ' M g 85 5E

~1 -

i: !

% g e .

g

.w 3 g i "'

% y a:

/ .

ssC&T' '

8 s ,

I,

'  ; E M

o E

C 1 I

s- t O - ."'

" ""~

8 o

a 3'esto"~ "

O 1365S/0049K 43 - "

_ - _ _ - - . 1

J R"

A ,

T E

I R .

P .

O .

R P

4 2

1 M

. E S

, A C

. R

..S C O E F O L E1 M -

I W T F T

O

. L P

. G

. I

.. F i

=. 25 =a 90 es =i O .O .

. 3ves:ce

_ _=wHx 2,

O 0 0

0 2

o Y o.

R s A I

't g i

t R o 2 ~

P c.

s O i

=

R /

P ,

1 o

c. 3

'4 i

e 2 s "

1 a M C 0 r 0 E o S f 2

1 A e C c r

.R o )

F 5 oC EF O t c _

O

c. S a o

'lo- p N E5 I m g M -W I

n l i T F l a p r

o T O W S(

c. L o s P t _

I k -

c

. a _

G R o

o I F

's. 0 1

6 e

0 r 0 u g _

4 i _

F o

o.

'2 o

c.

?7 h5 " 4_ 8d n4T hh e i'o O .

,O .

, ddiwuvE

=EC8en i*=e ll ! llL

Ill\il O . 0 0

0 2

[

0 Y 0 R 8 A

l T

E I

R 0 0

P O 6 1 2. -

R P =

(>

i

'l 0

0 4

( e 2 s ,

1 a ,

M C 0 r 0 E o S f 2 A 1 e C c r

.R o F

0 COF t

0. SE c O

a

'lO- 1 E 2 I1 M -W 2 I l T F l ao 0 T 0 O WN 4

L og P t n i

kr cp

. aS 0

0 0

1 R [(

1 F 1

'6 -

6

_ e

_ 1 r 1

u g

_ 0

_ 0 i F

_ 4 0

0

'2 0

0 ah gi'_'O 8d i =h 84A N.

D a".o e d>40E O .

= $n u 50rt '3'

'  ! llll'

,\IIf l ;l .

0 0

O 0 2

o U

c. m s

Y '

l R

A a ER

\. 0 0

6 P 1 O \

R 5-P . 0 0 =

' \ '4 1 >(

(e 0 s 0 a 2 C 1

, r o

\ f n]

o2

, i 1 \ o tn ao

'l o

ld se t ne ar

\ T rF

\ o f f c. ko c

a ae b Re r

2g 1 e U D o

c JR e

's. r I

8 u g

1 i

M F .

li~

n E _

o. S 4 A C

V R O -

A 0 0

F L

V

'2 -

b S I

V 0 0

D T

O A L -

o;. 7 & '0 P

~A 3: "g Q G

O I F

EEEx e '

l,il

~

O '

0 0

0 2

)/

I .

V o c.

V ' s l

0 0

b 6 1

. r 0

) 0 V 4

]8

'l

=

( 0 h 4'

0 3 2 e 1 s

, a C

. r 0C f o

Y E

0. S O ,<

Y

'0 -

l E

M I

i tm ld n]

o6 ao T se ne l

0 0

ar rF 6 T f

1 ko c -

ae _

Re r

o 3g 1 e

c. D

_9

's 8 o t e r

M u g

0 E i F

0 S I

4 A I

C

y R O

A 0 0

F .

V '2 6- .

\ S

/ I V o D

T O

n c. L

.n" ~ D*. o2- En n9"o P 7g8 O

G I

F

$eE% '8i

O 0 0

0 2

L '

!f

, , o c.

Y ( ht R ,.

A i T

E I

W 0 0

R f s

P 1 O I R '

P ,

n 0

8 J 0

=

4

'l f M A-h 0

(e 9 0 s a

JUj 2 C 1

r o

A l oC f]n0 o1

c. SE i O 8 L

'o -

l E

M tm ao ld se ne I

T ar 3n rF o T f

c. ko s c ae Re r

4g I 1 e o D

- o 6R

's. e 8 r u

I u

g M i

[ -

F o E

c. S

- 4 A

\

y C R

. O

/ 0 0

F

\

v '2 O

l

/ S v

I D

T 0

n 0 O L

q- c P

= 4 . 4 $ya *

.3

• O I G

F

=O10 $N b

l i

1 O .

Iw

,a s,

>"= " 8 s g m - 8 1

C -

2 l

N '

- T 8 ,

l 4 y

_ Lf e

8 u 5

4

- - i.

0 1 .

8- h 88 O -

• .s. e w

e E

p-8 =%

d 5g m.

N ~

g di

<= 8,

.- E C 8 W

' 4 5

% s ,

er 5> g 2 4 1

<> A s  ;

94*8 48 1 SE*0

(

00'0- 66'0- 41*g- gg g.E 8 E EL s

l l

'NI-dS10 C i

== I U l 1365S/0049K 1

.l

) '

8 N

i~ ., _

• >=

~ 8 N% ..-

~

b E

C3

_ g E

' 'o '

ca:: ,

• Y E W

-1 e a

so -

s.

8 w o g

• D' < e o g

.x 1

Sw a uo te f_ m, -

p W.2 --

i

>a- -o

==

I 8-e

.J

=.o e c. - .ec l

.w a um g

5 a D:

~

.. u. I W

I E i a <

8 .?.

m 8

i 8 l 29'Jr 00'O Et'sc- 00 set E

?~ co se tr s6 Cl* 8 7-dS

• J'-3803

(

4 13655/0049K  ;

L___ _

O o c.

o a

1 o Y c.

R ki A A T

E R o c.

P s ~ 8. -

O i R .

=

P [>

' A o

'4

c. (e i

8 s a

t C M r 0 o 0 E. f S

2 A e C No

. R F oC O t c

c.SE F a O 'lo-E 2 M

I 1

-W I2 l .

1 l o T FT aN

~ o W g O

c. L on o P ti r

kp cS a

C R [(

o 7 o I F

1

's. -

6 _

e r

u g .

o i

o. F .

4 _

o

o. _

'2 _

o _

o.

845'o O

$5  %.na_

N.3 :.oas

- e u9ET

=o.K h x . u"

,