ML20067D711

Nonproprietary VC Summer Evaluation for Tube Vibration Induced Fatigue

ML20067D711
Person / Time
Site:	Summer
Issue date:	10/31/1990
From:	Wootten M WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP.
To:
Shared Package
ML19310E606	List: ML20067D706 ML20067D711
References
SG-90-05-045, SG-90-5-45, WCAP-12593, NUDOCS 9102130194
Download: ML20067D711 (170)

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4

. ' HEST 8NGHOUSE CLASS 3-l.

HCAP 12593 SG-90-05-045 V. C. SUMMER EVALUATION FOR TUBE VIBRATION INDUCED FATIGUE OCTOBER 1990 f

M.a./

APPROVED: -

M. J. H00TTIK, MANhGER STEAP GENERATOR TECHNOLOGY AND ENGINEERING This ' document.contains information proprietary to Hestinghouse Electric

' Corporation. It is submitted in confidence and is to be used solely for the

. purpose for which it is . furnished and is to be returned upon request. This

document'and such information is not to be reproduced. transmitted, disclosed

or used otherwise in whole or in part without written-authorization.of Hestinghouse Electric Corporation, Energy Systems Business Unit.

WESTINGHOUSE ELECTRIC CORPORATION

'- NUCLEAR SERVICE DIVISION P.O. BOX-355

- PITTSBURGH, PENNSYLVANIA 15230

- c1990 Hestinghouse Electric Corporation

,06290:10/062890 l

i l

1 FOREHORD This nonproprietary report bears a Westinghouse copyright notice. The NRC is

- permitted to make the number of copies of this report necessary for its internal use and such additional copies which are necessary in order to have one copy available for public viewing in the appropriate docket files in the public document room in Washington, D.C. and in local public document rooms as may be required by NRC regulations if the number of copies submitted is insufficient for this purpose. The NRC is not authorized to make copies for the personal use of members of the public who make use of the NRC public document rooms. Copies of this report on portions thereof made by the NRC must include the copyright notice.

0629D:10/101190

= = = "

r4a -

> j,.Aes 2-M o s aa 1L.,e# _. - . m, 4 A ----g,._L 2: 51 _,.- k.,.-

l l

ABSTRACT l On July 15, 1987, a steam generator tube rupture event occurred at the North

.- Anna Unit 1 plant. The cause of the tube rupture has been determined to be high cycle fatigue. The source of the loads associated with the fatigue mechanism is a combination of a mean stress level in the tube with a superimposed alternating stress. The mean stress is the result of applied loading, manufacturing-induced residual stress and denting of the tube at the top tube support plate, while the alternating stress is due to out-of-plane deflection of the tube U-bend attributed to flow induced vibration. - For tubes without AVB support, local flow peaking effects are a significant contributor to tube vibration amplitudes.

This report documents the evaluation of steam generator tubing at V. C. Summer for-susceptibility to' fatigue-induced cracking of the type experienced at North Anna-Unit 1. The evaluation utilizes operating conditions specific to ~

- V. C. Summer to account for the-plant specific nature of the tube loading and response. The evaluation also includes reviews of eddy current data for s V. C. Summer to establish-AVB locations. This' report provides background of the event which occurred at North Anna, a criteria for fatigue assessment, a summary'of test data which support _the analytical approach, field measurement results showing AVB positions, thermal hydraulic analysis results, and calculations to determine tube mean stress, stability ratio, tube stress ratio, and' accumulated fatigue usage. This evaluation concludes that seven tubes were potentially susceptible to fatigue, and required ameliorative action.

Such action was completed :n April, 1990, with the installation of a cable damper, a hot leg solid plug, and a-cold leg sentinel plug, in each of the seven aforementioned-tubes. No further ameliorative action is required, and the tubes remaining in service in the V. C. Summer steam generators are not expected to be susceptible to high-cycle fatigue rupture at the top tube 4

support plate in a manner similar to the rupture which occurred at North Anna Unit #1 assuming operation of the plant through the end of the operating license at a full power steam pressure above 905 psia.

06290:1D/062690 i i

SUHHARY OF ABBREVIATIONS ASHE - American Society of Mechanical Engineers ATH0S - Analysis of the Thcrmal Hydraulics of Steam Generators AVB - Anti-Vibration Bar AVT - All Volatile Treatment ECT - Eddy Current Test EPRI -

Electric Power Research Institute FFT -

Fast Fourier Transform FLOVIB -

Flow Induced Vibrations HEVF - Hodal Effective Void Fraction OD - Outside Diameter RMS - Root Hean Square SR - Stability Ratio TSP - Tube Support Plate

'F - degrees Fahrenheit

~

hr - hour ksi - measure of stress - 1000 pounds per square inch lb - pound mils -

0.001 inch HH -

megawatt psi - measure of stress - pounds per square inch psia - measure of pressure - absolute 0629D:lD/062690 ii

TABLE OF CONTENTS o

h.

SECTION. 1

1. 0 Introduction

- 2.0 Summary and Conclusions ,

L2 1. Background

, 22 Evaluation Criteria

'2. 3 Denting Evaluation-2.~4 AVB Insertion Depths 2.5 : Flow -Peaking Factors 2.6 Tube Vibration Evaluation

'2.7 Overall Conclusion h 3.0  :

Background

L R .

3.1 North Anna Unit 1 Tube Rupture Event 3;2 Tube Examination Results g_, 3.3 _Hechanism Assessment ,

c4.0- Criteria f$r Fatigue Assessment -i 4.1 Stability Ratio Reduction Criteria 4.2 . Local Flow Peaking Considerations 04 4.3 ' Stress Ratio Considerations 1

50-

. Supporting Test Data 5 ?) ' Stability Ratio Parameters

' 5.2 -Tube' Damping Data

- 5.3 Tube Vibration Amplitudes with Single-Sided AVB Support

' 5.4 Tests to Determine the Effects on Fluidelastic Instability of Columnwise Variations in AVB Insertion Depths 5 .- 5 References 06290:10/062690 i ii L

r J

i i e ~. I.- -w + obs +k, - , - m- - ~- A w - - --,- - - - e - - en - ,,e -- ------ - - - -

TABLE OF CONTENTS (CONTINUED)

SECTION

, 6.0 Eddy Current Data.and AVB Positions 6.1 V. C.' Summer AVB Assembly Design 6.2 Eddy Current Data for AVB Positions 6.3 Tube Denting at Top Tube Support Plate 6.4 AVB Hap Interpretations 7.0 Thermal and Hydraulic Analysis

~7.1 V. C. Summer Steam Generator Operating Conditions and ID Relative Stability Ratio Analysis 7.2 ATH0S Analysis Model 7;3 ATH0S Results 7.4 Relative Stability Ratio Over Operating History l 7.5 Effect of Steum Pressure on . Relative Stability Ratio 8.0 Peaking Factor Evaluation L 8.1 North Anna 1 Configuration

8.2 Test Heasurement Uncertainties 8.3 Test Repeatability 8.4 Cantilever vs U-Tube 8.5 Air vs Steam-Hater Hixture 8.6 AVB Insertion Depth Uncertainty 8.7 ~0verall-Peaking Factor with Uncertainty 8.8 Peaking Factors for Specific Tubes 9.0- Structural and Tube Vibration Assessments 9.1 Tube Mean Stress 9.2 Stability Ratio Distribution Based upon ATH0S 9.3 Stress Ratio Distribution with Peaking Factor 9.4 Cumulative Fatigue Usage

^

9.5 Effect of Steam Pressure on Potentially Susceptible Tubes 9.6 Conclusions 06290:10/062690 iv

- . . - - - - . . . ~ - - - . - . . _ .

. - - - - ~ . .- -

LIST OF FIGURES-

• i FIGURE

' 3-1.' Approximate Mapping of Fracture Surface of Tube R9C51 S/G "C" iCold Leg, North Anna Unit 1 ,

.3-2.'SchematicRepresentationofFeaturesObserved.DuringTEM ,

Fractographic' Examination of Fracture Surface of Tube-R9C51, S/G i "C" Cold-Leg, North Anna Unit 1 3-3 ~ Calculated,and Observed-Leak Rates Versus Time 4-l' Vibration Displacement vs. Stability Patio 4-2 Fatigue' Strength of Inconel 600 in AVT Hater at 600*F l t 3i : Fatigue Curve for Inconel 600 in AVT Hater Camparison of Mean Stress l .

Correction Models 4-4 Modified' Fatigue with-10% Reduction in Stability Ratio for

! .Haximum-Stress Condition 4-5 Modified Fatigue with 5% Reduction in Stability Ratio for Minimum Stress Condition 5-1 Fluidelastic Instability Uncertainty Assessment i

l

5'-21 Instability Constant - B 5-3: Instability Constants, B, Obtained for Curved Tubes from Hind Tunnel Tests on the 0.214 Scale U-Bend Model

.A 5-4 Damping vs. Slip Void Fraction l

06290:1D/062690 v

+

<% e e U ' n w--- -.-,,w,> - -- v, v v , r- r n - in, - = , 1---, ,_,< ~ , . + ,,,-

LIST OF FIGURES (Continued)

~

FIGURE.

5 Overall View of Cantilever' Tube' Hind Tunnel Model 3 v

5-6' Top View of the Cantilever Tube Hind Tunnel Model 5-7: Fluidelastic Vibration Amplitude with Non-Uniform Gaps 5-8 Typical Vibration Amplitude and Tube /AVB Impact Force Signals for Fluidelastic Vibration with Unequal Tube /AVB-Gaps

'5-91 . Conceptual Designuof-the Apparatus for Determining the Effects on-m Fluidelastic Instability of Columnwise-Variations in AVB Insertion Oepths 5 10 Overall View of Hind Tunnel Test Apparatus h 5-11 Side View of Hind Tunnel Apparatus with Cover Plates Removed to b

show Simulated'AVBS and Top Flow Screen 5-12' AVB Configurations Tested for V. C. Summer 5-13 Typical. Variation of RMS Vibration Amplitude with Flow Velocity for Configuration la in Figure 5-12 6-1 AVB Insertion Depth Confirmation' 6-2 V. C. Summer - Steam Generator A AVB Positions l.

6-3 V. C. Summer - Steam Generator B AVB Positions 6-4 V. C. Summer - Steam Generator C AVB Positions 06290:10/062690 vi c

LIST OF FIGURES (Continued) flGUE

, 6-5 AVB Projection Depth = 9-00 6-6 AVB Projection Depth - 9.15 7-1 Plan View of ATHOS Cartesian Model for Reference Model D3 7-2 Elevation View of ATHOS Cartesian Model for Reference Model D3 7-3 Plan View of ATHOS Cartesian Model for Reference Model D3 Indicating Tube Layout 7-4 Flow Pattern on Vertical Plane of Symmetry 7-5 Vertical Velocity Contours on Horizontal Plane at the Entrance to the U-Bend Region (IZ-27) 7-6 Lateral flow Pattern on Horizontal Plane at the Entrance to the U-Bend Region (IZ 27) 7-7 Void Fraction Contours on Vertical Plane of Symmetry 7-8 Tube Gap Velocity and Density Distributions for Tube Row 10/ Column 3B 7-9 Tube Gap Velocity and Density Distributions for hoe Row 10/ Column 45 7-10 Tube Gap Velocity and Density Distributions for Tube Row 10/ Column 50 7-11 Average Velocity and Density in the Plane of the U-Bends Normal to Row 10 06290:10/062690 vii

-- - . . . _ . _ _ - - . - . . - - - - - - . - . ~ - - - _ . . _

LIST OF FIGURES (Continued)

FIGURE  !

i 7-12. V. C. Summer Normalized Stability Ratio Based on High Power (>61%) Operation 2

8-1. Original North Anna AVB C'snfiguration 8-2 Schematic of Staggered AVBs 8-3 AVB "P&ir" in ECT Trace 8-4 North Anna 1, Steam Generator C: AVB Positions Critical Review "AVB Visible" Calls

'8-5 North Anna 1 Steam Generator C, R9C51 Projection Matrix 4 8 North Anna R9C51'AVB Final Projected Positions 8-7 Final Peaking Factors for V. C. Summer f

9-1 Axisymmetric Tube Finite Element Model 9-2 Dented Tube Stress Distributions - Pressure Load on Tube 9-3 Dented Tube Stress Distributions - Interference Load on Tube E

9 Dented Tube Stress Distributions - Coccined Strest Results V. C. Summer 9-5 . Relative Stability Ratio Using HEVF Dependent Damping - V. C. Summer

! 0629D:10/062690 viii

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

LIST OF FIGURES (Continued)

WAE 9-6 Stress Ratio Vs. Column Number - Dented Condition - V. C. Summer 9-7 Stress Ratio Vs. Column Number - Undented Condition - V. C. Summer 9-8 Maximum Allowable Relative Flow Peaking - V. C. Summer 4

0629D:10/062690 ix i

l

. _ _ _ _ . _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ - _ _ _ . . a

LIST OF TABLES lAlLE 4-1 Fatigue Usage per Year Resulting from Stability Ratio Reduction 5-1 Wind Tunnel Tests on Cantilever Tube Model 5-2 Fluidelastic Instability Velocity Peaking Factors for Columnwise Variations in AVB Insertion Depths V. C. Summer 6-1 1 AVB Signals Determined to be Supported 6-2 1 AkB Signal Indicating Support for Flow Peaking Analysis 6-3 V. C. Summer Unsupported Tube Summary

~

7-1 V. C. Summer Steam Generator Operating Conditions and Comparison with l

Reference Model D3 ATHDS Analysis 7-2 V. C. Summer Operating History Data 8-1 Stability Peaking Factor Due to Local Velocity Perturbation l

B-2 Comparison of Air and Steam Hater Peaking factor Ratios 8-3 Effect of Locci Variation of AVB Insertion 8-4 Uncertainties in Test Data and Extrapolation 06290:10/062690 x

LIST OF TABLES (Continued)

IABli B-5 Extrapolation of Test Results to Steam Generator Conditions 8-6 Final Peaking Factors 8-7 Stability Peaking Factors for Specific Tubes - V. C. Summer 9-1 100% Power Operating Parameters - V. C. Summer 9-2 V. C. Summer Tubes with Significant Relative Stability Ratios or Stress Ratios 06290:10/062690 xi j

1

1.0 INTRODUCTION

This report documents the evaluation of steam generator tubing at V. C. Summer for susceptibility to fatigue-induced cracking of the type experienced at

. North Anna Unit 1 in July, 1987. The evaluation includes three-dimensional flow analysis of the tube bundle, air tests performed to support the vibration analytical procedure, field measurements to establish AVB locations, structural and vibration analysis of selected tubes, and fatigue usage )

calculations to predict cumulative usage for critical tubes. The evaluation  !

utilizes operating conditions specific to V. C. Summer in order to account for plant specific features of the tube loading and response. I Section 2 of the report provides a summary of the V. C. Summer evaluation results and overall conclusions. Section 3 provides background of the tube rupture event which occurred at North Anna Unit 1 including results of the examination of the ruptured tube and a discussion of the rupture mechanism.

The criteria for predicting the fatigue usage for tubes having an environment

( ,

- conducive to this type of rupture are discussed in Section 4. Section 5 l provides a summary of test data which supports the analytical vibration l .

evaluation of the candidate tubes. A summary of field measurements used to determine AVB locations and to identify unsupported tubes is provided in Section 6. Section 7 provides the results of a thermal / hydraulic analysis to establish flow field characteristics at the top support plate which are subsequently used to assist in identifying tubes which may be dynamically unstable. Section 8 presents an update of the methodology originally used to evalbate the tube rupture at North Anna Unit 1. The final section, Section 9, presents results of the structural and vibration assessment. This section describes tube mean stress, stability ratio and stress ratio distributions, and accumulated fatigue usage for the V. C. Summer steam generator small radius U-tubes.

i 1 ..

l l-1 1

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i 2.0

SUMMARY

.AND CONCLUSIONS The V. C. Summer steam generators have been evaluated for the susceptibility to a fatigue rupture of the type experienced at Row 9 Column 51 (R9C51) of

. Steam Generator C at North Anna Unit 1. The evaluation used Eddy Current Test

[ (ECT) data supplied by SCE&G and interpreted by Westinghouse.

2.1 Background

The initiation of the circumferential crack in the tube at the top of the top tube support plate at North Anna 1 has been attributed to limited displacement, fluidelastic instability. This condition is believed to have prevailed in the.R9C51 tube since the tube experienced denting at the support plate. A combination of conditions were present that led to the rupture. The tube was not supported by an anti-vibration bar (AVB), had a higher flow field due to local flow peaking as a result of non-uniform insertion depths of AVBs, had reduced damping due to denting at the top support plate, and had reduced -

. fatigue properties due to the environment of the all volatile treatment (AVT) chemistry of the secondary water and the additional mean stress from the denting.

2.2 Evaluation Criteria The criteria established to provice a fatigue usage less than 1.0 for a finite period of time (i.e., 40 years) is a 10% reduction in stability ratio that provides at least a 58% reduction in stress amplitude (to < 4.0 ksi) for a .

Row 9 tube in the North Anr3 1 steam generators (SG's). This reduction is required-to produce a fatigue usage of < 0.021 per year for a Row 9 tube in l North Anna and therefore greater than 40 year fatigue design basis. This same L fatigue criteria is applied as the principal criteria in the evaluation of V.

C. Summer tubing.

3 The fluidelastic stability ratio is the ratio of the effective velocity divided by the critical ~ velocity. A value greater than unity (1,0) indicates t

instability. The stress ratio is the expected stress amplitude in a 06290:10/062690 2-1 l

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

V..C. Summer tube divided by the stress amplitude for the North Anna 1. R9C51 tube.

Displacements are computed for unsupported U-bend tubes in Rows 13 ard inward,

. (descending row number) using relative stability ratios to R9C51 of North Anna 1 and an appropriate power law relationship based on instability displacement versus flow velocity. Different U-bend radius tubes and tube sizes have different stiffness and frequency and, therefore, different stress and fatigue usage per year than the Row 9 North Anna tube. These effects are accounted for in a stress ratio technique. The stress ratio is formulated so that a stress ratio of 1.0 or less produces acceptable stress amplitudes and fatigue usage for the V. C. Summer tubing assuming that the tubing remains in service for the balance of the plant operating license at the operating conditions for the reference fuel cycle analyzed. Therefore, a stress ratio less than 1.0 provides the next level of acceptance criteria for unsupported tubes for which the relative stability ratio, including flow peaking, exceed 0.9.

The stability ratios for V. C. Summer tubing, the corresponding stress and amplitude, and the resulting cumulative fatigue usage must be evaluated relative to the ruptured tube at Row 9 Column 51, North Anna 1, Steam Generator C, for two reasons. The local effect on the flow field due to AVB insertion depths is not calculable with available analysis techniques and is determined by test as a ratio between two AVB configurations. In addition, an

-analysis and examination of the ruptured tube at North Anna 1 provided a range of initiating stress amplitudes, but could only bound the possible-stability ratios that correspond to these stress amplitudes. Therefore, to minimize the influence of uncertainties, the evaluation of V. C. Summer tubing has been j- based on relative stability ratios, relative flow peaking factors, and i relative stress ratios.

l The criteria for establishing that a tube has support from an AVB, is that it

, must have at least one-sided AVB support present at the tube centerline. The criteria is based ~on test results which show that one-sided AVB support is sufficient to limit the vibration amplitude for fluidelastic excitation. AVB 06290:10/062690 2-2

support is established by analysis of eddy current (EC) measurements and is a key factor in determining the local flow peaking factors. The local flow peaking produces increased local velocities which cause an increase in stability ratio. A sull change in the stability ratio causes a significant

!. change in stress amplitude. The relative flow peaking factors of V. C. Summer l tubing without direct AVB support have been determined by test. These flow peaking factors, normalized to the North Anna R9C51 peaking, are applied to relative stability ratios determined by 3-D tube bundle flow analysis, to obtain the combined relative stability ratio used in the stress ratio determination.

2.3 Denting Evaluation The Eddy Current (EC) tapes were evaluated [

Ja c to determine the condition of the tube / top tube support interface of the unsupported tubes having potential flow peaking.

Because of the significance of the top tube support plate crevice conditions on the analysis and the potential for further corrosion at the top tube support plate since the October 1988 EC inspection, the EC analysis assumed that top tube support plate crevices were dented (i.e. having " corrosion with

!, magnetite" or " tube denting with deformation") unless they could conclusively be demonstrated to be otherwise. Analyses of eddy current (EC) data for V. C.

Summer shows the presence of " corrosion with magnetite" in roughly half of the tube / TSP crevices. Of the twenty-five (25) tube eddy current results from the October,1988, inspection that were evaluated for top tube support plate corrosion, eleven (11) were found to be magnetite-packed at one or both top tube support plate legs, none showed denting with deformation, and the remaining fourteen (14) showed no detectable magnetite or corrosion. For l

conservatism in the evaluation, all of the tubes evaluated are postulated to be dented. The effect of denting on the fatigue usage of the tube has been conservatively maximized by assuming the maximum effect of mean stress in the tube fatigue usage Waluation and by incorporating reduced damping in the tube

, vibration evaluation.

i i

I l

06290:1D/062690 2-3

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

I 2.4 AVB Insertion Depths The V. C. Summer SGs have two sets of Alloy 600 AVBs. The ' inner' or lower AVBs have a rectangular cross-section and extend into the tube bundle

, 'approximately as far as Row 10. They provide a nominal total clearance between a tube without ovality and the surrounding AVBs of ( Ja .c inch.

The outer (or upper) AVBs also have a rectangular cross section, and extend  :

into the tube bundle approximately as far as Row 21, providing a nominal tube-to-AVB clearance comparable to the inner AVBs. Since the purpose of this analysis is to evaluate the potentially unsupported tubes at or near the point 4 of maximum AVB insertion, only the dimensions and EC data pertaining to the inner AVBs are required.

The eddy current data were analyzed by Westinghouse to identify the number of tube /AVB intersections and the location of these intersections relative to the apex of a given tube. This information was used in calculations to determine the deepest penetration of a given AVB into the tube bundle. For the area of interest in the V. C. Summer steam generators, the AVB support of the tube can normally be verified if EC data shows both legs of the lower AVB, one on each side (hot leg - cold leg) of the U-bend. This is the preferred method of establishing tube support.

If caly the apex of a V. C. Summer AVB assembly is near or touching the apex of a tube U-bend, only one AVB signal may be seen. In this case, adequate tube support cannot be assumed without supplemental input. Support can be determined if ' projection' calculations based on AVB intercepts of higher row nurt.ber tubes in the same and cdjacent columns verify insertion depth to a point below the tube centerline. Haps of the AVB insertion depths for V. C. Summer are shown in Figures 6-2 thru 6-4. The AVB maps list the results

.of the ' projection' calculations from the smallest row tube for which suitable data exist to make a projection.

~

At tube locations where flow peaking effects could be significant, determination of only tube support conditions may not be sufficient to adequately define flow peaking factors. Flow peaking factor can, in some 06290:10/062690 2-4

. . _ . . . - . ___ _ . _ ___..._ _ _ _ _.-_.____m__ . . .m . . _ .

i cases [

3a ,c 2.5 Flow Peaking Factors Tests were performed modeling V. C. Summer tube and AVB geometries to determine the flow peaking factors for various AVB configurations relative to the North Anna R9C51 peaking factor. The test results were used to define an upper bound of the ratio relative to the R9C51 configuration.

2.6 Tube Vibration Evaluation i

The calculation.of relative stability ratios for V. C. Summer makes use of detailed tube bundle flow field information computed by the ATHOS steam generator thermal / hydraulic analysis code. Code output includes three-dimensional distributions of-secondary side velocity, density, and void fraction. along with primary fluid and tube wall temperatures. Distributions of these parameters have been generated-for every tube of interest-.in the

-V. C. Summer tube bundles based on recent full power operating conditions.

This information was factored into the tube' vibration analysis leading tc the relative stability ratios.

Relative stability ratios-of V. C. Summer (Row 8 through Row 12) +ubing versus R9C51 of. North Anna 1 are plotted in Figure 9-5. These relative stability ratios include relative flow peaking factors. The stress ratios for V. C. Summer are given in Figure 9-6 for tubes in the dented condition.- These

also include the relative flow peaking-effect, and-are. calculated based on-L clamped tube conditions with denting (with deformation) at the top tube support plate.

06290:10/062690 2-5 l

i Fatigue usages were calculated for current operating conditions and for the full power steam pressures calculated for plugging levels of 12% and 15%.

Four tubes, SG-A R9C83, SG-B R9C56 SG-C R12C5 and SG-C R13C5, if previously dented or if becoming dented at the beginning of an operating cycle with current operating conditions, such that the tube becomes rigidly clamped within the top tube support, could potentially have tube fatigue usage factors exceeding 1.0 within the cycle, and therefore require ameliorative action.

With the exception of SG-B R9C56, which was evaluated as having magnetite packing at one of the two top tube support plate intersections, all of these four tubes were evaluated from the October 1988 outage inspection data as

" clean" at the top tube support plate intersections. Two additional tubes, SG-C R9C29 (magnetite in one top TSP and clean in the other) and SG-C R10C23 (magnetite in both top TSP crevices), potentially have current accumulated fatigue usages as high as 1.0, if it is conservatively assumed that denting began at the start of the first fuel cycle, and also therefore require ameliorative action. SG-C R9C106 was evaluated as having no denting at the l top tube support plate elevation in the October 1988 EC inspection, but may have accumulated as much as 0.34 fatigue usage if it became dented or magnetite-packed at the beginning of the subsequent cycle. If dented and operating at Cycle 5 conditions, it could continue to accumulate fatigue usage l at the rate of 0.34 pr year, and was recommended for preventive action.

l Utilizing the past operating history and Cycle 5 operating conditions (941 psia steam pressure), the evaluation found that all other tubes are acceptable for continued operation through the end of the plant operating license.

To assist SCE&G in evaluating operational issues associated with cable damper modification options, the lowest added damping 'nlue determined from available tests was assumed to be provided by cable dampers in the seven tubes of interest for V. C. Summer. With this assumed minimum added damping value of

[ ],a c all of the stress ratios in the seven tubes of interest are below

( ),a,c with the highest being SG-C R13C5, having a stress ratio of

( ]A,c

- . R12C5 would have a stress ratio of ( Ja.c , and the remaining five tubes under consideration would have stress ratios of 3a .c or less. Hith this assumption, tubes that had not initiated a

~

! [

crack would be acceptable for continued operation with a cable damper installed.

l j 06290:10/062690 2-6

.-.~_.-mw---. , ~ . ,-.m. v. - - ,-, -r - , . , - - . . - . - - . , . .

v Based upon a review of the operational, maintenance, and modification inste11ation factors associated with the modification options, SCE&G decided

. -to install cable dampers into the seven tubes listed above. Since [

1 j a.c A summary listing of the unsupported critical tubes and pertinent vibration parameters (prior to installation of cable dampers) is given H ':51e 9-2.

An additional fatigue evaluation of the V. C. Summer tubing was performed to examine the effect of reduced steam pressure and coastdown power levels, with the obje'ctive of demonstrating the acceptability of the tube remaining in

, service with the highest stress ratio that does not exceed the 1.0 stress l ratio criterion. Parametric analysis was performed to determine the relative

- . stability ratio (RSR) multipliers and stress ratios for full power steam pressures below the referente steam pressure (941 psia) and it was determined L that the limiting tube, SG-A R9C55, does not exceed the 1.0 stress ratio criterion for steam pressures above 905 psia. Since SCE&G is considering power coastdown operation, the RSR multipliers were also evaluated assuming a constant volumetric steam flow for pressures below 905 psia. (The 905 psia steam pressure is a lower bound, full power steam pressure value; V. C. Summer turbine tests indicate lthe "best estimate" value of the Valves Hide Open (VHO) l~

steam pressure to te 915 psia). For the reduced power levels associated with operation belos the assumed 905 psia VHO limit, the RSR multipliers decrease, and the fatigue results remain bounded. Therefore, assuming that.the worst' case tube (SG-A R9C55) .as been dented since the first cycle and the turbine Valves Wide Open limit is not reduced below 905 psia, all tubes remaining in service at V. C. Summer are acceptable for operation through the end of the current operating license with power levels at or below 2785 MHt.

[ ..

0629D:10/100190 2-7

_ _ _ _ _ _ . _ _ _ _ _ _ _ _ . _ - _ _ . _ . - . ~ . . . _ _ _ _ _ . _ _ __ _ _ _ -

2.7 Overall Conclusion

, Seven tubes were recommended for preventive action: SG-A R9C83, SG-B R9C56, SG-C R12C5, SG-C Ri?C5, SG-C R10C23, SG-C R9C29, and SG-C R9C106. These tubes

- were removed from service in April 1990 with the installation of cable dampers, hot leg plugs, and cold leg sentinel plugs. The tubes remaining in service in the V. C. Summer steam generators are not expected to be susceptible to high-cycle fatigue rupture at the top tube support plate in a manner similar to the rupture which occurred at North Anna #1, assuming that the turbine Valves Wide Open lim',t is not reduced below 905 psia, through the eno of the current operating license with power levels at or below 2785 MHt.

06290:10/100190 2-8 l

3.0 BACKGROUND

, On July 15, 1987, a steam generator tube rupture occurred at the North Anna Unit 1. The ruptured tube was determined to be Row 9 Column 51 in steam generator "C". The location of the opening was found to be at the top tube support plate on the cold leg side of the tube and was circumferential in orientation with a 360 degree extent.

3.1 North Anna Unit 1 Tube Rupture Event The cause of the tube rupture has been determined to be high cycle fatigue.

The source of the loads associated with the fatigue mechanism has been determined to be a combination of a mean stress level in the tube and a superimposed alternating stress. The mean stress has been determined to have been increased to a maximum level as the result of denting of the tube at the top tube support plate and the alternating stress has been determined to be due to out-of-plane deflection of the tube U-bend above the top tube support' caused by flow induced vibration. These loads are consistent with a lower bound fatigue curve for the tube material in an AVT water chemistry environment. The vibration mechanism has been determined to be fluid elastic, based on the magnitude of the alternating stress.

A significant contributor to the occurrence of excessive vibration is the reduction in damping at the tube-to-tube support plate interface caused by the denting. Also, the absence of antivibration bar (AVB) support has been concluded to be required for vibration to occur. The presence of an AVB support restricts tube motion and thus precludes the deflection amplitude required for fatigue. Inspection data show that an AVB is not present for the Row 9 Column 51 tube but that the actual AVB installation depth exceeded the minimum requirements in all cases with data for AVBs_at many other Row 9 tubes. Also contributing significantly to the level of vibration, and thus loading, is the local flow field associated with the detailed geometry of the 06290:10/062690 3-1

4 steam generator, i.e., AVB insertion depths. In addition, the fatigue properties of the tube reflect the lower range of properties expected for an

. AVT environment. In summary, the prerequisite conditions derived from the evaluations were concluded to be:

l Fatigue Reauirements Prereauisite Conditions Alternating stress Tube vibration

- Dented support

- Flow excitation

- Absence of AVB Mean stress Denting in addition to applied stress Material fatigue properties AVT environment

- Lower range of j properties 3.2 Tube Examination Results Fatigue was found to have initiated on the cold leg outside surface of tube R9C51 immediately above the top tube support plate. No indication of significant accompanying intergranular corrosion was observed on the fracture face-or on the immediately adjacent 00 surfaces. Multiple fatigue initiation sites were found with major sites _ located at 110', 120', 135' and 150',

Figure 3-1. The plane of the U-bend is located at 45' with the orientation system used, or approximately 90' from the geometric center of the initiation zone at Section D-D. High cycle fatigue striation spacings approached 1 micro-inch near the origin sites, Figure 3-2. The early crack front is believed to have broken through-wall from approximately 100' to 140'. From this point on, crack growth is believed (as determined by striation spacing, striation direction, and later observations of parabolic dimples followed by equiaxed dimples) to have accelerated and to have changed direction with the o resulting crack front running perpendicular to the circumferential direction.

L I

06290:lD/062690 3-2 ll

.-m.m--r.- . _,, ,,w, r- e w- e r= - --m- , , w . - , ,-.e =

3.3 Hechanism Assessment To address a fatigue mechanism and to identify the cause of the loading, any loading condition that would cause cyclic stress or steady mean stress had to

. be considered. The analysis of Normal, Upset and Test conditions indicated a relatively low total number of cycles involved and a corresponding low fatigue usage, even when accounting for the dented tube condition at the plate. This analysis also showed an axial tensile stress contribution at the tube OD a short distance above the plate from operating pressure and temperature, thus providing a contribution to mean stress. Combining these effects with denting

' deflection on the tube demonstrated a high mean stress at the failure location. Vibration analysis for the tube developed the characteristics of first mode, cantilever response of the dented tube to flow induced vibration for the uncracked tube and for the tube with an increasing crack angle, beginning at 90' to the plane of the tube and progressing around on both sides to complete separation of the tube.

Crack propagation analysis matched cyclic deformation with the stress intensities and striation spacings indicated by the fracture inspection and

, analysis. Leakage data and crack opening analysis provided the relationship between leak rate and circumferential crack length. Leakage versus time was then predicted from the crack growth analysis and the leakage analysis with initial stress amplitudes of 5, 7, and 9 ksi. The comparison to the estimate of-plant leakage (performed after the event) showed good agreement, Figure 3-3. i Based on these results, it followed that the predominant loading mechanism responsible is a flow-induced, tube -vibration loading mechanism. It was shown that of the two possible flow-induced vibration mechanisms, turbulence and fluidelastic instability, that fluidelastic instability was the most probable cause. Due to the range of expected initiation stress amplitudes (4 to 10 ksi), the fluidelastic instability would be limited in displacement to a range of approximately ( 3a ,c This is less than the

^

distance between tubes at the apex, ( l a.c It was further confirmed that displacement prior to the rupture was limited since no indication of tube U-bend (apex region) damage was evident in the eddy-current signals of adjacent tubes.

06290:10/062690 3-3 1

Given the likelihood of limited displacement, fluidelastic instability, a means of establishing the change in displacement, and corresponding change in

. stress amplitude, was developed for a given reduction in stability ratio (SR). Since the rupture was a fatigue mechanism, the change in stress ,

, amplitude resulting from a reduction in stability ratio was converted to a fatigue usagt benefit through the use of the fatigue curve developed. Mean stress effects were included due to the presence of denting and applied loadings. The results indicated that a 10% reduction in stability ratio is needed (considering the range of possible initiation stress amplitudes) to reduce the fatigue usage per year to less than 0.02 for a tube similar to Row 9 Column 51 at North Anna Unit 1.

0629D:10/062690 3-4

_ _ _ _ _ _ _ _ _ _ _ -- J

l 00 - a f

W C

• C-C C

g 180*

Region of Herringbone f Pattern i

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' g, p IE A

5 ~ TAB A*A

%$ r.p 5 Coarse Texture and Dimpled K Rupture

+

( Indicates origins Figure 3-1. Approximate Mapping of Fracture surface of Tube R9051,

. S/G 'C' Cold Leg, North Anna Unit 1 i

a 3-5 4

. . , - - - - , - - , e v,--.m--w. .-,--.-m ,n--, ,_%.-,

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

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"" 3 5 = 21 9 in.

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$ = 1.0/1.E5 y in, ggg.

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/. and V Internal Neckin; 1-H

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5

• 2.E/4.0 v in. g,g l j 31 peeneg Nearly Ecui-Axed 5 = o.1/6.9 y in. Dimples l.

Note: Arrows Indicate Direction of Fracture Propagation Figure-3-2 Schematic Representation of Features Observed During.

TEM Fractographic Examination of Fracture Surface of Tube R9C51, S/G "C" Cold Leg, North Anna Unit 1 l

l l

04420:10/062190 3-6

!, ^^

l l l l l l l l l l l Calculated and observed leak rates versus time.

Observed values based on gaseous species condenser atr ejector SIGMA A = 5 KSI BIGNA A = 7 KSI i

SISMA A = 9 KSI l a O Ar-4; o

g same- - O Xe-135 a Kr-a7 sd s

• e E .

X i

y see- -  :

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o a  :  :  :  :

e e.e sees same an c sees asas sees mee mee esse amm eew TIMr., MIAJTts Figure 3-3 Calculated and Observed Leak Rates Versus Time 3-7

}

4.0 CRITERIA FOR FATIGUE ASSESSMENT The evaluation method and acceptance criteria are based on a relative comparison with the Row 9 Column 51 tube of Steam Generator C, North Anna

. Unit 1. This approach is necessary because (1) methods for direct analytical prediction of actual stability ratios incorporate greater uncertainties than a relative ratio method, and (2) the stress amplitude (or displacement) associated with a specific value of stability ratio can only be estimated by the analysis of North Anna Unit 1. For these reasons, the North Anna Unit I tubing evaluation was done on a relative basis to Row 9 Column 51 and a 10%

reduction in stability ratio criteria was established to demonstrate that tubes left in service would be expected to have sufficiently low vibration stress to preclude future fatigue rupture events.

To accomplish the necessary relative assessment of V. C. Summer tubing to Row 9 Column 51 of North Anna Unit 1 several criteria are utilized. First, stability ratios are calculated for V. C. Summer tubes based on flow fields predicted by 3-D thermal hydraulic models and ratioed to the stability ratio for Row 9 Column 51 at North Anna Unit i based on a flow field obtained with a 3-D thermal hydraulic model with the same degree of refinement. These ratios of stability ratio (called relative stability ratios) for each potentially unsupported U-bend in the V. C. Summer steam generators should be equivalent to 10.9 of R9C51, North Anna 1-(meeting the 10% reduction in stability ratio criteria). This provides the first level of screening of susceptible tubes incorporating all tube geometry and flow field differences in the tube dynamic evaluation. It has the inherent assumption, however, that each tube has the same local, high flow condition present at Row 9 Column 51, North Anna Unit

1. To account for these differences, flow peaking factors can be incorporated in the relative stability ratios and the stress ratios.

06290:10/062690 4-1 l

._ l

The next step is to obtain stress ratios, the ratio of stress in the V. C. Summer tube of interest to the stress in Row 9 Column 51, North Anna ,

. Unit 1, and after incorporating the requirement that the relative stability ratio to Row 9 Column 51 (R9C51) for the tube of interest is equivalent to

- -1 0.9, require the stress ratio to be 11.0. The stress ratio incorporates the tube geometry differences with R9C51 in relation to the stress calculation and also incorporates the ratio of flow peaking factor for the tube of interest to the flow peaking factor for R9C51 (flow peaking factor is defined in Section 4.2). This should provide that all tubes meeting this criteria have stress amplitudes equivalent to 1 4.0 ksi.

Finally, the cumulative fatigue usage for plant operation to date and for continued operation with the same operating parameters is evaluated. A fatigue usage 11.0 may not be satisfied by meeting the stress ratio criteria using the reference operating cycle evaluation since the reference cycle does not necessarily represent the exact duty cycle to date. Therefore, the time history of_ operation-is evaluated on a normalized basis and used together with the stress ratio to obtain a stress amplitude history. This permits the calculation'of current and future fatigue usage for comparison to 1.0.

4.1 Stability Ratio Reduction Criteria For fluidelastic evaluation, stability ratios are determined for specific configurations of a tube. These stability ratios represent a measure of the potential _for flow-induced tube vibration during service. Values greater than unity (1.0) indicate instability (see Section 5.1).

Motions developed by a tube in the fluideiastically unstable mode are quite large in comparison to the other known mechanisms. The maximum modal displacement (at the apex of the tube) is linearly related to the bending stress in the tube just above the cold leg top tube support plate. This relationship applies to any vibration in that mode. Thus, it is possible for an-unstable, fixed boundary condition tube to deflect an amount in the U-bend which will produce fatigue inducing stresses.

06290:1D/062690 4-2 l

The major features of the fluidelastic mechanism are illustrated in Figure 4-1. This figure shows the displacement response (LOG D) of a tube as a function of stability ratio (LOG SR). A straight-line plot displayed on log-log coordinates implies a relation of the form y - A(v)", where A is a

. constant, x is the independent variable, n is the exponent (or power to which x is raised), and y is the dependent variable. Taking logs of both sides of this equation leads to the slope-intercept form of a straight-line equation in log form, log y - c + n log x, where c - log A and represents the intercept and n is the slope. In our case the independent variable x is the stability ratio SR, and the dependent variable y is tube (fluidelastic instability induced) displacement response D, and the slope n is renamed s.

From experimental results, it is known that the turbulence response curve (on log-log coordinates) has a slope of approximately [ ]8'b'C. Test results also show that the slope for the fluidelastic response depends somewhat on the instability displacement (response amplitude). It has been shown by tests that a slope of [ l a,b,c is a range of values corresponding to J .c, a

displacement amplitudes in the range of [

whereas below [ 3a ,c are conservative values.

The reduction in response obtained from a stability ratio reduction can be expressed by the following equation:

a,c

[ 3 where D j and SR) are the known values at the point corresponding to point 1 of Figure 4-1 and D2 and SR2 are values corresponding to any point lower on this curve. Therefore, this equation can be used to determine the reduction in displacement response for any given reduction in stability ratio.

This equation shows that there is benefit derived from even a very small percentage change in the stability ratio. It is this reduction in displacement for a quite small reduction in stability ratio that formed the basis for demonstrating that a 101 reduction in stability ratio would be sufficient to prevent Row 9 Column 51 from rupturing by fatigue.

06290:10/062890 4-3

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

The fatigue curve developed for the North Anna Unit 1 tube at R9C51 is from i

4 Ja,c . Thus, a,c

~

where, ca is the equivalent stress amplitude to oa that accounts for a maximum stress of yo , the yield strength. The -3 sigma curve with mean stress effects is shown in Figure 4-2 and is compared to the ASME Code Design Fatigue-Curve for Inconel 600 with the maximum effect of mean stress.

. . The curve utilized in this evaluation is clearly well below the code curve reflecting the effect of an AVT environment on fatigue and [

3a ,c for accounting for mean stress that applies to materials in a corrosive environment.

.Two other mean stress models were investigated for-the appropriateness of-  !

their use in providing a reasonable agreement with the expected range _of i 4  ; initiating- stress -amplitudes. These wer's the [

.3a .c shown in Figure 4-3. With a [

a J .c. tne_[

~

3a.c ,

L.

1 06290:10/062690 4-4 4

The assessment of the benefit of a reduction in stability ratio begins with the relationship between stability ratio and deflection. For a specific tube geometry, the displacement change is directly proportional to change in stress so that stress has the same relationship with stability ratio, a,c The slope in this equation can range from [ 3a',c on a log scale depending on the amplitude of displacement. Knowing the stress resulting from a change in stability ratio from SR) to SR 2 , the cycles to failure at the stress amplitude were obtained from the fatigue curve. A fatigue usage per year was then determined assuming continuous cycling at the natural frequency of the tube. The initial stress was determined to be in the range of 4.0 to 10.0 ksi by the fractography analysis. .

It was further developed that the maximum initiating stress amplitude was not more than 9.5 ksi. This was based on [

]*'C . The corresponding stress level is 5.6 ksi.

8 The maximum stress, 9,5 ksi, would be reduced to [ 3 'C with a 10%

-reduction in stability ratio and would have a future fatigue usage of

[ ]"'C per year at 75% availability, Figure 4-4. The minimum stress, 5.6 ksi, would be reduced to [ Ja .c ksi with a 5% reduction in stability ratio and.would have future fatigue usage of [ l a,c per year, Figure 4-5; In addition, if a tube were already cracked, the crack could be as large as-[ 3a ,c inch in length and thru-wall and would not propagate if the stress amplitudes are reduced to 1 4.0 ksi.

06290:10/062690 4-5 l

Subsequent to the return to power evaluation for North Anna Unit 1, the time history of operation was evaluated on a-normalized basis to the last cycle.

I 1

j a.c ,

cumulative fatigue usage may then be computed to get a magnitude of alternating stress for the last cycle that results in a cumulative usage of 1.0 for the nine-year duty cycle. ,he result of the iterative analysis is that the probable stress associated with this fatigue curve during the last cycle of operation was approximately [ Ja.c for R9C51, North Anna Unit 1, Steam Generator C, and that the major portion of the fatigue usage came in the second, third and fourth cycles. The first cycle was conservatively omitted, since tienting is assumed, for purposes of this analysis, to have occurred during that first cycle. Based on this evaluation, the tube fatigue probably occurred over most of the operating history of North Anna Unit 1.

A similar calculation can be performed for the time history of operation assuming that (

Ja ,c On this basis, the effect of a 10% reduction in stability rM io is to reduce the stress amplitude to 4.0 ksi and results in a future fatigue usage of ( Ja ,c ,

Other combinations of alternating stress and mean stress were evaluated with

-3 sigma and -2 sigma fatigue curves to demonstrate the conservatism of the 10% reduction in stability ratio. Table 4-1 presents the results of the cases analyzed clearly demonstrating that the 10% reducU on in stability ratio combined with a -3 sigma fatigue curve and with maximum mean stress effects is conservative. Any higher fatigue curve whether through mean stress, mean stress model, or probability, results-in greater benefit for the same reduction in stability ratio. Further, for any of these higher curves, a smaller reduction in stability ratio than 10% would result in the same benefit. In addition, there is a large benefit in terms of fatigue usage for relatively small changes in the fatigue curve.

06290:10/062690 4-6

4.2 Local Flow Peaking Considerations Local flow peaking is a factor on stability ratio that incorporates the effects of local flow velocity, density and void fraction due to non-uniform

. AVB insertion depths. The flow peaking factor is applied directly to the stability ratio obtained from thermal-hydraulic analysis that does not account for these local geometry effects. Being a direct factor on stability ratio, a small percentage increase can result in a significant change in the prediction of tube response.

Since the evaluation of V. C. Summer tubing is relative to R9C51, North Anna Unit 1, the flow peaking factors are also applied as relative ratios, i.e., a ratio of V. C. Summer tubing to R9C51 at North Anna Unit 1. The flow peaking relative instability is obtained by testing in the air test rig described in Section 5.4, where the peaking factor is defined as the critical velocity for R9C51 AVB pattern compared to critical velocity for a uniform AV8 pattern. ' As explained in Section 8.0, the minimum value of [ l a,b,c is appropriate for R9C51 of North Anna 1. The peaking factor for a tube in V. C. Summer tubing is therefore divided by [ 3a ,b,c and the resulting relative flow peaking is multiplied times the relative stability ratio based on ATH0S results. If the peaking factor is 1.0, the relative flow peaking is [

3a ,b,c ,

As a further demonstration of the conservatism of [ l a,b,c as the minimum flow peaking factor for R9C51, the stress amplitude of 7.0 ksi obtained from iterating on cumulative fatigue usage (and selected as the nominal-value from i fractography analysis) was used to back calculate the apparent stability ratio and then the apparent flow peaking factor. Allowing for a range of slopes of the instability curve from 10 +' 30, the stability ratio is in the range of

, 1.1 to 1.4 and the flow peakit -: tor is in the range of 1.8 to 2.2. This range of flow peaking agrees with the range of flow peaking factors measured i- in the air tests and is considered to be the best estimate of the range of the R9C51_ flow peaking factor.

i J

! 0629D:1D/062690 4-7 1

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

The range of stability ratios, 1.1 to 1.4, is based on a value of 0.59 obtained with ATHOS results without flow peaking and with nominal damping that

. Is a function of modal effective void fraction. The nominal damoing reflects the nominal reduction in damping that occurs with denting at the tt te support plate. Therefore, a minimum damping scenario that is independent of void fraction is not considered to be credible and is not addressed in the evaluation that follows.

4.3 Stress Ratio Considerations In Section 4.1, a 10% reduction in stability ratio was established to reduce the stress amplitude on the Row 9 Column 51 tube of North Anna Unit I to a level that would not have ruptured, 4.0 hsi. To apply this same criteria to another tube in the same or another steam generator, the difterences in [

3a ,c ,

6,c

{$f

1. 2 P5

',d t

4 06290:10/062690 4-8

__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ E

E h

a,C

.c

?

where the stability ratio (SR) includes the flow peaking effect.

By eschlishing their equivalent effect on the stress amplitude produced the, tube rupture at North Anna 1, several other 6ffects may be accounted-for.

These include-a lower mean stress (such as for non-dented tubes), different frequency, tubes from the [ 3 8 'C hertz frequency of R9C51, North Anna'1,.

.and'. shorter design basis service.

I l

b 4-9 06290:1D/062690 l l '

l_______f___i___. s _ _ . . . . . , . . . . . , . . . - . _

In the case of lower mean stress, the stress ainplitude that would have caused the failure of R9C51, North Anna 1, would have been higher. [

j a.c ,

A lower or higher frequency tube would not reach a usage of 1.0 in the same length of time as the R9C51 tube due to the different frequency of cycling.

The usage accum" lated is proportional to the frequency and, therefore, the allowable number of cycles to reach a usage of 1.0 is inversely proportional to frequency. The equivalent number of cycles to give the usage of 1.0 for a different freauency tube [

3a ,c ,

, for a different time basis for fatigue usage evaluation, [

j a,c.e ,

Knowing the magnitude of the stress ratio allows 1) the determination of tubes that do not meet a value of I 1, and 2) the calculation of maximum stress in the acceptable tubes, a,c Having this maximum stress permits the evaluation of the maximum fatigue usage for V. C. Summer based on the time history expressed by normalized stability  ;

ratios for the duty cycle (see Section 7.4).

1 06290:10/062690 4-10 1

Table 4-1 Fatigue Usage per Year Resulting a from Stability Ratio Reduction

- S R , 1. STRESS FATIGUE MEAN STRESS USAGE REDUCTION BASIS (I} CURVE (2) H0 DEL PER YEAR

- - a,c

5. 9 yrs to fail [ la,c

5. 9 yrs to fail [ 3a,c

5. 9 yrs to fail [ Ja,c 10.

max,stresg) amplitudet

[ ]a.C 10.

max.stregg) amplitudet

[ 3a,c 10.

max. stresg) amplitudeW

[ 3a,c 10.

max.stregg) amplitudek

[ ]a.C

10. max. stress based on duty cycle (5) _ -

[ 3a,c (1) This gives the basis for selection of the initiating stress amplitude and its value in ksi.

(2) Sn is the maximum stress applied with Sm " Smean + Sa (3) [ 3a,c,

- (4) Cycles to failure implied by this combination of stress and fatigue properties is notably less than implied by the operating history.

Consequently this combination is a conservative, bounding estimate.

(5) Cycles to failure implied by the operating history requires [

Ja,c fatigue curve at the maximum stress of [ la.c, l

l 0629D:lD/062690 4-11

a,b,c Figure 4-1 Vibration Displacement vs. Stability Ratio p.

4-12 l

4 a,e 1

Figure 4-2 Fatigue Strength of Inconel 600 in AVT Water at 600*F l

. 4-13 l i

1

4

- a,c j-i

\

\

e 3

l i.. . Figure 4-3 Fatigue curve for Inconel 600 in AVT Water Comparison of Mean Stress correction Models i-I i

4-14 i

e

- . _ . . - _ _ _ _ - - _ - _ _ . . - -... . . . + , . = . . . - . . . . - - ,

i a,e l

.1

~

Figure 4-4 Modified Fatigue with IC% Reduction in Stability Ratio for Maximum Stress condition 4-15

l 8,C d.

1 1

4 Figure 4-5 Modified Fatigue with 5%. Reduction in Stability Ratio for Minimum Stress condition 4-16

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

l 5.0 SUPPORTING TEST DATA

, This section provides a mathematical descr.iption of the fluidelastic

. mechanism, was determined to be the most likely causative mechanism for the.

- North Anna tube rupture, as discussed in Section 3.3, to highlight the i physical conditions and corresponding parameters directly related to the event and associated preventative measures. The basis for establishing the  ;

appropriate values and implications associated with these parameters are provided. Where' appropriate, test results are presented.

5.1 -Stabil.ity Ratio Parameters Fluidelastic stability ratios are obtained by evaluations for specific configurations, in terms of active tube supports, of a specific tube. These

. stability ratios represent a measure of the potentici for tube vibration due to instability during service. Fluidelastic stability evaluations are performed with a computer program which provides for the generation of a finite element model of the tube and tube support system. The finite element model provides the vehicle to define the mass and stiffness matrices for the

- tube and its support system. This information is used to determine the modal frequencies (eigenvalues) and mode shapes (eigenvectors) for the linearly

-supported tube being considered.-

The methodology is comprised of the evaluation of the following equations:

Fluidelastic stability ratio - SR = Uen#U cfor mode-n, where Uc (critical velocity) and Uen (effective velocity) are determined by:

2 gj)

Uc

• 0 #n 0 [(m g.6n)~# (P o 0 )) W

and;

. N 2

g(p3p)U3/o +jn j Z I- .V en

- (2) i H

2

)

(*j/*o) *jn Z j

0442D:lD/062890 5-1 1

-- ~_. _ _ _ . . _ _

where, D - tube outside diameter, inches .

4*.

.V en

- effective velocity for mode n, inches /sec  ;

N - number of nodal points of the finite element model m3 , Uj ,'p) - mass per unit length, crossflow velocity and fluid density at node j, respectively p,mg. g

- refsrence density and a reference mass per unit g .ength, respectively (any representative values) 6 n

- logs-ithmic decrement (damping)

• jn - normalized displacement at node j in the nth mode of vibration 2 -- ' average of distances between node j to j-1, and j to al 3

-6 - an. experimentally correlated stability constant a Substitution of Equations (1) and [2] into the expression which oefines stabil.ity ratio, and cancellation.of like' terms, leads-to an expression in fundamental terms (without the arbitrary reference mass and density parameters). From this resulting expression, it-is seen that the stability 1

' ratio is directly related to the flow field in terms of the secondary fluid-velocity times square-root-density distribution (over the tube mode shape),

and inversely related to the square root of the mass distribution, square root

- of modal damping, tube modal . frequency, and the -stability constant (beta).

o

.he uncertainty in each of these parameters is addressed in a conceptual manner in Figure 5-1. The remainder of this section (Section 5.0) provides a discussion, and, where appropriate, the experimental bases to quantitatively i establish the uncertainty associated with each of these parameters. In L,

I f-0442D:10/052190 5-2

addition, Section 5.3 provides the experimental basis to demonstrate that tubes with [

a

, Jc . This a

implies that those tubes [ l .c would not have to be

- modified because their instability response amplitude (and stress) would be small. The very high degree of sensitivity of tube response (displacements and stresses) to changes in the velocity times square-root-density distribution is addressed in Section 4.0. This is important in determining the degree'of change that can be attained through modifications.

Freauency It has been demonstrated by' investigators that analytically determined frequencies are quite close to their physical counterparts obtained from measurements on real structures. Thus, the uncertainty in frequencics has been-shown to be quite small. This is particularly appropriate in the case of dented _(fixed boundary condition) tubes. Therefore, uncertainty levels introduced by the frequency parameter are expected to be insignificant (see also~ " Average Flow Field" subsection below).

Instability Constant (Betaf The beta (stability constant) values used for stability ratio and critical velocity evaluations (see above equations) are based on an extensive data base comprised of both Hestinghouse and other experimental results. In addition,

previous field experiences are considered. Values have been measured for full length U-bend tubes in prototypical steam / water environments. In addition, measurements in U-bend air models have been made 'with both no AVB and variable AVB supports (Figure 5-3).

a To help establish the uncertainties associated with ATHOS flow velocity and density distribution predictions on stability analyses, the Model Boiler j ,

.(PB-3) tests performed at Mitsubishi Heavy Industries (MHI) in Japan were modeled using ATHOS. A beta value consistent with the ATH0S predicted flow I conditions and the MB-3 measured critical velocity was determined. These

analyses supported a beta value of [ l a,b.c ,

06290:10/062690 5-3 I

A summary of the test bases and qualifications of the beta values used for

~ these assessments 1s provided by~ Figure 5-2. The lowest measured beta for tubes without AVSs was a value of [ J ,b c This value is used for the a

beta parameter in all stability ratio evaluations addressed in this Report

. (see also Average Flow Field" subsection below).

Mass Distribution The mass distribution parameter is based on known information on the tube and primary and secondary fluid physical properties. The total mass per unit length is comprised of that due to the tube, the internal (primary) fluid, and

, the external (secondary) fluid (hydrodynamic mass). Data in Reference 5-2 suggests that at operating void fractions (

j .c a

Tube Damoina Test data are available to define tube damping for clamped (fixed) tube 4

supports, appropriate to dented tube conditions, in steam / water flow

- conditions. Prototypic U-bend testing has been performed under conditions leading to pinned supports. The data of Axisa in Figure 5-4 provides the principal data for clamped tube conditions in steam / water. This data was obtained for cross flow over straight tubes. Uncertainties are not defined for the data from these' tests. Detailed tube damping data used in support of the stability ratio evaluations addressed in this report are provided in Section 5.2, below.

f1pw Field - Velocity Times Sauare-Root-Density Distribution

. . Average and U-bend-local flow field uncertainties are addressed independently in the following.

06290:10/062690 5-4

Averaae Flow Field

- Uncertainties in the average flow field parameters, obtained from ATHOS analyses, coupled with stability constant and frequency, are essentially the

_same for units with dented or non-dented top support plates. If the errors associated with these uncertainties were large, similar instabilities would be expected in the non-dented units with resulting wear at either the top support plate or inner row AVBs. Significant tube wear has not been observed in inner row tubes in operating steam gen rators without denting. Thus, an uncertainty estimate of about [ ]C for the combined effects of average flow field, stability constant and frequency appears to be reasonable. To further minimize the impact of these uncertainties, the V. C. Summer tubes are evaluated on a relative basis, so that constant error factors are essentially eliminated. Thus, the uncertainties associated with the average velocity times square-root-density (combined)' parameter are not expected to be significant.

U-Bend Local Flow Field

- Non-uniform AVB insertion depths have been shown to have effects on stability ratios. Flow peaking, brought about by the " channeling" effects of non-uniform AVBs, leads to a-local perturbation in the velocity times square-root-density parameter at the apex of the tube where it will have the largest.effect (because the apex is where the largest vibration displacemer.ts occut). Detailed local flow field data used in support of the stability ratio evaluations addressed in this report are provided in Section 5.2, below.

OyfJ31 1 Uncertai_nties Assessment Based on the above discussions, and the data provided in the following sections, it is concluded that local -flow peaking is likely to have contributed significantly to the instability and associated increased

. -vibration amplitude for the failed North Anna tube. Ratios of stresses and stability ratios relative to the North Anna tube, R9C51, are utilized in this

- report to minimize uncertainties in the evaluations associated with instability constants, local flow field effects and tube damping.

06290:1D/062690 5-5

5.2 Tube Damping Data

- The damping ratio depends on several aspects of the physical system. Two primary determinants of damping are the support conditions and the flow field. It has been shown that tube support conditions (pinned vs clamped) affect the damping ratio significantly. Further, it is affected by the flow conditions, i.e., single-phase or two-phase flow. These effects are discussed below in more detail.

l Reference (5-1) indicates that the damping ratio in two phase flow is a sum of contributions from structural, viscous, flow-dependent, and two-phase -damping.

The structural damping will be equal to the measured damping in air. However, in two-phase flow, the damping ratio increases significantly and is dependent on the void fraction or quality. It can be shown that the damping contribution from viscous effects are very small.

Damping ratios for tubes in air and in air-water flows have been measured and

. reported by various authors. However, the results from air-water flow are poor representations of the actual conditions in a steam generator

- (steam-water flow at high pressure). Therefore, where available, results from prototypic str'm-water flow conditiens should be used. Fortunately, within the past few p ars test data on tube vibration under steam-water flow has been

-developed for both pinned and clamped tube support conditions.

Two sources of data are particularly noteworthy and are used here. The first is a'large body of recent, as yet unpublished data from high pressure steam-water-tests conducted by Mitsubishi Heavy Industries (MHI). These data were gathered under pinned tube support conditions. The second is comprised of the results from tests sponsored by the Electric Power Research Institute (EPRI) and reported in References (5-2) and (5-3).

The damping ratio results from the above tests are plotted in Figure 5-4 as a function of void fraction. It is important to note that the void fraction is  ;

l a,c determined on the basis of [

06290:10/062690 5-6 l

.. - - - . .- - . . - __A

(Reference (5-4)). The upper curve in the figure is for pinned support conditions. This curve represents a fit to a large number of data points not

, shown in the figure. The points on the curve are only plotting aids, rather than specific test results.

The lower curve pertains to the clamped support condition, obtained from Reference (5-3). Void fraction has been recalculated on the basis of slip flow. It may be noted that there is a significant difference in the damping ratios under the pinned and the clamped support conditions. Damping is much larger for pinned supports at all void fractions. Denting of the tubes at the top support plate effectively clamps the tubes at that location. Therefore, the clamped tube support curve is used in the current evaluation to include the effect of denting at the top tube support plate.

The Reference 5-3 data as reported show a damping value of .51 at 100% void fraction. The 100% void fraction condition has no two phase damping and is considered to be affected principally by mechanical or structural damping.

Hestinghouse tests of clamped tube vibration in air have shown that the mechanical damping is only [ lca rather than the 0.5% reported in

- Reference (5-3). Therefore the lower curve in Figure 5-4 is the Reference (5-3) data with all damping values reduced by [ l a,c ,

l 06290:1D/062690 5-7

5.3_ Tube Vibration Amplitudes Hith Single-Sided AVB Support 2 A series of wind tunnel tests were conducted to investigate the effects of 4

tube /AVB' eccentricity on the vibration amplitudes caused by fluidelastic

. vibration.

[

3a ,c Prior test results obtained

- during the past year using this apparatus have demonstrated that the fluidelastic vibration characteristics observed in the tests performed with the cantilever tube apparatus are in good agreement with corresponding characteristics observed in wind tunnel and steam flow tests using U-bend tube

= arrays. A summary of these prior results is given in Table 5-1.

An overall view of the apparatus is shown in Figure 5-5. - Figure 5-6 is a top view of the apparatus. [

i

.. l a.c ,

06290:1D/062690 5-8

i As shown in Figure 5-7, the tube vibration amplitude below a critical velocity is caused'by [

a ,c, 3

Figure 5-7 shows the manner in which the zero-to-peak vibration amplitude, expressed as a ratio normalized to [ l a,c , varies when one gap remains at [ 3a ,c For increasing velocities, up to that corresponding to a stability ratio of [

Ja ,c . Figure 5-8 shows typical vibration amplitude and tube /AVB impact force signals corresponding to those obtained from the tests which provided the respits shown in Figure 5-7.

As expected, impacting is only observed in the [ ]a,c ,

It is concluded from the above test results that, [

3a ,c ,

5.4 Tests to Determine-the Effects on Fluidelastic Instability of Columnwise Variations in AVB Insertion Depths

This section summarizes a series of wind tunnel tests that were conducted to investigate.the effects of variations in AVB configurations on the initiation of fluidelastic vibration. Each configuration is defined as a specific set of insertion depths for the individual AVBs in the vicinity of an unsupported U-bend tube.

The. tests were conducted in the wind tunnel using a modified version of the cantilever tube apparatus described in Section 5.3. Figure 5-9 shows the 06290:10/062690 5-9

.i

conceptual. design of the apparatus. The straight cantilever tube, [

5

'i i

1

.4-a .C, J

.[

v i

a

- J .c . Figure 5-11 shows the AVBs,.when the side panel of the test section is removed. -Also shown is the. ,

1. - Ttop flow screen which.is -[

3a ,c The . l LAVB. configurations ~ tested are shownrin Fig. 5-12. Configuration la  !

corresponds to tube R9C51,-the failed tube at' North Anna. Configuration ;a 2

-corresponds' to one of the . cases in which the AVBs are! inserted to a uniform i depth-and no local' velocity peaking effects are expected.-

cAs-shown in Figure 5-9, C r-

.. j a.c , ,

j.

0629D:10/062690 5-10 L

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

t i

All the tubes except'the instrumented tube (corresponding to Row 10) are a

[' J c. As discussed in Section-5.3, prior

.) - testing indicates that this situation provides a valid model. The

-instrumented tube (- ]C as shown'in Figure 5.10. :Its (' Ja,c direction vibrational motion is~ measured using a .

non-contacting transducer.

L 1 J

-Ja , c

. The instrumented tube corresponds to a Row 10 tube as shown in Figure 5-9. However, depending on the particular AVB configuration, it can  :

reasonably represent a -tube in Rows 8 through 11. The AVB profile in the straight tube modelLis-the average of Rows 8 and 11. The difference in profil'e is quite small for these bounding rows.

[ l a.c using a x . hot-film anemometer located-as shown in Figure 5-9.  ;

s Figure 5-13 shows the rms vibration amplitude, as determined from PSD (power spectral density) measurements made using an FFT 4ectrum analyzer, versus flow velocity for Configuration la. Configuration la corresponds to the final, evaluated positions of AVBs near tdi Eytbi in North Anna (See Figures B-6'and 8-7). Data for three repeat tests are shown and.the critical velocity

~ is identified.' The typical rapid increase in vibration amplitude when the

- critical velocity for fluidelastic vibration is exceeded is evident.

The main conclusions.from the tests are: i

1. Tube vibration below the critical velocity is relatively small, typical of turbulence-induced vibration, and increases rapidly when the-: critical velocity for the initiation of fluidelastic vibration is exceeded.

. l l

4 l

06290:10/062690 5-11 ,

l l

i

J

2. ' Configuration lb '(which was initially thought' to represent AV8 positions near R9C51 in North Anna until re-evaluation indicated  ;

r.- Configuration la) has the lowest critical velocity of all the

. configurations tested.

a.

3. . Configuration 'Ib is repeatable and the configuration was rerun periodically to verify the consistency of the test apparatus.

The' initial test results obtained in support of the V. C. Summer evaluation are summarized in Table 5-2. The test data are presented as velocity peaking ratios, the ratio of critical velo:ity for North Anna tube R9C51 configuration la, to that for each V. C. Summer AVB configuration evaluated. i 5.5 References

-- ,a,b,c 1

g i'

G L .-

l l p :.  ;

4 l

L i .

I: l l

06290:1D/062690 5-12 l

l_ -.a_.._-_. .

Table 5-1 ,

Hind Tunnel Tests on Cantilever Tube Model OBJECTIVE: Investigate the effects of tube /AVB fitup on flow-induced tube vibration.

APPARATUS: Array of cantilevered tubes with end supports [

j a .C ,

HEASUREMENTS: Tube vibration amplitude and tube /AVB impact forces or preload forces.

RESULTS:

a,b,c L _

0629D:10/062690 5-13

h Table 5-2 a Fluidelastic Instability Velocity Peaking Ratios for Columnwise Variation in AVB Insertion Depths (V. C. Summer)

Type of Insertion Peaking Ratio Configuration Ula/U n

. a,b,c la Ib ik lw 1x ly 2a 4a

, 4b 4c 4d 40 4x Sa Sb Sc 8p 84 . -

Note: U is instability velocity at inlet for type n n

of AVB insertion configuration.

06290:10/062690 5-14

, a,c 4

Figure 5-1 Fluideiastic Instability Uncertainty Assessment 5-15

U-Bend ~ Test Data

1) MB-3 Tests

~~

B values of [ ]a,b,c

, 2) MB-2 Tests S of'[ Ja,b,c

3) Air Model Tests S of [ Ja,b,c without AVBs Tendency for B to increase in range of [ Ja,b,c with inactive AVBs (gaps at AVBs)

Tendency for B to decrease toward a lower bound of

[ ]a,b,c with active AVBs Verification of Instability Conditions

1) Flow conditions at critical velocity from MB-3

2) Measured damping for the specific tube

-. 3) Calculated velocities from ATH0S 3D analysis

4) s determined from calculated critical values

- Good agreement with reported S values

' 5) . ATHOS velocity data with S of [ ]a,b,c and known damping 4 should not significantly underestimate instability for regions of uniform U-bend flow ,

Figure 5-2 Instability Constant - S 5-16

= ---

a,b,c

,)

~

~

Figure 5-3 Instability Constants A, obtcined for Ctirved Tubes from Wind Tunnel Tests on the 0.214 Scale U-Bend Nx!el 5-17

1 l

l a,b,c 4

Figure 5-4 Damping vs. Slip Void Fraction 5-18

~

i a,b,c i

a-

-! (

Y 4l 1

i 4

Figure 5 5 ; Overall View of Cantilever Tube Wind Tunnel Model-253681

f 5

a,b.c Figure 5 6 Top View of the Cantilever Tube Wind Tunnel Model 25368 2

s b.e 4

l l .

i l

Figure 5-7 Fluidelastic Vibration Amplitude with Non-Uniform Gaps 5-21

a ,b .c

. Figure 5-8 Typical Vibration Amplitude and Tube /AVR lupact Force signals for Fluideiastic Vibration with unequal Tube /AVS Gaps 5-22

a .t .t Figure 5 g Conceptual Design of the Apparatus fcr Determining the Effects of Fluideiastic Instability of Columnwise Variations in AYB Insertion Depths 5-23

~

a,b,c Figure 510 Overall View of Wind Tunnel Test Apparatus

' 2$368 3 -

~

a,b.c I 1

Figure 511 Side View of Wind Tunnel ~ Apparatus with Cover Plates Removed to Show Simulated AVBs and Top Flow Screen l -

L I-l 253684

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

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

l TYPE OF AVB T(PE OF AVB l INSEP, TON INSERTON a, c - - a,c 4

1 e

a L

(

l t

I l

1 .

8 Figure 5-12 AVB Configurations Tested for V. C. Summer 5 26

a,b,c s

~

Figure 5-13 Typical Variation of RMS Vibration Amplitude with Flow Velocity for Configuration la in Figure 5-12 4

6.0 EDDY CURRENT DATA AND AVB POSITIONS from the eddy current tapes provided by SCELG for the October 1988 inspection of the V. C. Summer steam generators, Westinghouse performed a review of eddy current signals in the U-bend region. Approximately 1700 eddy current traces in locations in Rows 7 through 16 were analyzed for the presence of signals indicating AVBs. In addition, twenty-five (25) tubes with potential local flow field effects were examined for the presence of denting.

6.1 V. C. Summer AVB Assembly Design

[

~

3a ,c.e Review of the EC data for V. C. Summer shows that AVB insertion depth is fairly uniform in the regions between Columns 31 and 84 (corresponding to the " flat" contour of the tube bundle in this region) with insertion depth in most cases to Row 9 or lower. AVB insertion depth in the remainder of the columns is more variable, tending to a higher depth of insertion.

6.2 Eddy Current Data for AVB Positions The AVB insertion depths were determined on the basis of interpretation of the eddy current data. To locate the AVBs, the ECT data traces were searched for the characteristic peaks seen in the signals which indicate the intersection of an AVB (or a tube support plate) with the tube (Figure 6-1). Since ambiguity can occur in the interpretation of the ECT data, due to inability of 0443D:lD/061990 6-1

L l

ECT to differentiate on which side of a tube a " visible" AVB is located, other information was used to assist in establishing the location of the AVBs.

I f

j a.c The number of these AVB intersections, including zero (meaning no AVB present), was evaluated for each tube to indicate the presence or absence of AVBs. Figures 6-2 through 6-4 show a representation of AVB insertion distance based on evaluation of the EC data. All inspscted tubes in these figures, with the exception ~of-those indicated with a "0" or a "1", have two or more

" visible" AVB signals. In cases where no AVBs were indicated, a "0" is shown.-

and likewise, a "1" is shown where "one AVB" is indicated.

The direct observation data (the number of AVB intersections seen by the eddy ,

current probe) are the principal basis for determining the AVB positions.

Hhere the direct observations are ambiguous or there is a conflict between observations and projections, the more conservative data are used to determine the AVB positions. Since ' direct observation' gives a 'yes - no' type of i

answer, the projection method 1s used to-' interpolate' AVB insertion depths 4 -

between rows of tubes. Greater conservatism is generally interpreted as the AVB being less inserted although consideration must also be given to the resulting flow peaking factors.

In the case where the AVB characteristic signals can not be confidently determined due to a noisy signal or pre-existing plugged-tubes, location data for the AVBs is provided for (

l l

l-l 0443D:10/061990 6-2 1

_, .. . . _ _ - . . . , - , _ . - - - . - - - - , - . + , , , , _ , . . . - . . . , .,- - _

j a.c 6.3 Tube Denting at Top Tube Support Plate Subsequent to identifying the AVB signals, the Eddy Current (EC) tapes were evaluated i Ja ,c to determine the condition of the tube / top tube support interface of the unsupported tubes having potential flow peaking. Because of the significance of the top tube support plate crevice conditions on the analysis and the ,

potential for further corrosion at the top tube support plate since the October 1988 EC inspection, the EC analysis assumed the top tube support plate crevices to be dented (i.e. having " corrosion with magnetite" or " tube denting with deformation") unless they could conclusively be demonstrated to be otherwise. Analyses of eddy current (EC) data for V. C. Summer showed the presence of " corrosion with magnetite" in roughly half of the tube / TSP crevices. Of the twenty-five (25) tube eddy current results from the October, 1988, inspection that were evaluated for top tube support plate corrosion, eleven (11) were found to be magnetite packed at one or both top tube support plate legs, none showed denting with deformation, and the remaining fourteen (14) showed no detectable magnetite or corrosion. For conservatism in the evaluation, all of the tubes evaluated are postulated to be dented. The effect of denting on the fatigue usage of the tube has been conservatively maximized by assuming the maximum effect of mean stress 'en the tube fatigue usage evaluation and by incorporating reduced damping in the tube vibration evaluation.

04430:10/062190 6-3 l C-

6.4 AVB Map Interpretations 6.4.1 Description by Steam Generator To review the relationship of tube stability and tube row number, it is useful to examine Figure 9-8, at the end of Section 9. This figure combines the effects of the tube position (row and column), tube bundle flow-field (velocities, densities, and damping), and tube geometry (bend radius, etc.) to develop an allowable flow peaking ratio for each tube. The allowable flow peaking ratio is the highest flow peaking factor that a particular tube may

, experience before exceeding a stress ratio of 1.0 as compared to the North Anna R9C51, previously established in Section 4.0. Changes in the flow field account' for some of the variation in the allowable peaking ratio, and the peripheral tubes (Column 2) can accept higher peaking ratios, since their allowables are determined from an approach velocity developed from a square-root-sum of-the-squares formulation of the gap velocity on one side of the tube and the comparatively low bulk flow velocity on the periphery.

Observing the variation in allowable flow peaking versus row number, a

[ ]a,c decrease in the allowable flow peaking factor per row can be seen. Since a flow peaking ratio of 1.0 indicates that the flow peaking ,

factor for the tube being examined is identical to that of North Anna R9C51, it can be seen from Figure 9 8 that nearly all V. C. Summer Row 9 tubes would require a peaking factor equivalent or greater than North Anna R9C51 to exceed the stability ratio criteria.

SG-A The AVB map is given in Figure 6-2. All Row 12, Row 11 and Row 10 tubes are supported. Thirty-eight (38) Row 9 tubes, ninety-four (94) Row 8 tubes, and one hundred and nine (109) Row 7 tubes are unsupported. AVB insertion depths vary 'slightly from Column 2 through Column 30, gradually from Column 31 to Column 81, and to a greater extent between Columns 82 and 113.

R9C83 is the highest loaded. tube in this steam generator, having a relative stability ratio, including the effects of local flow peaking, of [

0633D:lD/062990 6-4

+

).a,c No appreciable magnetite was

. evaluated as being present in the top tubes support plate cret .ces of this tube, based upon a review of the October 1988 eddy current tapes.

The AVB positions near R9C83 [

ja,c AVB insertion depths near SG-A R8Cll were evaluated to determine the potential for flow peaking. Based on the [

]a,c With this conservative arrangement of AVBs, SG-A RSCll is evaluated to have no flow peaking.

Insertion depths near SG-A R8C92 were also evaluated to determine the potential for flow peaking. Based on the [

la,c With this insertion depth, as shown in Figure 6-2, SG-A RBC92 is evaluated to have no flow peaking. In the unlikely event that [

Ja,C 06330:10/062990 6-5

_ _~___.-._.._._ _._ _ _. _ _. _ ._._ _ . _ _ _ _ - _ _ . _ . _ _ _ _

i l

Of the remaining tubes in SG A, R9055 is the highest loaded. This tube has a j flow peaking ratio of ( )"'C i c ,. Flow peaking factor selections for all tubes having significant relative stability' ratios or stress ratios are discussed in Section 8.8.

SG-B The AVB map is given in Figure 6-3. All Row 12, Row 11 and Row 10 tubes are t supported. Four (4) Row 9 tubes, sixty-three (63) Row 8 tubes, and I ninety nine (99) Row 7 tubes are unsupported. AVB insertion depths vary gradually from Column 3 to Column 31 and from Column 84 to Column 113.

Insertion depths generally vary slightly Column 32 to Column 83, except for a depth variation between Columns 50 60.

R9C56 is the highest loaded tube in this steam generator, having a relative

- stability ratio, including the effects of local flow peaking, of (

1 Ja,c Based upon a review of the October 1988 eddy current tapes, magnetite was evaluated as.being present at the top hot leg tube support plate crevice of this tube, and no appreciable magnetite was evaluated as being present on the cold leg top tube support plate crevice.

The AVB positions near R9C56 [

ya,c L' Of the remaining tubes in SG-B, .R9C110 is the highest loaded. This tube has a

. flow peaking ratio of (

l

]a,c Flow peaking factor selections for other, lower row tubes are l

reviewed in Section 8.8. ' '

i 0633D:10/062990 6-6

l l

l

.SG C The AVB map is given in Figure 6 4. No Row 14, one Row 13, and one Row 12 tubes are unsupported. Five (5) Row 11 tubes, twelve (12) Row 10 tubes, ,

twenty-eight (28) Row 9 tubes, forty-eight (48) Row 8 tubes, and.one hundred and five (105) Row 7 tubes are unsupported. AVB insertion depths vary significantly from Column 2 to_ Column 31, slightly from Column 32 to Column -

83, and gradually from Column 84 to 113.

R13C5 is the highest loaded tube in this steam generator, having a relative

' stability ratio including the effects of local flow peaking (

Ja,c Other tubes having significant relative stability ratios are R12C5 ( Ja,c; R10C23 (

);a,c R9C29( Ja,c; and R9C106 (

Ja,c All five of the above listed tubes underwent ameliorative action (

) a,c The flow peaking factor selected for R13C5 is (

).a,c This is higher than

- the.1,47 flow peaking factor determined for North Anna R9C51, and gives a relative flow peaking ratio of ( ).a c Based upon a review of the October 1988 eddy current tapes, no magnetite was evaluated as being present -

at the top hot leg tube support plate crevice of R13C5, R12C5 and R9C106.

Magnetite signals were indicated at both tube support plate crevices of R10C23 and in the cold leg crevice of R9C29.

To account for (- .

),a,c The.AVB positions near Column 23 were (

4 0633D:10/062990 6-7 l . . . .

. l

Jac and is acceptable for continued operation as described in Section 9. Tube R10C23 underwent ameliorative action.

The AVB [

3a ,c The positions of AVBs C105/106 and C106/107 were both determined [

]a,c tube R10C106, resulting in the flow peaking factor described in Section 8.8.

The AVB projections near R9C106 were in good agreement, and a [

ja.c Of the remaining tubes in SG-C, RllC4 through RllC8 are the highest loaded.

These tubes have [

]a,c value for these row and column numbers.

Flow peaking factor selections for other, lower row tubes are reviewed in Section 8.8.

6.4.2 Summary of Support Conditions Tubes which were evaluated as havin0 "1" AVB signals, and determined to be supported based upon projection data and adjacent tube checks are listed in Table 6-1. With the exception of tubes listed in Table 6-2, "I AVB Signals Indicating Support for Flow Peaking Analysis", all tubes which are drawn with 0633D:lD/062990 6-8 f

l an AVB inserted to a depth even with the tube centerline are supported. The tubes in Table 6 2, although unsupported, are less limiting than neighboring

, tubes in which flow peaking is produced, and therefore are generally not included among the "significant" tubes in Section 9. Table 9-2. Table 6 3,

- which includes those tubes listed in Table 6-2, provides a summary listing of all unsupported tubes. The AVB projections shown are in nearly all instances the projected values from the tube in the next highest row in a particular column. If the projection from a particular next highest row tube varies significantly with those adjacent and higher row tubes, possibly due to a signal from a deposit, all surrounding data are analyzed, and a revised projection value determined.

l l

l 06330:10/062990 6-9

l TABLE 6-1 V. C. Summer

. 1 AV8 Signals Determined to t'e Supported V. C. Summer Steam Generator A Row 12 None Row 11 None Row 10 None Row 9 Columns 3, 4, 109 Row 8 None Row 7 Columns 28, 29 V. C. Summer Steam Generator _B Row 12 None Row 11 None Row 10 None Row 9 Column 113 Row B Columns 98 Row 7 None V.C. Summer Steam Generator C Row 12 Column 4, 6, 7, 8 Row 11 Columns 2, 3, 4 Row 10 Columns 103, 108 Row 9 Column 28 Row 8 None Row 7 Column 26 0633D:10/062690 6-10

i TABLE 6-2

. 1 AVB Signal Indicating Support for flow Peaking Analysis i l

1 V. C. Summer Steam Generator A l

l Row 12 None Row 11 None Row 10 None Row 9 None Row 8 None Row 7 Column 87 V. C. Summer Steam Generator B

, Row 12 None Row 11 None

. Row 10 None Row 9 None Row 8 Columns 42 Row 7 None V. C. Summer Steam Generator C Row 12 None Row 11 Column 4 Row 10 None Row'9 None Row 8 None Row 7 None 0633D:1D/062690 6-11

TABLE 6-3

. V. C. Summer Unsupported Tube Summary l l

l V. C. Summer Steam Generator A j Row 12 None Row 11 None

. Row 10 None Row 9 Columns 2, 5, 6, 52-83, 111-113 Row 8 Columns 2-12, 15-23, 31-84,91-100, 104-113 Row 7 Columns 2-27, 30-85,87-113 V. C. Summer Steam Generator B Row 12 None

. Row 11 None Row 10 None

. Row 9 Columns 56, 109-111 Row 8 Columns 2-8, 32-42, 44-50, 55-80, 96, 97, 104-113 Row 7 Columns 2-12, 15-24, 27, 31-84,91-113 V. C. Summer Steam Generator C Row 14 None Row 13 Column 5 Row 12 Column 5 Row 11 Columns 4-8 Row 10 Columns 2-8, 11, 12, 23, 106, 113 Row.9 Columns 2-8, 11-13, 16-20, 23, 27-29, 105-113 Row 8 Columns 2-20, 23, 24, 27-30, 53-55,92-113 Row 7 Columns 2-20, 23, 24, 27-84,88-113 l

0633D:lD/062690 6-12 l

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1

I 7.0 THERMAL AKO >lYORAULIC AKAcVSIS

.- Thf 3 section presents the results of 1 therra: and hydramic aillysis of the flow field on the secondary side of tne steam generator using the 3-0 ATHOS computer coda, Reference (7-1). The major results of the ana' lysis are the water / steam velocity components, density, void fraction, and the primary and

' secondary fluid and tube wall temperatures. The distributions of the tube gap g velocity and density along a given tube wtre obtained by reducing the ATH0S results The bundle parameter distributions used in the V. C. Summer analysis are based -on ATHOS results for another Model 03 steam generator (which will be k referred to as the R6/erence Model) having similar operating conditions. The effect of small differences in operating conditions between the V. C. Summer generators and the other D3 generator were accounted for by applying an adjustment factor to the computed stability ratios. ,

l In the following subsections, operating lata for V. C. Summer are presented along with a comparison to corresponding conditions of the Reference Model

. 03. As part of this comparison, a one-dimensional relative stability ratio ,

calculation is described. The stability ratios for V. C. Summer are adjusted

- in this manner. A description of the Reference 03 ATHOS model and sample results are included in the next two sections. Section 7.4 deccribes an analysis of the operating history data for V. C. Summer. The final section discusses the effect of future operation at differing full power steam pressures.

/

7.1 V. C. Summer Steam Generator Operating Conditions and 10 Reittive

-Stability Ratic Analysis Recent steam generator operating condition data for the V. C. Sun;ner unit were provided by SCEM. The data are representativo of full power operation durin3 the most recently completed fuel cycle, Cycle 5. Table 7-1 provides the data

-for only the most limiting of the three steam generators, SG-C..

.4 With these data, calculations were completed usino the Hestinghouse SG

. performance computer code, GENDS, to verify the plant data and to esttblish a complete list of operating conditions required for the ATHOS analysis. The s

0633D:10/062990 7 -1 l

GENO 3 code determines the primary side temperatures and steam flow rate required to obtain the specified steam pressure at the given power rating.

Besides confirming these parameters, the code calculates the circulation ratio which is of primary impartance to the stability ratio analysis since it.

together with the steam ' low establishes the total bundle flow rate and average loading on the tuber. It also provides an overall indication of the voids within the tube bundie since the bundle exit quality is inversely proportional to the circ ratic (x> d,. - 1/ circ ratio). The calculated circulation ratio is also listed in fable 7-1. In addition, the operating ronditions on which the Reference M7dt! 03 ATHOS study was based are listed.

With respect to their effect on tube stability ratios, three of the operating f traneters listed in Table 7-1 are of crime importance: [

I 3a .c An overall measure of the effect of different operating conditions on the stability ratio can be obtained from a parameter termed the ID relative

/luidelastic stability ratio. This ratio compares the fluidelastic stability ratic r.omputed for a , ticular set of operating conditions to a reference sta bility ratto. For the V. C. Summer analysis, the relative stability ratio techn que is usad to dufine an adjustment factor which is applied to the Refereccs Model 93 stability ratios to account for the differences in operating cq',diticas. The same technique is used to evaluate the effect of

. past operation on the stability ratio (Section 7.4) and the effect of future operation with 'Juced steam pressure / increased tube plugging (Section 7.5).

063?D:10/062990 7-2

The fluidelastic stability ratio is defined as the ratio of the effective I' fluid velocity acting on a given tube to the critical velocity at which large amplitude fluideiastic vibratioii uitiates:

0

, Fluidelastic D effective Stability Ratio, SR - Cl3 Ucritical at onset of instability .

In this ratio, the effective velocity depends on the distributton of flow velocity and fluid density, and or the mode shape of vibration. The critical velocity is based on experimental data and has been shown to be dependent upco the tube natural frequency, damping, the geometry of the tube, tae tube pi.ttern, and the fluid density, along with the appropriate correlstion roefficients. ]

The detailed calculation of this ratio using velocity and density ,

distributions, etc., requires three-dimensional thermal / hydraulic and tube vibration calculations which are lengthy. Therefore, a simplified,

.- one-dimensional version of this ratio has been used to provide a relative

• assessment technique for determining the effect of changes in operating conditions on the stability ratio. The relative stability ratio is defined by tae following equation:

aC (23 In this equation " SUM" refers to V. C. Summer and "REF" to the Reference Model D3 operating condition. While this simplified approach cannot account for three-dimenstonal tube bundle effects, it does consider the major operational carameters affecting the stability ratio. Four components make up this 2

ratio: a loading term based on the dynamic pretsure (pV ), a tube incremental mass (m) term, the natural frequency of the tube (fn ), and a damping ratio (6) term. It should be noted that the ratio is relative, in that each component is expressed as a ratio of the value for a given operating condition to that of a reference operating point.

0443D:10/061990 7-3

A I

-[

t j a ,C,

' The particul'ar damping correlation which is used for all normalized stability ratio calculations'is. based on a dented condition at.the top tube support plate (a clamped ~ condition,-as discussed in Section 5.2). =The clamped condition is also assumed in calculating the tube natural frequency.

-As shown at the bottom of-Table 7-1, the effect of the difference in operating

. conditions results in a [- =3 ,c decrease in relative stability ratio for a  ;

V. C. Summer compared to the Reference Model D3. The higher-pressure for

7. 'C." Summei '[ l a,c is the primary factor leading to this-

.: decrease. .'The stability. ratios for the Reference Model-03 steam generator are thus tidjust'ed by a [ ]"'C' multiplier to generate a set of 3D stability

1. ratios for V. C. Summer.

-s Justification for use of a one-dimensional relative stability ratio adjustmant

. factor is-(

4-e g.c

w g

a .C 1.

-0633D:1D/062990 7-4

7.2 ATHOS Analysis Model

- The calculation of relative stability ratios involves comparing the stability ratio calculated for one or more tubes in a given plant to the ratio calculated for the ruptured Row 9 Column 51 tube in the North Anna Series 51 steam generator. It makes use of ATH0S computed flow profiles for both tube bundles. Since the presence of AVBs in the U-Nnd ceo'cn of a tube oundle could influence the overall flow field and/or the local flow parameters for a particular tube of interest, some discussion of the treatment of AVBs is necessary before presenting a description of the ATH0S model.

The ATH0S code does not include the capability to model the presence of the AV8s in the U-bend region. However, Westinghouse has modified the code to include the capability to model the AVBs via flow cell boundary resistance factors. Practical lower limits of cell size in the ATHOS code, however, prevent a fine grid representation of the AVB V-bar shape which, in turn, limits the accuracy of the AVB representation. ATH0S calculations have been

. performed with and without AVBs in the model. [

4 3a ,c The Reference Model D3 analysis is based on a Cartesian coordinate system for the array of flow cells instead of the typical, and more widely used,

- cylindrical coordinate system. Hith a Cartesian coordinate system the tube 06330:10/062990 7-5

array and any AVBs are arranged in a square pitched configuration which is in 'ine with the coordinate axes. This alignment provides an improved

. representation of the tube region of interest in the bundle.

The ATHOS Cartesian coordinate system model for the Reference Model D? steam generator consists of 18,720 flow cells having 30 divisions in the x-axis (perpndicular to the tubelane) direction,16 divisions in the y-axis (along the tubelane) direction and 39 divisions in the axial (2-axis) direction. In the ATHOS analysis, the steam generator is considered to be symmetrical about the x-axis of the tube bundle. The model therefore, consists of one-half of the hot leg and one-half of the cold leg sides of the steam generator.

Figures 7-1 and 7-2 show the plan and the elevation views of the model. These two figures show the layout of the flow cells and identify locations for some

] of the geometric features.

As shown in Figure 7-1, with the Cartesian coordinate system, the circular wrapper boundary is represented by a step-wise wall as indicated by the heavy

. lines. All of the flow cells outside the simulated wrapper boundary above the first axial slab were blocked off by specifying extremely high flow resistances on the faces of the appropriate cells. Tubelane flow slots in the tube support plates are modeled also.

Figure 7-2 shows the elevation view of the model on the vertical plane of symmetry of the steam (enerator. The feedwater nozzle is located at axial indices 12-11 and 12. Ten axial layerc of cells were included in the U-bend near the top tube support (Figure 7-2, I2-27 to IZ-36) to mote closely model the flow conditions in the area of interest.

Figure 7-3 reproduces the plan view of the model but with the tube layout arrangement superimposed. This figure illustrates the locations of the tubes in the various flow cells. The grid lines in the Cartesian model are in-line with the tube array, providing for all of the tubes to be within the boundary of the flow cells. The fineness of the cell mesh is evident; the largest cells contain only 25 tubes while some of the smallest cells include only

. three tubes. Note, in particular, that additional detail was added near the bundle periphery (IY-13-16) to more closely model the inner radius tubes.

0633D:10/062990 7-6

l 7.3 ATHOS Results

. The results from the ATH0S analysis consist of the thermal-hydraulic flow parameters necessary to describe the 3-D flow field on the secondary side of

- the steam generator (velocity, density, and void fraction) plus the distributions of the primary fluid and mean tube wall temperatures. The secondary side mixture velocity is composed of three components (Vx, Vy, and Vz) which ATH0S computes on the surfaces of the flow cell. Since the local gap velocity surrounding a tube is required in the vibration a'nalysis, a post-processor is used which: a) interpolates among the velocity components for the cells located nearest to the tube of interest and, b) accounts for the minimum flow area between tubes to calculate the tube-to-tube gap velocity.

The post-processor performs the necessary interpolations to determine both in-plane and out-of-plane gap velocities at specific intervals along the length of a tube. It also interpolates on the ATH0S cell-centered density and void fraction to determine the required local parameters along the tube length. The output of the post-processing is a data f'!e which contains these

. parameter distributions for all the tubes in the generator and which provides a portion of the input data required for tube vibration analyses.

Figure 7-4 shows a vector plot of the flow pattern on the vertical plane of symmetry of the steam generator (the vectors are located at the center of the flow cells shown in Figure 7-2). The zig-zag flow pattern through the split flow preheater is clearly shown in the figure. On the hot leg side the vertical flow upward through the half-moon cut-out at the center of flow distribution Plate A is also clearly shown. The vertical velocity (V )

Z component entering the U-bend region on the hot leg side is about twice that of the cold leg side as seen in Figure 7-5 (at model vertical layer index IZ-27). The figure also shows the high V Z-component of the flow leaving the three flow slots on the top tube support plate (PLATE T) at the middle of the 2

figure. The lateral velocity components, VR - (Vx2 ,yy)U2 on the same horizontal plane (12-27) are shown in Figure 7-6. Viewing Figures 7-5 and 7-6 it is seen that at the entrance to the U-bend region the vertical velocity component is about twice that of the lateral velocity resultant on J

I the hot leg side, whe 06330:10/062990 7-7 I

l is several times greater than that on the cold leg side. Figure 7-7 shows the plot of the void fraction contours on the vertical plane of symmetry of the

. steam generator. In the preheater the void fraction is essentially zero. By comparison, the hot leg side void fraction develops rapidly from the lower bundle region. In the U-bend region the void fraction is above 0.95 on the hot leg side, decreasing to about 0.70 at the bundle periphery on the cold leg side.

Figures 7-8, 7-9 and 7-10 shov a sample of the individual tube gap velocity and density distributions along three tubes at Row 10. In each figure the gap velocity and density along the length of the tube are plotted from the hot leg tubesheet end on the left of the figure to the cold leg end on the right.

The mixture gap velocity and density distributions are required as part of the input for tube vibration analysis to determine the tube stability ratios.

These data were generated by the ATHOS post-processor for each tube in the model and stored in a data file. The data file was then utilized in the subsequent stability ratio calculations. Figure 7-11 shows the plot of the

, average in-plane gap velocity normal to the tube and density profiles as a function of the column number along Row 10. The average values were taken as

- the numerical average of the parameter over the entire 180* span of a U-bend at a given column location. The average velocity values are between 10.0 and 11.0 ft/sec. The velocity variations seen in the figure between Columns 35 and 55 are related to the effects of the flow slots along the tubelane of the top tube support plate.

7.4 Relative Stability Ratio Over Operating History One aspect of the evaluation of the V. C. Summer steam generators is to examine the operating history data and use it to determine the susceptibility to fatigue from fluidelastic vibration resulting from the 7-1/2 years of operation. This assessment has been completed through the use of the relative stability ratio technique described previously in Section 7.1. In this application a normalized stability ratio is defined which compares the fluidelastic stability ratio for each period of a plant's operation (fuel

. cycle) to a reference stability ratio based on a recent operating condition.

0633D:10/062990 7-8

A plot of this ratio against operating time, therefore, provides a relative indication of the effect of past operation on the plant's fluidelastic stability ratio. This normalized time-dependent ratio is subsequently combined with an absolute stability ratio.for the reference operating point derived from detailed three-dimensional thermal / hydraulic and tube vibration calculations. [

3a ,c As discussed previously in Section 7.1, the reference three-dimensional stability ratio calculations for the V. C. Summer steam generators were based on Reference Model D3 ATH0S study results along with an adjustment to account for the difference in operating conditions between V. C. Summer and the e

referenca plant. .In addition to the reference stability ratios for the recent operating conditions, a series of calculations were completed to generate a

. normalized stability ratio for each of the five fuel cycles since V. C. Summer

-became operational in October, 1982. Data for this evaluation are summarized

- in Table.7-2. Included are typical values for full load steam pressure and primary fluid average temperature in each cycle. . The number of days that the plant has operated within three power intervals (36-60%, 61-95%, and 96-100%)

are also listed. [

3a ,c

-The .resulting normalized stability ratios are shown in Figure 7-12. In this figure, the normalized stability ratio is plotted against cumulative operating

-time above 61% power. The reference value (-1.00) is based on the recent op'erating condition. The results indicate that, as a result of the general decrease in steam pressure which has occurred, the relative stability ratio has increased about [ Ja,c from Cycle 1 to the current cycle. Note that

- the calculations for Cycle 5 were projected forward from 11/27/89 to 3/16/90.

06330:10/062990 7-9

7.5 Effect of Steam Pressurc on Relative Stability Ratio

- Typically, future fatigue usage is computed assuming continued operation through the end of the 40 year design basis with the current reference operating conditions and relative stability ratios (RSRs). In addition to this calculation, the effects of future long-term increases in tube plugging have been evaluated. Plugging has an adverse effect on the fatigue usage because it results in lower ste3m pressures. Reduced pressure leads to higher U-bend velocities for the same flow rate and reduced damping. Both of these factors result in higher RSRs.

During the most recent fuel cycle, the average plugging level among the three generators was 7.8%. SCE&G estinated that the plugging for Cycle 6 may average 11%. Based on levels selected by SCE&G, two future plugging scenarios have been examined. In the first, it was assumed that at the next startup, 12% plugging is present and that this condition exists through 3/93, at which time the plugging incren.es to 15% for operation through 3/96. In the second scenario, the plugging is assumed to be 15% at the next startup and is maintained at this level for the six years of operation, through 3/96.

Based on average tube plugging, GEND performance calculations predict that the steam generator exit pressure will change from the current 941 psia to 926 psia for 12% plugging and to 911 psia for 15% plugging. These calculations are based on the assumption that the current 587*F T avg will be maintained, and indicate that the relative stability ratio will increase by [ 3a ,c for the SG exit pressures calculated for 12% plugging and by [ lc for a

15% plugging. These results have been included in Figure 7-12. Note that the pressure calculated for the assumed 15% plugging (911 psia) is close to the valves wide open pressure (915 psia) below which full power cannot be maintained without turbine moolfications. Therefore, the ( l a,c RSR multiplier represents a reasonable bounding value for future operation assuming full power operation.

0633D:10/062990 7-10

Although these calculations were based on specific levels of tube plugging,

[

'd j a .C

References:

7-1 L. H. Keeton, A. K. Singhal, et al. "ATHOS3: A Computer Program for Thermal-Hydraulic Analysis of Steam Generators", Vols. 1, 2, and 3, EPRI NP-4604-CCM, July, 1986.

06330:10/062990 7-11

Table 7-i  !

V. C. Summer Steam Generator Operating Conditions and Comparison with J

Reference Model D3 ATHOS Analysis V. C. Summer Reference Model (SG-C) D3

_ a,c

' Thermal Power (MHt)- 950 Steam Flow Rate (1bm/hr) 4.13 x 10 6

-'Feedwater' Inlet 1 Temperature-(*F) 432

-Steam Pressure (psla) 941 l

Water Level (%:of span) 63.6

'l Primary Inlet / Outlet Temperatures 618/556 g egy.

4 Calculated Parameters

. - a, c

- Circulation. Ratio' Bundla Flow Rate'(1bm/hr) 1D' Relative Stability Ratio

.(Normalized to' Reference'Model 03)

I y

n 0443D:1D/061990' 7-12

i Table 7-2 )

V. C. Sumer Operating History Data Distribution of Days in full Load Values Steam Frimary Feedwater Calculated Each Power Interval Calculated Pressure

• Avg. Temp." Temperature" Steam flow *

(Dea F) _LDeq F) E bm/hrl_ Circ R 311g*

geginning 61-95% 36-60% (Psia)

Cyrig [nd 36-100%

- _ ac 964 587 435 28-Sep-84 175 101 101 1 22-Oct-82 960 587 435 05-Oct-85 711 32 8 2 18-Dec-84 958 587 434 14-Dec-85 06-Mar-87 368 44 10 3

948 587 433 06-Jun-87 16-Sep-88 406 15 9 4

941 587 432 5 26-Dec-38 16-Mar-90** _1Q3 _13 _Z1 _

1569 210 151 Notes:

• Basis: most limiting generator, SG-C.

• • Projected end of cycle 5, last data on 11/27/89. All projected operation assumed to be at full power.

7-13 0443D/062190 l

aCr a

l.

1 .-

l Figure 7-1 Plan View of ATHOS Cartesian Hodel for Reference Model D3 -

t 0443D:10/050190 7-14

s,c

~

l -

t Figure 7-2 Elevation View of ATH0S Cartesian Model for Reference Model 03 1

04430:10/050190 7-15

a,e 1

i l

i l

i a _

Figure 7-3 Plan View of ATHOS Cartesian Model for Reference Model 03

- Indicating Tube Layout 04430

10/050190 7-16

a,e l

l l .

Figure 7-4 Flow Pattern on Vertical Plane of Symmetry l 0443D:10/050190 7_17

a,c Figure 7-5 Vertical Velocity Contours on a Horizontal Plane

, at the Entrance to the U-Bend Region (IZ-27) 0443D:1D/050190 7-18

1 a,c l

. ~

Figure 7-6 Lateral Flow Pattern on Horizontal Plane,

• at the Entrance to the U-Bend Region (IZ-27) t 0443D:10/050190 7-19

a,C

~"

Figure 7-7 Void Fraction Contours on Vertical Plane -

of Symetry 0443D:10/050190 7-20

.J43 ac r

Figure 7-8 Tube Gap Velocity and Density Distributions

.. for Tube Row 10/ Column 38 04430:10/050190 7 ~i

a,c Figure 7-9 Tube Gap Velocity and Density Distributions for Tube Row 10/ Column 45 i

I 0443D:10/050190 7-22 l

A,C

~~ -

Figure 7-10 Tube Gap Velocity and Density Distributions

, for Tube Row 10/ Column 50 0443D:lD/050190 7-23

a,c 4

Figure 7-11 Average Velocity and Density in the Plane'of the

.. U-Bends Normal to Row 10 0443D:10/050190 7-24

a,c 1 --

l 1

l _

Figure 7-12 V. C. Summer Normalized Stability Ratio Based

. on High Power (>61%) Operation 0443D:10/050190 7-25

8.0 PEAKING FACTOR EVALUATION

- This section describes the overall peaking factor evaluation to define the test based peaking factors for use in the tube fatigue evaluation. The evaluation of the eddy current data to define the AVB configuration for North Anna 1 Tube R9C51 is described. This configuration is critical to the tube fatigue assessments as the peaking factors for all other tubes are utilized relative to the R9C51 peaking factor. Uncertainties associated with applying the air model test results to the tube fatigue assessments are also included in this section. Included in the uncertainty evaluation are the following contributions:

o Extrapolation of air test results to two phase steam-water o Cantilever tube simulation of U-bend tubes o Test measurements and repeatability o AVB insertion depth uncertainty

- B.1 North Anna 1 Configuration 8.1.1 Background The AVB configuration of the ruptured tube in North Anna, R9C51, is the reference case for the tube fatigue evaluations for other plants. In accordance with the NRC Bulletin 88-02, the acceptability of unsupported tubes in steam generators at other plants is based on tube specific analysis relative to the North Anna R9C51 tube, including the relative flow peaking factors. Thus, the support conditions of the R9C51 tube are fundamental to the analyses of other tubes. Because of the importance of the North Anna tube, the support conditions of this tube, which were originally based on "AVB Visible" interpretations of the eddy current test (ECT) data (Figure 8-1),

were re-evaluated using the projection technique developed since the North Anna event. The projection technique is particularly valuable for

. establishing AVB positions when deposits on the tubes tend to mask AVB signals such as found for the North Anna 1 tubes. The results of this evaluation are

- summarized below, l

06330:10/062990 8-1

i 8.1.2 Description of the Method The basic method utilized was the projection technique in which the AVB position is determined based on measured AVB locations in larger row tubes

- in the same column. In this study, the projection technique was utilized in the " blind" mode, (AVBs called strictly based on the data) as well as the reverse mode (data examined on the basis of predicted AVB positions). The objective of this application was, with the greatest confidence possible, to establish the cositions of the AVBs in an 8 column range around the R9C51 tube in North Anna 1. Steam Generator C, 8.1.3 Data Interpretation The ECT traces for the U-bends in Rows 8-12 (in one case,13) were examined for Columns 48-55. The original AVB visible calls are shown in Figure 8-1.

The data were examined by an eddy current analyst experienced in reading these traces, and by a design engineer knowledgeable in the geometry of the Model 51 U-bend region.

The intent of this review was to determine if the presence or absence of AVBs as shown in Figure 8-1 could be confirmed using the AVB projection technique. Preliminary projected AVB positions were based on ;eometric data provided for a few of the tubes near R9C51. The features which were sought were evidence of data " spikes" where AVBs were predicted, offset indications (multiple spikes) where offset AVBs were predicted, single indications where single AVB intersections were predicted, etc. The data evaluation method used was a critical examination of the data, which was biased toward the presence of AVBs unless a confident call of "no AVB" could be made, and then checking the consistency of the data among the tubes in a column and against the theoretical data for the predicted AVB positions. [

0633D:10/062990 8-2

I I

3& ,c ,

I Figure 8-4 is the "AVB visibt a" map for coluains 48 through 55, based on the critical review of the data. It snould be noted that the original clata interpretations and the review trterpretations are consistent. a 8.1.4 Projections The [ l a,c ECT traces were utilized for projecting the position of tile AVBs according to the standard format of the projection Nothod.

The results of the projections ate presented in Figure 8-5, which shows a matrix of projections for tube rows 8 through 13 in columns 48 through 55.

For many of the tubes, more than one, and as many as three, projection 06330:10/062990 8-3

values are shown. Multiple projections are expecteti for a tube if the AVBs 01 either side of the tube are not at the same elevat non, or if the upper and lower AVB support that tube. As many as four different projections are possible if it is assumed that the tube is supported by the upper and lower

. AVBs, and both upper and lower bars are staggered in elevition as show.i in Figure 8-2.

The logic in arranging the projection data is based on the fol;owing two rules:

Rule 1. The projections of the same AVB based on different tubes in the same column [ l a.c ,

[

3a ,c ,

Rule 2. Two adjacent tubes in the same row [

a 3 .c . Consequently, the difference in the [

a 3c ,

I o

06330:10/062990 8-4 i

-- . x _,

j

The implementation of tai is that if the position (either lef t or right) of a projected AVB is a'aur c for a column, then the projections in the adjacen' colerv are also E 5

]a,c ,

S .

1 The ar angement of the AVBs as shown in Figure 8-5 satisfies the rules above

? Od is consistent with the rupture of R9C51. The resulting AVB arrangements, based on the projection matrix of Figure 8-5 is shown in Figure 8-6.

8.1.5 Conclusions The general AVB arrahgemert surrounding the ruptured "ibe in North . Ma 3 , /

Steam Generator C, which was the basis for the analysis, is confirmed by a

- detailed critical review of the ECT data. Differences exist in to AVB

- pattern o? tween tube columns 48-49, in which the AVBs appear to b; lesk ,

inserted than previously indM&ted. The pattern of Fig tc B-6 is the best '

fit to the rules which were adc,..s,1 tar determining the ;;Mtion of the AVBs, .s well as consistent with exp yaation of the tube fatiure-The bas!s of the ' review was a projection technique which utilizes data from tubes one or more rows removed from the actual inserted pos) tion cf the AVB to Jetermine the position of the AVB. The intent of the review was to establish the positions of the AVBs by confirming or eliminating features of AVP alignments such as *.ide to s'ide offsets, etc. of the AVBs adjacent to i the tube.s. Overcil, the conclusions .egarding the positions of the AVBs around R9C51 in North Anna-1, Steam Generator C are based on consistency <

among all the available data.

8.2 T+st Hetsurement Uncertaintin I

Tht: descr'ipt/lont of the peaMng factor tests and apparatus were provided in Sectior. 5.t . All pracMca~t measures were taken to reduce uncertainties.

Neverthe'tets, some still et:c.ain and should be properly accounted for. The impcrtant pilmot<.r rnaasured during testing that has a significant impact on 06330:1D/0629'i0 8-5

peaking factor is the air velocity. The air velocity at test section inlet was measured using a [ Ja,c . Based on considerable experience with the use of such instruments, it is known that the magnitude of uncertainty is very small. A( Ja,c measurement uncertainty is ustJ in this analysis based on past experience.

8.3 Test Repeatability During the peaking factor testing of AVB configuration, each test was perrormed at least two times to '.*nfirm repeatability. It has been demonstrated that the tests are quite repeatable with the results often falling within 2 or 3% of one another for the repeat tests. An upper bound value of 5% was used in the current uncertainty analysis.

8.4 Cantilever vs U Tube A first order estimate can be made of the validity of modeling a U bend tube by a cantilever tube in tests to determine the effects of AVB insertion

. depth on the initiation of fluidelastic vibration. The following assumptions are used:

a,c l

0443D:lD/061990 86

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

a,c 0

For the purposes of this estimate, the geometry of the cantilever measuring tube in the air test model is compared with the geometry of a prototypical Row 10 tube. [

ja,c ,

The comparison between a U-bend tube and the model tube involve the consideration of an effective velocity associated with the flow perturbation caused by-the AVBs. [

ja,c 04410:10/061990 8-7 l

[

a J c. Using these values, the ratio of the effective velocity for the cantilever measuring tube to that for the U-bend tube is about ( 3a ,c for the case treated.

A similar evaluation can be made for a Row 10 tube that lies in the projection or shadow of an AVB that is inserted to a depth required to support a Row 9 tube. [

ja,C, The net result is that the ratio of the effective velocity for the cantilever tube to that for the U-bend tube is about [ ['C.

These *esults indicate that, for the particular assumptions used, the tantilever tube model appears to be a reasonable representation of the U-bend with respect to determining relative peaking factors for different AVE configurations. This evaluation also shows that, on the average, the 5; magnitude of the systematic uncertainty associated with the use of cantilever tube to simulate the U-bend is about [ 3 ,c a

8.5 Air vs Steam-Hater Mixture The local peaking factors from the air tests can be applied to the steam

. generator steam / water conditions either as a direct factor on the mixture 06330:10/062990 8-8

l i

velocity and thus a direct factor on a stability ratio, or as a factor en the steam velocity only with associated impacts on density, void fraction and damping. This method leads to a reduction in tube damping which enhances the peaking factor compared to the direct air test value. For estimating an absolute stability ratio, this application of the peaking f actor is a best estimate approach. However, for the evaluation of tubes relative to stability ratio criteria, it is more conservative to minimize

^he peaking factor for the North Anna Unit I tube R9C51 through direct application of the air test peaking factor. This conservative approach is therefore use6 for evaluating tube acceptability.

Under uniform AVB insertion (or aligned AVB insertion). there are no local open channels for flow to escape preferentially. The'efore, air flow is approximately the same as steam / water flow relt.tive to velocity perturbations. Under non uniform AVB insertion the steam / water flow may differ from air, as the steam and water may separate from each other when an -

obstruction, such as an AVB, appears downstream. The water would continue along the saue channel while steam readily seeks a low resistance passage

- and thus turns into adjacent open channels. Two phase tests indicate a tendency for steam to nreferentially follow the low pressure drop path compared to the water phase.

Based on the above discussion, the F are considered to more appropriately 4

apply to the steam phase. Thus, it follows that mixture mass velocity for the tube subject to flow perturbation can be written as follows:

a,c where Dg is the vapor density, Of the water density, Fa the velocity peaking factor determined from air tests, jg* the nominal superficial

~

vapor velocity, and jf* the superficial water velocity. Steam quality can then be determined as follows:

0443D:10/061990 B9

a,c The Le11ouche-Zolotar correlation (algebraic slip model), as used in the ATH0S code, is applied to determine void fraction. Subsequently, mixture l density, velocity and damping coefficients for the tube which is not l

-supported and subject to flow perturbation is evaluated. Therefore, similar to the air velocity peaking factor, local scaling factors of mixture density and velocity and damping coefficient can be readily determined. Finally, a local stability peaking factor for fluidelastic vibration can be calculated as follows:

~ ~

a.C where Fs is the stability peaking factor, Fd the density ccaling factor, ,

Fy the velocity scaling factor, and F dp the damping coefficient scaling factor. If we use the air velocity peaking factor without translating to steam / water conditions, then a,c

, . l As shown in Table 8-1 stability peaking factors for the steam / water mixture are slightly higher than air velocity peaking factors. The difference between the steam / water and air peaking factors increases as the air peaking factor increases.

l For appilcation to tube fatigue evaluations, the ratio of the peaking factor for a specific tube to that for North Anna R9C51 is the quantity of interest. Larger values for this ratio are conservative for the tube fatigue assessment. The North Anna R9C51 peaking factor is one of the

. highest peaking factors.- As discussed in Section 8.7, a peaking factor of nearly ( l a,c is determined for the R9C51 tube. The differences between

[

J a ,c. Typical values are shown in Table 8-2. These 0443D:10/062190 8-10

results show that the direct application of the air test data yields the higher relative peaking factor compared to R9C51. To obtain conservatism in

, the peaking factor evaluation, (

3a.c, Comparing the vt. lues in the first and last columns of Table 8-1, it may be a

noted that the stability peaking factor for steam water is [ J .c higher than the air velocity peaking factor. On the average, the uncertainty associated with the conservative use of air velocity peaking factor is [ J a .c, The conclusion that peaking factor for steam / water flow would be higher due to the dependency of damping ratio on void fraction was supported by an '

alternate study. In this study, a section of steam generator tubes were simulated using the ATHOS code under prototypic flow conditions. The objective of this study was to examine the magnitude of the changes in void fraction and thus stability ratio as a consequence of non-uniform AVB

. insertion patterns. The current version of ATH0S has modeling limitations that prevent accurate modeling'of local geometry effects. In addition, it

. is believed that an analysis using two-fluid modeling procedure is mandatory to a calculation of the peaking factors for a steam generator to account for the preferential steam flow along the low resistance path. Consequently, the intent of this analysis is only to help bound the uncertainty on void fraction = effects from extrapolating the air tests to steam-water.

First the analysis was conducted with uniformly inserted AVBs in the ATHOS model. The ATH0S results were processed by the FLOVIB code to determine stability ratios for the specific tubes of _ interest. The calculation was repeated using a non-uniform AVB insertion pattern in the model. The results show that the void fraction distribution changes as a result of flow ,

perturbation. Further, the impact on stability ratio resulting from the

• a changes in void fraction profiles was about [ 3 .c. This alternate calculation provides-independent corroboration of the prior discussion regarding the stability peaking factors under steam-water conditions

. vs in air.

0633D:10/062990 8-11

8.6 AVB Insertion Depth Uncertainty f

4

. The most significant uncertainty for the low peaking configurations is not L in-the test results, but in the determination of actual AVB insertion

- patterns adjacent to specific tubes. The methodology used for obtaining the AVB insertion patterns from eddy current data can ascertain the AVB location l only approximately. The effect on peaking factor resulting from this uncertainty is addressed using test results of AVB configurations that varied from one another by up to ( Ja .c ,

. Based on maps of AVB insertion depth of various plants, several configurations have been tested for determining fluidelastic instability flow rate by an air cantilever model. Stability peaking factors were then determined from the ratio of critical flow rate for a uniform AVB insertion j configuration to a specific configuration. Figure 8-7 summarizes the AVB configurations tested. i j .

Position of AVB insertion depth is determined from Eddy Current Test (ECT) l data. Positioning of AVB from ECT data reading is subject to uncertainty; 8 A change of an AVB

. its accuracy is probably about [ 3 'C.

insertion depth in a given configuration leads to a different configuration, I

and thus a different peaking factor. A review of the tested AVB type has been made and results summarized in Table 8-3. As can be seen, a decrease in depth.of an appropriate AVB tends to decrease the peaking factor, for instance, a [

a ,c. Such a trend can be explained; a decrease in a specific-3 AVB depth will open up more channels for incoming fluid to distribute and thus less flow perturbation. However, this applies only to those changes without inducing the reinforcement of flow perturbation from upstream to downstream.

On the average, the uncertainty in peaking factor resulting from small variations in AVB insertion (of the order of 1/2 tube pitch) is found to be

[ 3a ,c ,

06330:10/062990 8-12

8.7 Overall Peaking Factor with Uncertainty

. As df russed in the previous subsections, there are several aspects to be considered in applying the laboratory test data to steam generator i

conditions. These considerations were reviewed one at a time in those subsections. This section will integrate the pieces into one set of stability peaking factors.

Looking forward to how these peaking factors are used in the analysis (Section 9), the relative stability ratio calculated for a given tube without the consideration of flow peaking is corrected using the ratio of the peaking factor of the specific tube to that of the North Anna R9C51 tube (Configuration la).

l I

It is to be noted that the test results would be applied as ratios of a specific tube peaking factor to the R9C51 peaking factor. This will reduce the influence of some uncertainties since the systematic uncertainties would

l. affect both the numerator and the denominator in the ratio of peaking factors. -The major difference will be in those configurations whose peaking

. factors are significantly lower than.that of R9C51. The approach employed here is intended to provide that conservative peaking factors are employed j for such apparently low peaking configurations.

l l The uniform AVB configuration (2a) is selected as a reference configuration, and the peak hg factors of all configurations tested are recomputed on the basis of this reference. As discussed below, some of the test uncertainties are applied to the reference case to account for its significantly low peaking relative to the R9C51 configuration.

The uncertainties in the test results and their extrapolation are those due

'to test measurements, test repeatability, cantilever tubes in the test vs U-tubes in the steam generator, and air tests vs steam-watar mixture. These were discussed in more detail in the previous subsections. The magnitude of these uncertainties are listed in Table 8-4.

s 0633D:1D/062990 8-13 l

L

l Of these uncertainties, those due to measurement and repeatability of tests are random errors and can occur in any test. Therefore, these are treated

- together. The total random uncertainties are calculated by (

a J .c. The RSS value of these is ( 3a ,c Since these can occur in any test, these are to be applied to all tests. One way of doing this is to apply it to the R9C51 value, that being in the denominator of the final peaking factor ratio. Thus the peaking factor for configuration la (R9C51) is reduced by this amount to yield a value of ( 3a .c instead of the [ Ja.c appearing in Table 5-2.

The nut three uncertainties in Tabla e,-4 are systematic uncertainties. It could be argued that these appear in the peaking factors of both the specific tube under consideration and the R9C51 tube and are therefore counter balanced. However, the relative magnitude of these may be different, particularly for configurations with much lower peaking than R9C51. Therefore it was judged that the [

a ,c.

. J Similarly, as noted above, the effect or ceaking factor due to the uncertainty in the field AVB

- configuration is also included in this reference case. Thus, (

3 a ,c. The peaking factor of the reference configuration 2a (Table 8-5) is raised by this amount to a value of (

jC a

The change in peaking factors of configurations la and 2a resulting from the application of uncertainties as described above are shown in Column 3 of Table 8-5. The peaking factors of all configurations are recomputed on the basis of this reference configuration (2a). These values are displayed in Column 4 of Table 8-5.

Some of the uncertainties were applied to the reference configuration (2a) in order to apply them to all low peaking configurations conserva"ively.

Thus, no configuration should have a lower peaking factor than this

- reference configuration. Therefore, when a peaking factor value less than

( l a,c is calculated for any configuration, (in Column 4 of Table B-5),

it should be altered to ( ]"'C Further, for some of the 0633D:10/062990 8-14

configurations that are conceptually similar, the more limiting (higher) value is used. For example, a peaking factor of ( Ja ,c is used for

-configurations 5a and 5b based on their similarity to configuration Sc.

. The final stability ratio peaking factors calculated on this basis (with configuration 2a as the reference) are shown in Table 8-6.

The overall conclusions from the peaking factor assessment are:

1. As noted in Table 8-4, five elements have been included in the uncertainty evaluation for the peaking factors. The uncertainty

-estimates were developed from both test and analysis results as deccribed in Sections 8.2 to 8.6. The largest single uncertainty of

( J a c is attributable to uncertainties of up to (

Ja,c on determination of AVB insertion depths from field eddy current data. This relatively large uncertainty is applicable only to low peaking conditions where the AVB uncertainties can contribute to small. peaking factors. The definition of "no flow peaking" was increased to encompass the small peaking effects from AVB insertion uncertainties. For the AVB patterns leading to significant peaking factors, AVBs were positioned within uncertainties to maximize the peaking factor. For these configurations, variations of AVB insertion within these uncertainties are expected to reduce the peaking factor compared to the final values of Table 8-6 and Figure 8-7.

2. Including uncertainties directed toward conservatively decreasing the peaking factor for the North Anna tube R9C51, the final R9C51 peaking factor is [ 3a ,c relative to a no flow peaking condition such as with uniform AVB insertion depths.

8.8 Peaking Factors for Specific Tubes Peaking factors for V. C.~ Summer were determined using the methodology

-described above. Table 8-7 summarizes the results of peaking factors. The AVB positions on each insertion pattern of Figure 8-7 should be carefully 0633D:1D/062990 8-15

i noted. Where the AV8s are shown [

3a ,c In applying the methodology to V. C. Summer, maps of the AVB insertion depths shown in Figures 6-2 throunk 5-4 were first reviewed. The second step was to identify locations having signifir'.nt AVB insertion configurations. In doing so, ma"imum allowaole flow peaking factors were also reviewed column by column for Rows 8 through 13. Based on the V. C.

Summer tube vibration analysis, flow peaking factors greater than

[ l a.c for Row 8 and [ 3a .c for Row 9 tubes would indicate the potential for tube fatigue.

After conservative estimates of peaking factors were made for specific

. tubes, those having peaking factors near the maxi.num allowable value were identified and AVB insertion depth was reviewed in the vicinity of the subject tube. If needed, the stability velocity, or the velocity at which unstable tube vibration initiates, was determined for the subject tube by testing the AVB insertion pattern in the Westinghouse Science and Technology Center Cantilever, Air Model. The peaking factor was then calculated using the stability velocity. 'or V. C. Summer, two supplementary configurations were tested. [

3a ,c Determination of peaking factors for identified tubes shown in Table 8-7 are described in detail below. Sections 8.8.1 to 8.8.3 are divided into small tables for ease in following the description.

8.8.1 Steam Generator A

' The following table gives the peaking factors for tubes with unique configurations of AVB insertion depths.

06330:10/062990 8-16

Steam Type of AVB Peaking Generator Row No Column No insertion Depth Factor a,c A 8 22 11 9 83 i 71, 70 63 55 For R8C22, type (' Ja,c was' selected and a peaking factor of ( Ja,c resulted. Tube R8Cll belonged to type [ Ja,c and thus a peaking factor of ( ']a,c was obtained. Type [ ]C was a good match for R9C83 and it then had a' peaking factor of ( Ja c . Type ( Ja,c was considered .

for tubes R9071-and R9C70, and a peaking factor of ( ]a.c was obtained.: Both'R9C63 and R9C55 had a peaking factor of ( Ja,c for a selection of type [ Ja c, 8.8.2 Steam Generator B Tubes with unique AVB configurations are listed together with their peaking l factors.

Steam Type of AVB raaking l ^ Generator Row No Column No Insertion Depth Factor

_ a,c B 7 11 8 74 66 9 110 56 ,

~ ~

0443D:10/061990 8-17

Type [ Ja,c was a conservative call for R7Cll, R8C74, R8C66 and R9C110 and a peaking factor of ( ]a,c resulted for all of them. R9C56 tube belonged to type [ Ja,c and a peaking factor of [ Ja,c was obtained.

8.8.3 Steam Generator C The following table presents results of peaking factors.

Steam Type of AVB Peaking Generator Row No Column No insertion Depth Facte-

_ a,C C 7 88 8 98, 97 93 9 106 -

29 1

23 12, 11 ,

10 106

. 23  ;

1 12 5 13 5 l

Type ( ]a,c was selected for R7C88 and a peaking factor of ( Ja,c  !

resulted. Both R8C98 and R8C97 belonged to type [ Ja,c and a peaking  !

factor of [ Ja,c was obtained.

0443D:10/061990 8-18 l

Type ( Ja.c was selected for R8C93 and thus a conservative peaking factor of ( Ja,c resulted. Type ( Ja.c was considered for R9C106 and R9C29 a

c and a peaking factor of ( Ja.c was obtained. Type [ J ,c was selected for tube R9C23 and a peaking factor of ( Ja ,c resulted. Type a

( Jc was considered for both R9C12 and R9C11 and a peaking factor of

[

a J .c was obtained. Type ( 3a ,c was used for R10C106 and a peaking a

factor of ( 3a ,c resulted. Tube R10C23 belonged to type [ J .c which has a peaking factor of [ JC a

. Type [ l a,c was selected for R12C5 and a peaking factor of r, Ja c resulted. As for R13C5, it could be identified with type ! Ja .c and a ceaking factor of [ Ja .c occurred.

Note that the bar between Columns 25 and 26 [

1 l

i i

i 3a .c The same discussion applies to the tests configuration for R9C23, Configuration 84 All of the remaining SG-C tubes have no flow peaking, however, the fatigue and vibration analyses included several of the larger radius unsupported tubes without flow peaking, inclur'4na R10Cll3, R10Cll, R10Cl2, R10C2-8, and R11C4-8. (See Table 9-2.)

I 0633D:1D/062990 8-19 f

l Table 81 Stability Peaking Factor Due to local Velocity Perturbation Scaling Factors for 5 team / Water Air Velocity Void Stability Peaking Fraction Density Velocity Damping Peaking Factor, Scaling, Scaling, Scaling, Scaling, Factor, F, F y F d

F y F dp F

3 a,C NOTE: 1. Stability peaking factor for steam / water mixture is calculated as follows:

a,c

2. Damping scaling factor is calculated using modal effective void fraction of ( Ja.c for R9C51 tube.

1 0443D:10/052190 8-20

Table 8-2 Comparison of Air and Steam Water Peaking Factor Ratios Air Air Steam Steam Peaking Peaking Peaking Peaking Factor Ratio Factor Ratio

_ _ a,c 0443D:10/052190 8-21

Table 8 3 Effect of Local Variation of AVB Insertion A to B AVB Peaking Peaking Ratio Type A Type B Variation Factor A Factor B (B/A)

. _ a,c

. a,c 0443D:lD/052190 8-22

Table 8-4 Uncertainties in Test Data and Extrapolation Source of Uncertainty Maanitude. Y.

1121

~ a,c

1. Velocity measurement Random

2. Test repeatability Random

3. Cantilever vs U tube Systematic

4. Air vs steam-water mixture Systematic

5. Field AVB configuration

• This is not an uncertainty associated with the test data, it results from the inaccuracy in determining the true AVB position in the field using eddy current data.

0443D:10/052190 8-23

Table 8-5 Extrapolation of Test Results to Steam Generator Conditions Peaking Fletor Test Data with Referenced to Configuration Data Uncertainties Configuration 2a

. _ aiC la ib ik Iw 1x ly 2a 4a 4b 4c 4d 4o 4x Sa Sb Sc 6a 8p 8q

~

l

\ ~

0443D:10/062190 8-24

Table 8-6 Final Peaking Factors Configuration Peaking factor

. _ a,c la ib ik lw 1x ly 29 4a ,

4b 4C 4d 4o 4x Sa Sb Sc 6a 8p 8q 0443D:10/062190 8-25

Table 8 7 Stability Velocity Peaking Factors for Specific Tubes V. C. Summer Steam Type of AVB Peaking Generator Row No Column No insertion Factor a,c A 8 22 11 9 83 71, 70 63 55 B 7 11 .

8 74 66 9 110 56 C 7 88 8 98, 97 93 9 106 29 23 12, 11 10 106 23 12 5 13 5 1

0443D:10/062190 8-26

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@ PLUGGsD 8-27

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~. * ... m. ,, x

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Figure 8-2 Schematic of Staggered AVBs 8 28

_ - - . . .z. _

=

, a,c Figure 8-3 AVB ' Pair" in ECT Trace 8-29

e U O 000 O 000 it OO Ge o OOO 2'

GOO O OOOO ODD DD@ DOOOO

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O@@D@@@ODOOOO e*- ,, ,, 54 53 52 sils ol n o u u u e % m. 6 'ad ='

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• L L-n s 4a al ess eu ess esa est eso ea eu

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L Figure 6-5 North Anna 1 Steam Generator C, R9C51 AVB l -

[ Ja,c Matrix 8-31

____ _ U

4 22 0000 OO dOOO 22 0000 O 0000 ta OOOO OO 0 0;O.0..

5 0 00 0000 O'OOO

.0000000000000 56 55 I 54 $3 52 51 50 49 44 47 46 45 44 i [

Figure 8-6 North Anna R9C51 Final [ la,e Positions (Configurationla) 8-32

i l

TNFE OF ,\VB PEAX NG TYPE OF AVB PEAKING INSERTON FACTOR INSERTON FACTOR

- a, c s c. - a, c 1

Figure 8 7 Final Peaking Factors for V. C. Summer  ;

8 33

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

9.0 ' STRUCTURAL AND TUBE VIBRATION ASSESSMENTS 9.1 Tube'Mean Stress This section summarizes the analysis to determine stresses in a dented, but

. undeformed, tube at 100% power. Loads imposed on the tube correspond to steady-state pressure, differential thermal expansion between the tube and

.the support plate, and a thru-wall thermal gradient. The analysis assumes the tube to be [ Ja,c at cold shutdown.

A summary of the temperature and pressure parameters used for mean stress calculations at .100% power in the vicinity of the top support plate is provided in lable 9-1. The tube temperature corresponds to thL average of the primary-side water temperature and the plate temperature. The resulting tub'e/ plate radial interference is [ Ja,c, Stresses due to differential pressure and interference loads are calculated -

using finite -element analysis with the model shown in Figure 9-1. The model prescribes [L Ja,c Two . reference ' cases were run using the finite element model, the first for a primary-to-c._ondary side pret tre gradient of 1000 psi','and the second for a[~ ]a,c inch radial interference between the tube and plate. The pressure case incorporates the axial load on the tube by applying a pressure loading along the top face-of the model. Plots showing the stress distributions on the tube' outer surface are provided for the two reference cases in Figures.9-2 ano 9-3. Thermal bending stresses due to the thru-wan thermal gradient are calculated to be 8.0 ksi using conventional . analysis

~

techniques. The combined stress distribution along the tube length, shown 4

0643D:10/062990 91

i

' t in Figure 9-4, was obtained by combining the thermal bending stresses and the reference solutions with appropriate multipliers based on.1007. power

. operating parameters.

f The maximum axial-tensile stress is 20.3 ksi and occurs approximately 0.133 inch above the top surface of the support plate. Adding, for conservatism, the surface stress due to pressure, 0.94 ksi, gives an applied mean stress of 21.24 ksi. In addition to the applied stress, residual stresses exist _in the tube as a result of -the manufacturing process. For mill annealed tubes with subsequent straightening and polishing, residual stresses are compressive at the tube surface, but 5-10 mils below the :urface, the stress

. levels change to 10-15 ksi tensile. Combining the applied and residual  !

stresses results in a cumulative mean stress of approximately 36-ksi, l assuming tube denting without deformation.

Ifl a tube is dented with deformation, the mean stress is limited by tube

. yielding. For the case of dented tubes with deformation,-the maximum l

. effect of 'mean stress was incorporated by using max " 'y in determining

-stability ratios.and fatigue usage.

h - 9.2 Stabi_lity Ratio Distribution Based Upon ATH0S i

- An assessment of the potential for tubes to experience fluidelastic instability in-the U-bend region has been performed for each of the tubes in l

l rows eight through-thirteen. This analysis utilizes FASTVIB, a Hestinghouse proprietary finite element based computer code, and PLOTVIB, a. post processor to FASTVIB. These codes predict the individual responses of an entire row of i'

steam generator tubing exposed to a location dependent fluid velocity and

-density profile. The program calculates tube natural frequencies and mode

(-

l- shapes using a linear finite . element model of the tube. The fluid elastic

-stability ratio U e/Uc (the ratio of the effective velocity to the critical L velocity) and the vibration ' amplitudes caused by turbulence are calculated .for

+ a'given velocity / density / void fraction profile and tube support condition.

The velocity, density.and void fraction' distributions are-determined using the ATH0S computer code as described in Section 7.3. The HECAN-generated mass and i-l:

e

'0444D:1D/062190 9-2

stiffness matrices used to represent the tube are also input to the code.

!(WECAN is also a Westinghouse computer code.)_ Additional input to FASTVIB/PLOTVIB consists of tube support conditions, f_luidelastic stability constant, turbulence constants, and location dependent flow peaking factors.

This process was performed for the steam generator tubes of a Reference Model 03 and- also for the North Anna Row 9 Column 51 tube (R9C51), using similarly appropriate ATH0S models. Ratios of the Reference results to those for North Anna Unit 1 R9C51 provided a-quantity that could be used for an initial assessment of the V. C. Summer tubes relative to the ruptured tube at North Anna Unit 1.

These_ initial relative stability ratios (RSR) were subsequently updated to account for the differences in operating conditions between the Reference Model D3 ATH0S model used in the evaluation and the V. C. Summer conditions.

A 1D multiplier _was developed and then applied to the RSR corresponding to each tube. A discussion of the 10 ratio methodology has been discussed in Section 7.0. The result.of this process is a quantity that describes a

. specific V C. Summer tube relative to the ruptured tube at North Anna Unit 1.

..- -Figure 9-5 shows the- results of this process for Rows 8 through 12. The

. relative ratios are obtained using the following conditions for V. C. Summer and North' Anna Unit 1:

.1) Tube is fixed-at the top tube support plate,

2) Void fraction-dependent damping,

3) .No AVB supports-are active,

4) . Location-dependent flow peaking factors.

i It_ is to be noted that the stability ratios plotted in Figure 9-5 are composites of'all steam generators using mirror image tubes. That is, any

~

peaking effect for a'given tube location indicated on the plot represents the maximum value of the peaking factor in all steam generators at that location.

0643D:10/062990 9-3

A horizontal line is drawn at the relative stability ratio value of 0.90.

This identifies the point where a ten percent reduction in stability ratio exists relative to North Anna R9C51. (See Section 4.1 for a discussion of the stability ratio reduction criteria.) All the tubes with ratios above this line would be considered to have stability ratios larger than ninety

~

percent of North Anna R9C51.

Figure 9-5 indicates that most tubes in Rows 7 through 11 of the V. C.

Summer steam generators are below the 0.9 RSR line. The RSR values for all Row 7 through 13 tubes are below 0.9, with the exception of the following seven tubes:

SG A SG B SG C R9C83 R9C56 R9C29 R9C106 R10C23 R12C5 R13C5

. 9.3 Stress Ratio Distribution with Peaking Factor An evaluation was performed to determine the ratio of the V. C. Summer tube stress over the North Anna R9C51 tube stress. This ratio is determined using relative stability ratios discussed in the previous section, relative flow peaking f actors (Table 8-7 f actors divided by

[ ]a,c), tube size, and bending moment factors. Sections 4.2 and 4.3 ccntain additional information and describe the calculational procedure used to obtain the results presentsd in this section. The results presented below are based upon the following conditions:

1) Tube is fixed at the top tube support plate,

2) Damping is void fraction dependent, 0643D:lD/062990 9-4

L 2

~

3) Tubes.have no AVB. support,

-)

4 10% criteria with frequency effects,

• 4-

[i. .

5)L Location-dependent flow peaking effects

6) Tubes are assumed to be dented with deformation (labeled with

- denting) or clamped at the top support plate due to crevice corrosion (labeled without denting).- J A tube can be considered acceptable if_ the stress ratio is less than 1.0.

when calculated using-the procedure described in Sections 4.2 and 4.3, including the conditions. listed above,_ and subject to confirmation of-fatigue usage' acceptability. Conformance to these-requirements implies that the stress acting on a given tube is expected to be-insufficient to produce a fatigue-event-in a manner similar to the rupture that occurred-in the R9C51 tube at North Anna Unit 1.

.- Figure 9-6 shows the results of the stress ratio calculations for each of-the V. C. Summer tubes in Rows 7 through 12. Similar to the stability .

. ratios'in Figure 9-5, the stress ratios in Figure 9-6 represent-the-

> - composite' ratios for1all V.- C. Summer steam generators. (Refer to Table 9-2 for salient tubes in individual' steam generators). These ratios-are applicable _for ' tubes that are dented (tube deformation) oat the top : tube support plate. This case bounds the clamped tube condition with no tube deformation, i.e., the case corresponding to the NRC definition of denting with' top; tube support plate corrt ;on plus magnetite in~the_ crevice

without tube deformation. . Figur s-7 contains the results for the case

'where tube deformation is'not present. These figures demonstrate the effects of varying the applied mean stress on the-tube. Using the mean stress present in the undented results produces stress ratio values that -i

~ are' lower than stress ratios calculated for; tubes in the _ dented condition.

0643D:lD/062990 9-5

_________-~--_-

- - - , ~ - - e e c -w~ v - w - r -~a-r- en - sm-~-- r n, --.e+.

. . ._ - . . .- . - _ . ._ - . . - - - - ~ -. - .-.- _-

I As can be observed in Figures 9 6, Figure 9-7 and Table 9-2, several tubes 4 have stress ratios that-are_ greater than 1.0. The following tubes have been identified as having stress ratios (both with and without denting) greater than~1.0:

10 A 1G_B 1Q C R9C83 R9C56 R9C29 R9C106 R10C23

.1 i

R12C5 R13C5 As noted. in Section 9.5, its is recommended that all tubes with-stress ratios exceeding 1.0 and that have cumulative usage greater than 1.0 (such as the tubes listed above) be removed-from service.

To assist SCE&G in evaluating operational issues associated with the

- installation of cable dampers, the lowest added damping value determined from the-available tests was assumed to be provided by cable dampers in

-- - the seven tubes of interest for V. C. Summer. With this assumed mi.:'eum added damping value of ( ),a,c all of the stress ratios in the seven tubes of-interest are below [

],a,c R12C5 would have-a stress ratio of

(

Ja,c or less. With this assumption,. tubes that had not initiated a crack would be predicted to be acceptable for continued

. operation with a cable damper installed.

An evaluation has also been performed to determine the required relative flow peaking that will produce a = stress ratio not greater than 1.0.

Figure-9-8 contains the results of this process for all tubes in Rows 7

- through 12. The ficiure was generated using the conditions outlined previously with the additional constraint that.the tubes are dented. Note

^

that this figure reads opposite of the previous figures, i.e., the top 4

0643D:lD/062990 9-6

_ - ._ _ _. ~. ._ _ . _ _ __ -_ _

curve in the figure corresponds to Row 7 and the bottom curve corresponds to Row 12. Maximum Allowable Relative Flow Peaking is the required

-relative flow peaking. (0.68 corresponds to no flow peaking) which, if used on the given tube, will produce a stress ratio (with denting) not to exceed 1.0. This curve can be used to identify the relative flow peaking required before preventive action would be recommended and, when used in conjunction with the actual flow peaking associated with each tube, to determine the margin (if any) present. This has also been performed in I

Table 9-2. The column with heading " Max Allow Rel FPEAK" identifies the

! relative flow peaking factor that would be permitted, on a tube by tuce L basis, before the stress ratio criteria would be exceeded. As can be i

observed in the table and figure, the inner row tubes have larger values of allowable relative flow peaking when compared to the outer rows.

9.4 Cumulative Fatigue Usage 1

! All unsupported tubes having stress ratios 1 1.0 will have a maximum stress' amplitude that'is <: 4.0 ksi (from 9.5 ksi), since a 10% reduction

- in the stability ratio for the North Anna Row 9 Column 51 tube was the criteria basis. The stability ratios for the V.'C. Summer tubing are

. based on the Cycle 5 operating parameters and assume future operation with

( the same parameters. The ' tubes are not expected to rupture as a result of l-fatigue if 1) they meet the stress ratio criteria of $1.0 and 2) their 1 current and future fatigue usage will total less than 1.0, Based on the above analyses, most V. C. Summer tubes meet the relative f

stress ratio criteria. Seven tubes do'not meet the stress ratio criteria. Table 9-2 provides a summary of the combined relative stability ratios and the stress ratios for salient unsupported tubes in Rows 7 through 13.

Of the seven tubes mentioned above, SG-A R9C83, SG-B R9C56, SG-C R12C5 and SG C R13C5, if previously dented or if becoming dented at -the beginning of an operating cycle with current operating conditions, could potentially ,

have tube fatigue' usage factors exceeding 1.0 within the cycle, and I .

0643D:1D/062990 9-7

- . . . -- .- . . - .. . . .- -. . . - - - . .~ - . _ .

therefore require preventive action. Note that with the exception of SG-B R9C56, which was evaluated as having magnetite packing at one of the two g_ top tube support plate intersections, all of these four times were evaluated from the October 1988 outage inspection data as " clean" at the

.. . top tube . support plate intersections. Two additional tubes, SG-C R9C29 (magnetite in one top TSP and -clean in the other) and SG-C R10C23 (magnetite in both top TSP crevices), potentially have current accumulated

-fatigue usages as =high as 1.0, if it is conservatively assumed that denting began at the start of the first fuel cycle, and also therefore l require preventive action.- SG-C R9C106 was evaluated as having no denting at the top tube support plate elevation based upon examination of the

.0ctober 1988 inspection data, but may have accumulated as much as 0.34 fatigue usage if it became dented or magnetite-packed at the beginning of

, Cycle 5.- If dented and operating at Cycle 5 conditions, it will continue to. accumulate fatigue usage at the rate of 0.34 per year, and is also recommended for-preventive action. .

l Acceptability of the V. C.- Summer tubing for fatigue is accomplished by demonstrating' the acceptability of the tube remaining in service with the highest stress ratio that does not exceed the 1.0 stress ratio criteria. ,

I For V. C. Summer this tube is SG-A R9C55 and has a stress ratio of

[ 3a ,c for.Cyclt 5 operating conditions. Assuming this worst case tube (R9C55)'has been dented since the first cycle and continues to operate.with. steam pressures at or above 941 psia, the total usage including the remaining term of the operating license would be 0.36. J 9.5 Effect of Steam Pressure on Potentially Susceptible Tubes An additional fatigue evaluation of the V. C. Summer tubing was performed to examine the effect of reduced steam pressure and coastdown power levels, with the objective of demonstrating the acceptability of the tube remaining-in service with the highest stress ratio.that.does not exceed

.the-1.0 stress ratio criterion. Parametric analysis was performed to determine the relative stability ratio (RSR) multipliers and stress ratios 06430:lD/092890 9-8

.. - . - . . . _ - . . . - - - - . . _ - . - . ~ . - - - - - .. -. .-

for full power steam pressures below the reference _ steam pressure (941

, psia) and it _was_ determined that the limiting tube, SG-A R9C55, does not

= exceed _ the 1.0 stress ratio criterion for steam pressures above 905 psia.

Since SCE&G is considering-power coastdown operation, the RSR multipliers

. were also evaluated assuming a coastant volumetric steam flow for pressures below 905 psia. (The 905 psia steam pressure is a lower bound, full power steam pressure value; V. C. Summer turbine tests indicate the j "best estimate" value of the Valves Hide Open (VHO) steam pressure to be 915 psia). For the reduced power levels associated with operation below the assumed 905 psia VHO limit, the RSR multipliers decrease, and the fatigue results> remain bounded. Therefore, assuming that the worst case l tube .(SG-A R9C55) has been dented since the first cycle and the turbine Valves Hide Open limit is not reduced below 905 psia, all tubes remaining in service at V. C. Summer are acceptable for operation through the end of' the current operating license with power levels at or below the 2785 MHt.

9.6 Conclusions Seven tubes were recommended for preventive action: SG-A R9C83, SG-B-R9C56 SG-C R12C5, SG-C RISC5, SG-C R10C23, SG-C R9C29, and SG-C R9C106.

These tubes were removed from service in April 1990 with the installation of cable dampers, hot leg plugs, and cold leg sentinel plugs._ -The tubes remaining in service in the V. C. Summer steam generators are not expected to be susceptible to high-cycle fatigue' rupture at the top _ tube support Lplate in a manner similar to the rupture which occurred at North Anna #1, assuming that the turbine Valves Hide Open limit is not-reduced below 905 -

psia, through the end of the current operating license with power levels at or below 2785 HHt.

e 4

06430:1D/100190 9-9

Reference:

9-1 Westinghouse Research & Development Report 77-ID2-TUCOR-R2,

" Residual Stresses in Inconel 600 Steam Generator Tubes - Part II: Straight Tubes", Westinghouse Research Laboratories, Proprietary Class 2, D. L. Harrod, October 21, 1977.

4 0643D:10/062990 9-10

e Table 9-1 100% Power Operating Parameters V. C. Summer Bounding Values for Mean Stress Calculations Primary Pressure - 2250 psia Secondary Pressure - 941 psia Pressure Gradient - 1309 psi Primary Side Temperature * - 587'F Secondary Side Temperature - 537'F Tube Temperature - 562*F

_ Average of Thot - 618'F and Tcold - 556*F.

0643D:10/062690 9-11

TA8LE 9-2 V. C. Sumer Tubes Hith Significant RSRs or Stress Ratios Steam Row Col. Flow Hax Allow RSR* Stress Ratio Gen. No. No. Peaking Rel. FPEAK FPEAK H/ Dent H/0 Dent

. 1 A 8 11 a,c 0.549 0.10 0.10 22 0.524 0.08 0.08 l

9 55 0.818 0.76 0.70 63 0.801 0.68 0.62 70 & 71 0.725 0.39 0.36 83 1.155 >2.00 >2.00 B 7 11 0.546 0.12 0.11 8 66 0.672 0.31 0.29 74 0.607 0.18 0.16 9 56 1.168 >2.00 22.00 110 0.737 0.43 0.39 C 7 88 0.544 0.12 0.11 8 93 0.555 0.11 0.10 97 & 98 0.595 0.16 0.14 9 11 & 12 0.710 0.35 0.32 )

23 0.636 0.19 0.17 29 0.946 1.78 1,63 i 106 0.937 1.63 1.49 1 1

10 2-8 0.740 0.37 0.34 l 11 & 12 0.738 0.36 0.33 l 23 0.968 1.88 1.73 106 0.738 0.36 0.33 113 0.545 0.07 0.06 11 4-8 0.856 0.70 0.64 12 5 1.403 >2.00 >2.00 13 5 1.751 >2.00 >2.00 1

a e

04440:10/062190 9-12

. . - . - ~ - . - - _ - . _ - . - _ .-

e .-

1

.l-TUBE g

.MM l ...

f SUPPORT PLATE l  : :

M.W l

-i ...

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t

(

9.

Figure 9-1 Axisymmetric Tube Finite Element Model 0444D:10/ 050190 '9-13

a,c

~ _

o

= ,

I l

l l

)

1 Figure 9-2 Dented Tube Stress Olstributions Pressure Load on Tube 0444D:1D/050190 9-14

a,c e

l 1

4 l

-'t t

Figure 9-3 Dented Tube Stress Distributions Interference Load on Tube 0444D:1D/050190 9-15

a, O

Figure 9 4 Dented Tube Stress Distributions Combined Stress Results for V. C. Summer 0444D:10/050190 9-16

a,e Figure 9-5 Relative Stability Ratios Using HEi!F Dependent Damping V. C. Summer - (Composite of All Steam Generators with Umbrella Flow Peaking) 1 04c 0:10/050190 9-17

a,C r

4 Figure 9-6 Stress Ratio vs. Column Number - Dented Condition - V. C. Summer (Composite of All Steam Generators with Umbrella Flow Peaking) 04440:10/050190 9-18

.,c e

1 l

l l

1 l

m Figure 9-7 Stress Ratio vs. Column Number - Undented Condition - V. C. Summer ,

-(Composite of All Steam Generators with Umbrella Flow Peaking)

- 04440:1D/050190 9-19

a,e o.

t Figure 9-8 Maximum Allowable Relative Flow Peaking - V. C. Summer 4

04440:10/050190 9-20

_ _ _ _ _ _ _