ML20207L778

Nonproprietary WCAP 11936, McGuire Unit 2 Evaluation for Tube Vibration Induced Fatigue

ML20207L778
Person / Time
Site:	Mcguire, McGuire, 05000000
Issue date:	10/06/1988
From:	Connors H, Frick T, Hall J WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP.
To:
Shared Package
ML19312B199	List: ML20207L752 ML20207L765 ML20207L778
References
WCAP-11936, NUDOCS 8810170437
Download: ML20207L778 (149)

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WESTINGHOUSE CLASS 3 WCAP 11935 I

r MCGUIRE UNIT 2 EVALUATION FOR TUBE VIBRATION INDUCED FATIGUE AUTHORS:

H. J. CONMORS M. H. HU T. M. FRICK A. Y. LEE J. M. HALL M. R. PATEL G. W. HOPKINS R. M. WILSON J. L. HOUTMAN R. M. WEPFER APPROVED:

b b d

T.A.PITTERLE,kANAGER STEAM GENERATOR ENGINEERING This document contains information proprietary to Westinghouse 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, trans:nitted, disclosed or used otherwise in whole or in part without written authorization of Westinghouse Electric Corpuration, Energy Systems Business Unit.

WESTINGHOUSE ELECTRIC CORPORATION NUCLEAR SERVICE DIVISION P.O. BOX 3377 PITTSBURGH, PENNSYLVANIA 15230

ABSTRACT On July 15, 1987, a steam generator tube rupture event eccurred 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 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 McGuire #2 for susceptibility to fatigue-induced cracking of the type experienced at North Anna Unit 1.

The evaluation utilizes operating conditions specific to McGuire

1. 2 to account for the plant specific nature of the tube loading and response.

The evaluation also includes reviews of eddy current data for McGui,re #2 to establish AVB locations. This report provides bar.kground of the event which cccurred at North Anna, a criteria for fatigue assessment, a summary of test data which surport the analytical approach, field measurement results showing AVB positions, thermal hydraulic analysis results, and calculations to determine tube mean stress, stabd ity ratio and tube stress distributions, and accumulated fatigue usage.

This evaluation concludes that none of the tubes potentially susceptible to fatigue require corrective action.

4 0248M:49/081288 3

SUMMARY

OF ABBREVIATIONS American Society of Mechanical Engineers ASME

~

Analysis of the Thermal Hydraulics of Steam Generators ATH0S Anti-Vibration Bar AVB All Volatile Treatment AVT Eddy Current Test ECT Electric Power Research Institute EPRI Fast Fourier Transform FFT Flow Induced Vibrations FLOVIB Modal Effective Void Fraction MEVF Outside Diameter OD RMS Root Mean Square Stability Ratio SR Tube Support Plate TSP degrees Fahrenheit

'F hr hour measure of stress - 1000 pounds per square inch

)

ksi pound lb mils 0.001 inch MW mega watt measure of stress - pour.ds per square inch psi measure of pressure - absolute psia 1

I 0248M:49/081288 4

.. i

r TABLE 0F CONTENTS SECTION 1.0 Introduction 2.0 Summary and Conclusions

2.1 Background

s 2.2 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

3.0 Background

3.1 North Anna Unit 1 Tube Rupture Event 3.2 Tube Examination Results 3.3 Mechanism Assessment s

4.0 Criteria for Fatigue Assessment 4.1 Stability Ratio Reduction Criteria a

4.2 Local Flow Peaking Considerations 4.3 Stress Ratio Considerations 5.0 Supporting Test Data 5.1 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 0248M:49/081288-5

TABLEOFCONTENTS(CONTINUED)

SECTION 6.0 Eddy Current Data and AVB Positions 6.1 McGuire #2 AVB Assembly Design 6.2 Eddy Current Data for AVB Positions 6.3 AVB Insertion Depths 6.4 AVB liap Interpretations 7.0 Thermal and Hydraulic Analysis 7.1 McGuire #2 Steam Generator Operating Conditions 7.2 ATH0S Analysis Model 7.3 ATH0S Results 7.4 Relative Stability Ratio Over Ooerating History 8.0 Peaking Factor Evaluation 8.1 North Anna 1 Configuration 8.2 Test Measurement Uncertainties 8.3 Test Repeatability 8.4 Cantilever vs U-Tube 8.5 Air vs Steam-Water Mixture 8.6 AVB Insertion Depth Uncertainty 8.7 Overall Peaking Factor with Uncertainty 9.0 Structural and Tube Vibration Assessments 9.1 Tube Maan Stress j

9.2 Stability Ratio Distribution Based Upon ATHOS 9.3 Stress Ratio Distribution with Peaking Factor 9.4 Cumulative Fatigue Usage 0248M:49/082488 6

4 LIST OF FIGURES FIGURE 3-1 Approximate Mapping of Fracture Surface of Tube R9C51 S/G "C" Cold Leg, North Anna Unit 1 3-2 Schematic Representation of Features Observed During TEM Fractographic Examinatien of Fracture Surface of Tube R9C51, S/G "C" Cold Leg, North Anna Unit 1 3-3 Chlculated and Observed Leak Rates Versus Time 4-1 Vibration Displacement vs. Stability Ratio 4-2 Fatigue Strength of Inconel 600 in AVT Water at 600'F 4-3 Fatigue Curve for Inconel 600 in AVT Water Comparison of Mean Stress Correction Models s

4-4 Modified Fatigue with 10% Reduction in Stability Ratio for Maximum Stress Condition 45 Modified Fatigue with 5% Reduction in Stability Ratio for Minimum Stress Condition 5-1 Fluidelastic Instability Uncertainty Assessment 5-2 Instability' Constant - $

53 Instability Constants, S, Obtained for Curved Tubes from Wind Tunnel Tests on the 0.214 Scale U Bend Model 54 Damping vs. Slip Void Fraction 1

l 0248M:49/082488 7

LIST OF FIGURES (Continued)

EIGURE 5-5 Overall View of Cantilever Tube Wind Tunnel Model 5-6 Top View of the Cantilever Tube Wind Tunnel Model 5-7 Fluidelastic Vibration Amplitude with Non-Uniform Gaps 58 Typical Vibration Amplitude and Tube /AVB Impact Force Signals for Fluidelastic Vibration with Unequal Tube /AVB Gaps 59 Conceptual Design of the Apparatus for Determining the Effects on Fluidelastic Instability of Columnwise Variations in AVB Insertion Depths l

5-10 Overall View of Wind Tunnel Test Apparatus 5-11 Side View of Wind Tunnel Apparatus with Cover Plates Removed to Show Simulated AVBS and Tcp flow Screen 5-12 AVB Configurations Tested for McGuire #2 5 13 Typical Variation of RMS Vibration Amplitude with Flow Velocity for Configuration la in Figure 5-12 6-1 AVB Insertion Depth Confirmation 62 McGuire #2-Steam Generator A AVB Positions I

63 McGuire #2 Steam Generator B AVB Positions 64 McGuire #2 Steam Generator C AVB Positions i

f 65 McGuire #2 Steam Generator D AVB Positions 0248M:49/081288 8 L

._ _ __.__.___., _ ~,._-__ _,__ ______ _ _

3 l

LIST OF FIGURES (Continued) l

\\

FIGURE 6-6 AVB Projection Depth = 9.00 6-7 AVB Projection Depth = 9.15 7-1 Plan View of ATH0S Cartesian Model 7-2 Elevation View of ATHOS Cartesian Model 7-3 Plan View of ATH0S Cartesian Model 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 7-6 Lateral Flow Pattern on Top of Top Tube Support Plate 7-7 Void Fraction Contours on Vertical Plane of Symmetry l

7-8 Tube Gap Velocity and Density Distributions for Tube Row 10/ Column 5 79 Tube Gap Velocity and Density Distributions for Tube Row 10/ Column 20 1

7-10 Tube Gap Velocity and Der,sity Distributions for Tube Row 10/ Column 40

~

3 7-11 Average Velocity and Density in the Plane of the U Bends Normal to Row 10

)

0248M:49/081288 9

i I

~

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(

LISTOFFIGURES(Continued)

FIGURE l

7-12 McGuire #2 - Normalized Stability Ratio Based on i

High Power (>85%) Operation i

8-1 Original North Anna AVB Configuration 8-2 Schematic of Staggered AVBs 8-3 AVB "Pair" in ECT Trace 84 North Anna 1, Steam Generator C: AVB Positions Critical Review "AVB Visible" Calls 85 North Anna 1, Steam Generator C, R9C51 Projection Matrix 8-6 North Anna R9C51 AVB Final Projected Positions 8-7 Final Peaking Factors for McGuire #2 91 Axisymmetric Tube Finite Element Model 9-2 Dented Tube Stress Distributions - Pressure Load on Tube 93 Dented Tube Stress Distributions - Interference Load on Tube 94 Dented Tube Stress Distributions - Combined Stress Results l

McGuire #2 95 Relative Stability Ratio Using MEVF Dependent Damping - McGuire #2 l

96 Stress Ratio Vs. Column Number Dented Condition - McGuire #2 I

1 i

)

024BM:49/081288 10 i

i LIST OF TABLES IbEL 4-1 Fatigue Usage per Year Resulting From Stability Ratio Reduction 1

5-1 Wind Tunnel Tests on Cantilever Tube Model 5-2 Fluidelastic Instability Velocity Peaking Factors for Columnwise Variations in AVB Insertion Depths McGuire #2 l

6-1 1 AVB Signals Determined to be Supported I

6-2 1 AVB Signal Indicating Support for Flow Peaking Analysis i

63 Summary Listing of Unsupported Tubes - McGuire #2 7-1 McGuire #2 Steam Generator Operating Conditions Used for ATHOS Analysis 7-2 McGuire #2 Operating History Data 81 Stability Peaking Factor Due to Local Velocity Perturbation 82 Comparison of Air and Steam Water Peaking Factor Ratios 83 Effect of Local Variation of AVB Insertion 84 Uncertainties in Test Data.and Extrapolation i

85 Extrapolation of Test Results to Steam Generator Conditions i

1 86 Final Peaking Factors 87 Stability Peaking Factors for Specific Tubes l

1 0248M:49/082488 11 a

1 l

1

l l

I l

LIST OF TABLES (Continued)

TABLE 1

i 9-1 100% Power Operating Parameters - McGuire #2 l

1 92 Sumary of McGuire #2 Evaluation of the Salient Unsupported U-Bends I

1 i

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l l

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i 1

0248M:49/08128812 1

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i

1.0 INTRODUCTION

This report documents the evaluation of steam generator tubing at McGuire #2 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 tlie tube bundic, 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 evalustion utilizes operating conditions specific to McGuire #2 in order to account for plant specific features of the tube loading and response.

Section 2 of the report provides a summary of the McGuire #2 evaluation results and overall conclusions. Section 3 provides background for 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 mecha.nism. 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 provides a summary of test data which supports the analytical vibration 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 evaluate 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 McGuire #2 steam generator small radius U-tubes.

0248M:49/081288 13 i

2.0

SUMMARY

AND CONCLUSIONS s

The McGuire #2 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 supp led by Duke Power Company and interpreted by Duke Power and 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, fluid elastic 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 provide a fatigue usage less than 1.0 for a finite period of time (i.e., 40 years) is a 107. reduction in stability ratio that provides at least a 58Y. reduction in stress amplitude (to < 4.0 ksi) for a Row 9 tube in the North Anna 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 North Anna and therefore greater than 40 year fatigue life objective. This same fatigue criteria is applied as the principal criteria in the evaluation of McGuire #2 tubing.

0248H:49/081288-14

The fluidelastic stability ratio is tie ratio of the effective velocity divided by the critical velocity. A value greater than unity (1.0) indicates instability. The stress ratio is the expected stress amplitude in a McGuire #2 tube divided by the stress amplitude for the North Anna 1, R9C51 tube.

Displacements are computed ?or unsupported U-bend tubes in Rows 12 and inward, (descending row number) ut,ing 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 will have different stiffness and frequency and, therefore, different stress ared 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 ratigue usage for the McGuire #2 tubing for the reference fuel cycle snalyzed. Therefore, a stress ratio less than 1.0 provides the next level of acceptance criteria for unsupported tubes for which the rehtive stability ratio, including flow peaking, exceed 0.9.

The stability ratios for McGuire #2 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 various AVB insertion depths is not within the capability of 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 influe'-' 'ncertainties, the evaluation of McGuire #2 tubing has been bosai " M ;ive stability rr.tios, relative flow peaking factors, and relative strca

.~.ios.

The criteria for establishing that a tube has support from an AVB and therefore eliminate it from further considerations 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 sideo AVP support is sufficient to limit the 0248M:49/081288 15 t

vib ation amplitude for fluidelastic excitation. AVB suppcrt is established by ant. lysis of eddy current (EC) measurements and is a key factor in determining the local flow peaking factors. The local flow peaking produces increased r

local velocities which cause an increase in stability ratio. A small percentage change in the stability ratio causes a significant change in stress amplitude. The relative flow peaking factors of McGuire #2 tubing without direct AVB support have been determined by test. These flow peaking factors, normalized to the North Anna R9C51 praking, 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 to determine the condition of the tube / tube support interface of the first row of unsupported tubes inboard of the AVBs. Analyses of eddy current (EC) data for McGuire #2 shows the presence of ' corrosion with magnetite' in the major!ty of.the tube / TSP crevices. No

' dent' (denting with deformation) signals were observed at the top tube supporc plate of any McGuire #2 tubes examined.

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 in the tube fatigue usage evaluation and by incorporating reduced damping in the tube vibration evaluation.

2.4 AV3 Insertion Depths

• nire #2 SGs have two sets of Alloy 600 AVBs. The ' inner' AVBs have a

'a ur cross ser. tion and extend into the tube bundle approximately as far as.v 10.

They provide a nominal total c,1earance between a tube without ovality and the surrounding AVBs of inch.

The outer AVBs also have a rectangular cross section, And extend into the tuba bundle approximately as far as Row 21, providing a nominal tube to AVB clearance comparable to the inner AV8s.

Since the purpose of this analysis is to evaluate the potentially unsupported tubes at or near the point of maximen L

AVB insertion, only the dimensions and EC data pertaining to the inner AVBs are required.

0248M:49/081288 16 J

l

The eddy current data supplied by Duke Power were reviewed 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 McGuire #2 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 data, indicated by a listing of two or more AVBs in the insertion depth plots, is the preferred method of establishing tube support.

If only the apex of a McGuire #2 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 number tubes in the same and adjacent columns verify insertion depth to a point below the tube centerline. Maps of the AVB insertion depths for McGuire #2 are shown in Figures 6-2 thru 6 5.

These AVB maps list the results of the

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

2.5 Flow Peaking Factors Tests were performed modeling McGuire #2 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.

It was found that the worst case flow peaking results for McGuire #2 were less than for North Anna R9C51.

2.6 Tube Vibration Evaluation The calculation of relative stability rat e for McGuira #2 makes use of detailed tube bundle flow field informaticn computed by the ATHOS steam generator thermal /h,draulic 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(8M:4C/Odl288 17

of these parameters have been generated for every tube of interest in the McGuire #2 tube bundles bas'ed on recent full power operating conditions.

This information was factored into tf i tube vibration analysis leading to the relative stability ratios.

Relative stability ratios of McGuire #2 (Ruw 8 through Row 12) tubing 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 McGuire #2 are given in Figure 9-6.

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

For all four steam generators, the stress ratios of all tubes in Rows 8 through 12 are less than 1.0, even when the tubes are assumed to be unsupported.

A summary listing of the unsupported critical tubes evaluated is given in Table 9 2.

The maximum relative stability ratio and stress ratio occur in SG B:R9C88.

For this limiting tube, the m:..imum cumulative fatigue usage for a 40 year operating period is calculated to be less than 0.01.

Since this is much less than 1.0, all analyzed tubing in McGuirs #2 is acceptable for continued service. The fatigue calculation utilized plant operating history to date and assumed future operation at 100% availability with current fuel cycle parameters.

2.7 Overall Conclusion The analysis described above indicates that the McGuire #2 tubes currently in service are not expected to be susceptible to fatigue rupture at the top support plate in a manner similar to the rupture which occurred at North Anna 1.

Therefore, no modification, preventive tube plugging, or other measure to preclude such an event is judged to be necessary.

0248M:49/081288 18 3

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 circumfereatial 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 supertmposed 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 siternating 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 alternatir.g 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 cetailed geometry of the t

0243M:49/081288 19

l.

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:

Fatiaue Reauirements Ettreouisite Conditions Alternating stress Tube vibration

- Dented support 6

Flow excitation

- Absence of AVB Mean stress Denting in addition to applied stress 4

Material fatigue properties AVT environment

- Lower range of 3

properties 3.2 Tube Examination Results fatigue was found to have initiated on the cold leg outside surface of tube R9C51 imediately above the top tube support plate. No indication of significant accompanying intergrauular corrosion was observed on the fracture j

face or on the immediately adjacent 00 surfaces. Multiple fatigue initiation 3

sites were found with major sites located at 110', 120', 135' and 150',

i Figure 3-1.

The plane of the U-bend is located at 43' with the orientation 7

system used, or approximately 90' from the geometric center of the initiatittt

]

zone at Section D 0.

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, j

striatien direction, and later observations of parabolic dimples followed by t

j equiaxed dimples) to have accelera'.ed and to have changed direction with the J

resulting crack front running perpendicular to the circumfarential direction.

)

]

l 0248M:49/081288 20 J

i 3.3 Mechanism 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 correspording low fatigue usage, even when account'.ng 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 I

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, i

j beginning at 90' to the plane of the tube and progressing around on both I

sides to complete separation of the tube.

l j

Crack propagation analysis matched cyclic deformation with the stress intensities and striation spacings indicated by the fracture inspect'on and i

analysis. Leakage data and crack opening analysis provided the relationship between leak rate and circumferential crack length.

Leakage versus time was 4

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 best l

estimatc of plant leakage (performed after the event) showed good agreement, j

Figure 3 3.

Based on these results, it followed that the predominant loading mechanism l

responsible is a flow induced, tube vibration loading mechanism, it was shown i

i that of the two possible flow induced vibration mechanisms, turbulence and fluidelastic instability, that fluideiastic 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 (

nJa.c. This is less than the distance between tubes at the apex, (

Ja,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.

0248M:49/081288-21 l

Given the lik911 hood of limited displacement, fluidelastic instability, a means of establishini; 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 usage 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 0.0?. for a tube similar to Row 9 Column 51 at North Anna Unit 1.

024BM:49/080188 22

4 l

DD {

^

s g

i et w

C C-C C

q 180' Regien of Herrir.;t:re f Pattern

\\

- so-m-

r E

A l-B O'

F tot i

g I

g TAB F-T t

s Cearse Texture 3

and Diepted j

i o

Rupture

(

( Indicates origins i

i Figure 3-1 Approximate Mapping of Fracture Surface of Tube R9C51.

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

l

)

5 = 1.5/1.8 e in.

Heavy Omide Attack

=

3 5 ar21 y in.

y

\\

/

f3t p

1. ,3-D g

5 = 1.0/1.85 v in.

180' b

\\

/

3,g vm i

Db es

~ IO*

270* - l 1-G and V

Interr.a1 Neckin; 35 I

s

,I1f 5 = 2.8/4.0 v in.

g A

3,3

,, red aA l

/

Nearly Ecut-Axed i

5 = 6.1/6.9 9 in.

Ote;1es 1

Note: Artsws Indicate Dirt: tion of Fracture Frepagation Figure 3 2 Schematic Representation of Features observed During TEM Fractograhi: Examination of Fracture surface of Tube R9C51. S/G 'C' Cold Leg. North Anna Unit 1

t l

l l

l l

l l

l l

l l

Calculated and observed leak rates versus time.

Observed values thesed on gaseous species condenser air ejector i,

S

\\

g SIGMA A = 5 KS!

SIGMA A = 7 M31 t:n FIGM A A = 9 KS!

l a 3

O At'-d1 O

Xe-135 A

Ki -a7 9,

N<

I l

i C'

C g

w i-

/

I o

a i...

d 1

o l

.4.

i.k.

sein 6.

a i.

ai.

h.

.i.

i.

TIME (Minutes) l Figure 3 3 Calculated and Observed Leak Rates Versus Time J

i 4.0 CRITERIA FOR FATIGUE ASSESSMENT i

i 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 j

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 1 tubing evaluation was done on a relative basis to Row 9 Column 51 and a 10%

reduction in stability r!.tio 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 McGuire #2 tubing to Row 9 i

l Column 51 of North Anna Unit 1, several criteria are utilized.

First, stability ratios are calculated for McGuire #2 tubes based on flow fields i

predicted by 3 D thermal hydraulic models and ratioed to the stability ratio for Row 9 Column 51 at North Anna Unit 1 based on a flow field obtained with a 3 D thermal hydraulic model with the same degree of refinement. These ratios i

of stability ratio (called relative stability ratios) for each potentially i

I unsupported U bend in the McGuire #2 steam generators should be equivalent to 1 0.9 of R9C51, North Anna 1 (meeting the 10% reduction in stability ratio l

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 j

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 ratto!, and the relative stress ratios.

l

\\

i 0248M:49/081288 26

The next step is to obtain stress ratios, the ratio of stress in the McGuire #2 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 $1.0. The stress ratio incorpo -es 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 ud for continued operation with the same operating parameters is evaluated. A fatigue l

usage s 1.0 may not be satisfied by meeting the stress ratto criteria using l

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 dui ng service. Values greater than unity (1.0) indicate instability (see Section 5.1).

Motions developed by a tube in the fluidelastically unstable mode are quite large in comparison to the other known uechanisms. The maximum medal displacement (at the apex of the tube) is linearly related try 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.

0248M:49/081288-27 l

-=

The major features of the fluideiastic 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 l

coordinates ir.. plies a relation of the form y A(x)n, 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 l

form, log y c + n log x, where c = log A and represen6s the intercept and n is the slope.

In our case the independent variable x is the stability ratio i

SR, and the dependent variable y is tube (fluidelastic instaoility induced) displacement response D, and the slope n is renamed s.

i From experimental results, it is known that the turbulence, response curve (on f

log log coordinates) has a slope of approximately ( Ja,b c.

Test results also show that the slope for the fluidelastic response depend: somewhat on the instability displacement (r'esponse amplitude).

It has been shown by tests that a slope of (

Ja,b,cisarangeofvaluescurrespondingtodisplacement l

amplitudesintherangeof(

Ja.c, whereas below

(

]C are conservative values.

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

ac where Dg and SR; are the known values at the point corresponding to point 1 of Figure 41 and D2 ano SR2 are values corresponding to any point lower on this curve. Therefoce, this equation can be used to determine the reduction in displacement response for,#y 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 rctio that formed the basis for demonstrating that a 10% reduction in stability ratio would be sufficient to prevent Row 9 Column 51 from rupturing by fatigue.

024BM:49/080188-28

The fatigue curve developed for the North Anna Unit I tube at R9051 is from

(

jac. Thus, ac where, a is the equivalent stress amplitude to o that accounts a

a for a maximum stress of o, the yield strength. The 3 sigma curve with y

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 (

Ja.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 initiating stress amplitudes. These were the [

Ja.c shown in Figure 4 3.

Witha(

Ja.c,the(

ja,C, 0248M:49/080388-29

F i

I The assessment of the benefit of a reduction in stability ratto begins with the relationship between stability ratio and deflection.

For a specific tube 4

geometry, the displacen nt change is directly proportional to change in striss l

so that stress has the same relationshir, with stability ratio, a,C i

i l

J The slope in this equation can range from (

Ja.c on a log scale depending on the amplitude of displacement. Knowing the stress resulting from

}

a change in stability ratio from SRg to SR, the cycles to failure at the

[

2 l

stress amplitude were obtained from the fatigue curve. A fatigue usage per l

4 year was then determined assuming continuous cycling at the natural frequency l

]

of the tube. The initial stress was determined to ue in the range of 4.0 to l

l 10.0 ksi by the fractegraphy analysis.

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

r i

l I

1 I

l 4

l l

)

Ja.c.

The corresponding I

stress level is 5.6 ksi.

The maximum stress, 9.5 ksi, would be reduced to (

]a,c with a 10%

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

(

Ja,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 j

ratio and would have future fatigue usage of (

Ja.c per year, Figure l

4 5.

In addition, if a tube were already cracked, the crack could be as large

)'

as [

Ja.c inch in length and thru wall and would not propagate if the j

stress amplitudes are reduced to s 4.0 ksi, i

4 l

i 024BM:49/081288 30

l l

I 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.

lt

[

i j

Ja,c, cumulative fatigue usage may then be computed to get a l

magnitude of alternating stress for the isst cycle that results in a cumulative f

usage of 1.0 for the nine year duty cycle.

The result of the iterative analysis is that the probable stress associated with this fat Que curve during thelastcycleofoperationwasapproximately(

Ja,c for R9C51, North l

Anna Unit 1 Steam Generator C, and that the major portion of the fatigue usage came in the second, third aad fourth cycles. The rirst cycle was l

conservatively omitted, since denting is assumed, for purposes of this l

l 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 j

Anna Ur.it 1.

j A similar calculation can be performed for the time history of operation j

assuming that (

4 l

Ja,c, j

On this basis, the effect of a 10% reduction in stability ratio is to reduce

)

j the stress amplitude to 4.0 ksi and results in a future fatigue usage of j

(

la.c, l

Other combinations of alternating stress and mean stress were evaluated with 3 sigma and 2 sigma fatigue a rves to demonstrate the conservatism of the 4

i 10% reduction in stability ratio. Table 4-1 presents 'the results of the cases analyzed clearly demonstrating that the 10% reduction in stability ratio

=i 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 i

small changes in the fatigue curve.

j 0248M:49/080188 31 i

1 i

4.2 Local Flow Peaking Considerations i

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 tasettion 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 1,ignificant chang 6 in the prediction of tube response.

l Since the evaluation of McGuire #2 tubing is relative to R9C51, North Anna Unit 1, the flow peaking factors are also applied as relative ratios, i.e., a ratio I

of McGuire.52 tubing to R9C51 at North Anna Unit 1.

The flow peaking relative j

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 3

l pattern compared to critical velocity for a uniform AVB pattern. As explained 1

J in Section 8.0, the minimum value of (

Ja,b,c is appropriate for R9C51 of North Anra 1.

The peaking factor for a tube in McGuire #2 tubing is therefore divit.ed by (

Ja,0,c and the resulting relative float peaking is multiplied j

times the relative stability ratio based on ATHOS results.

If the peaking i

ftctor is 1.0, the relative flow peaking is (

Ja,b,c, i

As a further demonstration of the conservatisin of (

Ja,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 i ominal value from

)

fractography analysis) was used to back calculate the apparent stability ratio l

ard then the apparent flow peaking factor. Allowing for a range of slopes of j

the instability curve from 10 to 30, the stability ratio is in the range of 1,1 l

to 1.4 and the flow peaking factor is in the range of 1,8 to 2.2.

This range j

of flow peaking agrees with the range of flow peaking factors measured in the j

air tests and is considered to be the best estittate of the range of the R9C51 flow peaking factor.

l l

I t

1 0248M:49/081288 32

\\

The range of stability ratios,1.1 to 1.4, is based on a value of 0.63 obtained with ATHOS results without flow peaking and with nominal dampin'g that is a function of modal effective void fraction. The nominal damping reflects the nominal reduction in damping that occurs with denting at the tube 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 statility 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 ksi.

To apply this same criteria to anothertubeinthesameoranothersteamgenerator,thedifferencesin[

ja.c, a,c f

d s

l 024BN:49/080188-33 l

1 i

d I

i I

I I

i

)

i i

1 l

l 1

a,c j

t i

i i

l i

i I

l a

t

)

l 1

i i

\\

where the stability ratio (SR) includes the flow peaking effect, i

i t

)

By establishing their equivalent effect on the stress amplitude that produced I

i the tube rupture at North Anna 1, several other effects may be accounted for, j

These include a lower mean stress (such as for non dented tubes), different j

frequencytubesfromthe(

Ja c.e hertz frequ'ency of R9C51, North Anna 1.

j and shorter design basis service.

l i

a 0248M:49/080188 34

)a--.------.--...

_ = -

l In the case of lower mears stress, the stress amplitude that would have caused l

the failure of R9C51, North Anna 1, wou'Id have been higher.

(

i ja,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 accumulated is proportfonal to the frequency and, therefore, the allowable number of cycles to reach a usage of 1.0 is inver.tely proportional to frequency. The equivalent number of cycles to give the usaga of 1.0 t'ar a different frequency tube [

la.c, Foradifferenttimebasisforfatigueusageevaluation,[

i i

l Ja.c.e, Knowing the magnitude of the stress ratio allows 1) the determination of tubes that do not meet a value.of s 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 McGuire #2 based on the time history expressed by normalized stability e

ratios for the duty cycle (see Section 7.4).

024BM:49/080188 35

. - =.

l Table 4 1

)

Fatigue Usage per Year Resulting From Stability Ratic Reduction

{

i SR, %

STRESS FATIGUE MEAN STRESS USAGE l

REDUCTION BASIS (I)

CURVE (2)

MODEL PER YEAR i

l d

a,c 5.

9 yrs to J

fail (

Ja.c I

5.

9 yrs to y

j fail (

Ja.c i

i 5.

9 yrs to j

1 fail (

Ja.c

]

{

10.

max,stresk)

J amplitudel

(

ja.c j

10.

max stresg) amplitudel

[

ja,c j'

10.

max, stres )

i amplitudel 1

i i

1*

10.

j max.stresg) amplitudgt

(

)

'C 10.

max. stress based on duty c glj(5) i 1

(1)

This gives the basis for selection of the initiating stress amplitude and

{

its value in ksi.

(2) 5 is the maximum stress applied with 5, = Smean + S '

3 a

I (3)

[

la.c, I,

1 (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.

'4 (5) Cyclestofailureimpliedbytheoperatinghistoryrequires{

]a.c fatigue curve at the maximum stress of (

Ja, 0248M:49/080188-36 l

I t

. a,b,c l r

e I

i l

1 i

l 1

i 1

I I

l 1

t 1

I

)

i i

+

l l

4 I

l I

)

}

i 1

N i

4 I

A i

a l

4 Figure 4-1 Vibration Displacement vs. Stability Ratio i

i

)

1 1

4 l

1 i

. ~ - -

-. - -,. - ~

I I

l l

i t

i J

a,c 4

l t

i 1

i i

t 4

I i,

1 i

l' f

?

i i

I F

1 r

i I

I

\\-

i 1

l j

i l

l j

1 1

j l

I t

)

1 J

f I

.i a

1 1

I t

i l

1 i

r i

Figure 4 2 Fatigue Strength of Inconel 600 in AVT Water at 600'F I

i l

1 l

I I

i l

i

4 J

l l

u

}

9 I

a,e i

l i

i 1

I L

I i

i j

1 I

I I

i 1

i i

I I

I f

4 a

I l

i j

1 Figure 4-3 Fatigue Curve for Inconel 600 in AVT Water Comparison of Mean Stress Correction Models s

i I

i l

1 l

l l

f j

aC 1

I

)

i i

1 1

l i

1 i

1 4

1 i

i e

I 1

I j

l i

i Figure 4-4 Modified Fatigue with 10% Reduction in Stability j

Ratio for Maxtu m Stress Condition 1

l i

}

.O.

+. ' e.

g

\\'{ q:.

O. O IMAGE EVALUATION A ' 's.

\\:;

q90' TEST TARGET (MT-3)

/

fl.,Y %,

Q fff,

N '! y?N'

%f/ gyfp frf f' kt l.0 L "t "i

,_ m 22 u

E",, - q 2.0 l,l

[ '

1 :

Uh3 1.25 l' l.4 b-ma mjl,.6 y

=

4 150mm 4

6"

%g lIi%y,y, f

4%

L;../4;b

+ ;g.

.;j

A

_M+

,O :

' '?, h '

sp?/.

?..

////p'N[s'/# T ' 'S

/s'O, IMAGE EVALUATION O ' st, O

s "' 8*

TEST TARGET (MT 3)

We\\////

ggs 4

' 4,

/t

.i e

gg,$5 Q s[,'

y l.0 F: M3

.m 22

[

7,.

= 4 L' r.

; 23 lll l,l i<=

p)4

.c 1.25 1=l. 4 cil I.6 m

==

4 150mm l

4 6"

Os Df,

pf, %

O$'1 0

4l,,,

• .?

s&@n;c Af

/g o

p e

g 4

e.

c V

jf g

.;/k\\

a m

s Op u

c.

z o

l 1

i i

4 a,c 4

J f

I 4

i 1

1 M

4 4

1 1

i j

Figure 4-5 Modified Fatigue with 5% Reduction in Stability l

Ratio for Minimum Stress Condition 4

i I,

i

5.0 SUPPORTING TEST DATA This section provides a mathematical ' ascription of the fluid elastic mechanism, which was determined to tx the most likely causative mechanism for the North Anna tube rupture, as discussed in Section 3.3, to highlight the physical conditions and correspondino parameters directly related to the event and associated preventative measures. The basis for estaolishing the appropriate values and implications associated with these parameters are provided. Where appropriate, test results are presented.

5.1 Stability Ratio Parameters Fluid elastic 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 potential for tube vibration due to instability during service.

Fluid elastic 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:

Fluid elastic stability ratio - SR = Ven/Uc for mode n, where Uc (critical velocity) and Uen (effective velocity) are determined by:

2D ))l/2 (3)

U =$f 0 ((m, 6 ) / (#o g

n n

and; N

2 2

g(#/p)U 4

g 3 o j jn j

U (2)

N 2

jf(*j/*o)4 3

jn z) 0248M:49/080188 42

where, D

tube outside diameter, inches

=

V effective velocity for mode n, inches /sec

=

en N

number of nodal points of the finite element model

=

mj, Uj, pj =

mass per unit length, crossflow velocity and fluid density at node j, respectively reference density and a reference mass per unit po, mo

=

length, respectively (any representative values) 6 logarithmic decrement (damping) n djn normalized displacement at node j in the nth mode of vibration

=

Zj average of distances between node j to j-1, and j to J+1

=

an experimentally correlated stability constant

=

Substitution of Equations (1) and (2) into the expression which defines stability 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 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).

The uncertainty in each of these parameters is addressed in a conceptual manner in Figure 51. The remainder of this section (Section 5.0) provides a discussion, and, where appropriate, the experimental bases to quantitatively establish the uncertainty associated with each of these parameters.

In 0248M:49/080188 43

[

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

implies that those tubn (

Ja,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 addrcssed in Section 4.0.

This is importar.t in determining the degree cf change that can be attained through mcdifications.

Frecuency I

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 frequencies has been j

shown to be quite small. This is particularly appropriate in the case of dented (fixedbour9evcondition) tubes.

Therefore, uncertainty levels introduced by the frequency parameter are expected to be insignificant (sea also "Average Flow Field" subsection below).

i Instability Constant (Beta)

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 Westinghouse 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, j

measurements in U-bend air models have been made with both no AVB and variable l

AVB supports (Figure 5-3).

1 To help establish the uncertainties associated with ATH0S flow velocity and j

density distribution predictions on stability analyses, the Model Boiler (MB-3) tests performed at Mitsubishi Heavy Industries (MHI) in Japan were modeled using ATHOS. A beta value consistent with the ATHOS predicted flew conditions and the NB 3 measured critical velocity was determined. These analyses supported a beta value of (

Ja,b,c, i

i i

0248M:49/080188 44 l.

r - _

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

I these assessments is provided by Figure 5-2.

The lowest measured beta for tubss without AVBs was a value of l Ja,b,c. This value is used for the beta parameter in all stability ratio evaluations addressed in this Report (see also ' Average Flow Field" subsection below).

l 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 (

i

]a c, Tube Damoina i

Test data are available to define tube damping for clamped (fixed) tube supports, appropriate to dented tube conditions, in steam / water flow j

j conditions.

Prototypic U bend testing has been performed under conditions

]

leading to pinned supports. The data of Axisa in Figure 5-4 provides the i

principal data for clamped tube cenditions in steam / water. This data was obtained for cross flow over strainht tubes. Uncertainties are not defin6J 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 j

5.2, below.

l Flow Field - Velocity Times Souare-Root-Density Distribution I

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

0248M 49/080188 45

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 i. nits with dented or non dented top support plates.

If the errors associated with these uncertainties were large, similar instabilities would be j

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 generators without denting. Thus, an uncertainty estimate of about (

]a,e 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 McGuire #2 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.

i U-Bend local Flow Field Non uniform AVB insertion depths have been shown to have effects on stability ntios.

Flew peaking, brought about by the "channaling" effects of nnn-uniform AVBs, leads to a local perturbation in the velocity times squaro root density parameter at the apex of the tube where it will have the largest effect (because the apex is where the largest vibration displat.ements occur).

Detailed local flow field data used in support of the stability ratio j

evaluations afdressed in this report are provided in Section 5.2, below.

Overall Uncertainties 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 l

significantly to the instability and associated increased vibration amplitude for the failed North Anna tube. Ratios of stresses and stability ratios j

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.

l 0248M:49/080188 46 4

i 5.2 Tube Damping Data L

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.

I Reference (5-1) indicates that the damping ratio in two phase flow is a sum of contributions frcm 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 <ir and in air-water flows have been measured and reported by variou's authors. However, the results from air water now are poor 1

representations of the actual conditions in a steam generator (steam water flow at high pressure). Therefore, where available, results from prototypic steam-water flow conditions should be used.

Fortunately, within the past few l

years test data on tube vibration under steam water flow has been developed for i

l both pinned and clamped tube support conditions.

l 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 i

steam water tests conducted by Mitsubishi Heavy Industries (MHI). These data were gathered under pinned tube support conditions. The second is comprised of I

the results from tests sponsored by the Electric rawer 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 j

function of void fraction.

It is important to note that the void fraction is determined on the basis of (

]a,c l

J 1

I t

024BM:49/080188-47

)

l (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.

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

Westinghouse tests of clamped tube vibration in air has shown that the mechanical damping is only (

Ja c rather than the.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 (

Ja c, I

l

\\

l

]

i 4

1' i

1 l

024BM:49/080188-48

l 5.3 Tube Vibration Amplitu. des With Single-Sided AVB Support

]

)

A series of wind tunnel tests were conducted to investigate the effects of tube /AVB eccentricity on the vibration amplitudes caused by fluidelastic vibration, j

I Ja,c.

Prior test results obtained i

j during the past year using this apparatus have demonstrated that the fluidelastic vibration characteristics observed in the tests performed with the j

cantilever tube apparatus are in good agreement with corresponding characteristics observed in wind tunnel and steam flow tests using U bend tube l

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

An overall view of the apparatus is showri in Figure 5-5.

Figure 5 6 is a top view of the apparatus.

(

4 l

l J

l 1

)

l 1

1 1

Ja.c, l

t i

i l

0248M:49/080189 49

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

Ja.c, j

l Figure 5 7 shows the manner in which the zero-to peak vibration amplitude, expressed as a ratio normalized to (

Ja,c, varies when one gap remains at(

Jac.

For increasing velocities, up to that corresponding to a stability ratio of (

Ja,c.

Figure 5-8 shows typical l

vibration amplitude and tube /AVB impact force signals corresponding to those obtained from the tests which provided the results shown in Figure 5-7.

As expected, impacting is only observed in the [

]a,c, It is concluded from the above test results that, (

ja.C, 5.4 Tests to Determine the Effects on Fluidelastic Instability of i

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 0248H:49/080188 50 l

i

]

m

conceptual design of the apparatus.1 The straight cantilever tube; li

[

1 l

1

i ja.c, i

i I

j i

I

]a.c.

Figure 5-11 shows the l

AVBs, when the side panel of the test section is removed. Also shown is the j

top flow screen which is (

e l

i l

la.c. The AVB j

configurations tested are shown in Fig. 5-12. Configuration la corresponds to l

l tube R9C51, the failed tube at North Anna. Configuration la corrtsponds to one

{

l of the cases in which the AVBs are inserted to a uniform depth and no local j

velocity peaking effects are expected.

1 1

G l

0248M:49/080188 51 i

. _ = -

i As shown in Figure 5 9, (

i l

Ja,c, i

l All the tubes except the instrumented tubed (corresponding to Row 10) are

(

Ja,c. As discussed in Section 5.3, prior testing indicates that this situation provides a valid model. The instrumented Ja c as shown in Figure 5.10.

j tube (

Its(

Ja.c direction vibrational motion is measured using a non-contacting 4

transducer, I

(

i l

e 1

j Ja,c. The instrumented tube corresponds to a Row 10 tube as shown in i

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 +,he j

straight tube model is the average of Rows 8 and 11. The difference in profile j

is quite small for these bounding rows.

i i

('

]a.c using a l

4 l

hot film anemometer located as shown in Figure 5 9.

j Figure 5 13 shows the rms vibration amplitude, as determined from PSD (power spectral d o sity) measurements made using an FFT spectrum analyzer, versus flow velocity for Configuration la. Configuration la correspnds to the final.

l evaluated positions of AVBs near tube R9C51 in North Anna (See Figures 8 4 and i

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.

i i

l 1

l i

0248M:49/001288 52 1

The main conclusions from the tests are:

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.

f 2.

Conf,iguratio.n Ib (which was initially thought to represent AVB positior.s near R9C51 in North Anna until re evaluation indicated Configuration la)

]

has the lowest critical velocity of all the configurations tested.

r L

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 McGuire #2 evaluation are summarized in Table 5 2.

The test data are presented as velocity peaking ratios, the ratio of critical velocity for North Anna tube R9C51 configuration la, to that for each McGuire #2 AVB configuration evaluated.

l 5.5 References a,b,e r

5-1 i

i

.i l

l l

52 1

53 1

l 54 l

]

l i

i I

j 0248M:49/081288 53 1

l

Table 5 1 Wind 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 (

Ja.c, MEASUREMENTS: Tula vibration amplitude and tube /AVB impact forces or preload forces.

RESULTS:

a,b,c p

b l

0248M:40/080188-54

i l

i I

i Table 5 2 Fluidelastic Instability Velocity Peaking Ratios j

j for Columnwise Variation in AVB Insertion Depths

{

(McGuire#2) l l

1 i

r 1

j Type of Insertion Peaking Ratio j

1 Configuration Ula/Un l

1 t

a,b,c 1

I" l

[

lb 2a f

3 l

2b j

l 3

4a l

I 4b l

j I

4C l

4d

l 4f i

l 4g j

e 4p i

i 4q j

f 5a i

F 5b 4

j 5c 5e 1

6a 6e j

j Note: U is instability velocity at inlet for type n of AVB insertion n

configuration.

I i

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I i

t sbt i

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1 t

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d

'j l

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l i

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1 i

l l

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i Figure 5 1 Fluidelastic Instabt11ty Unsertainty Assessment i

U Bend Test Data 1)

MB 3 Tests A values of (

Ja,b,c 2)

MB 2 Tests A of (

Ja,b,c 3)

Air Model Tests A of (

Ja,b,c without AVBs Tendency for A to increase in range of (

]a,b,c with inactive AVBs (gaps at AVBs)

Tendency for 4 to decrease toward a lower bound of

(

Ja,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 ATHOS 3D analysis 4)

A determined from calculated critical values Good anraa-ant with rerneted A values 5)

ATHOS velocity data with A of (

Ja,b,c and known damping should not significantly underestimate instability for regions of uniform U bend flow i

A l

l I

l Figure 5-2 Instability Constant - A j

,,e o,b,c a

i

,t r

J J

l j

i i

)

1 I.

l d

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Figure 5 3 Instability Constants. A, obtained for Curved Tubes from Wind Tunnel Tests on the 0.214 Scale U Bend Model I

)

l

l j

j l

4 I,

4 I

a,b,c j

t j

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t 3

ti E

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i 0

I i

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1

(

t Figure 5 4 Damping vs. Slip Void Fraction i

1 j

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i THIS FIGURE IS CONSIDERED PROFRIETARY 1

IN ITS ENTIRETY 1

i t

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Figure 5 5 Overall Vies Cantilever Tube Wind Tunnel Model

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_ _ _ _ _ _ _ _ _ _ _ _ _ - ~_

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THIS FIGURE 15 CONSIDERED PROFRIETMY i

IN ITS ENTIRETY i

i i

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j I

t 1

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i Figure 5 6 Top View of the Cantilever Tube Wind Tunnel Model I

I a

I l

I i

l

l a,b c

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t l

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Figure 5 7 Fluidelastic Vibration Ampittude with Non Uniform $sps

(

(

l I

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_ _ - - = _.

- - -(

4 1

l a,b.c

{

I a

l 1

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i Figure 6 4 Typical Vibration Anplit ade and Tube /AVI lopect Force Signals for Fluidelsstic Vibration with Unequal Tube /AVB Saps l

)

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l Figure 5 9 Conceptual Desitn of the Apparatus for Determining the j

Effects af Fluidelastic Inst 31)lty of Col anwise j

1 Verlattens in AVB Insertion Depths I

i i

i 1

(

4 e

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p 1

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i, Figure 510 Overall View of Wind Tunnet h.si Apparatus

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1 l

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Figure 511 Side View of Wind Tunnel Apparatus with Cover Plates i

Removed to Show Simi.'ated AVBs and Tcp Flow Screen l-l l

l

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

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TYPE OF AVB TYPE OF AVO LiggTcN INSERTON df

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a,b c s

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Figure 5 13 Typical Variation of RMS Vibration A plitu's wit.6 Flow 1

j Velocity fer Configuration la in Figure 512 l

i l

6.0 EDDY CURRENT DATA AND AVB POSITIONS To reduce the number of tubes to be inspected for the presence of AVB support during the May-June, 1988, outage at McGuire #2, Westinghouse performed a review of eddy current information provided by Duke Power in the 1985, 1986 and 1987 outages. Approximately 870 eddy current readings (nearly 225 per steam generator) from diverse tubes in Rows 7 through 20 were analyzed to estimate AVB positions for each data point.

From 6his information, tube positions in each of the four steam generators were individually identified for eddy current inspections. This preliminary AVB projection effort reduced the number of tubes to be inspected in May June,1988, from 2,387 tubes (formerly all tubes in Rows 7-12, minus 301 already inspected) to 1,277 tubes, a net reduction of 1,110 tubes.

6.1 McGuire #2 AVB Assembly Design

[

la,c.e Review of the EC data for McGuire #2 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 slightly lower depth of insertion.

\\

0248M:49/081288 61

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 characterietic peaks seen in the signals which indicata 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, dua to inability of 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.

Consistency with the design of the AVB assembly, consistency of data with adjacent columns, and projection methods were utilized to evaluate the depth of insertion.

In the case of single AVB contacts, the length of the contact signal, and verification by projet. tion were used in some instances to confirm or deny support of the tube with a single contact.

4 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 6-5 show a representation of AVB insertion distance based on evaluation of the EC data. The values indicated below the tubes are the AVB depth projections of the smallest row tube which has two AVB indications.

In cases where no AVBs were indicated, a "0" is shown, and likewise, a "1" is shown where "one AVB" is indicated. All other tubes examined have two or more AVB indications.

The direct observation data (the number of AVB intersections seen by the eddy current probe) are the principal basis for determining the AVB positions.

Where the direct observations were ambiguous or there is a conflict between observations and projections, the more conservative data are used to determine the AVB positions. Since ' direct observaticn' gives a 'yes - no' type of answer, the projection method is used to ' interpolate' AVB insertion depths 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.

l 0248M:49/081288 62

The projection technique is useful where noisy or spurious ECT signals prevent direct observation of the AVBs and where data is unavailable due to plugged tubes.

(

l ja,c 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 l

for the AVBs is provided for (

l l

l c

ja,c

(

ja,c 6.3 Tube Denting at Top Tube Support Plate I

i Subsequont to identifying the AVB signals, eddy current data were examined to evaluate the incidence of corrosion and/or denting at the top tuba support plate.

In the denting evaluation, the EC tapes were evaluated to determine the condition of the tube / TSP interface for potentially unsupported tubes in locations which could be susceptible to flow peaking. Analysis of the data for

.I 4

0249M:49/082488 1

McGuire #2 shows the presence of ' corrosion with magnetite' in the majority of the tube / TSP crevices examined. Of the forty-two June,1988, tube eddy current results evaluated for top tube support plate corrosion, 38 were found to be magnetite packed, none showed denting with deformation, and four showed no detectable magnetite or corrosion. Because the tube vibration analyses were based on the conservative assumption that all tubes in the area of interest were structurally ' fixed' in the TSP holes by denting or corrosion with associated tube deformation, the results of this phase of the examination do not influence the disposition of the tubes found to be susceptible to fatigue.

6.4 AVB MAP INTERPRETATIONS 6.4.1 Description by Steam Generator The McGuire #2 SGs AVBs, as previously noted, have a nominal design insertion depth to Row 10.

SG-A The AVB map is given in Figure 6-2.

A listing of unsupported tubes is given in Table 6-2.

No AVB signal was detected in any of the Column 113 tubes.

In this column, which ends at Row 12, the absence of indicated support for these tubes is less critical than for other Row 11 and 12 tubes, since the velocities which affect the stability ratio are on one side of the tube the lower bulk flow velocities, as opposed to gap velocities. The only other Row 10 tube (other than R10Cll3).in the four steam generators which was also unsupported was R10C112. Nine Row 9 tubes, seventy-seven (77) Row 8 tubes, and one hundred three (103) Row 7 tubes are not supported. The AVB insertion depth is uniform in the central region (Columns 31 to 84) with the majority of the insertion depths to Row 9.

The insertion depth varies gradually in the region between Row 2-14, some peaking was evaluated between Rows 14 to 30, and insertion depth again varies gradually between Columns 85 to 113.

R9C2? is the highest loaded tube in this steam generator, having.a relative stability ratio of 0.65.

1 0249M:49/081288 2

SG-B The AVB map is given in Figure 6-3.

A listing of unsupported tubes is given in Table 6-3.

All Row 12, 11 and 10 tubes are supported.

Eight Row 9 tubes, seventy-seven (77) Row 8 tubes, and one hundred (100) Row 7 tubes are not supported. AVB insertion depth varies gradually between Rows 6 and 7 from Columns 2 through 29, with a slight change between Columns 29 and 34.

Variations occur between Columns 84 to 113. R9C88 is the highest loaded tube in any of the steam generators, having a relative stability ratio of 0.66.

SG-C The AVB map is given in Figure 6 4.

A listing of unsupported tubes is given in Table 6-4.

All Row 12, 11 and 10 tubes are supported. Two Row 9 tubes, sixty-one (61) Row 8 tubes, and one hundred (100) Row 7 tubes are not supported. AVB insertion depth varies within about a two-and one half pitch distance between Columns 2 and 39. Variations between Columns 84 and 113 are "stepped", for the most part. R9C22 and R9C93 are the highest loaded tubes in this steem generator, both having relative stability ratios of 0.65.

~

SG-D The AVB map is given in Figure 6 5.

A listing of unsupported tubes is given in Table 6 5.

All Row 12, 11 and 10 tubes are supported.

Fourteen Row 9 tubes, ninety-one (91) Row 8 tubes and one hundred (103) Row 7 tubes are not supported. AVB insertion depth varies gradually across the tube columns.

Five Row 9 tubes ari the highest loaded tubes in this steam generator, having relative stability ratios of 0.57.

6.4.2 Summary of Tube Support Conditions Table 6-1 provides a listing of tubes which, although indicated as supported by 1 AVB by eddy current, were evaluated as being supported, based upon projection data and existing checks. Table 6 2 provides a listing of tubes, also with 1 AVB signals by eddy current, which are shown as supported, to provide a limiting evaluation of flow peaking of nearby tubes. Table 6-3 provides a summary listing of unsupported tubes based upon the limiting conditions.

0249M:49/081288-3

Table 6-1 McGuire #2 1 AVB Signals Determined to be Supported McGuire #2 Steam Generator A Row 9 Columns 2, 22, 27, 62, 106 Row 8 Columns 13, 29, 53, 88, 90 Row 7 None McGuire #2 Steam Generator B Row 9 Columns 32, 34, 37, 39, 43, 49, 52, 53, 54, 55, 62, 63, 64, 66, 68, 93, 95, 96, 111 Row 8 Columns 17, 30, 89, 101 Row 7 Columns 4, 8, 14 McGuire #2 Steam Generator C Row 9 Columns 2, 64, 65 Row 8 Columns 8, 11, 13, 104 Row 7 Column 29 McGuire #2 Steam Generator D Row o Columns 3, 8, 47, 65, 72, 73, 109 Row 8 Columns 8, 31, 101, 102 Row 7 Columns 25, 26, 86, 87 2

l 0249M:49/081288 4 1

Table 6-2 McGuire #2 1 AVB Signal Indicating Support for Flow Peaking Analysis McGuire #2 Steam Generator A i

Row 9 Column 22 Row 8 Column 100 McGuire #2 Steam Generator 8 Row 9 Column 57 9

McGuire #2 Steam Generator C Row 8 Columns 12, 16, 20, 21, 23, 31, 56, 78, 82 and 88 Row 7 Columns 86, 87 McGuire #2 Steam Generator D None I

i t

1 l

0249M:49/081288 5

Table 6-3 Summary Listing of Unsupported Tubes McGuire #2 McGuire #2 Steam Generator A Row 12 Column 113 Row 11 Column 113 Row 10 Columns 112, 113 Row 9

• -lumns 18, 19, 23, 108-113 Row 8 oolumns 17-24, 27, 28, 31-51, 54 84, 94-99, 105-113 Row 7 Columns 9, 10,13-113 McGuire #2 Steam Generator B Row 12 No unsupported tubes Row 11 No unsupported tubes Row 10 No unsupported tubes Row 9 Columns 33, 56, 65, 69, 70, 88, 92, 110 Row 8 Columns 2, 31-84, 88,91-100, 103 113 Row 7 Columns 2, 15-11S*

McGuira #2 Steam Generator C Row 12 No unsupported tubes Row 11 No unsupported tubes Row 10 No unsupported tubes Row 9 Column 22, 93 Row 8 Columns 2-5, 9, 17, 22, 32 35, 38-55, 58-7), 83, 84, 89, 92 99, 106 Row 7 Columns 2-27, 30 85, 88, 89,92-107 McGuire #2 Steam Generator D Row 12 No unsupported tubes Row 11 No unsupported tubes Row 10 No unsupported tubes Row 9 Columns 2, 5, 6, 7, 50 56, 64, 107, 108 Row 8 Columns 2 11, 16 23, 32 84,92-100, 103-113 Row 7 Columns 2 24, 27, 31 84,88-113 AVB positions C25/C26 and C28/C29 in Figure 6-3 are shown to support adjacent Row 7 tubes, although AVB support of these tubes was not evaluated j

by direct Row 7 eddy current data (no AVB data are available for these i

i tubes). These Row 7 tubes are stable in either case, and the AVBs are shown in this position for a bounding evaluation of flow peaking of nearby tubes.

j t

0249M:49/081288 6

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't 7.0 THERMAL AND HYDRAULIC ANALYSIS I

h

{,

This section presents the results of a thermal and hydraulic analysis of the flow field on the secondary side of the steam generator using the 3-D ATHOS computer code, Reference (7-1). The major results of the analysis are the o

water / steam velocity components, density, void fraction, and the primary and seco-9ry fluid and tube wall temperatures. The distributions of the tube gap l

vs and density along a given tube were obtained by reducing the ATHOS

[

]

reso, In the following subsections, the ATHOS model and some sample results of the analysis are described. Normalized stability ratios over the operating histories of the unit were also determined and are reported in Section 7.4.

f 7.1 McGuire C Steam Generator Operating Conditions

)

i l

Recent steam generator operating condition data for the McGuire #2 unit were provided by Duke Power. The data are representative of full power operation

)

during the most recent fuel cycle, Cyle 4.

With these data, calculations were i

completed using the Westinghouse SG performance computer code, GEND3, to verify l-the plant data and to establish a complete list of operating conditions required for the ATHOS analysis. The GEND3 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 l

code calculates the circulation ratio which is used to determine the total bundle flow rate and average loading on the tubes.

The calculated circulation

}

ratio klong with the other thermal / hydraulic conditions are listed in Table 1 1.

The ATHOS 3 0 flow field calculation was based on these parameters.

i 7.2 ATHOS Analysis Model 1

l 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 ATHOS computed flow profiles for both tube

~

j '-

bundles. Since the presence of AVBs in the U bend region of a tube bundle i

could influence the overall flow field and/or thi local flow parameters for a particular tube of interost, some discussion of the treatment of AVBs is j

necessary before presenting a description of the ATHOS model.

j 0249M:49/081288 12 4

.---n,-.

i The ATH0S code does not include the capability to model the presence of the AVBs 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. ATHOS calculations have been performed with and without AVBs in the model. Calculations of stability ratios relative to North Anna R9C51 show that the relative stability ratios for tubes l

near the center of the steam generator are essentially the same for models with or without AVBs. The ATHOS AVB modeling sensitivity studies with uniform insertion show some tendency for the AVB resistance effects to lower tube gap velocities near the central regions and to increase velocities near the peripheral tubes. However, the magnitude of this effect is uncertain due to the limitations in ATHOS for modeling the AVBs.

Further, the global flow i

resistance of staggered AVB insertion would be less than that from uniform insertion. Based on the sensitivity studies using ATHOS models with and I

without uniformly inserted AVBs, the most reliable relative stability ratios (for actual steam generators with non uniform AVB insertion depths) are expected using ATHOS models excluding AVBs and effects of variable AVB insertion depths by using flow test results of actual AVB geometries.

l The McGuire #2 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. With a Cartesian coordinate system the tube array and any l

AVBs are arranged in a square pitched configuration which is in line 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 McGuire #2 steam generator consists of 18,720 flow cells having 30 divisions in the x axis (perpendicular to the tubelanc) direction, 16 divisions in the y axis (along the tubelane)

I direction and 39 divisions in the axial (z-axis) direction.

In the ATH0S analysis, thG 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 1

0249M:49/081288 13 r

1 1

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 o

features.

t O

I 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 l

j lines. All of the simulated 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 generator. The feedwater nozzle is located at axial indices IZ-11 and 12. Ten axial layers of cells were included in the U-bend near the top tube support (Figure 7-2, IZ 27 to IZ 36) to more closely model the flow conditions in the area o,f interest.

1 Figure 7-3 reproduces the plan view of the model but with the tube layout j

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 l

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 naar the bundle l

periphery (!Y 12-16) to more closely model the inner radius tubes.

I 7.3 ATHOS Results i

The results from the ATH0S analysis consist of the thermal hydraulic flow 9

parameters necessary to describe the 3 D flow field on the secondary side of 1

the steam generator plus the distributions of the primary fluid and mean tube

)

wt.11 temperatures. Since the velocity components computed by ATHOS are defined

)

on the surfaces of a flow cell, the tube gap velocity and density distributions

~

c 1

l l

0249M:49/081288 14 1

i 1

i along a particular tube required for tube vibration evaluation are determined by a post-processor from the ATH0S output. The post-processor generates a dt sa file which contains this information for all the tubes in the model and the file serves as part of the input data required for tube vibration analyses.

Because the majority of the flow cells contain more than one tube inside a cell, the tube gap velocity and density surrounding a tut.e are obtained by interpolation of the ATH0S calculated velocities (defined on the cell surfaces) and density (defined at the center of the cell). The post-processor performs l

the necessary interpolations to determine in plane and out-of-plane velocities at specific intervals along the length of the tubes.

i l

a Figuro 7 4 shows a vector plot of the flow pattern on the vertical plane of symetry 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 !Z 27).

l The figure also shows the high V component of the flow leaving the three Z

flow slots on the top tube support plate (PLATE T) at the middle of the 2 + yy ', on the same 2

figure. The lateral velocity components, VR = /Vx horizontal plane (lZ 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 the hot leg side, but is about three times of that on the cold leg side.

Figure 7 7 shows the plot of the void fraction contours on the vertical plane of symetry 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 l

bundle region.

in the U bend region the void fraction is about 0.9 0.95 on the i

hot leg side, decreasing to atout 0.60 at the bundle priphery on the cold leg side.

Figures 7 8, 7 9 and 7 10 show a sample of the individual tube gap velocity and density distributions along three tubes at Row 10.

In each figure the gap j

velocity and density along the length of the tube are plotted from the hot leg

)

0249M:49/081288 15

4 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 tored in a data file. The data file was then utilized in the subsequent stability ratio calculations.

Figure 7-11 shows the plot of the l

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 7.3 l

and 8.4 ft/sec. The velocity variations seen in the figure at Columns 22, 38

)

and 50 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 McGuire #2 steam generators is to examine the operating history data and use it to determine the susceptibility to

• ~

fatigue from fluidelastic vibration resulting from the 5+ years of operation.

This assessment has been completed through the use of a parameter termed the normalized stability ratio. The normalized stability ratio 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.

I A plot of this ratio against operating time, therefore, provides a relative indication of the effect of past operation on the plant's fluidelastic i

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.

High values for the net stability ratto, in particular, over a significant q

period of operation, coupled with other prerequisite conditions (e.g., absence i

of AVB support and denting at the top tube support plate), could indicate an increased susceptibility to fluidelastic vibration instability and fatigue.

i l

l 0249M:49/081288 16 s

The fluidelastic stability ratio is defined as the ratio of the effective fluid velocity acting on a given tube to the critical velocity at which large amplitude fluidelastic vibration initiates:

o Fluidelastic Veffective s

Stability Ratio, SR =

[1]

Ucritical at onset of instability In this ratio, the effective velocity depends on the distribution of flow velocity and fluid density, and on the mode shape of vibration. The critical l

velocity is based on experimental data and has been shown to be dependent upon the tube natural frequency, damping, the geometry of the tube, the tube pattern, and the fluid density, along with the appropriate correlation coefficients.

i l

The detailed calculation of this ratio using velocity and density distributions, etc., requires three dimensional thermal / hydraulic and tube vibration calculations which are time consuming. Alternately, a simplified, one-dimensional version of this ratio has been used to provide a relative assessment technique for determining the effect of past operation on the stability ratio.

The normalized stability ratio is defined by the following equation:

a,c (2)

In this equation "cyc x" refers to each fuel cycle and "ROP" to the recent operating condition. While this simplified approach cannot account for three dimensional tube bundle effects, it does consider the major operational parameters affecting the stability ratio.

Four components make up this ratio:

l a loading term based on the Jynamic pressure (pV ), a tube incremental 2

mass (m) term, the natural frequency of the tube (f ), and a damping ratio n

(6) term.

It should be noted that the ratio is relative, in that each l

/

component is expressed as a ratio of the value for a given fuel cycle or power level to that af the recent operating point.

0249M:49/081288 17

i i

I i

o I

O g

L Ja,c,.The i

j particular 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 I

assumed in calculating the tube natural frequency, i

As discussed previously in Section 7.1, the reference three dimensional stability ratio calculation for the McGuire #2 steam generators was based on the following operating parameters which are representative of recent full

[

l, power operation-i i

Steam Flow 3.77 x 106 lbm/hr j

Steam pressure 1007 psia Circulation Ratio

[

Ja.c(Westinghousecalculation) i A series of calculations were completed to generate a normalized stability ratio for each of the four fuel cycles since the plant became operational in May, 1903. Data for this evaluation are summarized in Table 7-2.

Included are cycle average values for full load steam pressure and primary fluid inlet temperature. The number of days that the plant has operated within three power i

intervalt (85 90%, 90 95'/. and 95100%) above 85*, of full power are also j

listed. Since tube vibration and possible fatigue are associated with higher I

p w:r operation, only the higher power operating periods are considered

)

important to the evaluation. The operating parameters listed in Table 7 2 were i

then input to the Westinghouse GEND3 computer code todetermine the overall j

performance of the steam generator, in particular, the circulation ratio for each fuel cycle. These calculated values are also listed in the table.

l.:

i i

't

{

0249M:49/081288 18

)

o

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 85% power. Note that the ratio assigned to each of the high power intervals listed in Table 7-2 (85-90%, 90-95%, and 95 100%) and plotted in Figure 7 12 has been conservatively based on the highest power level in each interval. Figure 7-12 indicates that the full power normalized ratio has remained essentially constant throughout all four fuel cycles. This is a result of the fact that there have bean no power upratings, significant changes in primary temperature, or steam generator internal modifications which could alter either the bundle flow rate (circulation ratio) or the steam pressure.

The very small changes that have occurred in the full power ratio merely reflect the effect of small cycle-to cycle steam pressure variations.

Figure 7 12 also shows that the stability ratios and operating periods at the 1 wer 2

power intervals are negligible compared to the full power results.

References:

7-1 i.. W. 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.

l 0249M:49/081288 19

k t

J Table 7-1 McGuire #2 Steam Generator Operating Conditions Used for ATHOS Analysis Power 854.5 MWT (99.8% of full power) f i

1 Primary Flow Rate 3.68 x 107 lb/hr j

Primary Inlet Temperature 616.4'F J

Primary Outlet Temperature 559.4 'F i

Steam Flow Rate 3.77 x 106 lb/hr i

Feedwater Inlet 437.7'F Temperature l

I Water Level from Tubesheet 490 inches j

Steam Pressure 1007 psia (S/G Exit) 1010 psia (Dome for ATHOS Input) 1 Circulation Ratio 2.35 1

l i

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4 e

i 1

i f

I

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I 0249M:49/081288 20 s

..r.,

y.

_7,-.

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

,,.mm- - -,

,,y

.m,

,_rr--~7--,

. -. _ _~

. _ _ _ _ _... _ ~. _ _

y s

fable 1-2 McGuire #2 Operating History Data Otstributton of Days la

- ----- Full Load Values

[ach Power Interval Steam Pressure Thot Calculated Cycle Beginning

[nd 95-100%

90-95%

85-901 (Psta)

(Deg F)

Ctre. Ratto I

35-Ny-83 25-Jan-85 210 12 65 1000 616.9 2.36 2

05-hy-85 14-b r-86 210 11 1

1005 614.3 2.35 3

18-Jun-$6 01-m y-87 225 0

1 1003 616 2.35 f

4 03-Jul-87 26-Nr-88 233 1

1 1001 616.4 2.35 1

878 24 68 C249M.49/061288-21

a,e f

1

• e L

I l

I i

1 1

4 Figure 7-1 Plan View of ATl105 Cartesian Model for McGuire #2 1

a,c s

l I

i l

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l 1

l l

l 1

i

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Figure 7 2 Elevation View of A'll!05 Cartesian Model for McGuire #2 l

'BoC

=

I I

I f

i t

i Figure 7 3 Plan View of ATh05 Cartesian Model for P.cGuire #2 Indicating Tube Layout r

l

a,e t

)

i i

l 1

i i

I l

l l

l i

i i

i i

i l

l i

l i

l i

i l

?

I l

l 1

l t

I Figure 7-4 Flow Pattern on Vertical Plane of Symmetry

aCr

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l

.t I

i 1

i i

t 1

l l

I i

i i

I i

i l

i l

1 l

l I

l u

Figure 7-5 Vertical Velocity Contours on a Horizontal Plane at the Entrance to the U Bend Region

4,C

\\

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d 1

1 i

l i

1 Figure 7-6 Lateral Flow Pattern on Top of Top Tube Support Plate

Ar c q

l l

l l

l l

l i

1 l

J

~

Figure 7-7 Vold Fraction Contours on Vertical Plane of Sy n try 1

t 1

1

l 1

a,c

~1 i

l l

1 i

l 1

Figure 7-8 Tube Gap Velocity and Density Distributions for Tube Row 10/ Column 5 1

a,e e

O l

Figure 7-9 Tube Gap Velocity and Density Distributions for Tube Row 10/ Column 20

1 l

a,e 1

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l l

l l

l l

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t l

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Figure 7-10 Tube Gap Velocity and Density Distributions for Tube Row 10/ Column 40 i

l

4,C

~

I c.

4 l

l I

I i

}

i i

1 i

1 i

1 I

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

U-Bends Normal to Row 10 1

4 f

j 1

1 McGUIRE 2 NORMAIJZED STABILITY RATIO EstD oN HIO4 PUwW>&SM) oPD% TON 1.04

{

Reference MsR = 1.0 j

1.02 "

/ (Basis for AME hm)

/

---e 1-1 3

2

'3 k

/

l o.sa -

w, o.ss -

I I

o s4 -

N estPeer I'

o.s 2 -

E N

o.s -

l 1

J o sa -

\\ set Powr 5

cas -

g o.s4 -

I c a2 -

i oa o

o.a o.4 c.s o.n i

1.2 1.4 (tw.ve w e) l accumuim om 4spacre, reco wm 1

1 l

i i

I Figure 7-12 McGuire #2 Normalized Stability Ratio Based onHighPower(>85%) Operation 4

i d

I

8.0 PEAKING FACTOR EVALVATION This section describes the overall peaking factor evaluation to define the test j

based peaking factors for use in the tube fatigue evaluation. The evaluation of tN eddy current data to define the AVB configuration for North Anna 1 Tube j

R9CSI is described. This configuration is critical to the tube fatigue assessments as the peaking factors for all other tubes are utilized relative to j

the R9C51 peaking factor. Uncertainties associated with applying the air model test results to the tube fatigue assessments are also included in this se: tion.

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 j

o AVB insertion depth uncertainty I

i 8.1 North Anna 1 Configuration J

8.1.1

Background

j The AVB configuration of the ruptured tube in North Anna, R9C51, is the

]

reference case for the tube fatigue evaluations for other plants.

In 1

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 l

to the North Anna R9C51 tube, including the relative flow peaking factors.

I Thus, the support conditions of the R9C51 tube are fundamental to the analyses i

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 reevaluated using the prrsjection 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.

OM9M:49/081288-34 i

1 3

a 4

8.1.2 Description of the Method l

The basic method utilized was the projection technique in which the AVB 1

position is determined based on measured AVB locations in larger row tubes in 4

]**,

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 l

mode (data examined on the basis of predicted AVB positions).

The objective of this application was, with the greatest confidence possible, to establish the positions of the AVBs in an 8 column range around the R9C51 tube in North i

Anna 1. Steam Generator C.

I 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.

q 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 j

Model 51 U bend rt jion.

The intent of this review was to determine if the presence or absence of AV8s as shown in Figure 8-1 could be confirmed using the AVB projection technique. Preliminary projected AVB positions were based on geometric data l

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 4

(multiple spikes) where offset AVBs were predicted, single indications where single AVB inters-etions were predicted, etc. The data evaluation method used was a critical examination of the data, which was biased toward the 1

presence of AVBs unless a confidert call of "no AVB" could be made, and then

)

checking the consistency of the data among the tubes in a column and against i

the theoretical data for the predicted AVB positions.

[

l

]

}

I

}

i 0249M:49/081288 35

}

}

I l

]

l i

i i

l J

f 1

i l

i i

i l

)

I l

i i

i 1-1 1

{*

Ja,C, k

4 j

Figure 8 4 is the "AVB visible" map for columns 48 through 55, based on the l

1 critical review of the data.

It should be noted that the original data i

interpretations and the review interpretations are consistent.

l 8.1.4 Projections The (

Ja c ECT traces were j

utilized for projecting the position of the AVBs according to the standard j

format of the projection method.

l l

The results of the projections are 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, r. ore than one, and as many as three, projection values 1

i j

0249M:49/081288-36 1

=... _

.. =. -

i j

are shown. Multiple projections are expected for a tube if the AVBs on either side of the tube are not at the same elevation, or if the upper and lower AVB support that tube. As many as four different projections are possible if it is 1

assumed that the tube is supported by the upper and lower AVBs, and both upper and lower bars are staggered in elevation as shown in Figure 8 2.

i The logic in arranging the projection data is based on the following two rules:

Rule 1.

The projections of the same AVB based on different tubes in the l

samecolumn(

Ja.c,

(

i 4

j l

l 4

I l

l l

i l

l

{

Ja,C, I

Rule 2.

Two adjacent tubes in the same row (

Ja,c. Consequently, the difference in the (

Jac, i

l

~

4 I

j.*

1 1

l j

0249M:49/081288-37 I

i The implementation of this is that if the position (either left or right) of a projected AVB is assumed for a column, then the projections in the j

adjacent columns are also (

j 1**c.

l The arrangement of the AVBs as shown in Figure 8 5 satisfies the rules above and is consistent with the rupture of R9C51. The resulting AVB arrangements, i

based on the projection matrix of Figure 8 5 is shown in Figure 8 6, 1

l 8.1.5 Conclusions l

I

)

The general AVB arrangement surrounding the ruptured tube in North Anna 1, j

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

detailed critical review of the ECT data.

Differences exist in the AVB l

pattern between tube columns 48 49, in which the AVBs appear to be less inserted than previously indicated. The pattern of Figure 8 6 is the best fit i

to the rules which were adopted for determining the position of the AVBs, as l

well as consistent with explanation of the tube failure.

The basis of the review was a projection technique which utilizes data from l

j' tubes one or more rows removed from the actual inserted position of the AVB l

l to determine the position of the AVB.

The intent of the review was to i

establish the positions of the AVBs by confirming or eliminating features of i

AVB alignments such as side to side offsets, etc. of the AVBs adjacent to the I

tubes. Overall, the conclusions regarding the positions of the AVBs around l

)

R9C51 in North Anna 1. Steam Generator C are based on consistency among all j

the available data.

l i

8.2 Test Measurement Uncertainties

{

The descriptions of the peaking factor tests and apparatus were provided in I

Section 5.4.

All practical measures were taken to reduce uncertainties.

1 Nevertheless, some still remain and should be properly accounted for. The important paramoter measured during testing that has a significant impact on 4

I 1

1

~

i 0249M:49/081288 38 1

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 used in a

this analysis based on past experience.

8.3 Test Repeatability During the peaking factor testing of AVB configuration, each test was l

l performed at least two times to confirm 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 l

value of 5% was used in the current uncertainty analysis.

8.4 Cantilever vs b-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. Yhe following assumptions are l

used:

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s a,c I

l 1

l l

1 i

[

i 1

0249M:49/081288-39

~

a,c 1

l 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, 4

The s eparison between a U-bend tube and the model tube involve the eration of an effective velocity associated with the flow perturbation con

• causeo by the AVBs.

(

i i

l t

l Ja.C j

4

\\

0249M:49/081288 40

l I

(

I e

}

l f

f 1

Ja.c. Using these values, the ratio of the effective velocity

{

for the cantilever measuring tube to that for the U bend tube is about l

[

Ja,e for the case treated, f

t A similar evaluation can be made for a Row 10 tube that lies in the i

projection or shadow of an AVB that is inserted to a deptii required to support a Row 9 tube.

(T l

1 l

I I

i f

Ja,c, The net result is that the ratio of the effective velocity for the cantilever

(

tube to that for the U band tube is about (

18'C.

(

l These results indicate that, for the particular assumptions used, the I

cantilever tube model appears to be a reasonable representation of the U bind wig respect to determining relative peaking factors for different AVB configurations. This evaluation also shows that, on the average, the j

magnitude of the systematic uncertairty associated with the use of cantilever tube to simalate the U bend is about (

la c, 8.5 Air vs Steam Water Mixtare 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 j

0249M:49/081288 41

1 l

I velocity and thus a direct factor on a stability ratio, or as a factor on the l

steam velocity only with associated impacts on density, void fraction and

(

dwping. This method leads to a reduction in tube damping which enhances the peaking factor compared to the direct air test value.

For estimating an l

absolute stability ratio, this application of the peaking factor is a best estimate approach. However, for the evaluation of tubes relative to stability ratio criteria, it is more conservative to minimize the peaking factor for the North Anna Unit 1 tube R9C51 through direct application of the I

air test peaking factor. This conservative approach is therefore used for evaluating tube acceptability, i

l Under uniform AVB insertion (or aligned AVB insertion), there are no local open channels for flow to escape preferentially. Therefore, air flow is approximately the same as steam / water flow relative 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 same channel while sterm readily seeks a low resistance passage and thus turns into adjacent open channels. Two phase tests indicate a tendency for steam to preferentially follow the low pressure drop path compared to the water phase.

Based en the above discussion, the Fg are considered to more appropriately dpply to the steam phase. Thus, it follows that mixture mass velocity for the tube susject to flow perturbation can be written as follows:

a.C

~

where O is the vapor density, Dr the water density, F the velocity g

a peaking factor determined from air tests, j

• the nominal superficial vapor g

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

0249M:49/081288 42

. - ~

l

I t

~

~

I a,c l

The Le11ouche Zolotar correlation (algebraic slip model), as used in the ATHOS code, is applied to determine void fraction. Subsequently, mixture 1

density, velocity and damping coefficients for the tube which is not I

supported and subject to flow perturbation is evaluated.

Therefore, similar to the air velocity peaking factor, local scaling factors of mixture density f

and velocity and damping coefficient can be readily determined. Finally, a l

local stability peaking factor for fluid 61astic vibration can be calculated as follows:

r l

aC j

I t

where F is the stability peaking factor, Fd the density scaling factor, s

F the velocity scaling factor, and Fdp the damping coefdicient scaling y

factor, if we use the air velocity peaking factor without translating to steam / water conditions, then

(

~

~ a,c As shown in Table 81 stability peaking f&ctors for the steam / water mixture j

are slightly higher than air velocity peaking factors. The difference between the steam / water and air peaking factors increases as the air peaking j

factor increases.

J For application to tube fatigue evaluations, the ratio of the peaking facter 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 Anr,a R9C51 peaking factor is one of the highest peaking factors. As discussed in Section 8.7, a peaking factor of nearly

(

la.c is determined for the R9C51 tube. The differences between

~

Ja.c. Typical values are shown in Table 8 2.

These results show

(

0249M:49/081288-43 l

\\

l

(

1 i

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

factorevaluation,(

f

~

i Ja.C, l

t l

Comparing the values in the first and last columns of Table 81, it may be noted that the stability peaking factor for steam water is (

la.c higher than the air velocity peaking factor. On the average, the uncertainty l

associated with the conservative use of air velocity peaking factor is

[

18'C.

i l

The conclusion that peaking factor for steam water flow would be higher due I

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 protypic flow conditions. The objective of this study was to axamine 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 ATHOS 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 j

intent of this analysis is on1) to help bound the uncertainty on void J

fractior, effects from extrapolating the air tests to steam water.

First the analysis was conducted with uniformly inserted AVBs in the ATHOS model. The ATHOS results were processed by the FLOV!B 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 changes in void fraction profiles was about [

la.c. This alternate calculation provides independent corroboration of the prior discussion regarding the stability peaking factors under steam water conditions vs in

air, j

0249M:49/081288 44

_ _ - =_ - -.-

l t

8.6 AVB Insertion Depth Uncertainty The most significant uncertainty for the low peaking configurations is not in

[

the test results, but in the determination of actual AVB insertion patterns l

adjacent to specific tubes. The methodology used for ob,taining the AVB insertion patterns from eddy current data can ascertain the AVB location only approximately. The effect on peaking factor resulting from this uncertainty f

is addressed using test results of AVB configurations that varied from one l

anotherbyupto(

Ja.c, Based on maps of AVB insertion depth of various plants, several l

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 i

configuration to a specific configuration.

Figure 8 7 sumarizes the AVB configurations tested.

Position of AVB insertion depth is determined from Eddy Current Test (ECT) data. Positioning of AVB from ECT data reading is subject to uncertainty; its accuracy is probably about (

Ja,c. A change of an AVB l

insertion depth in a given configuration leads to a different configuration.

and thus a different peaking factor. A review of the tested AVB type has l

bean made and results sumarized in Table 8 3.

As can be seen, a decrease in

{

depth of an appropriate AVB tends to decrease the peaking factor, for j

instance,a(

Ja.c.

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

downstream.

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

[

Ja.c, 0249M:49/OS1288 45

i 8.7 Overall Peaking Factor with Uncertainty 1

I As discussed in the previous subsections, there are several aspects to be considered in applying the laboratory test data to steam generator l

These consideration.s were reviewed one at a time in those conditions.

j subsections. This section will integrate the pieces into one set of f

I 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 l

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 (Configurationla).

It is to be noted that, of all the configurations i

tested, configuration Ib produced the highest peaking factor, followed very closely by 4c, la and 5e. This is useful in the sense that it tends to explain why, of all the tubes in service, the R9C51 tube was the one to 1

experience the fatigue rupture, i

It is to be reted 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 affect both the numerator and the denominator in the ratio of peaking factors. The major difference will be in those confiriurations whose peaking factors are significantly lower than that of R9C51. lhe approach employed here is intended to provide that conservative peaking t' actors are employed for such apparently low peaking configurations.

The uniform AVB configuration (24) is sslected as a reference configuration, and the peaking factors of all configurations tested are recomputed on the basis of this reference. As discussed below, some of the test uncertaintics are applied to the reference case to account for its significantly low psaking 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 water mixture. These 0249M:49/081288 46

i j

1 l

l were discussed in more detail in the pr wious subsections.

The magnitude of i

these uncertainties are listed in Table 8 4.

j j

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

together. The total random uncertainties are calculated by [

j j

Ja.c. The RSS value of these is

( Ja 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 j

factor for configuration la (RSC51) is reduced by this amount to yield a l

valueof(

Jacinsteadofthe[

Ja.c appearing in Table 5 2.

j The next three uncertainties in Table 8 4 are systematic uncertainties.

It ceuld be argued that these appear in the peaking factors of both the specific t

tube under consideration and the U C51 tube and are therefore counter balanced. However, the relative magnitude of these may be different, j,

particularly for configurations with much lower peaking than R9C51.

Thereforeitwasjudgedthatthe(

l

).

1'C.

St.tilarly, as noted above, the effect on

{

8

{

peaking factor due to the uncertainty in the field AVB configuration is also l

)

included b this reference casa.

Thut

(

l Ja.c. The i

peaking factor of the reference configuration 2a (Table 8 5) is raised by l

this amount to a value of (

4 1,c, The change in peaking factors of configurations la and 2a resulting from the i

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 i

basis of this reference configuration (2a). These values are displayed in

)

Column 4 of Table 8 5.

i

.O i

j 0249M:49/082488 47 1

l l

Some of the uncertainties were applied to the reference configuration (2a) in l

order to apply them to all low peaking configurations conservatively. Thus, no configuration should have a lower peaking factor than this reference configuration. Therefore, when a peaking factor value less than (

Ja c is calculated for any configuration, (in Column 4 of Table 8 5), it should be l

l altered to [

Ja.c.

Further, for some of the configurations that are l

conceptually similar, the more limiting (higher) value is used.

For example, a peaking factor of (

Ja.c is used for configurations 5a and Sb based on their similarity to configuration Sc.

l l

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

It may be noted that the peaking factors vary in the range (

Ja,c, the RSC51 peaking factor being (

Ja.c. Figure 8 7 snows the final peaking factors with the pictorial representation of the AVB insertion patterns.

Table 8 7 shows the result of applytrg the peaking factors to specific tubes l

in the McGuire #2 and 2 steam generators, o

The overall conclusions from the oaaking factor assessmant 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 described in Sections 8.2 to 8.6.

The largest single uncertainty of (

Ja.cis

]

attributable to uncertainties of up to (

Ja.c on determination of AVB insertion depths from tield eddy current data.

This relatively large uncertainty i, 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.

l l

0249M:49/081288 48

I l

2.

Including uncertainties directed toward conservatively decreasing the l

peaking factor for the North Anna tube R9C51, the final R9C51 peaking l*

factoris(

Ja.c relative to a no flow peaking condition such as l

with uniform AVB insertion depths.

l.

3.

The final peaking factors include peaking effects g* eater than the R9C51 tube (such as configuration 4c) although this is believed to be a consequence of the conservative uncertainty analysis and is not likely to be representative of eqtual peaking effects.

6 O

I l

1 i

e e'

l l

0249M:49/081283 49

l l

l Table 8 1 l

l Stability Peaking Factor Due to Local Velocity Perturbation Scaling Factors for Steam / Water Air Velocity Void Stability l

Peaking Fraction Density Velocity Damping Peaking

Factor, Scaling,

scaling, scaling, Scaling.

Facter, F

F.

F Fd I

I y

V dp 3

t i

a,c I

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.

0249M:49/081288 50

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

i

)

l I

4 l

i 0249M:49/081283 51 1

e Table 8 3 Effect of Local Variation of AVB Insertion 1

l A to B AVB Peaking Peaking Ratio l

Type A Type B Variation Factor A Factor B (8/A) aC s

.g 0

(

l*

i I

l

.a 02(1"'19/081283 52 1

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

_ a,c 1.

Velocity measurement Random 2.

Test repeatability Random 3.

Cantilever vs U-tube Systematic 4.

Air vs steam water mixture Systematic 5.

Fie1d AVB configuration 1

l I

l This is not an uncertainty associated with the test data.

l it results from the inaccuracy in determining the true AVB position in the field using addy current data.

j 0249M:49/081288 53

.\\

Table 8-5 t

Extrapolation of Test Results to Steam Generator Conditions 2

Peaking Factor Test Data with Referenced to Confiauration QLt1 Uncertainties Confia. 2a a,C la lb F

2a 2b 3

4a 4b 4c 4d 4f 4g 4p 4q Sa Sb q

Sc 5e i

6a 6e i

0249M:49/081288 54 1

~

l l

Table 8-6 1

FINAL PEAKING FACTORS I

i Onfiauration Peakina Factor 4

a,c 4

la Ib P

2a 2b 1

3 4a 4b 4c i

4d 4f 4g i

4p 4q 4

Sa Sb Sc Se i

1 3

6a i

6c l*

~

s a

i i

i l

J 024SM:49/081288 55 1

-i

,i

Table 8-7 j

Stability Peaking Factor's fcr Specific Tubes McGuire #2 Steam Peaking Generator Row No Column No Factor

• a,c A

7 9, 10 8

27 8

23 9

18 9

19 9

23 All of the V!am21ning B

8 88 9

33 9

69, 70 9

88 9

92 All of the Remaining C

7 88, 89 8

9 8

17 8

22 8

83, 84 8

89 8

93 9

22 9

93 All of the Remaining D

9 5,6,7 9

107, 108 All of the Remaining The peaking factor is divided by [

la,c to obtain the flow peaking ratio to R9C51 of North Anna 1.

s j

0249M:49/081288 56

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'2 OO O O O O O O u

OO O O 9 0

0. 0

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is

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y,,**

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,)

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l l

l l

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l l

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1 l

l rigure 8-2 Scher".atic of Staggered AVBs 4

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)CaC l

i I

I s

l Figure 8 3 Ayg.Patr' in ECT Trace

G

~

00@O0000 00000 22 ODGOODGG OOOOO 22 0000 000 00000 to

.' G@DDD@DODOOOO O@@D@@@ODOOOO Column 56 55 54 53 52 51 50 49 48 47 46 45 44

$ Plugged Tube Q FaHedTube f.",M*L*%iel2"."C'"'n'^21'" 2"l2?

Figure t 4 North Anna 1. Steam Generator C. AVB Positions critical Review *AVB Visible' Calls

.n-----

/

an__

~

~ i i iEi$35iiiii E 55 nu -

u.

g;,,

....i u-

,,, i i o..

M BE H WHE H ERRE

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aln 5 55n$54f$

$ FM)$,

~-

g gg a gg usu gg 2

2.

.x,,,

2. =. r_

2. =.

C55 C54

.C53 C52 C51 C50 C49 C44 ll,%'",^r7 m u-e u.ume a,e E

• tow SW**

,,e

'High SWe'

}

Figure 8-5 Horth Anna,1, steam,Ge,nerater C.

R9C51 AVB Matrix

o O OO OOOOOO O O O O 12 O OO O O

00 0 0 0 0 tt O OO OOOOOO O.O..O.O to 0 00 00@

000000

.O'OOOOOOOOdOOO 8

$6 55 54

$3 52 51 50 49 48 47 46 45 44 I

i i

i e

a,e Figure 8 6 North Anns R9C51 AVB Final pesitjens

TYPE OF AVB PEAKING FACTOR TYPE OF AVB PEh0NG FACTOR INSERTON INSERTON

~

r I

a beC a,b,c l

u la 49 1b 4p 2a 44-2b Sa l

I 3

5b l

l i

4a!

Sc 4b 5e 4c 6a 4d 6c i

4f

?

Figure 8 7 Final Peaking Factors for McGuire 2 i

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 analysic 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 Table 9-1.

The tube temperature corresponds to the average of the primary-side water temperature and the plate tem,nerature. The resulting tube / 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 (

ja,c Two reference cases were run using the finite element model, the first for a primary-to-secondary side pressure gradient of 1000 psi, and the second for a

(

Ja,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 distribution of stress for the tube outer surface for the two reference cases are provided in Figures 9-2 and 9-3.

Thermal bending stresses due to the thru-wall thermal gradient are ca'Wited to be 7.03 ks! using conventional analysis techniq

m combined stress distribution along the tube length, in Figure 9-4, was obtained by combining the thermal bending stresses and the reference solutions with appropriate multipliers based on 100% power operating parameters.

i 0249M:49/082488-57 i

The maximum axial tensile stress is 18.7 ksi and occurs approximately 0.125 inch above the top surface of the support plate. Adding, for conservatism, the surface stress due to pressure,1.0 ksi, gives an applied mean, stress of 19.7 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 surface, the stress levels change to 10-15 ksi tensile. Combining the applied and residual stresses results in a cumulative mean stress of approximately 35 ksi, assuming tube denting without deformation.

If a tube is dented with deformation, the mean stress is limited by tube yielding.

For the case of dented tubes with deformation, the maximum in determining effect of mean stress was incorporated by using amax " Oy stability ratios and fatigue usage.

9.2 Stability Ratio Distribution Based Upon ATH0S An assessment of the potential for tubes to experience fluid elastic instability in the U-bend region has been performed for each of the tubes in rows eight through twelve. This analysis utilizes FASTVIB, a Westinghouse proprietary finito element based computer code, and PLOTVIB, a post processor to FASTVIB. These codes predict the individual responses of an entire row of steam generator tubing exposed to a location dependent fluid velocity and density profile.

The program calculates tube natural frequencies and mode shapes using a linear finite element model of the tube. The fluid elastic stability ratio V,/Uc (the ratio of the effective velocity to the critical 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 WECAN generated mass and stiffness matrices used to represent the tube are also input to the code.

(WECAN is also a Westinghouse proprietary computer code.) Additional input to tASTVIB/PLOTVIB consists of tube support conditions, fluid elastic stability constant, turbulence constants, and location dependent flow peaking factors.

0249M:49/081288-58

This process was performed for the McGuire #2 steam generator tubes and also for the North Anna Row 9 Column 51 tube (R9C51) using similarly appropriate ATH0S models. Ratios of the McGuire #2 results to those for North Anna Unit 1 R9C51 were generated to produce a quantity that could be used to provide an initial assessment of the McGuire #2 tubes relative to the ruptured tube at North Anna Unit 1.

Figure 9 5 shows the results of this process for each of the rows under investigation. The relative ratios are obtained using the following conditions for McGuire #2 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.

It is to be noted that the stability ratios plotted in Figure 9-5 are composites of all steam generators. 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.

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

This identifies the point where a ten percent reduction in stat;ility ratio l

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 all tubes in Rows 8 through 12 of the McGuire #2 steam generators lay below the 90% line.

0249M:49/081288 59

-r

9.3 Stress Ratio Distribution with Peaking factor An evaluation was performed to determine the ratio of the McGuire #2 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 factors (Table 8-7 factors divided by [

Ja,c) tube size, and bending moment factors. Sections 4.2 and 4.3 contain additional information and describe the calculational procedure used to obtain the results presented 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,

3) Tubes have no AVB support, 4) 10% criteria with frequency effects,

5) location dependent flow peaking effects

6) Tubes are assumed to be dented or undented (both situations were considered, but the evaluation is based on the more limiting, dented case).

A tubs 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 and 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 McGuire #2 tubes in Rows 8 through 12. As in Figure 9 5 for the stability ratio, the stress ratios in Figure 9-6 represent the composite ratios for all McGuire #2 steam generators.

(Refer to Table 9 2 for critical tubes in 0249H:49/081288 60

individual steam generators). These ratios are applicable for tubes that are dented (tube deformation) at 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 corrosion plus magnetite in the crevice without tube deformation. The current tube condi' ions at McGuire #2 correspond to this latter definition of denting.

As can be observed in Figure 9-6, all tubes in Rows 8 through 12 of all McGuire

1. 2 steam generators fall in the acceptance region with respect to U-bend fatigue, even when assumed to be unsupported. With the exceptions of SG-A tubes R12C113, R11C113, R10C113, and R100112, all McGuire #2 Row 10 tubes and above are currently supported.

9.4 Cumulative Fatigue Usage All tubes that are unsupported and have a stress ratio s 1.0 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 t

basis. The stability ratios for the McGuire #2 tubing are based on the current operating parameters and with future operation on the same basis, the tubes are not expected to rupture as a result of fatigue if 1) they meet the stress ratio criteria of 11.0 and 2) their current and future fatigue usage will total less than 1.0.

All tubes in the evaluation have conservatively been considered to be dented with deformation. Based on the above analytes, all McGuire #2 tubes meet the relative stress ratio criteria under the current AVB conditions. Table 9-2 provides a summary of the combined relative stability ratios and the stress ratios for the more salient unsupported tubes in Rows 8 through IP..

J Acceptability of the McGuire #2 tubing for fatigue is accomplished by demonstrating the acceptability of the tube with the highest stress ratio, 0.24 in W-B: R9C88. Assuming the tuJe has been cented since the first cycle and continue to operate under current conditions, the total usage including the remaining term of the operating license would be less than 0.01.

In the event of a future uprating of the plant, the potential for tube fatigue would need to be re evaluated.

0249M:49/082488 61

_y

Reference:

, a,c 9-1 l

0249M:49/0gg4ag.Sg

e Table 9-1 100% Power Operating Parameters McGuire #2 Bounding Values for Mean Stress Calculations 1

Primary Pressure

- 2250 psia Secondary Pressure - 1000 psia i

Pressure Gradient = 1250 psi l

Primary Side Temperature * = 588.3*F Secondary Side Temperature = 544.6'F Tube Temperature

= 566.5'F i

Average of Thot = 618'F and Tcold = 558.6'F.

1 i

i l

l I

0249M:49/081288 62

Table 9 2 j

Summary of McGuire #2 Evaluation of the Salient Unsupported U-bends PEAK RELATIVE STRES M

EDM GEL.

FACTOR STABILITY RATIO (I)

EM{I)

A 7

9 & 10 1.11

<.514

<.07 8

27 1.16

<.554

<.11 28 1.11

.476

.05 9

18 1.16

.564

.10 19 1.11

.540

.08 23 1.36

.647

.21 10 112

.596

.11 113

.414

.02 11 113

.511

.04 12 113

.627

.11 B

8 88 1.31

.554

.11 9

33 1.16

.572

.11 69 & 70 1.11

.548

.08 88 1.36

.663

.24 92 1.16

<.646

<.21 C

7 88 & 89 1.11

<.474

<.05 8

9 1.16

.514

.07 17 1.16

.485

.05 22 1.21

.532

.09 83 & 84 1.11

.474

.05 89 1.36

.569

.13 93 1.16

<.532

<.09 9

22 & 93 1.36

.646

.21 0

9 5-7, 107 1.11

.572

.11

& 108 All 7

(All remaining 1 445 1 93 8

not listed s.445 0 03 9

above) s.510 1 06 (1) All ratios are in comparison to R9C51, North Anna 51, Steam Generator C and include the effect of local flow peaking.

i r

i 0249M:49/081288 63 1

I i

40 f

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l AXISYMMETRIC TUBE MODEL i

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1 Ficure 9-1 Axisymetric Tube Finite Element Model 4,

J i

1 0249M:49/080488 64 i

.---,--m---_---

7

TUBE STRESSES - MODEL D2/D3/D4/E2 i

1000 PSI PRESSURE LOAD CASE

.i 8

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0.2 0.4 0.6 0.8 1

OtST44CE FROW TSP CEPUERLNE. N.

O AXIAL

+

HOOD l

Figure 9-2 Dented Tube Stress Distributions Pressure Load on Tube 4

a

)

0249H:49/080488 65

TUBE STRESSES - MODEL D2/D3/D4/E2 1.0 MIL INTERFERNCE CASE 30 20 j

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Figure 9 3 Dented lube Stress Distributions Interference Load on Tube i

0249H:49/080488 66 L-

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J Figure 9-5 Relative Stability Rattos Ustng MEVF Dependent Doping D7-26-88 McGatre #2 - (Composite of all Steam Generators with timbre 11a T h Peaking)

C249M.49/C60488-68

o.

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=

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J Ftgure 9-6 Stress Ratio vs. Cohari Nunber - Dented CondItton - McGu1re #2 (Composite of all %s utth thbrella Flow Peaking)

C24981:4?/060488-69

-