ML20059F157

Nonproprietary Analysis to Determine Relative Tube/Tube Support Plate Displacements Under Steam Line Break Loads for Catawba Unit 1 Sgs

ML20059F157
Person / Time
Site:	Catawba
Issue date:	10/31/1993
From:	WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP.
To:
Shared Package
ML19311B168	List: ML20059F137 ML20059F148 ML20059F157
References
WCAP-13887, NUDOCS 9311040155
Download: ML20059F157 (100)

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WESTINGHOUSE CLASS 3 (NON-PROPRIETARY)

WCAP-13887 ANALYSIS TO DETERMlHE RELATIVE TUBE / TUBE SUPPORT PLATE DISPLACEMENTS UNDER STEAM LINE BREAK LOADS FOR CATAWBA UNrr 1 STEAM GENERATORS October 1993 O

N e WESTINGHOUSE ELECTRIC CORPORATION O

NUCLEAR SERVICES DIVISION

, P.O. BOX 355 PITTSBURGH, FENNSYLVANIA 15230 C1993 WESTINGHOUSE ELECTRIC CORPORATION ALL RIGHTS RESERVED

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ABSTRACT j This report summarizes an analysis to determine relative motions between the tube support

)

plates (TSPs) and the tubes during a steam line break (SLB) event for the Catawba Unit 1 )

, steam generators. If the relative tube / TSP displacements during a SLB event are large, then the benefit of the TSP to prevent tube rupture could be reduced. Assuming uniform through-wall cracks of length approaching the TSP thickness, a relative tube / TSP displacement during the SLB event exceeding approximately 0.5 inch could expose the crack with the possibility of a tube rupture. TSP motions due to S LB loads are calculated by means of a nonlinear dynamic time-history analysis employing a c' :tural model of the complete Westinghouse Model D-3 S/G tube and tube support structural system.

Results from this evaluation are judged to be conservative bc&ed on sound engineering principles. The SLB dynamic analysis does not consider the effects of friction and all inction-like phenomenon which would act at the TSP-tube interfaces, and which would strongly mitigate TSP-tube relative motions. TP ominal manufacturing gap between the tubes and TSPs are conservatively used in the ar.alysis to govem the activation of nonlinear tube interaction effects. Finally, perhaps the most significant conservatism relative to displacements is that the maximum displacements considered in the burst probability calculations (summarized in WCAP-13494, Rev.1) are made with the TSPs assumed to remain at the maximum displacement (relative to the tubes) achieved at any time during the transient. Thus, these independent conservative assumptions are compounded and Oxaggerateo by assuming simultaneous occurrence in an unrealistically worst case construct.

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J TABLE OF CONTENTS i

I Section Page 1.O lntroduction .. ..... . .. . ..... . . .. . . ... . . . .. 1-1 ,

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2.0 TSP Loads Evaluation . . . ..... .. ... . .. . .. . . .....'2-1 2.1 initial Conditions of SLB Transient . ... . ....... . . .. ... 2-1  ;

2.2 Location of the Guillotine Break .. . . . ... . .. . . . .2-1 2.3 Computational Model ... ..... ... . ..... . ... .... 2-1 2.4 Loss Coefficient of Pressure Drop Through TSPs . . . . .. .. . .. 2-2 2.5 Results of Pressure Drops through TSPs and Baffles .. . . . .. . .2-2 3.0 Structural Modeling . .... .. .. . ... . .. . .. ... .3-1 3.1 Material Properties . . .. . . .. . .. .. 3-1 3.2 TSP Support System . ... . . .. . . .. ...... .3-1 3.3 Finite Element Model Geometry . . .. . ... . . ..... .. 3-2 ,

4.0 Application of Pressure Loading . . . . . . .. . .. . . .... . 4-1 5.0 WERWOLF Computer Program and Solution Capabilities . . . . .... ... 5-1 6.0 Displacement Results . . . . . ..... . ..... ....... ... .... 6-1

. 7.0 Stress Results . . . . . . . ..... . . ... .. .. ....... .... . 7-1 8.0 Displacement Categorization ... ...... ... ... .... . .. .. .. .. 8-1 9.0 References . . ............ .. ..... .. .............. .... .. 9-1

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LIST OF TABl.ES l.

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~- Table : Description Page 3- 1 Summary of Component Matenals . . ... .... . .3-6 3- 2 Summary of Material Properties l

SA-216 WCC . . .. .. . . . . . . . .. .. ....... 3-7 1

L 3- 3 Summary of Material Properties SA-508 Class 2 . .. . . .. . . ... .. . ... . . 3-8 3- 4 Summary of Material Properties SA-533, Gr. A - Class 2 ... . . . . . . 3-9 3- 5 Summary of Material Properties SA-285, Gr. C . . . . . . . . ... 3 - 10 3- 6 Summary of Material Properties SA-106, Gr. B .. . .... . . . . ... . .. 3 - 11 3- 7 Summary of Material Properties SB-166 . . . . ....... . . . .... ............... 3 - 12 l

3- 8 Summary of Model Sub-Structures Non-Plate Components ...... . .. . .. . . . .. 3 - 13 3- 9 Summary of Model Sub-Structures  ;

Baffle and Support Plates . . . . . ... . . .. . . .. .... .... .. . 3 - 14 3- 10 Summary of Non-Unear Spacer Stiffnesses . .. ....... .. .. . . . 3 - 15 3- 11 Summary of Equivalent Plate Properties .. .. . .. .. ... ...... . 3 - 16 3- 12 Calculation of Revised Tubesheet Density . . ...... ..... . . . . . . 3 - 17 3- 13 Summary of Effective Plate Densities .... .. ............... . . . . 3 - 18 3- 14 Comparison of Natural Frequencies Full Versus Reduced DOF . . . . . . ................ ...... .. . . . . 3 - 19 6- 1 Summary of TSPTTube Relative Displacements for Postulated SLB Event for Catawba D3 S/Gs .... ....................6-3 ,

e

- Continued -

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5 LIST OF TABLES (CONTINUED)

. Table : Description Page 7- 1 Summary of Distorted Geometry / Stress Plot Figure Numbers .. . . . . . . . . . . . . 7-3 8- 1 Summary of Results for Displacement Categorization . . . . .. . .. ... . .8-2 5

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l LIST OF FIGURES Figure : Description Page 2- 1 Secondary Side Nodes, and Tube Support Plates identification (See Figure 2 2 for Preheater Detail) .. . . . . 2-4 2- 2 Preheater Nodes, and Baffle Identification of Model D3 Steam Generator . . . . .. . . .. .... ... . 2-5 2- 3 Secondary Side Fluid Nodes and Flow Connectors for Model D3 Steam Generator . . .. . . . ..... . .2-6 2- 4 Primary Fluid Nodes and its Flow Connectors, Metal Heat Nodes and its Heat Transfer Connectors, and Secondary Fluid Nodes within Tube bundle . . . . . . . . . . . . .. . . ... .. . . 2-7 2- 5 Pressure Drops through Flow Distribution Baffes A and B during Steam Line Break of Catawba 1 Steam Genercor . .... ... . 2-8 2- 6 Pressure Drops through Tube Support Plates C, G and L during Steam Line Break of Catawba 1 Steam Generator . . . . .. 2-9 2- 7 Pressure Drops through tube Support Plates Ghot and Q cogo during Steam Line Break of Catawba 1 Steam Generator . . ..... . . . 2 - 10 2- 8 Pressure Drops through Tube Support Plates R, S and T during Steam Line Break of Catawba 1 Steam Generator . . . ....... . 2 - 11 2- 9 Pressure Drops through Preheater Baffles D, E and F during Steam Line Break of Catawba 1 Steam Generator ..... ....... 2 - 12

, 2- 10 Pressure Drops through Preheater Baffles H, J and K during Steam Line Break of Catawba 1 Steam Generator . ... . . 2 - 13 2- 11 Pressure Drops through Prehester Baffles M, N and P during Steam Line Break of Catewt>e 1 Steam Generator . . . . . . . . 2 - 14 2- 12 Pressure Differential Across Tubesheet during Steam Line Break of Catawba 1 Steam Generator . . . . . . . . . . . . . .. .. . 2 - 15 2- 13 Blowdown Flow through Steam Nozzle and Flow Rate through Tube Support Plate T . . . . . . . . . ..... ............ ... . 2 - 16

- Continued -

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LIST OF FIGURES (CONTINUED) 1

, Figure : Description Page 2- 14 Fluid Pressure at Steam Nozzle and Tube Support Plate T . . . . . . . . .. . . 2 - 17 2- 15 Steam Void Fraction at Tube Support Plate T . . .... .. .. .. . 2 - 18 3- 1 Tube Bundle Geometry . . .. . .... ... . . . 3-20 l l l 3- 2 Tierod / Spacer Locations . .. . . . . . . . . 3 - 21 3- 3 Plate / Wrapper Support Locations Plates A, C, L, 8, D, E, F, J, K, M, N, P . . . . ..... . .. . 3 - 22 34 Plate / Wrapper Support Locations Plates G, H . . . ... .... 3 - 23 3- 5 Plate / Wrapper Support Locations Plates Q, R, S, T . . . .... .. . . .. .... . . ..... . . . 3 - 24 i

3- 6 Plate / Partition Plate Support Locations

- Plates A, B . . . .... ...... .. ......... .. ....... ... .. 3 - 25 3- 7 Plate / Partition Plate Support Locations Plates C, D, G .. ....................... ........... . . . . . . . 3 - 26 3- B Plate / Partition Plate Support Locations Plates E, F. H, J, K, L, M, N, P . . . ..... .... ...................3-27 3- 9 Overall Finite Element Model Geometry . .. . .......... ..... .... 3-28 3- 10 Mode Shape Plot - Plate T Full Set of DOF Mode i . . . . . . . ... ......................................3-29 3- 11 Mode Shape Plot - Plate T Full Set of DOF Mode 2 . . .... ... . ............. .................. . . . . . 3 - 30 3- 12 Mode Shape Plot - Plate T Full Set of DOF Mode 3 . . . .... ... ................................ . . . 3 - 31

- Continued -

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LIST OF FIGURES (CONTINUED) i i

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• Figure : Description 1

.1 3- 13 Mode Shape Plot - Plate T Full Set of DOF Mode 4 ... .... .. . .. ...... ............. . . 3 - 32  ;

t 3- 14 Mode Shape Plot - Plate T Full Set of DOF 3 -

Mode 5 . . .. . . .. .. .. . ..... .. .......... ...

3- 15 Mode Shape Plot - Plate T Reduced Set of DOF Mode 1 . . . .. . . .. .. . .. .. . . 3 - 34 3-16 Mode Shape Plot - Plate T Reduced Set of DOF Mode 2 . . . . . ... .. . ...... .... . .... . . 3 - 35 3- 17 Mooe Shape Plot - Plate T Reduced Set of DOF Mode 3 . . . . . . . . .... .... ........ ... ....... ...... . 3 - 36 3-18 Mode Shape Plot - Plate T Reduced Set of DOF ,

Mode 4 . . . . . .. .. .... ........ .... . ......... ... . . . . 3 - 37 3-19 Mode Shape Plot - Plate T Reduced Set of DOF

Mode 5 . ... . .. .... . .......... ... ................ 3 - 38 6- 1 Plate A (Hot Leg) SLB Displacement Time-History ... ........ ...... . 6-4 l 6- 2 Plate B (Cold Leg) SLB Displacement Time History . . . . . . . . . . . . .. . ... 6-5 6- 3 Plate C (Hot Leg) SLB Displacement Time-History . . . . . . . . . . . . . . ... . . 6-6

• 6- 4 Plate D (Cold Leg) SLB Displacement Time-History . . . . . . . . . . . . . . ..... .6-7 6- 5 Plate E (Cold Leg) SLB Displacement Time-History . . . . . . . . . . . . . . . . . . . . 6-8

- Continued -

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LIST OF FIGURES (CONTINUED)

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. Figure . Description Page 6- 6 Plate F (Cold Leg) SLB Displacement Time-History ......... . . 6-9 6- 7 Plate G (Hot Leg) SLB Displacement Time-History ....... .. . . 6 - 10 6- 8 Plate H (Cold Leg) SLB Displacement Time-History . .... . . .. 6 - 11 6- 9 Plate J (Cold Leg) SLB Displacement Time-History . ... . . . 6 - 12 ,

6- 10 Plate K (Cold Leg) SLB Displacement Time-History . .... . . .... 6 - 13 l 6- 11 Plate L (Hot Leg) SLB Displacement Time-History . . . . . . . . .. 6 - 14 6- 12 Plate M (Cold Leg) SLB Displacement Time-History . ... .. .. . 6 - 15 ,

6- 13 Plate N (Cold Leg) SLB Displacement Time-History . . . . . . .. . 6 - 16

' 6- 14 Plate P (Cold Leg) SLB Displacement Time-History . . . . . . . . . . . ... . . 6 - 17 6- 15 Plate Q (Cold Leg) SLB Displacement Time-History . .... ..... . .. . 6 - 18 6- 16 Plate Q (Hot Leg) SLB Displacement Time-History . . . . . . . . . . . . . . . . . . . 6 - 19 6- 17 Plate R (Cold Leg) SLB Displacement Time History . . . . . . . ..... . . . . . . 6 - 20 -

-I 6- 18 Plate R (Hot Leg) SLB Displacement Time-History . . . . . . . . . . . . . . ... . 6 - 21 6- 19 Plate S (Cold Leg) SLB Displacement Time-History . . . . . . . . . . . . . . . . . . 6 - 22 6- 20 Plate S (Hot) SLB Displacement Time-History . . . . . . . . . . . . . . . . .. .. . 6 - 23 6- 21 Plate T (Cold Leg) SLB Displacement Time-History . . . . . . . . . . . . . . . . . . 6 - 24 22 Plate T (Hot Leg) SLB Displacement Time-History . . . . . . . . . . . . . . . . . . . . 6 - 25 1

7- 1 Distorted Geometry - Plate A ....................................7-4 l.

7- 2 Maximum Stress intensity l Plate A . .. .. ........................... ............ ... 7-5 l i

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LIST OF FIGURES (CONTINUED)

. Figure : Description Page 7- 3 Minimum Stress intensity Plate A . . . .. . ......... . ..... . . ... . . . . 7-6 7- 4 Distorted Geometry - Plate C . .. .. .. . . ...... .. . .7-7 7- 5 Maximum Stress intensity Plate C ...... . . . ..... ...... .. . . 7-8 7- 6 Minimum Stress Intensity Plate C . .. . .... . . 7-9 7- 7 Distorted Geometry - Plate G . . . .. . ... . .... .. . . 7 - 10 7- 8 Maximum Stress Intensity Plate G . . . . . ... . . . ......... . . 7 - 11 7- 9 Minimum Stress intensity Plate G ... . . .. . . ........ . . . . 7 - 12 7- 10 Distorted Geometry - Plate L . . . . . . . . ... .. ........... .. 7 - 13 7- 11 Maximum Stress Intensity Plate L . .. .......................... ................. . 7 - 14 l

1 7-12 Minimum Stress intensity l Plate L . .. . ... ..... ... .... ........... ............... 7 - 15  ;

7- 13 Distorted Geometry - Plate Q . . . . . ...... ............... . . . . . . 7 - 16 7- 14 Maximum Stress Intensity Plate Q . . ... .. . . . .. .............. ..... .. ... . 7 - 17 7- 15 Minimum Stress intensity Plate Q . . ........... ..................................7-18 l

7- 16 Distorted Geometry - Plate R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 - 19 j 7- 17 Maximum Stress Intensity Plate R . . . ............... .. .. ...................... 7 - 20

- Continued -

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LIST OF FIGURES (CONTINUED)

Figure : Description Page 7- 18 Minimum Stress Intensity Plate R . . .. .... .. ... . .. . ...... .... . 7 - 21 7- 19 Distorted Geometry - Plate S .. . . ... ..... ........... . 7 - 22 7- 20 Maximum Stress intensity Plate S . . . .. ... . .. ..... ........ . . 7 - 23 7- 21 Minimum Stress intensity Plate S . . . . . ..... .. . . . .. ....... .. 7 - 24 7- 22 Distorted Geometry - Plate T . . . ... . .. .. ..... ..... .7-25 7- 23 Maximum Stress intensity Plate T . .. . . . . .. .. ....... ..... . . 7 - 26 7- 24 Minimum Stress intensity ,

Plate T .. . .. . ... ... . ... . ... ... ...... .. . 7 - 27 L

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1.0 Introduction This report presents the analys:s of relative motions between the TSPs and the tubes during a SLB event. If the relative tubefiSP displacements during a SLB event are large, then the ,

benefit of the TSP to prevern tube rupture could be reduced Assuming uniform through-wall cracks (conservative relative to those typical of ODSCC) of length approaching the TSP

- thickness, a relative tube /T3P displacement during the SLB event exceeding approximate'y -

0.5 inch could expose the crack with the possibility of a tube rupture. TSP displacements are evaluated using nonlinear, dynamic, time history analyses to assess the potential for crack exposure. This SLB evaluation is specific to the Westinghouse D-3 S/Gs in Catawba-1.

Results from this evaluation are judged to be conservative based on sound engineering principles. The hot standby condition is used as the initial condition for the analysis, thus the .

pressure drops are conservative relative to normal operating conditions. Further, a water level of 392 inches above the top of the tubesheet is assumed. This compares with the expected Catawba-1 water level of 422 inches for hot shutdown conditions. The lower water level increases SLB pressure drops across the plates.

Major sources for conservatism in the analytical displacement responses are as follows. The  !

SLB dynamic analysis does not consider the effects of friction and all friction-like phenomenon which would act at the TSP-tube interfaces, and which would strongly mitigate TSP-tube relative motions. Further, this evaluation assumes no deposits at the TSP-tube interfaces. i Therefore, the possibility of both denting and deposits of magnetite formed by TSP corrosion are not considered and their effects on gaps are ignored. The nominal manufacturing gap between the tubes and TSPs are conservatively used in the analysis to govern the activation of the nonlinear tube interaction effects. Finally, perhaps the most significant conservatism relative to displacements is that the burst probability calculations are made with the TSPs r assumed to remain at the maximum displacement (relative to the tubes) achicved at any time during the transient. This is clearly extremely conservative since the displacements are calculated without friction effects to constrain them, and then it is assumed that they remain for more than 20 minutes in that configuration until the maximum tube pressure differential is ,

attained. In other words, there is no friction when it would mitigate the displacements, but there is friction (or some other mechanism) which acts to keep the plates at their maximum  ;

displacement for a very long (relative to the transient) time period. Thus, these independent conservative assumptions are compounded and exaggerated by assuming simultaneous occurrence in an unrealistically worst case construct.

The TSP. motions due to SLB loads are calculated by means of a nonlinear dynamic  :

time-history analysis employing a structural model of the complete Westinghouse Model D-3  ;

S/G tube and tube support structural system. Specifically, the model includes the tubesheet,

. channel head, lower shell, wrapper, partition plate, all TSPs and baffle plates, and the tierods and spacer pipes. In order to account for possible nonlinear interaction between the TSPs and the tubes due to plate rotations, tube substructures are also included. The analytical -

models and the results obtained from the analyses (both initial static and dynamic time-history

, solutions) are presented below.

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l 2.0 TSP Loads Evaluation .

I

-1 A postulated steam line break (SLB) event results in blowdown of steam and water out of steam generator. The fluid blowdown depressurizes the secondary side fluid and thus causes the fluid to move. Fluid motion leads to pressure drops across the tube support plates (TSP) and the flow baffles. Tube support plate deflections will occur as a result of the pressure

- drops. The SLB pressure loads are determined for the Catawba Unit 1 Model D-3 steam generator using the TRANFLO computer code (References (1) and (2)). The TRANFLO code j is capable of simulating the blowdown flow out of the pressure vessel due to the pipe break event (References (1) and (3)). This code is a network flow based code that simulates the thermal and hydraulic characteristics of fluid through the steam generator internals. Code outputs include flow rate, pressures and pressure drops as a function of time during the SLB transient.

2.1 Initial Conditions of SLB Transient When fluid is set in motion in the tube bundle, it will exert a higher pressure drop across the ,

TSPs and baffles when compared to steam. Hot standby of zero power provides a solid water pool in the tube bundle, while full power operation generates a water and steam mixture.

Thus, hot standby is conservative in determining pressure drops across the TSPs. Previous parametric studies have confirmed that the hot standby, zero load condition, yields larger pressure loads to the internal components when compared to full power operation. Therefore, '

this analysis simulates the SLB transient initiating from no load, hot standby conditions. The Catawba Unit 1 steam generators are maintained at a water level of 422 inches above the top of the tubesheet during hot standby. The computational model considers a water level of 392 inches above the top of the tubesheet. According to previous parametric evaluations, a lower water level tends to yield higher pressure loads across tube support plates because of the rapid flashing of water across the water level. The rapid water flashing generates water

- motion, and the closer the top tube support plate is to the water level, the higher the flow rate, and thus the higher the pressure drop. Use of the no load, hot standby condition and a water level of 392 inches is thus conservative in estimating the pressure loads to the TSPs. System )

parameters corresponding to no load conditions include a water and steam temperature -

initially at 557 F, a primary coolant pressure of 2350 psia, a tecondary side steam pressure of 1106 psia, and a feedwater temperature of 75 F.

2.2 Location of the Guillotine Break ,

A guillotine break of the steam line could be postulated to occur randomly along the whole l length of the line. The analytical model considers that the guillotine break occurs 18 inches  ;

from the outlet of the steam nozzle. This consideration is conservative when compared to the possibility of a break further downstream, such as outside the containment building. An additional 80 feet of piping extends to the inner wall of the containment, and about 180 to l J

- 200 feet lie between the steam outlet nozzle and the main steam isolation valve (MSIV) for the Catawba-1 plant. There are three 90" elbows between the steam generators and containment, and six to the MISV. The additional piping and elbows add to the flow resistance, and tend to decrease the blowdown flow. A reduction of the blowdown flow could ]

, reduce pressure drops through the tube support plates.

2.3 Computational Model The TRANFLO computer modelis composed of a network of nodes and connectors that j represent the secondary side fluid, tube metal heat transfer and primary coolant. Figures 2 and 2-2 show the nodal layout of the secondary side of the Model D-3 steam generator.

I 2-1 i

Figures 2-3 and 2-4 present the nodal network of the secondary fluid. primary fluid and tube j metal. The computational model consists of the following elements ,

i l

n

?

The Moody two-phase critical flow model determines the flow rate of the blowdown out of the steam  :

line break with a discharge coefficient of 1.0. Travis, Hirt and Rivard (Reference (4)) reported in 1978 that one-dimensional critical flow models such as Moody tend to over predict actual flow rates because iney neglect the two-dimensional nature of the flow at the entrance to the break. To predict - .

accurately the blowdown flow rate, a two-dimensicnal analysis would be required. In lieu of such an analysis, a one-dimensional analysis is conservatively used as it yields higher pressure drops than .

the actual ones.

2.4 Loss Coefficient of Pressure Drop Throuoh TSPs in the tube bundle area, [ .

t T-The pressure loads on each TSP is a result of the form loss pressure drop. The form loss pressure ,

drop depends on the form loss coefficient and flow rate across the plate. Based on test data of '

pressure drop across prototypical tube support plates with tubes in place, [

y'.

2.5 Results of Pressure Drops through TSPs and Baffles Blowdown flow induces fluid flow in the secondary side, and thus pressure loads to various baffle plates outside the preheater. Figures 2-9,2-10 and 2-11 depict the pressure loads through preheater baffles. Figure 2-12 shows the pressure differential time history across the tubesheet.

This rapid development of peak pressure drop corresponds to the fast blowdown flow rate and quick 2-2

pressure depressurization. For example, Figure 2-13 depicts the result of blowdown flow through the steam nozzle to the break and flow through TSP T. Figure 2-14 shows pressure transients at the steam nozzle and TSP T, respectively. Figure 2-15 illustrates the increasing trend of steam void

- fraction due to water flashing as a result of depressurization. The blowdown flow through the break  :

., is zero initially (i.e., at time zero) and increases to a maximum flow of about [

! ]** Internal fluid flow such as that inside the tube bundle lags behind the blowdown flow

. through the steam nozzle, but quickly develops, too. For instance (see Figure 2-13), the flow rate ,

through TSP T is essentially zero early in the transient, and then increases to its maximum of about [

j )**. Note that the flow area through TSP T is[

) x, i

j The flow rate peaks within one second while the void fraction increases with time, decreasing the

amount of water in the mixture. Since water exerts higher pressure drops than steam, as the former . ,

j is heavier than the latter, the peak pressure loads across TSPs or baffle plates typically develop i within one second after SLB initiation. The pressure drops then reduce to a small value or become

quasi-steady state.

i

)

4

+

e I

i I l l

e I

• i f .

i l i--

l

! e f*

4

{ -- 2 -_3 s  !

4

+,- -

1 6

s a

r.

M 1

t 4

A i

1 I

Figure 2-1

- Secondary Side Nodes, and Tube Support Plates .

2 Identification (See Figure 2-2 for Preheater Detall)-

2-4  :

s .

t

+

I

.l

'? .

a 5

Figure 2-2  :

Preheater Nodes, and Bame identification of Model D3 Steam Generator ,

.2-5

-9..  ;

i 7

c-i a ,

i i

i i

I

'i k

e >

e 4

T

.i L

.. t J

. -j

-q i

Figure 2-3 . ,

Secondary Side Fluid Nodes and Flow Connectors -!

for Model D3 Steam Generator

-I 2-6 .i

a 2

a h

5 P

t E

.E i

Figure 2-4 .

Primary Fluid Nodes and its Flow Connectors, Metal Heat Nodes' and its Heat Transfer Connectors, and Secondary Fluid Nodes within Tube bundle 2-7 W ,,

h 1

.a r

i v

1

-i 4

it .j Figure 24_ _

l' Pressure Drops through Flow Distribution Baffes A and B '

during Steam Line Break of Catawba 1 Steam Generator- '

2 .

. j--

l

?

2 1

a i

- i 1

9 i

L' t

1 f

4 e

f

^!

t

,. i i

k, .

i Figt,re s 24

- Pressure Drops through Tube Support Plates C, O and L during Steam Line Break of Catawba 1 Steam Generator

k. 2 ,9 3

I

i a 'l t

l .'

' \

i d

9 Figure 2-7 .

Pressure Drops through tube Support Plates Q%, and Qw during Steam Line Break of Catawba 1 Steam Generator 10 -

l5

i i

a I

a A

f i

4 i

J

~ .,

1 a ,

t b

Figure 2-8 ')

Pressure Drops tiirough Tube Support Plates R,8 and T during Steam Line Break of Catawba 1 Steam Generator 1 2 - 11

'l

i.

a-i, i

t I

t r

N 4

I"~ Figure 2-9 Pressure Drops through Preheater Bames D, E and F during Steam Line Break of Catawba 1 Steam Generator i

'-i 2 - 12 .;

- n

a

.o

)

l*

I l, -

Figure 2 '

Pressure Drops through Preheater Bames H J and K during Steam Line Break of Catawba 1 Steam Generator 2 - 13 l-

.---_-_-______-.:___---__:____L___-  ::____--_____-______-___________-.- .

a s,

Figure 211 Pressure Drops through Preheater Bames M. N and P

'during Steam Line Break of Catawba 1 Steam Generator .

2 - 14

a l.

't i P

}

1 i

t

' I i

i

- - Figure 212 )

Pressure Differential Across Tubesheet during

~

j Steam Line Break of Catawba 1 Steam Generator  ;

2 - 15  ;;

i s

v y. o-y y- - e y y

i I ;.

l a

4

,9'

"*' Figure 2-13 Blowdown Flow through Steam Nonle and Flow Rate .

through Tube Support Plate T-2 - 16 a

j j

.)/ ,

d 4

a 1

t!

Figure 214-Fluid Pressure at Steam Nonle and Tube Support Plate T 2 - 17 w'

a J

i

[

i l

7 Figure 215 Steam Vold Fraction at Tube Support Plate T l 2 - 18 i

3.0 Structural Modeling This section summarizes the structural modeling of the Model D3 preheater region. The model is converted into a number of substructures (super elements) that are used in the subsequent dynamic analysis to determine TSP displacements under SLB loads. Due to the support configuration for the TSPs, it is necessary to include essentially all of the [

]*".

The WECAN computer code, Reference (7), is used to develop the model. The model is composed mainly of plate elements, with beam elements used to model the tierods, spacers, and tubes.

3.1 Material Properties A summary of component materials is contained in Table 3-1, with the corresponding material properties summarized in Tables 3-2 through 3-7. The properties are taken from the 1971 edition of the ASME Code, Reference (8), which is the applicable code edition for Catawba Unit 1. It should be noted that although the properties are provided over the temperature range 70 -700 F, the average temperature during the transient is -550 F. Since temperature

• dependent properties cannot be used in substructures, properties for the finite element model correspond to the values at 550 F. In addition, the material properties for the tubesheet and tube support plates must be modified to account for the tube penetrations and flow holes.

- Also, in the case of the TSPs, the density must be modified to account for the added mass of the secondary side fluid. Additional discussion concerning these modifications is provided later in Section 3.4.

32 TSP Support System The support system for the TSPs is a combination of several support mechanisms. A schematic of the tubc bundle region is shown in Figure 3-1, with each of the plates identified.

The hot leg plates in the preheater region (A, C, G, and L), and the plates above the preheater (0, R, S, and T) are [

, ]*.'

The in-plane support for the TSPs is provided by [

3-1

~

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

[

}'

As noted above, [

.]* There would likely bo l -- some frictional resistance, however, this has been neglected for this analysis. For Plates L, Q, R, S, and T, where the [

]**. Recall, in the discussion above, that for Plates G andH,[

]*.

Regarding the tierods and spacers,[

i jb 4

1

]**.

The various support locations for the plates are shown in Figures 3-2 through 3-8. Figure 3-2 shows the locations of the tierods and spacers. Plate / wrapper support locations are shown in Figures 3-3 through 3-5, with partition plate support locations shown in Figures 3-6 through 3-8.

In reviewing the vertical support locations for Plate C, it is apparent that [

]**

.q 3.3 Finite Element Model Geometry

[ The overall finite element model is shown in Figure 3-9. In order to generate appropriate ' .

substructures for the tubes, the model includes [ .  ;

l yr. l o .;

3-2 I

__1_______:_2_

I .

p.c ,

Shown in Tables 3 8 and 3-9 is a listing of the substructures for the different component members. Note as discussed above, that the non-linear spacers are not included in any of

. the substructures. A summary of the non-linear spacer stiffness values is shown in .

Table 3-10. I 3.4 Revised Material Properties As noted earlier, the material properties for the tubesheet and tube support plates are modified to account for [

Ja.c in calculating revised values for [

t Y

i P

p.c For the tubesheet, [

T*. Calculations to determine the revised tubesheet density are contained in Table 3-12.

For the TSPs, there are [

y.c

' Several of the plates on the cold leg of ' tie preheater have flow slots in place of flow holes.

For these plates, [

p.c (continued).

3-3 l i

.l 1

[

]. This table provides a summary of the actual (structural) and modeled plate areas, the metal and added fluid masses, and the final effective plate densities.

,- 3.5 Dynamic Dearees of Freedom in setting up the dynamic substructures, it is necessary to define the dynamic degrees of 1 freedom. For this analysis, [

t ja.e, In all, [

]'*. A sample set of mode shape plots is provided for Plate T. Mode shap plots for the full set of DOF are shown in Figures 3-10 through 3-14, while mode shapes for the reduced set of DOF are shown in Figures 3-15 through 3-19. A comparison of the natural frequencies for the full and reduced sets of DOF for these plates is provided in Table 3-14.

l Based on both [  !

ja.e The DOF for the [

. .i

]'

• l-;

"' ' (continued)

It is expected that in the vicinity of the flow slots the [ >

e 3-4 l 1

1

with support plate locations for the plates. The DOF for the[

).t, 3.6 Displacement Boundary Conditions The displacement boundary conditions for the substructure generation consist primarily of [

ja.c, S&

nm I

3-5

.l r

e Table 3-1 l, Summary of Component Materials l t

) .

f l COMPONENT l MATERIAL l  ;

s ChannelHead SA-216 Grade WCC  !

Tubesheet SA-508 Class 2  !

Shell SA-533 Grade A. Class 2 i Tube Support Plate SA-285 Grade C l Wrapper SA-285 Grade C "!

Partition Plate SA-285 Grade C

', t Stayrod SA-106 Grade B  !

. Spacer SA-106 Grade B Tube inconel 600 -

i d

f

~!

., i l

i l

~

.'-l 1

i

)

3-6 I

,- - , , , _ ~, . . e _ _ _ _ _ _ _ _ _ , _ _ . - _~

Table 3-2 Summary of Material Properties

. SA-216 WCC I

ll TEMPERATURE l PROPERTY CODE ED. 70 200 300 400 500 600 700 Young's Modulus 71 27.90 27.70 27.40 27.00 26.40 25.70 -24.80 Coefficient of Thermal 71 6.07 6.38 6.60 6.82 7.02 7.23 7.41 Expansion Density -

0.283 0.282 0.282 0.281 0.280 0.280 0.279 7.324 7.303 7.287 7.269 7.252 7.234 7.215 c,

l PROPERTY l UNITS l Young's Modulus psi x 1.0E06 Coefficient of Thermal in/in/deg. F x 1.0E-06 Expansion Density Ib/in*3 a

lb-sec 2/in"4 x 1.0E-4

.t

-O A

3-7  !

)

i

I l

I Table 3-3 Summary of Material Properties j

- SA-508 Class 2  ;

i o

ll TEMPERATURE l PROPERTY CODE ED.l 70 200 300 400 500 600 700 Young's Modulus 71 29.90 29.50 29.00 28.60 28.00 27.40 24.90 t Coefficient of Thermal 71 6.07 6.38 6.60 6.82 7.02 7.23 7.41 Expansion  ;

Density - 0.283 0.282 0.282 0.281 0.280 0.280 0.279 7.324 7.303 7.287 7.269 7.252 7.234 7.215

, l PROPERTY l UNITS l Young's Modulus psi x 1.0E06

- Coefficient of Thermal in/in/deg. F x 1.0E-06 Expansion Density Iblin^3 l lb-sec^2/in^4 x 1.0E-4 )

l l

1 1 . .

3-8 l

Table 3-4 Summary of Material Properties

- SA-533, Gr. A - Class 2 ll TEMPERATURE PROPERTY CODE ED. 70 200 300 400 500 600 700 Young's Modulus 71 29.90 29.50 29.00 28.60 28.00 27.40 26.60 Coefficient of Thermal 71 6.07 6.38 6.60 6.82 7.02 7.23 7.41 t Expansion Density -

0.283 0.282 0.282 0.281 0.280 0.280 0.279 i 7.324 7.303 7.287 7.269 7.252 7.234 7.215 .

, l PROPERTY l UNITS l Young's Modulus psi x 1.0E06 Coefficient of Therrnal in/in/deg. F x 1.0E-06 Expansion .

Density lblin*3 '

lb-sec^2/in^4 x 1.0E-4 9

?

l 3-9

Table 3 Summary of Material Properties SA 285, Gr. C ll TEMPERATURE I PROPERTY l CODE ED. 70 200 300 400 500 600 700 Young's Modulus 71 27.90 27.70 27.40 27.00 26.40 25,70 24.80 s

Coefficient of Therma! 71 6.07 6.38 6.60 6.82 7.02 7.23 7.44 Expansion Density - 0.284 0.283 0.283 0.282 0.281 0.201 0.280 7.35 7.33 7.32 7.30 7.28 7.26 7.25 i PROPERTY l UNITS l r Young's Modulus psi x 1.0E06 Coefficient of Thermal in/in/deg. F x 1.0E-06 Expansion Density Iblina3 lb-sec^2/in"4 x 1.0E-4 O

a 3 - 10

Table 3-6 Summary of Material Properties

, SA-106, Gr. B ll YdMPERATURE l PROPERTY CODE ED. 70 200 300 400 500 600 700 Young's Modulus 71 27.90 27.70 27.40 27.00 26.40 25.70 24.80 Coefficient of Thermal 71 6.07 6.38 6.60 6.82 7.02 7.23 7.44 Expansion Density -

0.284 0.283 0.283 0.282 0.281 0.281 0.280 7.35 7.33 7.32 7.30 7.28 7.26 7.25

, l PROPERTY { UNITS l Young's Modulus psi x 1.0E06

- Coefficient of Thermal in/in/deg. F x 1.0E 06 Expansion Density lb/in^3 lbsec^2/in^4 x 1.0E-4

.e 9

)

a 3 - 11 e . _ - _ . _ _ _ _ . - _ . _ _ _ .

a Table 3 7 Summary of Material Properties

.. SB-166 ,

ll TEMPERATURE l PROPERTY CODE ED. 70 200 300 400 500 _ 600 700 Young's Modulus 71 31.70 30.90 30.50 30.00 29.60 29.20 28.60 Coefficient of Thermal 71 7.13 7.40 7.56 7.70 7.80 7.90 8.00 Expansion Density - -

0.306 0.305 0.305 0.304 0.303 0.302 7.923 7.905 7.386 7.867 7.847 7.828 4

I PROPERTY l UNITS l Young's Modulus psi x 1.0E06

,, Coefficient of Thermal in/in/deg. F x 1.0E-06 Expansion <

Density Ib/in^3 lb-sec^2/in^4 x 1.0E-4 6

i e

3 - 12

a Table 3-8 '

Summary of Model Sub Structures Non-Plate Components t

4 a

s 4

t f

4 h

6 2

M s

O

.A 3 - 13

Table 3 9 '

Summary of Model Sub Structures.

4 Baffle and Support Plates k

e t'

l 3 - 14

Table 3-10 Summary of Non Linear Spacer Stiffnesses e

) a l

l l

l 8 I-1 l

i 1

e e

3 - 15

'ot Table 311 Summary of Equivalent Plate Properties 5

4 1

I 6

2 O

- i am 1

4 w

2 e

4 i

e e

d 3 - 16 i

1 l

l Table 312 Calculation of Revised Tubesheet Density B

J

.e h

4 Gu 1

9 5

3 - 17 l

i Table 3-13 Summary of Effective Plate Densities S

t Metal Density = 727 lb-sec a2An*4 E-4 Plate thickness = 0.75 in S

4 I

t 3 -18

Table 3-14 Comparison of Natural Frequencies

• Full Versus Reduced DOF  ;

E a

3 r

b p

4 t

t M

W t

b I

W k

4 F O

i M

.3 - 19

[. ,

n

. I t

A > L .

l

.g.

f\ '

i n-I

'Q* I u

e- x

, *W ~ %

H

• L* q 'M"- N ,_

-. w- s _

4

.y - , .

i 1

SlW

, , "Ga m *H' - T _

.p. _ s

~

~

• 2 "

.c.

. -b

.D*-- ' '

.A* m *B' - N m, l emis a summi a4 Mr i

~

4

, 4

. NoTt: PRD4EATZR WODlMCAT10N NOT WCWM t .

Figure 3-1 Tube Bundle Geometry 3- 20

i

~

d Figure 3 2 Tierod / Spacer Locations 3 - 21

r P , :

)

)

- i,

~a.  !

. -i i

)

.i

'j. ..

i i

i

.'i t

't f

-5 3

i i

}

.  !)

e-

. Figure 3-3 Plate / Wrapper Support Locations .

Plates A, C. L. B D, E, F. J, K, M, N, P '

i i

3 - 22 ,

I e ve--,- v - > = y- w- -

4 A

3

^  ;

l i

\

l Figure 3-4 Plate / Wrapper Support Locations Plates G, H L

1 3 - 23

fI

~

a s

• Figure 3-5 Plate / Wrapper Support Locations Plates Q, R S, T 3 - 24

1

. a s

i i

i 1

1

• i 1

l l

l

. Figure 3-6 j Plate / Partition Plate Support Locations Plates A, B 3 - 25

. a a

i 1

l 1

=

A

. Figure 3-7 Plate i Partition Plate Support Locations Plates C, D, G 3 - 26 L .. ,. . .

i 1

~ a a

. Figure 34 Plate i Partition Plate Support Locations Plates E, F, H. J, K, L, M, N, P i 3 - 27  ;

)

a 2

Figure 3-9 overall Finite Element Model Geometry 3 - 28

1 1

]

a 1

Figure 3-10

• Mode Shape Plot - Plate T Full Set of DOF Mode 1 3 - 29

a 4

4 1

Figure 3-11 Mode Shape Plot - Plate T Full Set of DOF Mode 2 l

3 - 30

. 1 i

4, a

Figure 3-12 Mode Shape Plot - Plate T Full Set of DOF Mode 3 3 - 31

a 4

Figure 3-13  ;

- Mode Shape Plot - Plate T l Full Set of DOF Mode 4 3 - 32 L

b-a s

s' i

1 Figure 3-14

- Mode Shape Plot - Plate T Full Set of DOF Mode 5 3 - 33

a i

f 1

i l

?~

l l

Figure 3-15 Mode Shape Plot . Plate T Reduced Set of DOF Mode 1 3 - 34

((

a t

• 2 i

4 1

Figure 3-16

- Mode Shape Plot - Plate T Reduced Set of DOF Mode 2 3 - 35

1 i

1 i

J a l 1

8 I

1 1

l l

1 l

1 i

a  !

'I a

4 l

Figure 3-17

- Mode Shape Plot -Plate T Reduced Set of DOF Mode 3 3 - 36

, . .- . - . . - ~. . - . . . - . . .

$ '^t .

-)

1

-i i

.i t

a- t 9

a  !

e-

.l 3

1:

a f

i i

?

h

I

?

f i

'l

,. r 1.- l

.1 i

Figure 3-18 .l Mode Shape Plot Plate T ,

Reduced Set of DOF .  ;

l Mode 4  ;

?

j 3 - 37

~

, e ~ - - . -..L. ______-L-..-__-..-_._.._ __.-._--:L.>

a !

a 1

e Figure 3-19

• Mode Shape Plot - Plate T Reduced Set of DOF Mode 5 3 - 38

4.0 Application of Pressure Loading

. The SLB pressure loads act on the tubesheet and each of the TSPs. To accommodate this, load vectors are prescribed for each of the plate substructures using a reference load of

[ ]** The loads are applied to each component by [

]**, as defined in Section 2.0.

The transient pressures summarized in Section 2.0 are relative to the control volume for the thermal hydraulic analysis. The area over which the hydraulic pressure acts corresponds to the area inside the wrapper minus the tube area. These pressures [

]* * . A summary of the transient pressure drops obtained from TRANFLO are given in Section 2.0. These were modified as discussed above and applied to the structural model for the dynamic analysis.

4 e

S 6

9 m

9 J

4-1

5.0 WERWOLF Computer Program and Solution Capabilitics The purpose of the analysis is to obtain the relative motions between the tubes and tube support plates under the actions of the SLB loadings. Structural model superelements

. discussed previously in Section 3.0, which represent each of the linear structural components of the Model D3 S/G tubes, tubesheet and tube support plates physical system, provide the appropriate mass and stiffness matrices necessary to obtain both the required static and

, dynamic motion solutions.

The superelement properties are appropriately coupled together in the nonlinear solver program WERWOLF. Additional required model capabilities to simulate important physical  ;

effects are also implemented in WERWOLF. For the SLB analysis, the additional capabilities include: [

]*- More detail with respect to each of these capabilities follows.

The linear structural members are assigned DOFs as follows. [ ,

a,C I

a.C I

P 9

aC

, [

a.C 5-1

6.0 Displacement Results t

The purpose of this Section is to present the conservative relative motions between the TSPs

-. and the tubes which were obtained through the nonlinear dynamic WERWOLF solution described in Section 5.0, and which are required to establish the conservative potential crack length uncovered during the SLB event. ,

[ ,

]**. It is, therefore, important that these results be reviewed to determine that, indeed, there was no chance for gross plastic deformations in one or more areas of the model that could possibly significantly affect those relative TSP-tube motions. This section provides those required reviews.  !

We note that there are two major influences on the evaluation of the TSP-tubes relative displacements in the dynamic model. [

}*** .t The nonlinear dynamics analysis results establish that, [

r

[ ,-

]** These are addressed below (Section 7.0).

[ ,

]'* Specific displacements that are '

recommended for those calculations are given in Table 6-1. Actual time-histories of relative ,

tube / TSP displacements are provided in Figures 6-1 through 6-22. These figures address  ;

the plates in Westinghouse nomenclature and in alphabetical order. [ ,

]**. i We have reviewed the important absolute and relative displacements above. In Section 7.0, l the stresses and their implications are reviewed. [ ,

]**

6-1  ;

s 9

f f

I.

j 1

Js,c k

1. 5 b

t e

i-h I

h

-h t

F

.i ih

1. l

?

'I b

.6 i

.1

?

r

A. p a

b s

..)

"f

'I 3

?. )

J 3

9 r

..} .

s

.1 l

,- )

1

.4 ,

.k '

1

.h 6-2 p,

- !1 1

, w < ,

l Table 6-1 Summary of TSPITube Relative Displacements for Postulated SLB Event for Catawba D3 S/Gs

\

e 6

e m

6-3

a s

l d'

l I

i Figure 6-1 Plate A (Hot Leg) SLB Displacement Time-History 64

.l

- a a

a Figure 6-2 Plate B (Cold Leg) SLB Displacement Time-History l 6-5

i i

l a

e Figure 6-3 Plate C (Hot Leg) SLB Displacement Time-History 6-6

~ a i '

e 1

l 1

Figure 6-4 Plate D (Cold Leg) SLB Displacement Time-History 6-7 l l

. a a

t Figure 6-5 Plate E (Cold Leg) SLB Displacement Time-History 6-8

1 i

)

~ a ,

l I

i 8

3 i

b 4

Figure 6-6 Plate F (Cold Leg) SLB Displacement Time-History -

l 6-9

a

~

. .M 4

Figure 6-7 Plate G (Hot Leg) SLB Displacement Time-History 6 - 10

l l

i a l

.. 1 l

1

)

8 i

a

-o

.c  ;

i Figure 6 8 Plate H (Cold Leg) SLB Displacement Time History 6 - 11

t L

i I

a

[

f

. .t ,

3 f

C

- r

.I

?

t e .*

4 i

F t

J v

-]

.i '

P -

. Figure 6-9. Plate - J (Cold Leg) SLB Displacement Time-History  ;

6 - 12  :

4

--__Y--

('

l 1

1 I

l l

l

., a n

i

-4 Figure 610 Plate K (Cold Leg) SLB Displacement Time-History 6 - 13

a 4

J Figure 6-11 Plate L (Hot Leg) SLB Displacement Time-History 6 - 14

a s

Figure 612 Plate M (Cold Leg) SLB Displacement Time-History 6 - 15

. a l

I i

l i

i

• :l l

Figure 6-13 Plate N (Cold Leg) SLB Displacement Time-History 6 - 16 I

i

________._____._________________._._____________________._____._______.______.___a

l 1

l f l i 'a l I

J

^.,  ;

Figure 614 Plate P (Cold Le9) SLB Displacement Time-History i

1 6 - 17 l

i a

a-

-)

i . j

-!i

! i i

I l

i 1

, ') .

+- .j Figure 615 Plate Q (Cold Leg) SLB Displacement Time-History 6 - 18 q

-q j

, a 1j 1

s ,

1

.,: a {

b e-t, 1

e  ::

... zj A

1

')

z.

Figure 616 Plate Q (Hot Leg) SLB Displacement Time-History 6 - 19 ..

1

e

.i j

i 2

.1

'i L

i 4

Figure 6-17 : Plate R (Cold Leg) SLB Displacement Time-History 6 - 20

. a J

Figure 6-18 Plate R (Hot Leg) SLB Displacement Time-History 6 - 21

i a

4 Figure 6-19 Plate S (Cold Leg) SLB Displacement Time-History 6 - 22

y7 -

B W

.4 e

I

)1 Figure 6-20 Plate S (Hot) SLB Displacement Time-History 6 - 23 ,

I

e a

s 4

1 i

o l.

l Figure 6 21 Plate T (Cold Leg) SLB Displacement Time-History 6 - 24

F a

l i

l t

M Figure 6 22 Plate T (Hot Leg) SLB Displacement TimeMistory 6 25

I 7.0 Stress Results The appropriateness of the displacements calculated using the elastic dynamic analysis is in I part dependent on the amount of plasticity that occurs in the various structural members of the

, preheater during the SLB event. -Thus, in conjunction with the displacement results from the i dynamic analysis, stresses are calculated for the hot leg plates at the times corresponding to the maximum plate displacements. [

]'*. A summary of the maximum SLB displacements for each of the plates is summarized in Table 6-1. For the plates above the preheater, O, R, S, and T, maximum displacements are given for both the hot and cold legs.

1 The displacement values in Table 6-1 are relative displacements between the TSP and the l tubesheet relative to their initial starting position. The primary concem for the SLB event, is the relative motion of a tube and the TSP at any given TSP. In other words, how much would an axial crack that is inside a TSP move up or down relative to the TSP during a SLB event.

Since the tubes are assumed to move with the tubesheet, relative displacements are. )

calculated between the tubesheet and TSP.

Although, the values in Table 6-1 are not absolute displacements, is is anticipated that the

- times corresponding to the maximum relative displacements are also ine times of maximum 1 displacement amplitude for each of the TSP's. The transient response of the tubesheet during the first 1.5 seconds is a gradual decay of pressure drop. Thus, the transient response

- characteristic of the relative displacements also represents the transient response of the TSP, -

offset by the tubesheet displacement.

I  ;

l ja.c, Additional boundary conditions corresponding to lines of symmetry and appropriate rotational

. constraints are also applied to the model. The finite element results give a set of displacement and stress results for the overall plate. [ j

.l l

4.C In order to interpret the displacement and stress results, a distorted geometry plot and stress contour plots for the maximum and minimum stress intensities have been made for each 7-1 q

l plate. These plots show the distribution of stress throughout the plate. As expected, the maximum stresses occur near the tierod support locations, and along the plate neutral axis,

, where high plate flexure occurs. The plate stresses cannot be compared directly to the material yield strength, however, as these stresses correspond to an equivalent solid plate. In order to arrive at the plate ligament stresses, additional detailed stress analysis of the plates is required. Such an analysis is outside the scope of this program. The equivalent plate stresses do provide a general guideline as to those areas of the plate that are most limiting from a stress viewpoint. The distorted geometry and stress contour plots are provided in Figures 7-1 through 7-24. A summary of which figures apply to which plates is given in Table 7-2.

[

, ja.c I

, ]* '.

Thus, it is concluded that, although some local yielding of some of the plates is likely to occur, the maximum plate displacemetns are not expected to be significantly affected.

I l

l l

7-2 1

. r . 7- e., ,,, ,.

d, "% j

~;, '

1 Table 7-1 -l Summary of Distorted Geometry /

Stress Plot Figure Numbers  !

l i

Distorted SINT Plate Geometry Max l Min - ,

A 7-1 7-2 7-3 C 7-4 7-5 7 G 7-7 7-8 7-9 L 7-10 7-11 7-12 +

Q 7-13 7-14 7-15 R 7-16 7-17 7-18 I S 7-19 7-20 7-21 i T 7-22 7-23 7-24

, 6

+

.i b

o v

\

t h

a r

7-3 l

a a

a f

v Figure 7-1 Distorted Geometry . Plate A 7-4

r4 a

9 4

o i

l i

Figure 7 2 Maximum Stress intensity l Plate A i

=  ;

7-5 4

i

a a

1 I

(

1 l

1 l

l l

'W l

j- .

Figure 7-3 Minimum Stress intensity Plate A i'

7-6 I

t _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _

1 t.

l 1

1 a

a l

M Figure 7-4 Distorted Geometry - Plate C 1

1 7-7 )

i

a 4

r er

. Figure 7-5 Maximum Stress intensity ,

Plate C 7-8

a

• i i

~

i j

Figure 7-6 Minimum Stress intensity i Plate C I 7-9  ;

a t

9 Figure 7 7 Distorted Geometry - Plate G 7 - 10

a P

d Figure 7-8 Maximum Stress Intensity Plate G 7 - 11

a 1

Figure 7-9 l Minimum Stress intensity Plate G i

7 - 12

a 4

t o

9 Figure 7-10 Distorted Geometry - Plate L 7 - 13

a

'J 1

O

. l 1

Figure 7-11 Maximum Stress intensity Plate L 7 - 14

a W

o

~

Figure 7-12 Minimum Stress Intensity .

Plate L l

7 - 15 '

i

s.

]

a

<o t

e e

l i

Figure 7-13 Distorted Geometry - Plate Q 7 - 16

4 .

l l

.I 6

e l

1

-' Figure 714 Maximum Stress intensity Plate Q i

7 - 17  ;

4 a

0 i

o-Figure 7-15

• Minimum Stress intensity Plate Q 7 - 18

I a

9 4

1 1

t'.

I i l

4 l

L e

Figure 716 Distorted Geometry - Plate R 7 - 19

a

+

3 F

4 L

e Figure 7-17 Maximum Stress Intensity Plate R 7 - 20

l a ,

o.

t c

3 Figure 7-18 J

Minimum Stress intensity Plate R 7 - 21

p ~],

p l

l de 1

a a

4 9

k Figure 719 Distorted Geometry - Plate S 7 - 22

1 a

-O a

4, o

Figure 7-20 Maximum Stress intensity Plate S 7 - 23

a x

i o

L I

a 1

Figure 7-21 g

Minimum Stress intensity Plate S 7 - 24

r i.

I I-t s.

a 4

4 E

[

i o .

f 3

L

.L C

1I

)

1 Figure 7-22 Distorted Geometry - Plate T  !

7 - 25 i

J

-! r i_T-(

1

'a  :

i

.y. >

t t

t I

k i

L

,i

)

'I t

- b t

v i

,i 1;

.?

t

'L

.1 2 +

t f

a

,i t

t

+

3

.t t

Figure 7-23 Maximum Stress Intensity

' Phk T

• 7 ..

?

a

'i

(

)

'v Figure 7 24 Minimum Stress intensity Plate T 7 - 27

8.0 Displacement Categorization

, in order to establish probabilities for tube burst as a result of relative plate / tube movement, calculations are performed to determine how many tubes are associated with a given displacement magnitude for a given plate. The plate displacements are categorized into three groupings, [ ]^# It is the relative plate / tube 9 displacement that is of interest, with the tube and plate positions at hot shutdown defined as the reference position. Thus, the algorithm for calculating the relative displacements is as follows:

AD = (Dg,,,, - D 7o ,,,no,,), , 7 - (Dg,,,, - D ,eo,noi), 7 , o., where Dg,,,, = Plate Displacement Druno,no, = Tubesheet Displacement T = Time of maximum relative displacement from dynamic analysis In order to calculate the relative displacements across the full plate, displacement (stress) solutions are run for the tubesheet and for the plate being evaluated both at time equal zero, and at the time of maximum relative displacement. Reviewing the summary of maximum relative displacements for the hot leg plates in Table 6-1, the maximum displacement exceeds

[

ps Based on the results in Table 6-1, stress solutions are obtained for the tubesheet at the following times.

o a,c a

f 7,

s 8-1 l

i Table 81 Summary of Results for s - Displacement Categorization

-Q ,

a l

t

[

O I

4.

8-2

9.0 References v 1. Land, R. E.,1976, "TRANFLO Steam Generator Code Description," WCAP-8821, Westinghouse Proprietary Class 2, September 1976.

2. MPR 663, "TRANFLO: A Computer Program for Transient Thermal Hydraulic Analysis with

' Drift Flux," November 1980, MPR Associates, INC.

3. MPR 755, "Model D-3 Steam Generator Thermal Hydraulic Transients," January 1983, MPR Associates, INC.

4. Travis, J. R., Hirt, C. W., and Rivard, W. C.,1978, " Multidimensional Effects in Critical Two-Phase Flow," Nuclear Science and Engineering, Vol 68, pp. 338-348

5. Huffman, K. L. and Billman, T. A.,1977, " Baffle and Tube Support Pressure Drop Testing," WTD-PE-77-04, Westinghouse Proprietary Class 2.

6. APWR-SG-0597,1984, " Advanced PWR Steam Generator Design Review Report," Vol 2 June 1984, Westinghouse Proprietary Class 2.

7. 88-1E7-WESAD-R2, "WECAN - Westinghouse Electric Computer Analysis, User's Manual", Third Edition, Revision X, K. Thomas.  ;

,e 8. ASME Boiler and Pressure Vessel Code, Section Ill,1971 edition.

" 9. "Added Mass and Hydrodynamic Damping of Perforated Plates Vibrating in Water",

r D. F. DeSanto, Journal of Pressure Vessel Technology, May,1981. j I

l l

4 t

. .m 9-1