ML20153D705
| ML20153D705 | |
| Person / Time | |
|---|---|
| Site: | Farley  |
| Issue date: | 07/31/1988 |
| From: | Connors H, Frick T, Hall J WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML17201Q496 | List: |
| References | |
| WCAP-11876, NUDOCS 8809060018 | |
| Download: ML20153D705 (150) | |
Text
. _ - _ ___-_ _ _____ _____ _ __ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -__ __ _. _ _ _ _ - _ _ _
WESTINGHOUSE CLASS 3 WCAP-11876 d
JOSEPH FARLEY UNIT 1 AND 2 EVALUATION FOR TUBE VIBRATION INDUCED FATIGUE July 1988
. AUTHORS: H. J. CONNORS M. H. HU T. M. FRICK A. Y. LEE i J. M. HALL R. E. SMITH G. W. HOPKINS A. C. SMITH J. L. HOUTMAN M. P. PATEL APPROVED: d, T. A. PITTERLE, MANAGER STEAM GENERATOR ENGINEERING WESTINGHOUSE ELEOTRIC CORPORATION
, SERVICE TECHNOLOGY DIVISION P.O. f,0X 3377 PITTSBURGH, PENNSYLVANIA 15230
$88' O
288!*< Si88lhe
A85 TRACT
- On July 15, 1987, a steam generator tube rupture event occurred at the North Anna Unit 1 plant. The cause of the tube rupture has been determined to be high cycle fatigue. The source of the stresses 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 tu flow induced vibr; tion. For tubes without AVB support, local flow peaking effects are a significant contribution to tube vibration amplitudes.
This report documents the evaluation of steam generator tubing at Joseph Farley 1 and 2 for susceptibility to fatigue-induced cracking of the type experienced at North Anna Unit 1. The evaluation utilizes operating conditions specific to
. Joseph Farley 1 and 2 to account for the plant spscific nature of the tube loading and response. The evaluation also includes reviews of eddy current a
data for Joseph Farley 1 and 2 to establish AVB locations. This report provides background of the event which occurred at North Anna, a criteria for fatigue assessment, a summary of test data which suppt.t the analytical approach, field measurement results showing AVB positions, thermal hydraulic analysis results, and calculations to determine tube mean stress, stability ratio and tube stress distributions, and accumulated fatigue usage. This evaluation leads to the conclusion that there are no potentially susceptible tubes in either Farley Unit. No tubes require corrective action to minimize the likelihood of a fatigue induced tube rupture even if tube denting deformation should occur in the future. Consequenty, future inspections for denting deformation are not required for tube fatigue assessments.
s e
l 0209M:49/072588-3 J
SUMMARY
0F ABBREVIATIONS ASME - American Society of Mechanical Engineers ATH0S - Analysis of the Thermal Hydraulics of Steam Generators AVB - Anti-Vib;-ation Bar
. AVT - All Volatile Treatment ECT - Eddy Current Test EPRI - Electric Power Research Institute FFT - Fast Fourier Transform FLOV!B - Flow Induced Vibrations MEVF - Modal Effective Void Fraction OD - Outside Diameter RMS - Root Mean Square Stability Ratio SR TSP - Tube Support Plate
'F - degrees Fahrenheit hr - hour ksi - measure of stress - 1000 pounds per square inch lb - pound mils - 0.001 inch '
MW - mega watt psi - measure of stress - pounds per square inch psia - measure of pressure absolute i
0209M:49/063088-4
1 1
l l
l TABLE OF CONTENTS SECTION 1.0 Introduction 2.0 Summary and Conclusions
2.1 Background
2.2 Evaluation Criteria 2.3 Denting Evaluation 2.4 AVB Insartion Depths 2.5 Flow Peaking Factors 2.6 Tube Vibration Evaluation 2.7 Prior Fatigue Usage 2.8 Overall Conclusion 3.0 Background 3.1 North Anna Unit 1 Tube Rupture Event 3,2 Tube Examination Results ,
3.3 Mechanism Assessment i 4.0 Criteria for Fatigue Assessment 4.1 Stability Ratio Reduction Criteria 4.2 Local Flow Peaking Considerations
- 4.3 Stress Ratio Considerations i
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 l 5.5 References !
r t
I I I
i t
0209M:49/071188 5 i
i TABLEOFCONTENTS(CONTINUED) )
SECTION 6.0 Eddy Current Da':a and AVB Positions
- 6.1 Modified AVB Design 6.2 Eddy Current Inspection 6.3 Eddy Current Data for AVB Positions 6.4 AVB Insertion Depths 7.0 Thermal Hydraulic Analysis 7.1 One Dimensional Relative Stability Ratio Calculation Methodology and Justification 7.2 ' Relative Stability Ratio Calculations for Farley 7.3 3 D Tube Bundle Flow Field for Reference Series 51 Steam Generator i
8.0 Peaking Factor Evaluation 8.1 North Anna 1 Configuration 8.2 Test Measurement Uncertainties 8.S Test Repeatability !
8.4 Cantilever vs U Tube 8.5 Air vs Steam Water Mixture 8.6 AVB Insertion Depth Uncertainty :
l 8.7 Overall Peaking Factor with Uncertainty 9.0 Structural and Tube Vibration Assessments 9.1 Tube Mean Stress ,
9.2 Stability Ratio Distributions Based Upon ATHOS 9.3 Stress Ratio Distribution j 9.4 Cumulative Fatigue Usage i
I i
0209M:49/071188 6 i
LIST OF FIGURES FIGURE
_' 1-1 Modified. AVBs Installed in Joseph Farley 1 and 2 Steam Generators 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 Examination of Fracture Surface of Tube R9C51, S/G "C" Cold Leg, North Anna Unit 1
+
33 Calculated 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 43 Fatigue Curve for Inconel 600 in AVT Water Comparison of Mean Stress Correction Models 44 Modified Fatigue with 10% Recuttion 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 - A 5-3 Instability Constants, A, Obtained for Curved Tubes from Wind Tunnel Tests on the 0.214 C:d'a U-Bend Model 54 Damping vs. Slip Void Fraction 0209M:49/071188-7
LISTOFFIGURES(Continued)
- f.M E E 5-5 overall View of Cantilever Tube Wind Tunnel Model 5-6 Top View of the Cantilever Tube Wind Tunnel Medal 5-7 Fluidelastic Vibration Amplitude with Non-Uniform Gaps 5-8 Typical Vibration Amplitude and Tube /AVB Impact Force Signals for Fluidelastic Vibration with Unequal Tube /AVB Gaps 59 Conceptual Design of the Apparatus for Determining the Effects on Fluidelastic Instability of Columnwise Variations in AVB Insertion Depths
- 5-10 Overall View of Wind Tunnel Test Apparatus b ll Side View of Wind Tunnel Apparatus with Cover Plate: Removed to ,
Show Simulated AVBS and Top Flow Screen 5-12 AVB Configurations Tested for Farley 1 and 2 ,
5-13 Typical Variation of RMS Vibration Amplitude with Flow Yciocity for Configuration la in Figure 5-12 i 6-1 AVB Insertion Depth Confirmation 6-2 Joseph Farley 1 - Steam Generator 'A' - AVB Positions 6-3 Joseph Ferley 1 Steam Generator 'B' - AVB Positions 6-4 Joseph Farley 1 - Steam Generator 'C' - AVB Positions 65 Joseph Farley 2 - Steam Generator 'A' - AVB Positions 0205M:49/071188 8
LISTOFFIGURES(Continued)
FIGURE 66 Joseph Farley 2 - Steam Generator 'B' - AVB Positions 67 Joseph Farley 2 - Steam Generator 'C' - AVB Positions 7-1 Comparison of Relative Stability Ratios Calculated From 10 and 30 Methods 7-2 Plan View cf ATHOS Cartesian Model for Reference Plant 7-3 Elevation View of ATHOS Cartesian Model for Reference Plant 7-4 Plan View of ATHOS Cartesian Model Indicating Tube Layout t'
7-5 Flow Pattern on Vertical Plane of Symmetry 7-6 Lateral Flow Pattern on Horizontal Plane in the U-Jend Region 7-7 Lateral Flow Pattern on Top of Tebatheet 7-8 Tube Gap Velocity and Density Distributions for Tube at R10/C3 79 Tube Gap Velocity and Density Distributions for Tube at R10/l20 7-10 Tube Gap Velocity and Density Distributions for Tube at R10/C40
- 7-11 Average Velocity and Density in the Plane of the U Bends Normal to Row 10 0209M:49/071188-9
l LIST 0FFIGURES(Continued)
ElElE 81 Original North Anna AVB Configuration 82 Schematic of Staggered AVBs 83 AV8 'Patr' in ECT Trace 84 North Anna 1, Steam Generator C: AVB Positions Critical Review 'AVB Visible' Calls 8-5 North Anna 1, Steam Generator C, R9C51 Projection Matrix 86 North Anna R9C51 AVB Final Projected Positions 8-7 Final Peaking Factors for Farley 1 and 2.
9-1 Axisy metric Tube Model 92 Dented sube Stress Distributions Pressure Load on Tube 93 Dented Tube Stress Distributions Interference Load on Tube 94 Dented Tube Stress Distributions Combined Stress Results Joseph Farley I and 2 95 Relative Stability Ratio Using MEVF Dependent Damping 96 Stress Ratio Vs. Column Number Dented Condition i
0209M:49/071188-10
L!$T OF TABLES IARLE 21 Farley 1 Tubes Examined for Denting and Corrosion 22 Farley 2 Tubes Examined for Denting and Corrosion 4-1 Fatigue Usage per Year Resulting From Stability Ratio Reduction 51 Wind Tunnel Test on Cantilever Tube Model 52 Fluidelastic Instability Peaking Ratios for Columnwise Variations in'AVB Insertion Depths 61 Summary Listing of Unsupported Tubes 7-1 Typical Fa: ley Operating Conditions and Relative Stability Ratio Predictions 81 Stability Peaking Factor Due to Local Velocity Perturbation l L
82 Comparison of Air and Steam Water Peaking Factor Values 83 Effect of Local Variation of AVB Insertion l
l 84 Uncertainties in Test Data and Extrapolation '
1 i
85 Extrapolation of Test Results to Steam Generator Conditions l l
8-6 Final Peaking Factors :
2 l l
8-7 Stability Peaking Factors for Specific Tubes [
I i
0209M:49/071188 11
P M Y2%%%M M.9:hW M LISTOFTABLES(Continued) f TABLE 9-1 100% Power Operating Conditions for Joseph Farley 1 and 2 92 Joseph Farley 1 and 2 Evaluation of Salient Unaupported U Bends 9-3 0'isposition Criteria Relative to U-bend Fatigue t
0209M:49/071188-12
, ~ . - - - - - - . - __ _ _ _
1.0 INTRODUCTION
This report documents the evaluation of steam generator tubing at Joseph Farley 1 and 2 for potential for fatigue-induced cracking of the type experienced at North Anna Unit 1 in July, 1987. The evaluation includes one dimensional extrapolation from a three dimensional flow analysis of a similar reference
. steam generator, air-tests performed to support the vibration analytical procedure, field measurenients to establish AVB locations, structural and vibration analysis of selected tubes, and fatigue usage calculations to predict cumulative usage for critical tubes. The evaluation utilizes operating conditions specific to Joseph Farley 1 and 2 in order to account for plant specific features of the tube loading and response. Furthermore, the evaluation is based on the current Farley tube bundle configuration incorporating modified AVBs. A sketch of the modified AVBs is shown in Figure 1 1. Con ~ sideration is also given to previous operation with the as built AVBs.
Section 2 of the report provides a sumary of the Joseph Farley 1 and 2 evaluation results and overall conclusions. Section 3 provides background f;r the tube rupture event which occurred at North Anna Unit 1 including results of the examination of the ruptured tube and a discussion of the rupture mechanism. The criteria for predicting the fatigue usage for tubes having an environment conductive to this type of rupture are discussed in Section 4.
Section 5 provides a sumary of test data which supports the analytical vibration evaluation of the candidate tubes. A summary of field measurements used to determine AVB locations and ultimately to identify unsupported tubes is provided in Section 6. Section 7 provides the results of a thermal hydraulic l analysis to estabitsh flow field characteristics at the top support plate which i 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.
l
- presents results of the structural and vibration assessment. This section l
detemines tube mean stress, stability ratio and tube stress distributions, and j
- accumulated fatigue usage, fort: g the heis for the conclusions for Joseph Farley 1 and 2. ,
1 i
n l 0209M:49/063088-13
- i N\ t I
( h 7
'. [~ -
l 5 i
~'
~
/ .-
,- E ;
'116:
~
iis .
i :
g ,$\
- . / .
~
p -
- l*/._
d.
Y
[
,W f I
- f ']' f
- 4. * ' / -
p ,
, $N$ aki; h, ,$$1,'$ll!!!!lf<' 1 it!llill;I l! o ttil ti i ti t t y 4 ()
~
.\
I
\Y \
~
\
\
f
. \ - - - .
.\ %
1wr
\ .52Ei N- '
v_i .
t i rigure 1-1 Modified AVBs Installed in Farley 1 and 2 Steam Generators. 5G18 Has a slightly Different Retaining Mechanism outside of the Tube Bundle.
0209M:49/071188-14
2.0 SUMARY AND CONCLUSIONS The Joseph Farley 1 and 2 steam generators have been evaluated for the
.' susceptibility of unsupported U-bend tubes with denting at the top tube support plate to a fatigue rupture of the type experienced at Row 9 Column 51 (R9C51) '
- of Steam Generator C North Anna 1.
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. The unstable condition prevailed in the R9C51 tube when the tube experienced denting at the support plate. A combination of conditions were present that led to the rupture. The tube is not supported by ;
an anti-vibration bar (AVB), has a higher flow field due to local flow peaking as a result of non-uniform insertion depths of AVB's, has reduced damping because of denting at the top support plate, and has reduced fatigue properties consistent with a lower bound fatigue curve for the tube material in an all volatile treatment (AVT) water chemistry environment and because of 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 10% reduction in stability ratio that .
provides at least a 58% reduction in stress amplitude (to < 4.0 ksi) for.a Row 9 tube in the North Anna 1 steam generators. 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 a 40 year fatigue life objective. This same criteria is
- being appi.ied as the principal criteria in the evaluation of Farley tubing, o The determination of stability ratio is the evaluation of a ratio of velocities, the effective velocity divided by the critical velocity. A value greater than unity (1.0) indicates instability. The stress ratio is the l expected stress amplitude in a Farley tube divided by the stress amplitude for !
l the North Anna 1, R9C51 tube. !
l
! 0209M:49/072588-15
Assuring a stress amplitude that corresponds to a stability ratio equivalent to los lower than R9C51 of North Anna 1 is required of Row 9 tubes in Joseph Farley 1 and 2 as well as in larger and smaller U bend radius tubes. Prior to the antivibration bar modification (AVB), Row 11 and Row 12 tubes are expected to have had AVB support and consequently negligible prior fatigue usage. This permits the consideration of a modification of the 10% criteria to a less
. conservative criteria for these row tubes. However, in spite of the low likelihood for any significant fatigue usage, the 10% criteria basis has been conservatively retained for all tubes in Joseph Farley 1 and 2. Displacements are computed for these tubes using relative stability ratios to R9C51 of North Anna 1 and an appropriate power law relationship based on instability displacement versus flow velocity. Different U-bend radius tubes will have different stiffness and frequency and, therefore, different stress and fatigue usage per year than the Row 9 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 cumulative fatigue usage for the Jowh Farley tubing based on the reference fuel cycle analyzed. ,
j The stability ratios for Joseph Farley 1 and 2 tubing, the corresponding stress and amplitude, and the resulting cumulative future fatigue usage must be evaluated relative to the ruptured tube at Row 9 Column 51, North Anna 1 Steam i
Generator C, for t e 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 provides a range of initiating stress amplitudes, but can only bound the possible stability ratios that correspond to these stress amplitudes. Therefore, to minimize the influence of uxertainties, the evaluation of Joseph Farley 1 and 2 tubing has been bued on relative stability ratios, relative flow peaking factors, and relative stress ratios, j-l The criteria for establishing that a tube has support from an AVB and therefore lt eliminate it from further considerations is that at least one sided support is j present to the tube centerline. Test results show that one sided AVB support I l- is sufficient to limit the vibration amplitude for fluidelastic excitation, i
i 0209M:49/063088 16
AVB support at the tube centerline is established by analysis of eddy current (EC) measurements and is a key factor in the assessment of fatigue failure susceptibility since the AVB positions determine the local flow peaking factors. The local flow peaking factor is a direct factor on the apparent
- stability ratio and a small percentage change causes a significant change in stress amplitude. The relative flow peaking factors for Joseph Farley 1 and 2 tubing without direct AVB support have been determined by instability tests.
These factors have been applied to relative stability ratios determined by 3 0 tube bundle flow analysis adjusted to Faricy conditions and the combined relative stability ratio used in the stress ratio determination.
2.3 Denting Evaluation i All Row 11 tubes and ten (10) tubes in each of Rows 8, 9, 10 and 12 were evaluated for tube denting (with deformation) and top support plate corrosion (Tables 21 and 2 2). Essentially all tubes were found to have top tube support plate corrosion plus magnetite in the crevice which corresponds to the NRC definition of ' denting" in NRC Bulletin 88-02. None of the tubes in Farley I were found to have deformation due to denting. Se,me of the tubes in Farley 2, indicated in Table 2-2, have possible, but questionable, tube deformt. tion.
2.4 AVB Insertion Depths The eddy current data was reviewed to identify individual legs of the AVBs and to provide angular data on AVB le ations. To locate the lowest penetration of each AVB at the hinge olate, extrapolation methods have been applied to determine the depth of penetration and the distance between AVB bars at the lowest measurable row number.
Overall, the evaluation shows that all Row 12 tubes are supported by AVBs.
Row 12 is the design depth of insertion for the modified AYBs except for a 1 special AVB at each side of the tube bundle which penetrates to about Row 9.
5 The evaluation also shows that the AVBs have very uniform insertion depths with the bottom hinge i. late located between Rows 11 and 12. Only a few Row 11 tubes were found to be supported by the AVBs. Haps of the AVB insertion depths are shcwn in the attached figures. Figures 6.2, 6.3 and 6.4 show AVB locations in
- Farley 1. Figures 6.5, 6.6 and 6.7 show AVB locations in Farley 2.
0209M:49/071183-17
2.5 Flow Peaking Factors
. Tests were performed to determine the flow peaking factors for Joseph Farley 1 and 2 AV8 configurations relative to the North Anna R9C51 peaking factor. The modified AVB design was used in the tests for the Joseph Farley 1 and 2 values and the original AVB design was used for R9C51. Since the Joseph Farley 1 and 2 AVBs show uniform AVB insertion to one tube pitch, the tests focused on sensitivity to uncertainties in determining the AVB depth of insertion. The test results were used to define an upper bound of the ratio for ' uniform AVB insertion" relative to the R9C51 configuration. Based on the AVB maps, it is found that the flow peaking affects are bounded by the "uniform AVB insertion" ratio relative to R9C51.
2.6 Tube Vibration Evaluation One-dimensional analyses have been used to develop a relative stability ratio between Farley and another Model 51 unit for which three dimensional vibration analyses have been performed. The ID based adjustments lead to a 2.4% increase in stability ratios relative to the unit used for the 30 analyses. Based on applications of the 10 adjustment ratio and comparisons with direct 3D ratios for other analysis results, it is estimated that the 2.4% adjustment is accurate to better than 1%. The assumed operating conditions for the 1D analyses envelop the operating conditions provided by Alabama Power for both Unit 1 and 2.
Figures 9 5 and 9 6 show the Farley adjusted stability and stress ratios relative to North Anna 1 tube R9C51. These figures are based on no flow peaking for the Farley tubes and are applicable to both Unit 1 and 2. The overall criteria is that the relative stress ratios be < 1.0.
The results show that, based on the 1D adjusted analyses, all Farley tubes meet the relative stress ratio criteria under the assumption of tube denting with i
deformation and no flow peaking (Figure 9 6). The stress ratios based on clamped tube conditions with no tube deformation is conservatively assumed to
. correspond to a tube with top TSP corrosion plus magnetite in the crevice (NRC definition of denting). The evaluation is based on the more conservative assumption of dented tubes, however.
0209M:49/063088 18
No tubes require corrective action to minimize the itkelihood of a fat,igue induced tube rupture even if tube denting deformation should occur in the
(, future. Consequently, future inspections for denting deformation are not required for tube fatigue assessments.
2.7 PRIOR FATIGUE USAGE Only Row 11 and smaller tubes in Farley 1 and 2 are unsupported and subject to future fatigue usage. These tubes meet stress ratio criteria based on continued operation at the same stability ratio. The predicted fatigue usage for the limiting tube is -0.01 per year or about 0.4 over a period of operation of approximately 40 years. The original AVB locations and tube fatigue usage, prior to installation of the AVB modificaiton, were not determined. By the prior design, Row 11 tubes are expected to have had AVB support and consequently negligible prior fatigue usage. Even though AVB position evaluations for other units of similar design have indicated an occasional Row 11 tube that was not supported, the frequency of such an occurrence is less than 0.5% based on a sample of over 2800 tubes. Table 9 3 provides justification for acceptance of Row 11 tubes based on analyses which indicate that Row 11 tube stress levels in Farley Units 1 and 2 would not lead to rapid propcgation of postulated or existing cracks.
2.8 Overall Conclusion Based on the results of the tube fatigue evaluation, it is concluded thit no modification, preventive tube plugging, or other measure is necessary in Joseph Farley 1 and 2 to preclude a fatigue rupture similar to the North Anna 1 event.
t 0209M:49/072588 19
Table 8-1 FARLEY 1 TUSES EXAN!NED FOR DENTIN 8 AND CORR 0510N R0W COLUMN ,
SG A 8 6 15 9 6-15 10 6 9, 11-16 11 All 12 27, 28, 50 59 13 27, 28, 51-59 <
SG B 8 2 8, 14-16 9 2 4, 16, 88 93 10 2-4, 16, 88 93
- - 11 All 12 2-4, 83 93 l 13 3, 4, 14, 16, 17, 88 92 i j SG C 8 25 32, 48, 57 ,
! 9 25 32, 48, 49 10 25 32, 48, 49 11 All ;
12 11 17, 26-28 i i
13 11-17, 26 28 i
f i
l Note: None of the tubes were found to have deformation due to denting. All l tubes show the presence of corrosion plus magaetite at the top tube
- l. i support plate.
s
(
i l
l 0209M:49/063088-20 ;
Table 2-2 FARLEY 2 TUSES EXANINED FOR DENTING AND CORR 05!0N I
- R0W COLUPW SG A 8 55, 562 , 57, 61, 42, 70 74 9 10 12, 132 , 14 16, 60, 43, 65 10 102 , 112 , 12, 132, 14 16, 60, 63, 65 l 11 All 12 102 , }12, 12, 13 2, 14 16, 60, 63, 65 13 10 16, 60, 63, 65 SG B 8 55 57, 60, 61, 64, 66, 67, 70, 71 9 27-31, 33 37 f
10 27 31, 33-37 l 11 All i
~
12 27 31, 33 37 !
l 13 27-36 '
I SG C 8 7-16 9 52 55, 60, 65, 67-70
- 10 52 55, 57, 65, 67-70 j j
11 All j 12 53 55, 57, 58, 65, 67 70 ;
13 53 55, 57, 58, 65, 67-70 :
I :
1 Notes:
. 1. All tubes show presence of corrosion plus magnetite at the top TSP. !
i j5 2. Possible, but questionable, indications of small tube deformation {
! attributed to denting, j i
l \
I i :
l 0209M:49/063088 21 I
3.0 BACKGROUND
On July 15, 1987, a steam generator tube rupture occurred at the North Anna <
Unit 1. The ruptured tube was determined to be Row 9 Column 51 in steam
.' generator 'C'. The location of the opening was found to be at the top tube support plate on the cold leg side of the tube and was circumferential in
- orientation with a 360 degree extent.
3.1 North Anna Unit 1 Tube Rupture Event l
The cause of the tube rupture has been determined to be high cycle fatigue.
The source of the stresses associated with the fatigue mechanism has been determined to be a combination of a mean stress level in the tube and a superimposed alternating stress. The mean stress has been determined to have been increased to a maximum level as the result of denting of the tube at the l top tube support plate and the alternating stress has been determined to be due to out of-plane deflection of the tube U bend above the top tube support caused by flow indu:ed vibration. These stresses are consistent with a lower bound fatigue curve for the tube material in an AVT water chemistry environment. The vibration mechanism has been determined to be fluid elastic, based on the magnitude of the alternating stress.
A significant contributor to the occurrence of excessive vibration is the reduction in damping at the tube to tube support plate interface caused by the denting. Also, the absence of antivibration bar (AVB) support has been concluded to be required for ruuisite vibration to occur. The presence of an AVB support restricts tube motion and thus precludes the deflection amplitude required fo; fatigue. Inspection data shows that an AVB is not present for che Row 9 Column 51 tube but that the actual AVB installation depth exceeded the minimum requirements in all cases with data for AVBs at many other Row 9 tubes. Also contributing significantly to the level of vibration, and thus loading, is the local flow field associated with the detailed geometry of the steam generator, i.e., AVB insertion depths. In addition, the fatigue properties of the tube reflect the lower range of properties expected for an 0209M:49/063088 22
l AVT environment. In sunmary, the prerequisite conditions derived from the I evaluations were con:1uded to be:
Fatiaue Raouirements Prereauisite Conditions Alternating stress Tube vibration
- Dented support i
. Flow excitation
- - Absence of AVB Mean stress Denting in addition l to applied stress i i Material fatigue properties AVT environment i Lower r, ge of l properties !
3.2 Tube Examination Results Fatigue was found to have initiated on the cold leg outside surface of Tube l' R9C51 innediately above the top tube support plate. No indications of significant accompanying intergranular corrosion was observed on the fracture l face or on the immediately adjacent 00 surfaces. Multiple fatigue initiation l sites were found with major sites located at 110', 120', 135' and 150', ,
Figure 3-1. The plane of the U bend is located at 45' with the orientation
- system used, or approximately 90' from the geometric center of the initiation zone at Section D D. High cycle fatigue striation spacings approached 1 l
- micro inch near the origin sites Figure 3 2. The early crack front is believed a to have broken through wall at a position of from approximately 100' to 140'F. From this point on, crack growth is believed (as determined by l 2
striation spacing, striation direction, and later observations of parabolic
,- dimples followed by equiaxed dimples) to have accelerated and.to have changea direction with the resulting crack front running perpendicular to the
! circumferential direction. '
i 1
i l j
l 0209M:49/063088 23 f
, t
3.3 Mechanism Assessment 4
To address a fatigue mechanism and to identify the cause of the loading, any loading condition that wot'.d cause cyclic stress or steady mean stress had to be considered. The analysis of Normal, Upset and Test conditions indicated a relatively low total number of cycles involved and a corresponding low fatigue
~
usage, even when accounting for the dented tube condition at the plate. This analysis also showed an axial tensile stress contribution at the tube 00 a short distance above the plate from operating pressure and temperature, thus providing a contribution to mean stress. Combining these effects with denting deflection on the tube demonstrated a high mean stress at the failure location. Vibration analysis for the tube developed the characteristics of first mode, cantilever response of tha dented tube to flow induced vibration for the uncracked tube and for the tube with an increasing crack angle, beginning at 90' to the plane of the tube and progi ning around on both sides to complete separation of the tube.
Crack propagation analysis matched cyclic deformation with the stress intensities and striation spacings indicated by the fracture inspection and analysis. Leakage data and crack opening analysis provided the relationship between leak rate and circumferential crack 1cngth. Leakage versus time was then predicted from the crack growth analysis and the leakage analysis with initial stress amplitudes of 5, 7 and 9 ksi. The comparison to the best I estNte of plant leakage (performed after the event) showed good :greement, Figure 3-3, 1
Based on these results, it followed that the predominant loading mechanism
! responsible is a flow-induced, tube vibration loading mechanism. It w&s shown 1
that of the two possible flow-induced vibration mechanisms, turbulence and fluidelastic instability, that fluidelastic instability was the most probable l' cause. Due to the range of expected initiation stress amplitudes (4 to 10ksi),
the fluidelastic instability would be limited in displacement to a range of l
approximately ( Ja c. This is less than the distance l between tubes at the apex, ( Ja c. It was further confirmed that l' displacement prior to the rupture was limited since no indication of tube to l tube contact in the U-bend (apex region) was evident in the eddy-current signals for adjacent tubes.
0209M:49/072588 24
Given the likelihood of limited displacement, fluidelastic instability, a means of establishing the change in displacement, and corresponding change in stress amplitude, was developed for a given reduction in stability ratio (SR). Since the rupture was a fatigue mechanism, the change in stress amplitude resulting l 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 0.02 for a tube similar to Row 9 Column 51 at North Anna Unit 1.
~
i 0209M:49/063088 25
D-0 - s g
ID y '
C
- C-C C
q zw Region of Herringbone f Pattern ,
I g /
- 9o. .
- no.- ;
i s I
B
- 3*8 F E-E
' 0 A
l A
A-A N TAB l s F-F
/
!
- Co4rse Texture and Dimpled e Rupture
+
( Indicatas Origins i:
Figure 3-1 Approximate Mapping of Fracture Surface of Tube R9C51
. S/G 'C' Cold Leg, North Anna Unit 1 0209M:49/062988-26
t l
l l
5 = 1.5/1.6 y in.
l Heavy
- Oxida t l
Att1ck j 5 ar21 y in.
l g
3 = 1.0/1.85 y in. 180' 3-C j
i $ Parabolic l
~ 80* 270' - l 1-G Dirwies
/ and
~
V Internal Necking l 38 l
5 = 2.8/4.0 v in. h
\
l j g.g
. a d, pe,n[d !
I Nearly Equi-Axed 5 = 8.1/6.9 y in. Dimples l
Note: Arrows Indicate Direction of Fracture Propagation Figure 3-2 Schematic Representation c/ Features Observed During TEM Fractograhic Examination of Fracture Surface of Tube R9C51, S/G 'C' Cold Leg, North Anna Unit 1 0209M:49/063088 27
s::- : l l l j l l l l l l l Calculated and observed leak rates versus time.
Observed values based on gaseous species condenser air ejector g SIGMA A = 5 KS!
@ SIGNA A = 7 MSI ,
g SIGMA A = 9 KSI l a a O Ar-d1 0 Xe-135 g see. ~ g gp_g7 c
< 1
% i o x see- -
- g .-
/
/-
o a so-- --
l l 0 l : : : : : : : : : :
- s. s see. see. m. as m sua I
I l TIME (Minutes) l l.
i:
Figure 3-3 Calculated and Observed Leak Rates Versus Time l
0209M:49/063088-28
l 4.0 CRITERIA FOR FATIGUE ASSESSMENT Evaluation against criteria to show that Joseph Farley 1 and 2 steam generator tubing will not rupture by fatigue in the manner of North Anna Unit 1 can only
." be done by an assessment relative to the Row 9 Column 51 tube of Steam Generator C, North Anna Unit 1, since,1) methods for direct analytical prediction of actual stability ratios incorporate greater encertainties than a relative ratio, 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 evaluetion was done on a relative basis to Row 9 Column 51 and a 10% reduction ',n stability ratio criteria was established to demonstrate that tubes left in service would be expected to have sufficiently low vibration stress to preclude future fatigue rupture events.
To accomplish the necessary relative assessment of Joseph Farley 1 and 2 tubing to Row 9 Column 51 of North Anna Unit 1, several criteria are utilized. First, stability ratios are calculated for Joseph Farley 1 and 2 steam generators based on flow fields predicted by 3 D thermal hydraulic models end ratioed to tha stability ratio for Row 9 Column 51 at North Anna Unit 1 based on a flow field obtained with a 3-D thermal hydraulic mods 1 with the sane degree of refinement. These ratios of stability ratio (called relative stability ratios) for each potentially unsupported U-bend in the Joseph Farley 1 and 2 steam generators shnuld be equivalent to 10.9 of R9C51, North Anna 1 (meeting the 10% reduction in stability ratio criteria). This provides the first level of screening of susceptible tubc incorporating all tube geometry and flow field differences in the tube dyeamic evaluation. It has the inherent assumption, however, that each tube has tne samo local, high flow condition present at Row 9 Column 51, North Anna Unit 1, and does not account for tube geometry differences in the stress calculation. Te account for these differences, flow peaking factors can be incorporated in th:: relative stability ratios or, as noted below, in the relative stress ratios.
0209M:49/063008-29
l The second criteria is to obtain stress ratios, the ratio of stress in the Joseph Farley 1 and 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 Coltan 51 (R9C51) for the tube of interest is
,- equivalent to 1 0.9, require the stress ratio to be 11.0. The stress ratio incorporates the tube geometry differences with R9C51 in relation to the stress calculation and also incorporates the ratio of flow peaking factor for the Joseph Farley 1 and 2 tube of interest to the flow peaking factor for R9C51 j (flow peaking factor is defined in Section 4.2). This should provide that all tubes meeting this criteria have stress amplitudes s 4.0 ksi.
4.1 Stability Ratio Reduction Criteria For fluidelastic evalui. tion, stability ratios are determined for specific configurations of a tube. These stability ratios represent a measure of the potential for flow-inouced tube vibration during 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 mechanisms.
The maximum modal displacement (at the apex of the tube) is linearly related to the bendinl 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 possiole for an unstable, fixed boundary condition tube to deflect an amount in the U bend which will produce fatigue inducing stresses.
The major featuros of the fluideiastic mechanism are 111uster.ted in Figure
( 4-1. This figure shows the displacemen', response (LOG D) of a tube as a I function of stability ratio (LOG SR). A straight-line plot displayed on log log coordinates implies a r91ation of the form y = A(x)n, where A is a constant,
. x is the independent variable, n is the ex'ponent (or power to which x is raised), and y is the dependent variable. Taking logs of both sides of this
- equation leads to the slope-intercept form of a straight-line equation in log form, ly y c + n log x, where c - log A and represents the intercept and n
. is the slopr:. In our case the independent variable x is the stability ratio SR, and the dependent variable y is tube (fluidelastic instability induced) disp 17. comer.t response D, and the slope n is renamed s.
0:09M:49/063088-30
I From experimental results, it is known that the turbulence response curve (on log-log coordinates) has a slope of approximately [ la,b,c. Test results
. also show that the slope for the fluidelastic response depends somewhat on the instability disolacement (response amplitude). It has been shown by tests that a slope of ( Ja,b,c is a range of values corresponding to displacement amplitudes in the range of ( Ja c, whereas below
, [ ]a,c are conservative values.
The reduction in response obtained from a stability ratio reduction can be expressed by the following equation:
a,c where 03 and sri are the known values at the point corresponding to point 1 of Figure 4-1 and D2 and SR2 are values corresponding to any peint lower on this curve. Therefore, this equation can be used to determines the reduction in displacement response for any given reduction in stability ratio.
This equation shows that there is benefit derived from even a very small percentage change in the stability ratio. It is this reduction in displacement for a quite small reduction in stability ratio that formed the basis for demonstrating that a 10% reduction in stability ratio would be sufficient to prevent Row 9 Column 51 from rupturing by fatigue.
i The fatigue curve developed for the North Anna Unit 1 tube ed R9C51 is from
( ,
1 i
. Ja,c. Thus,
- - a,c l
l . -
0209H:49/061588-31
where, a, is the equivalent stress amplitude to aa that accounts for a maximum stress of yo , the yield strength. The 13 sigma curve with mean stress effects is shown in Figure 4-2 and is compared to the ASME Code
. Design Fatigue Curve for Inconel 600 with the maximum effect of mean stress.
~
The curve utilized in this evaluation is clearly well below the code curve reflecting the effect of an AVT environment on fatigue and (
~
]a,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 [ ]a,c shown in Figure 4-3. With a (
]a,c, the [
. Ja,c, Tne assessment cf the benefit of a redcetion in stability ratio b;oins with the ralationship betwe3n stabiitty ratio and deflection. For a specific tube geometry, the displacement change is directly proportional to change in stress so that stress nas the same relationship with stability ratio, a,c
= .
The slope in this equation can range from ( }a,c on a log scale depending on the amplitude of displacement. Knowing the stress resulting from a change in stability ratio from sri to SR2 , the cycles to failure at the stress amplitude was obtained from the fatigue curve. A fatigue usage per year 2
was then determined assuming continuous cycling at the natural frequency of the tube. The initial stress was determined to be in the range of 4.0 to 10.0 ksi by the fractography analysis.
0209M:49/061588-32
It was further developed that the maximum initiating stress amplitude was not more than 9.5 ksi. This was based on (
Ja,c. The corresponding stress level is 5.6 ksi.
The maximum stress, 9.5 ksi, would be reduced to [ Ja,c with a 10%
reduction in stability ratio and would have a future fatigue usage of
( 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 ratio and would have future fatigue usage of ( Ja,c per year, Figure 4 5.
Subsequent to the return to power evaluation for North Anna Unit 1, the time ,
l-history of operation was evaluated on a normalized basis to the last cycle.
C la,c, cumulative fatigue usage may then be computed to get a magnitude of alterneting stress for the last cycle that results in a cumulative usage of 1.0 for the nine-year duty cycle. The result of the iterative analysis is that the probable stress associated with this fatigue curve during the last cycle of operation was approximately (~ .]a c for R9C51, North ,
. Anna Unit 1, Steam Generator C, and that the major portion of the fatigue usage came in the second, third and fourth cycles. The first cycle was a conservatively omitted, since denting is assumed, for purposes of this ,
analysis, to have occurred during that first cycle. Based on this evaluation, the tube fatigue may have been occurring over most of the operating history of North Anna Unit 1.
0209M:49/063088-33
, , , , - - - - - - - - - - . , _ - - - - - - - - - - - - - - - - - ,,,._n---,w.,-- -
A sil31ar calculation can be performed for the time history of operation assuming that (
ja c,
. On this basis, the effect of a 10% reduction in stability ratio is to reduce the stress amplitude to 4.0 ksi and results in a future fatigue usage of
( Ja,c, Other combinations of alternating stress and mean stress were evaluated with
-3 sigma and -2 sigma fatigue curves to demonstrate the conservatism of the 10% reduction in stability ratio. Table 4-1 presents the results of the cases analyzed clearly demonstrating that the 10% reduction in stability ratio combined with a -3 sigma fatigue curve and with maximum mean stress effects is conservative. Any higher fatigue curve whether through mean stJ]ss, mean stress model, or probability, results in greater benefit for the same reduction in stability ratio. Further, for any of these higher curves, a smaller reduction in stability ratio than 10% would result in the same benefit. In
. addition, there is a large benefit in terms of fatigue usage for relatively small changes in the fatigue curve.
4.2 Local Flow Peaking Considerations Local flow peaking ic a factor on stability ratio that incorporates the effect on local flow velocity, density and void fraction due to non-uniform AVB :
insertion depths. The flow peaking factor is applied directly to the stability ratio obtained from thermal-hydraulic analysis that does not secount for these local geometry sffects. Being a direct factor on stability ratio, a small ,
percentage ir. crease can result in a significant change in the prediction of tube response. <
Since the evaluation of Joseph Farley 1 and 2 is relt.tive to R9C51, North Anna Unit 1, the flow peaking factors are also applied as relative ratios, i.e., a
, ratio of Joseph Farley 1 and 2 to R9C51 at North Anna Unit 1. The flow peaking relative instability is obtained by testing in the air test rig described in Section 5.4, where the peaking factor is defined as the critical velocity for 0209M:49/063088 34
-9 R9051 AVB pattern compared to critical velocity for a uniform AVB pattern. As explained in Section 8.0, the minimum value of ( ]a,b,c is appropriate for R9C51 of North Anna 1. The pecking factor for a tube in Joseph Farley 1 and 2 is therefore divided by [ ]a,b,c and the resulting relative flow peaking l is multiplied times the relative stability ratio based on ATHOS results. If the peaking factor is 1.0, the relative flow peaking is (
, ja,b,c, As a further demonstration of the conservatism of 1.47 as the minimum flow peaking factor for R9C51, the stress amplitude of 7.0 ksi obtained from iterating on cumulative fatigue usage (and selected as the nominal value from fractography analysis) was used to back calculate the apparent stability ratio and then the apparent flow peaking factor. Allowing for a range of slopes of the instability curve from 10 to 30, the stability ratio is in the range of 1.1 to 1.4 and the flow peaking factor is in the range of 1.8 to 2.2. This range of flow peaking agrees with the range of flow peaking factors measured in the air tests and is considered to be the best estimate of the range of the R9C51 flow peaking factor.
The range of stability ratius, 1.1 to 1.4, is based on a value of 0.63 obtained with ATH05 results without flew peaking and with nominal camping that is a function of aodal effective void fra: tion. The nominal dattping reflects the ,
nominal reduction in damping that occurs with denting at the tube suoport plate. Therefore, a minimum damping scenario that is independent of void fraction is not consiaered to be credible and is not addressed in the evaination that follows.
4.3 Stress Ratio Considerations In Section 4.1, a 10% reduction in stability ratio was established to reduce
. the stress amplitude on the Row 9 Column 51 tube of North Anna Unit 1 to a level that would not have ruptured, 4.0 ksi. To apply this same criteria to
. another tube in the same or another steam generator, the differences in (
. Ja.C, 0209M:49/063088-35 l
A a , c, i
- i f
i t
l i
i J p f;
t a ,
7 i
1 1 i f l d 6 4 h i,
l
\
E
.b t
i i i 1
l t P
F I
I i
l i
h t
0209M:49/061788-36 ,
l r
, . . - - _-__-n,-n,-a,-.--,---- .--ww-,-,,
Thus, the stress ratio to be evaluated and compared to 1.0 is
' ~
a,c
.' where the stability ratio (SR) includes the flow peaking effect.
. By establishing their equivalent effect on the stress amplitude that produced the tube rupture at North Anna 1, several other effects may be accounted for.
These include a lower mean stress (such as for non-dented tubes), different frequency tubes from the ( Ja,c.e hertz frequency of R9C51, North Anna 1, and shorter design basis service.
In the case of lower mean stress, the stress amplitude that would have caused the failu,re of R9C51, North Anna 1, would have been higher. (
Ja,c, A lower or higher frequency tube would not reach a usage of 1.0 in the sare length of time as the R9051 tube due to the different frequency of cycling.
The usage accre.ulated is proportional to the frequency and, therefore, the allowablo number of cycles to reach a usage of 1.0 is invorsely proportional to frequency. The equivalent number of cycles to give the usage of 1.0 for a differant frequency tube (
l Ja,c, For a different time basis for fatigue usage evaluation [
l ja,c.e, 0209M:49/063088-37
Knowing the magnitude of the stress ratio allows 1) the determination of tubes that do not meet a value of 11, 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 Joseph Farley 1 and 2 based on the time history expressed by normalized stability ratios for the duty cycle (see Section 7,4).
l l
l l
! 0209M:49/061588 38 1
Table 4-1 Fatigue Usage per Year Resulting From Stability Ratio Reduction
$R, % STRESS FATIGUE MEAN STRESS USAGE REDUCTION BASIS (I) CURVE (2) MODEL PER YEAR
,. . a,c
- 5. 9 yrs to fail ( Ja,c
- 5. 9 yrs to fail ( Jac
- 5. 9 yrs to fail ( Ja.c
- 10. max.stresg) amplitudet
[ Ja.c
. 10. max.stresg) amplitudet
[ Ja,c
- 10. I wax. stres )
amplitudet
, ( Ja,c 10.
max. stres )
amolitudet
[ Ja,e
- 10. max. stress based on 1 duty c (5)
(1) This gives the basis for selection of the initiating stress amplitude and its value in ksi.
(2) S,is the maximum stress applied with S,= Smean + Sa '
(3) ( Ja.c, (4) Cycles to failure implied by this combination of stress and fatigue l
properties is notably less than implied by the operating history.
Consequently this combination is a conservative, bounding estimate.
(5) Cyclestofailureimpliedbytheoperatinghistoryrequires{
Ja,c fatigue curve at the maximum stress of ( Ja, ,
0209M:49/061588-39
t
. a,b, a .
1 i
!. i 6
P 1 ;
. I I
i I
i i i
t i i
I l .
- Figure 4 1 Vibration Displacement vs. Stability Ratio i
0209M:49/062988-40 i :
i a,c ;
~
i l
i l
l l i l
l l ,
. t i
t
. Figure 4 2 Fatigue Strength of Inconel 600 in AVT Water at 600'F [
l l
i 0209M:49/062988 41 !
e - - - - - - - __._,,___--..--_,--,-,_-..m ,,_ ,, . , ,__.-_-.y.,-_ _ , ,,,~-, y .. __,,, ,,,__ - . _ , _ _ - _ _ __-_, ___ , _7--..
a,c s
1 Figure 4-3 Fatigue curve fo? Inconel 600 in AVT Water Comparison of Mean Stress Correction Models
) !
0209M:49/062988-42 ,.
J
l I
a,c i
1 l
Figure 4-4 Modified Fatigue with 10% Reduction in Stability
. Ratio for Maxtaum Stress Condition ,
0209M:49/062988 43
a,c s
d l.
l l
Figure 4-5 Modified Fatige.1 with 5% Reduction in Stability Ratio for Minimum Stress condition l
0209M:49/062988 44
5.0 SUPPORTING TEST DATA This section provides a mathematical description of the fluid-elastic mechanism, which was determined to be the most likely causative mechanism for the North Anna tube rupture, as discussed in Section 3.3, to highlight the physical conditions and corresponding parameters directly related to the event and associated preventative measures. The basis for establishing the appropriate values and implications associated with these parameters are provided. Where appropriate, test results are presented.
5.1 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 dafine the mass and stiffness matrices for the tube and its support system. This information is used to determine the modal frequencies (eigenvalues) and .aoaa shapes (eigenvectors) for the linearly supported tube being corsidered The methodology is c.omprised of the evaluation of the fallowing eq ntions:
(
l Fluid elast'c stability ratio - SR - Ven/Uc for mode n, where Uc (critical velocity) and Uen (effective velocity) are determined by:
, u-Af e Dn ((m,6 )n / (#o }
and; 2 2 I j jn Zj 2, f(p/p,)ud j
W un I (m3/mo) (jn j=1 Zj 0209M:49/063088 45
where, D - tube outside diameter, inches V
en
- effective velocity for mode n, inches /sec N = number of nodal points of the finite element model ej, Uj, pj = mass per unit length, crossflow velocity and fluid density at node j, respectively po, mo = reference density and a reference mass per unit length, respectively (any representative values) on = logarithmic decrement (damping)
(jn - normalized displacement at node j in the nth mede of vibration zj - average of distances between node j to j-1, and j to J+1
- = an experimentally correlated stability constant l Substitution of Equations (1) and (2) into thi expression which aefines I
stability ratio, and cancellation of like terns, 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 ('.;sta).
The uncertainty in each ot' these parameters is addressed in a conceptual >
manner in Figure 5 1. The remainder of this section (Section 5.0) provides a
. discussion, and, where ap1ropriate, the experimental bases to quantitatively establish the uncertainty associated with each of these parameters. In 0209M:49/063088 46
addition, Section 5.3 provides the experimental basis to demonstrate that tubes with(
Ja,c. This implies that those tubes [ Ja c would not have to be a modified because their instability response amplitude (and stress) would be small. The very high degree of sensitivity of tube response (displacements and stresses) to changes in the velocity times square-root density distribution is addressed in Section 4.0. This is important in determining the degree of r i
change that can be attained through modifications.
i Frecuency 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 shown to be quite small. This is particularly appropriate in the case of ;
dented (fixed boundary condition) tubes. Therefore, uncertainty levels !
introduced by the frequency parameter are expected to be insignificant (see j also 'Averago Flow Field" subsection below). I Instability Constant (Beta) ,
i l The beta (stability constant) values used for stability ratio and critical i velocity evaluations (see above equations) are based on an extensiva data base :
comprised of both Westinghouse and other experimental results. In addition, l previous field experiences are conside. red. Values have been measured for full
! length U-bend tubes in prototypical steam / water environments. In addition, !
measurements in U bend air models have been made with both no AVB and variable AVB supports (Figure 5 3).
I To help establish the uncertainties associated with ATHOS flow velocity and '
density distribution predictions on stability analyses, the Model Boiler (MB 3) tests performed at Mitsubishi Heavy Industries (MHI) in Japan were modeled l l
using ATHOS. A beta value consistent with the ATHOS predicted flow conditions :
and the M8 3 measured critical velocity was determined. These analyses supported a beta value of [ ja,b,c, i
0209M:49/063088-47 l
A sumary of the test bases and qualifications of the beta values used for these assessments is provided by Figure 5-2. The lowest measured beta for tubes without AVBs was a value of ( 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).
Mass Distribution The mass distribution parameter is based on known infor. nation 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 [
. . . . )
Tube Damoina Test data are available to define tube damping for clamped (fixed) tube supports, appropriate to dented tube conditions, in steam / water flow conditions. Prototypic U bend testing has been performed under conditions leading to pinned supports. The data of Axisa in Figure 5 4 provides the principal data for clamped tube conditions in steam / water. This data was obtained for cross flow over straight tubes. Uncertainties are not defined for the data from these tests. Octailed tube damping data used in support of the stability ratio evaluations addressed in this report are provided in Section 5.2, below.
Flow Field - Velocity Times Souare-Root Density Distribution Average and U bend local flow field uncertainties are addressed independently 8
in the following.
)
0209M:49/063088-48
Averaae Flow Field Uncertainties in the average flow field parameters, obtained from ATHOS
~
analyses, coupled with stability constant and frequency, are essentially the same for units with dented or non dented top support plates. If the errors associated with these uncertainties were large, similar instabilities would be
~
expected in the non-dented units with resulting wear at either the top support plate or inner row AVBs. Significant tube wear has not been observed in inner row tubes in operating steam generators without denting. Thus, an uncertainty estimate of about [ ]a,c for the combined effects of average flow field, stability constant and frequency appears to be reasonable. To further minimize the impact of these uncertainties, the Joseph Farley 1 and 2 tubes are evaluated on a relative basis, so that constant error factors are essentially eliminateo. Thus, the uncertainties associated with the average velocity times square root density (combined) parameter are not expected to be significant.
U-Bend local Flow Field Non-uniform AVB insertion depths have been shown to have effects on stability ratios. Flow peaking, brought about by the "channeling" effects of non uniform AVBs, leads to a loc.a1 perturbation in the velocity times square root density parameter at the apex of the tube where it will have the largest effect
- (because the apex is where the largest vibration displacements occur).
Detailed local flow field data used in support of the stability ratio t evaluations addressed in this report are provided in Section 5.2, below.
l
( Overall Uncertainties Assessment l
l Based on the above discussions, and the data provided in the following sections, it is concluded that local flow peaking is itkely to have contributed significantly to the instability and associated increased vibration amplitude for the failed North Anna tube. Ratios of stresses and stability ratios relative to the North Anna tube, R9C51, are utilized in this report to minimize uncertainties in the evaluations associated with instability constants, local flow field effects and tube damping.
0209M:49/063088 49
5.2 Tube Damping Data The damping ratio depends on several aspects of the physical system. Two
. primary determinants of damping are the support conditions and the flow field.
It has been shown that tube support conditions (pinned vs clamped) affect the damping ratio significantly. Further, it is affected by the flow conditions, i.e., single phase or two-phase flow. These effects are discussed below in more detail.
Reference (5-1) indicates that the damping ratio in two phase flow is a sum of contributions from structural, viscous, flow dependent, and two-phase damping.
The structural damping will be equal to the measured damping in air. However, in two phase flow, the damping ratio increases significantly and is dependent on the void fraction or quality. It can be shown that the damping contribution from visc'ous effects are very small.
. Damping ratios for tubes in air and in air water flows have been measured and reported by various authors. However, the results from air water flow are poor
. representations of the actual conditions in a steam generator (steam water flow at high pressure). Therefore, where available, results from prototypic steam watcr flow conditions should be used. Fortunately, within the past few years test data on tube vibration under steam-water flow has been developed for both pinned and clamped tube support conditions.
Two sources of data are particularly noteworthy and are used here. The first l is a large body, of recent, as yet unpublished data from high pressure steam water tests conducted by Mitsubishi Heavy Industries (MHI). These data were gathered under pinned tube support conditions. The second is comprised of the results from tests sponsored by the Electric Power Research Institute (EPRI) and reported in References (5-2) and (5 3).
, The damping ratio results from the above tests are plotted in Figure 5 4 as a function of void frr, . iij'. It is important to note that the void fraction is detemined on the bW- [ la.c l
l 0209M:49/063088 50
1 (Reference (5-4)). The upper curve in the figure is for pinned support conditions. This curve represents a fit to a large number of data points not
~
shown in the figure. The points on the curve are only plotting aids, rather than specific test results.
The lower curve pertains to the clamped support condition, obtained from Reference (5-3). Void fraction has been recalculated on the basis of slip flow. It may be noted that there is a significant difference in the damping ratios under the pinned and the clamped support conditions. Damping is much larger for pinned supports at all void fractions. Denting of the tubes at the top support plate effectively clamps the tubes at that location. Therefore, the clamped tube support curve is used in the current evaluation to include the effect of denting at the top tube support plate.
The Refer'ence 5 3 data as reported show a damping value of 0.5% at 100% void fraction. The 100% void fraction condition has no two phase damping and is considered to be affected principally by mechanical or structural damping.
Westinghouse tests of clamped tube vibration in air has shown that the mechanical damping is only [ ]8'C rather than the 0.5% reported in Reference (5-3). Therefore the lower curve in Figure 5 4 is the Reference (5 3) dat with all damping values reduced by ( Jac, i
i I
(
0209M:49/063088 51
5.3 Tube Vibration Amplitudes With Single Sided AVB Support A ,eries of wind tunnel tests were conducted to Investigate the effects of tube /AVB eccentricity on the vibration amplitudes caused by fluidelastic
. vibration.
[
Ja.c. Prior test results obtained during the past year using this apparatus have demonstrated that the fluidelastic vibration characteristics observed in the tests performed with the cantilever tube apparatus arn in good agreement with corresponding characteristics observad in wind tunnel and steam flow tests using U-bend tube arrays. A summary of these prior results is given in Table 5-1.
An overall view of the apparatus is shown in Figure 5 5. Figure 5 6 is a top view of the apparatus. (
i d
4 I
s
}a,c, i
i
~
0209M:49/063088-5?
As shown in Figure 5-7, the tube vibration amplitude below a critical,' velocity iscausedby[
~
Ja,c, Figure 5-7 shows the manner in which the zero-to peak vibration amplitude, expressed as a ratio normalized to ( Ja.c,varieswhenonegapremains at ( la.c. For increasing velocities, up to that corresponoing to a stability ratio of (
la c. Figure 5 8 shows typical 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 [ la,c, l
It is concluded from the above test results that, (
ja c, 5.4 Tests to Determine the Effects on Fluidelastic Instability of Columnwise Variations in AVB Insertion Depths This section summarizes a series of wind tunnel tests that were conducted to investigate the effects of variations in AVB configurations on the initiation '
i 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
- cantildver tube apparatus described in Section 5.3. Figure 5-9 shows the conceptual design of the apparatus.1 The straight cantilever tube, (
0209M:49/063088 53
}a,c,
(
Ja,c. Figure 5-11 shows the
. AVBs, when the side panel of the test section is removed. Also shown is the top flow screen which is (
I
]**C, The AVB configurations tested are shown in Figure 5-12. Configuration la corresponds !
to tube R9C51, the ruptured tube at North Anna. Configuration 12a corresponds :
to one of the cases in which the AVBs are inserted to a uniform depth and no local velocity peaking effects are expected. '
i I
l l
.l i
I 1
1 l 0209M:49/063088-54
As shown in Figu're 5-9, (
Ja.c, All the tubes except the instrumented tubed (corresponding to Row 10) are 4
( -]a.c. As discussed in Section 5.3, prior l testing indicates that this situation provides a valid model. The instrumented (
i . tube [ ]a.c as shown in Figure 5.10. .
4 Its ( Ja,e direction vibrational motion is censured using a non contacting l transducer.
l i ,
i
, ja.c. The instrumented tube corresponds to a Row 10 tube as shown in !
Figure 5 9. However, depending on the particular AVB configuration, it can t . reasonably represent a' tube in Rows 8 through 11. The AVB profile in the l j straight tube model is the average of Rows 8 and 11. The difference in profila [
l 1s quite small for these boending rows. j l
i
! ( Ja.c using a ,
l hot film anemometer located as shown in Figure 5-9.
! i l
Figure 5-13 shows the ras vibration amplitude, as determined from PSD (power spectral density) measurements made using an FFT spectrum analyzer, versus flow l
velocity for configuration la (which corresponds to tube R9C51 in North Anna).
f Data for three repeat tests are shown and the critical velocity is identified. [
l' The typical rapid increase in vibration amplitude when the critical velocity for fluidelastic vibration is exceeded is evident.
I l: l l ~
l, 1. The AVBs shown in Figure 5-9 correspond to original AVBs. Modified l l model AYBs ccrresponding to those used in field modified units, such as i Joseph Farley 1 and 2, were made using the same procedure as for the original AVBs and are shown installed in Figure 5-11.
7 l ;
[ 0209M:49/063089 55 i
The main conclusions from the tests are:
- 1. Iuba 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.
~
- 2. Configuration 1b (R9C51 in North Anna) has the lowest critical velocity of all the configurations test 6d.
- 3. Configuration 1b is repeatable and the configuration was rerun periodically to verify the consistancy of the test apparatus.
The initial test results obtained in support of the Joseph Farley 1 and 2 evaluation are summarized in Table 5 2. The test data is presented as a velocity peaking ratio; a ratio of critical velocity for North Anna tube R9C51
, configuration la, to that for each Joseph Farley 1 and 2 AVB configuration I
evaluated.
. 5.5 References a q.
e I
r i
I' 4
1 0209M:49/061783 56
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: Tube vibration amplitude and tube /AYB impact forces or preload '
forces.
RESULTS:
l
,a,b.c
- e l
1 i
(
i:
i ;
- i 1
- 1 i
0209M:49/061588 57
Table 5-2 Fluidelastic Instability Velocity Peaking Ratios for Columnwise Variation in AVB Insertion Depths
. (Joseph Farley 1 and 2 with Modified AVBs)
Type of Insertion Peaking Ratio Configuration Ula/Un*
a,b,c la**
lb**
2a 12a 13
. 14d 14e
- 15b 17c 17d 17e 18a 18b ,
Note:
- Un is instability velocity at inlet fr type n of AVB insertion configuration.
- Test was conducted with original AVBs.
0209M:49/061588 58
t 1
l
. a,c i I'
r l
l I
i i
1 l
- L f
{
\ : ,.
. Figure 5-1 Fluidelastic Instability Uncertainty Assessment t
i I ..
! 0209M:49/063088-59 i
' i
U-Band Test Data
- 1) MB-3 Tests Avaluesof( Ja,b,c
- 2) MB-2 Tests J'of( Ja,b,C
, 3) Air Model Tests .
A of ( Ja,b,c without AVBs Tendency for A to increase in range of ( Ja,b,c with inactive AVBs (gaps at AVBs)
Tendency for A to decrease toward a lower bound of
[ la,b,c with active AVBs ,.
Verification of Instability Conditions
- 1) Flow conditions at critical velocity from MB-3
- 2) Me&sured damping for the specific tube
- 3) Calculated velocities trom ATHOS 3D analysis .
- 4) A determined from calculated critical values Good agreement with reported 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
. Figure 5-2 Instability Constant - A 4 i
0209M:49/063088 60 .
1
{
\
,,4 a,b,c i
l i
I P
i :
j . l.
3 Figure 5-3 Instability Constants, 4, obtained for curved Tubes from l Wind Tunnel Tests on the 0.214 Scale U-Bend Model I
f P
k 0209M:49/062988 61 1
I
1 l
i 1
. a,b,c I
I I
i l'
i l-l 3
i i
Figure 5-4 Damping vs. Slip Void Fraction 0209M:49/061088-62 t
. - - . -. _ _______I
a,b,c e
THIS FIGURE IS C0fl51DERED PROPRIETMY IN ITS ENTIRETY Figure 5 5 Overall View of Cantilever Tube Wind Tunnel Model 25364 1
a,b :
THIS FIGURE IS CONSIDERED PROPRIETMY IN ITS ENTIRITY i
l Figure 5-6 Top View of the Cantilever Tube Wind Tunnel Model l
l :
l :siss.:
1
a ,b ,c f
i i
i t .
P L
i l
t 1 I i
I.
I e i f
Figure 5-7 Fluidelastic Vibration Amplitude with Non-Uniform Gaps i 1
- I {
l '
0154M:49/032888 65 1
i I
I l
l l
1 l
a ,b ,e
= . _
- i i
l 1
i f I i
I
. l 1 ;
I l
1 1 '
I l
l t
i i i
i
)
i l
1:
} Figure 5 4 Typical Vibration Amplitude and Tube / Ave tapact Force i signals for Fluidelastic Vibration with Unequal !
t Tube /AVB taps i l
1 Ol!M.:49 02 !!!.!! f
. a,b c
?
i i
i l
l 3
I
[
- Figure 5 9 Conceptual Design of the Apparatus for Determining the Effects of Fluidelastic Instability of Columnwise
. Variations in AVB Insertion Depths '
i
)
O!!4?t:49/0328SS 67 r
i
~~ ~
a,b,i i i
THIS FIGURE IS CONSIDERED PROPP.!ETARY IN ITS ENTIRETY t
I l-l i
(
l l
Figure 510 Overall View of Wind Tunnel Test Apparatus
.i 6
l ma !
- - a,b,c t
. Figure 5-11 Side View of Wind Tunnel Apparatus with Cover Plates Removed to Show Simulated AVBs for Field Modified Units and Top Flow: Screen 25 M S
I TYPE OF AVB TYPE OF AVB INSERTION INSERTION
<- t ' t FIS CCCCCCCO
- ,. c p r y e p + p c, + n
. C&? tf J55 U :5 5?? cf 5 1a CC COSC00 14e 00000000 0C000000 00000000 00000000 00000000 O c : :- C +
+
0 0 : :. C c
^
_ _ o CCCCCCC0 C C C C F '7 0 1b c C C CCC C o 1cb
'W
't'cc0' cCOOOOOOO C C COSCC O CCOOOOCO 00000000 00000000 00000000 CC000C00 C ^% ^: ^ ^
CO CCCCCCCO c % t :Xc 3 QQ Qf CCCCCCCO cF lrf ffc3 12A 0000'000 00000000 17C 6C50e6Co l 00000000 00000000 00000000 00000000 CCCCCCC0
, as 00000000 CC CCCCCO o Of 0000o000 17d C r CC0 00 13 o
- oo C 00000000 00000000
,. 00000000 00000000 C C C CCCCO 2 C CO C C C CCCCO .
1 0 C0 C C C CCC C O j79 Cb0 4C C C C OeC C o OOOOeOOO CCC00CCO 00000000 00000000 00000000 C C C CC C C O CC I C CC O C C ^: C C ; C 3 C l;l l.; ; C C2 0 C : 0 M C F '^7F 1 183 COOOOOCO
_. C C E # 6e C3 C 5 300000 00000000 CooOOOOO 00000000 rin C cl.* C c o C CI ckn ct, ,
o eT- F ri- r c: o 14d m 5m OOOOSCOO
, m IOU w' ci:
000000 w3 00000000 00000000 00000000 00000000
. Figure 5-12 AVB CONFIGURATIONS TESTED FOR FARLEY 1 & 2
a,b,c l
i i
l I
l i
l $
t 1
i l
t l
I I
l i
j l
Figure 5 13 Typical Variation of RMS Vibration Amplitude with Flow Velocity for Configuration la in Figure 5-12 i
i I
F 6.0 ED0Y CURRENT DATA AND AVB POSITIONS 6.1 Modified AVB Design The AVBs originaly supplied with the Farley steam generators were replaced
, between 1985 and 1987. The design of the replacement AVBs uses V-bar AVB assemblier, made primarily of 405 stainless steel, having a rectangular cross section, which are positioned in pairs between each column of tubes from column 4/5 to column 90/91. One V-bar assembly is located on each side of the U bend centerline. Each V-bar assembly includes an upper and a lower bar which are joined by a hinge at the apex. These AVBs are designed to extend inward from the periphery of the tube bundle, so that the bottom of the bar is located between rows 11 and 12. Outboard of these AVB pairs, special assemblies are used in columns 3/4 and 91/92. The special assemblies consist of single V bar assemblies which straddle the U bend centerline, and extend to locate the bottom of the bar between rows 8 and 9. No AVBs are installed in columns 1/2, 2/3,92/93,or93/94.
The nominal insertion depth of the replacement AVBs was controlled during installation by the use of temporary spacers between the outermost tube, and the attachment head on the outer end of each bar. This spacing and insertion depth was verified separately by inspection prior to permanently fixing the AVBs to their retainer plate.
At the ' nominal' point of the AVB assembly tolerance, the bottom of the replacement AVB is positioned at 11.14 tube pitches, lacking 0.14 tube pitches of supporting a' row 11 tube. The AVB assembly tolerance was plus or minus 0.3 tube pitches. Thus, it follows that within the assembly tolerance, at'the maximum insertion distance (inward tolerance) possible, the AVB could extend to 10.84 pitches, marginally supporting a row 11 tubes while at the maximum outward tolerance, the AVB could extend to 11.44 pitches, still continuing to
- support a row 12 tube.
. 6.2 Tube Denting at Top Tube Support Plate Eddy current data from the 1986 and 1987 outages were examined to evaluate the corrosion and/or denting at the top tube support plate for the tubes in rows 8 0209M:49/072588-64
l through 13. 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, as if by denting or corrosion, the results of this phase of the examination, which are plotted, are informative, but do not have an impact on
. the final decision as to whether to plug a tube or not.
- 6.2.2 Tube Wall Thinning at the AVB Supports No tube wall thinning was observed at the modified AVB/ tube intersections in rows 8 through 13 of the bundle.
6.3 Eddy Current Data for AVB Positions The AVB insertion depths were determined on the basis of interpretation of the eddy current data. To locate the AVBs, the ECT data traces were searched for the characteristic peaks seen in the signals, which indicate the intersection of an AVB (or a true support plate) with the tube (Figure 6.1). The number of these intersections, including zero, were logged for each tube to indicate the presence or absence of AVBs. Where only a single intersection was indicated by the drta, the length of this intersection was recorded to provide additional information to assess the adequacy of support for the tube. Figures 6.2, 6.3, and 6.4 for Unit I and 6.5, 6.6 and 6.7 for Unit 2 show the number of AVB signals found for each tube, as well as the condition of the tube to T5P interface at +.he locations when it was evaluated.
The 405 stainless steel used for the modified AVBs is ferritic. As a result, it produces a much stronger eddy current signal than the original Inconel AVBs. For this reason, the AVB assembly hinge plate, in the proximity of a Row 11 tube, produces an eddy current signal which may, or may not, indicate the AVB assembly is in contact with the tube. Likewise, resolution of the eddy current results is insufficient to differentiate between the nominal and minimum tolerance installation. As a result, the AVB indications for Row 11 1 tubes are heavily discounted. The AVB insertion depths for the Farley steam generators art based primarily on projection calculations.
4 0209M:49/071188 65
Since ambiguity can occur in the interpretation of the ECT data, due to
. inability of ECT to differentiate at 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 for adjacent columns and verification by projection were utilized to determine the depth of insertion which was plotted. For the cases of single AVB contacts, the length of the contact signal and verification by projection was used in a few instances to confirm or deny support of the tube with a single contact.
Data from the 1986 outage were used to determine the positions of the AVBs for ll nit 1. Data from the 1987 inspection were used for Unit 2. The Eddy Current data analysis was performed principally by the SG Inspection and Analysis group of Westinghouse STD.
6.4 AVB Insertion Depths AVB position maps for Unit 1 steam generators A through C are given in Figures 6.2 through 6.4. Similarily, maps for Unit 2 steam generators A through C are given in Figures 6.5 through 6.7. The number of visible AVB indications per tube, projections of AVB insertion, and the condition of the tube to TSP interface are shown on these figures.
Th6 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 observation' gives a 'yes - no' type of answer, the projection method is used to ' interpolate' AVB insertion depths
. between rows of tubes. The visual images thus produced being more easily understood when fluid flow peaking situations are evaluated.
l.
Greater conservatism is generally interpreted as the AVB being less inserted although consideration must also be given to the resulting flow peaking factors. No attempt was made to inflate the flow peaking factors through conceptually possible, but unreasonabla, interpetation of the data.
0209M:49/072588 66
i l !
6.4.1 AV8 Projection The depth of insertion of the replacement AVBs can be determined on the basis of the measured location of the legs of the AVB in larger radius tube rows in i I* the same column. This is useful if the direct observations of the AV8s fcr the !
) potentially susceptible tubes are unavailable (i.e., due to tube plugging or signal masking) or if the direct observations are ambiguous (i.e., 2 :
indic.ations in cach of 2 adjacent rows in the same column). Projections of i AVBs are never the method of choice where unambiguous direct data for Rows 9 !
l through 13 are available. !
l l The fundamental assumption of the projection technique is that the included 1 angle between the upper and lower bars is within the specified tolerance of the I AVB modification assembly drawing. The included angle cannot be larger than i the specified tolerance since the maximum angle is limited by a mechanical stop ,
- on the hinge which connects the upper and lower bars, and a protective cable l,
which limits the separation of the two heads of the assembly during ,
j installation. (The cable is removed after installation of the assembly). If
- l. the actual included angle is smaller than the specified angle, the actual insertion of the assembly will be farther than the predicted insertion, since l
l the basis of the projection is the measured arc length. Consequently, any l l
error in the AVB positions introduced through the projection technique will be f in the conservative direction, i.e. the AVB will not be inserted as far. !
l l
A projected position of 11.0 indicates that the Row 11 tube is marginally j
}
supported. The maximum possible inserted position of the AVBs is defined by l j
the attachment head of the assemblies in contact with the outer tubes, although l this position is less than the minimum specified spacing tolerance relative to l the outside tube. The projection value for this position is 10.85, based on j l
the end of the lower bar relative to the centerline of the tubes. The minimum !
installed position of the AV8s is defined by the maximum tolerance spacing l
) between the attachment head and the outer surface of the outer tube. The !
( corresponding projection value for this position is 11.6, based on the same f f,
i reference features, f
l i I
l G
l i
i 0238M:49/071188 2 !
I
i l
l l
The projection method is based on consistency of the projections from more than one row of tubes in the same column to assure that the projections are not based on potentially spurious data from a single tube. If consistency is shown among several tubes in the same column, exper'9nce has shown that the best
. prediction of the position of the AVB is based on the tube nearest to the predicted position. For example, if projections are based on data for Rows 13,
. 14 and 15 in a column, and the predicted positions are within approximately half a pitch, e.g., 11.8, 12, 12.3 for each of the tubes respectively, the best prediction is the one based on Ror 13 in this example.
In each column, two projected positions may be obtained, one for each of the two assemblies on the opposite sides of the bundle centerline. The predicted deepest insertion of the two projections is the applicable AVB position. The rationale for this is that a tube in the potentially susceptible row range, when supp'orted by one AVB on either side of the centerline, becomes unsusceptible (i.e., fluidelastically stable) regardless of the other boundary conditions. Thus if the two insertion predictions in a column are N.0 and N.6, tube N will be considered supported because the AVB at N.0 provides the necessary support as noted above, c 6.4.2 Analysis of Plant Data The evaluation of the plant data from the latest addy current inspections shows that all of the Row 12, and higher, tubes in both plants are supported. Row 12 is the design depth of insertion for the modified AVBs, except for a special ;
j AVB at each side of the tube bundle which penetrates to about Row 9. The i evaluation also shows that the AVBs have very uniform insertion depths with the bottom hinge plate located between Rows 11' and 12. This is apparent in the
- maps of the AVB locations, given in Figures 6.2 through 6.7. Only a few Row 11 tubes were found to be supported by AVBs. The unsupported tubes are sumarized on Table 6.1.
i: -
I 1
I 0238M:49/071188-3
Table 6.1 SUMARY LISTING OF UNSUPPORTED TULES Unit 1 Steam Generator A Row 12 No unsupported tubes except: C93, C2 Row 11 All unsupported except: C91, C92, C80, C79, C40, C39, C30, C29 C3, C4 Row 10 All unsupported except: C92, C91, C4, C3 Unit 1 Steam Generator 8 Row 12 No unsupported tubes except: C93, C2 Row 11 All unsupported except: C92, C91, C27, C26, C4, C3 Row 10 All unsupported except: C92, C91, C4, C3 Unit 1 Steam Generator C Row 12 No unsupported tubes except: C93, C2 Row 11 All unsupported except: C92, C91, C15, C14, C4, C3 i Row 10 All unsupported except: C92, C91, C4, C3 l Unit 2 Steam Generator A Row 12 No unsupported tubes except: C93, C2 Row 11 All unsupported except: C92, C91, C4, C3 Row 10 All unsupported except: C92, C91, C4, C3 Unit 2 Steam Generator B ,
No unsupported tubes except: C93, C2 Row 12 Row 11 All unsupported except: C92, C91, C4, C3 !
I Row 10 All unsupported except: C92, C91, C4, C3 Unit 2 Steam Generator C Row 12 No unsupported tubes except: C93, C2 Row 11 All unsupported except: C92, C91, C72, C71, C60, C59, C58, C57 C4, C3 i Row 10 All unsupported except: C92, C91, C4, C3 i
l L
i 0238M:49/063088 4 i l
- 04 6 m = De 4 et a Osseekee - e m se ses 4# GE Bt
- . - .. 4.
- Wee - 868 Setatite = 887 50 d LM9 f*et' OeWT l men.e - 6, I Pts - =. Iet tum e 1 yes - sta anvertes rt ans 0198 PWI* OeFf CDee - Fr Met - to ese spues - les
' ea W
t e.TT 7
i 1
. nr. i e s6 am IWIWtles . 84F M4
.) . ..~o
~~
~
. h[.. .. .'. . f~ SiF8ElfP2 e er een 8
. . . ...,..p....
k E:
<> d;..I'? t .m
- me s m ,n u
. ew 1E1' M
. 68 Puot?
. De 6 g, *
- Os 8 ett = OoeseL e = 0 m a mas ta QL si
.- i. to tree - see WTnTItBe. IIP 30
. I ts* rete oso? i ae.e - ..
i p nae Suee ==== ISS
- se .. I e
] l movie . m oss i 1
-- e t >+ , to oest see - e. t, Pett === t 9 4 et '
.g= a., g"Ai =
r .- t=mi
-- ite
.:Pm,i
. . ._4,N P c, . aniu ,t L-
'.. == - = a.u
. . . O.e.
..o . ...
.._T..-
( _
M m -
l,'
2
.k . ._ k .
1.h.- -
it oue, .i t i.4 a. .m J.m.Fdel LEY l 0 aff(ET I&th Figure 6 1 AVB Insertion Depth Confirmation
! 0238M:49/063088-5
ee
- a ___
f J
l
@@ 2 a1 GG 12 -
OG : a GO : a OOOG '
68: 2 OGG 12 OOOOG i lOGGi2 06 .12 GG 12 88 1 _
09 : 2 OG ila OG ai GG n a OG -
1 89 -
1 OG a OGG : a OOO - a 66 15 OS ir OGG [5 GG E:
OOG OG
[i ir
}{
?j.E eG c a Ge i; eG i';
b]>
ee II OG !*
ee si GO a eee Ei OOO : ;
}$g<
OG ir GG t! OO Ti OG il GG 12 GG EE OG il GG il OG ir OG il GG 12 OG ir ;
eG a a-GG : a Os n a j
9G 11 GG il OG 55 i OG 8.1 GG 12 OG is 1 l OG il GG 8
. 2 GG is '!
2 OG is ir ,flf !
09 1 OG 5 GG Ge 12 t a OO is li l]
i.
3 00 ,
s ii c n ii c
30 3 2
li c
il c
00 .
s iI c 60O ,
- ,l sl c O00 s n
Il c 0O il 1
, c 00 .
s iI c @0O il L 6 p. c !
00 s li c 0O c ii 00 ,. c ii 00 .
li c 0O c il 0G ,, c il 00 .
2 ll c 0O c i i
'000 ,, ci i 00 =
li c 0O c .
000 i,lc 00 i. c li 0O c ii 600 ,. c ii 00 ,4 ll c 0O c .
600 i, l c 00 2 ii c 0O ,. c il B
000 ,. c ,
00 .
il c 6O ,, c o.
n 3Go s
n 600 ,, c ii 00 s.
ll c 0O ,. c ii
- /
6:isSt i
60 ,. c 00 .
1l c 0O c ii
- e o uP r 1 60 i.ic 00 1 4
li c 0O i.lc s, ig yB FeV O60 c il 00 =
ll c 0O c .
lrA F
a O66 - c i, i 00 =
li c 0O ,. c i i O66 4lc .
00 o s
ii c 0O c iI O66 .c ii 00 i s
il c 0O. c .
O66 c i
l 00 s, c 0O c ii 8 O66 c i, i 0 0~ ss Il c 0O ,, c il 6
^
=
G66 c il 00 s.
ii c 0O u c ^
66 ,. c ii 00 s s
il c
0O n c ii O66 c !.
l 00 s e
ii c
0O ,. c ii 66 c ii 00 i s
il c
OO n c il
_ O66 e c 00 u c @OO c .
O66 . c il li i1 00 u c
. o, _
ii ll c
4> O iI c
l I
l
-_- i~
OO 12 8 1 Ge s o GO n o -
069 12 00 2 OOOO ; _
. 066 8
- 90 2 OOOOO 1 _
066 12 OS 2 90 1 _
966 : 1 90 2 00 11 OO6 11 00 2 00 1:
966 12 99 3 00 11 666 11 00 1: OO -
966 E1 00 1: 00 1 OOG e o 000 2 OO e a 966 : o OO : a 00 11" 1 OS6 c "
OO :o OO = E ,
4 OOe T! OO i! -
OO i!-
il
' T8$ OOO -! OS I OO T GO D2 OOG li OO li OO 5E
.g O@ i OO 31 OO L1 a< OOe s o OO ro OO : o OOO li OO 3- OO [- 088 12 @@ 22 00 11 OOS E1 OO 21 OO L1 4 008 12 OO 2 00 11 ]! 080 11 90 2 00 11" lj OOO 8 o OO : o OO n
- j a OO@ T! OO i! OO i D[!
eee II ee II es ii fi eee ir ee n Oe s1 -! OOO 8 o OO : o OO n o "1 T
7 ee n o E
. GO z o GO : a l
GO : o GO : o OOOO 2_ i OO s a OO o 99999 1_ l OS : " OO x u OO - Ge s a GO : a OO a - Ge ir OO x OO 1-06 : 1 GO E 90 11 Ge :1 ee . ee . -
- OG E
- Ge ir OO "-
- SO : a OG 11 OO e "
Oe ir OS a 00 : a }<
;i OG E: GO L: OO = = ~'
< GO o GO : o- GO : a GO
~
Tj'.] 09 13 Ge i2 OO a:
%..s GO : o OS : o OO "
M 99 7- OS I- - OS I 9'3 OS I; OO i- OO E'
?c OO l-2 OO i OO Eo Ge l Ge t 00 :=
OO le OO 12 OO a *" 98 1 OG E: OO n 3 OO l OO i OO n a y]j: OO 8 89 1 a OO 12 1 :; OO S.2 Oe a s 00 : o - GO 8 a OS : o OO c o ee -
= .
ee . . ee . . I;',{j i-ee r ee r ee T prj l - I
Ge : a b
~
Ge : o ee n u - 66 1 Ge i: GOOO 1 _ 966 12 OG E 99998 1 _ SSS S: 66 x 2 SO L _ OOG GO E2 00 11 66 12 80 x 2 00 11 66 12 Ge i: 00 1
@@ t OO -
1 66 " OG - a OO - " 66 53 GO i OO i t 66 : u GO o 00 :
" Ij Ge i-Se i OO F- !!
m GG r a OG ea- OO : " 40
@G TU
' a?d.$ OO i - OO T -
% *9 eG T7 ee ? OO F
[6%$ OG li GG ii OO Se@ x 2 Se t: OO Y hk , OG 12 Ge t: OO E ! OG 1: GG El ,@,,Q O O O il ! OG 12 80 12 00 11 OG - - ee 2 . ee - - i ,3 GG -13 GO E5 00 55 17 GG 8 " GO : o OO n a i OG l3 88 53 OO i
,' l i 2
3 eG 8.2 ee ir GO E ee s: OO El ee f."j il" , ee n a ee - o Oe = taj
T. 80 11 e GOO 11 GO : a -
?
00 11 GG : a GOOO ~ 000 : a Se s o 99990 1 _ 00 1 Ge x . ee - . 406 1 a GO : o GO - = SS EL 66 LL OO L1 66 11 OO il OO 11 66 11 GG il OO 11 00 11 Ge ir OO 11 66 11 @@ it OO
- 1 00 11 00 11 00 11 1 Se c . ee .
ee = . 1 j Ge l GO [i OO [i 3$ a8E 00 11 GO 11 OO il 90 e k' 00 11 00 11 OO 11
- $)f f
u. O 3 51 Oe s _o
@@ L1 Ge ir OO OO 77 a
00 11 Ge OO E.1. t ee T;
= .
ee : . Oe OOO 00 3 00 i7 3 OO TT - GO : -o GO i!-
'] a' 00 11 88 [2 090 51
, 00 11 00 11 OO 11 , l l 00 11 00 11 00 11 GG GO 888GG il" OO OO OO s o c ' t o j'i gg 2 l l OO s a ee s ; OO n o uij l ee I - ee n e ese = =
7.0 THERMAL AND HYDRAULIC ANALYSIS This section presents the results of calculations of the relative stability ratio, a parameter which is used in assessing the susceptibility to
; fluidelastic vibration. The ratio is based on analysis of secondary side tube bundle velocity, density and void fraction distributions which are derived from , three dimensional ATHOS3 computer code (Reference 7-1) calculations. For application to the Farley evaluation, a ID-to-3D ratioing technique is described which permits the use of existing ATH053/ tube vibration / stability ratio results for a similar Reference 51 Series Plant. Adjustments to these reference plant results are made to account for the effects of the specific operating conditions for the Farley units.
In the following subsections, the relative stability ratio calculation technique is described along with specific results for the Farley generators. A description of the ATHOS3 analysis model and sample results for the Reference 51 Series Plant are also presented. 7.1 One-Dimensional Relative Stability Ratio Calculation Methodology and <
~
Justification ! The assessment of the susceptibility to fluidelastic vibration and tube fatigue makes use of a parameter termed the relative stability ratio. The relative stability ratio compares the fluidelastic stability ratio for a particular plant to the stability ratio calculated for the North Anna 1 steam generators (SRplant x/SR n . anna). High values of this parameter over a significant period of operation, coupled with other prerequisite conditions (e.g., absence of AVB support and denting at the top tube support plate), could indicate an increased susceptibility to fluidelastic vibration instability.
. 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.
. Fluidelastic V Stability Ratio, SR = effective U
critical at onset of instability I 023BM:49/063088 9
In this ratio, the effective velocity depends on the spanwise distributions of flow velocity and fluid density, and on the mode shape of vibration. The critical 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. The detailed calculation of this ratio using spanwise velocity and density distributions, etc. requires three-dimensional thermal / hydraulic and tube vibration calculations which are very time consuming. Alternately, a simrlified, one-dimensional version of this ratio has been used to provide a more rapid, relative assessment technique for determining the susceptibility to fluidelastic vibration. It is defined by
- a,e (1)
While this simplified approach cannot account for the three-dimensional tube bundle effects, it does consider the major factors affecting the stability ratio. Four components make up this ratio: a loading term based on the dynamic pressure (pV 2 ), a tube incremental mass (m) term, the natural frequency of the tube (fn), and a damping ratio (6) term. Note that the overall ratio is relative, in that each component is expressed as a ratio of the plant's value to the value for North Anna 1. The calculation of the relative stability ratio makes use of the overall steam generator operating conditions (steam flow, steam pressure, and circulation ratio), along with the geometry, to calculate an average secondary-side U bend void fraction, density, and radial tube gap velocity. The velocity and density are then used in forming a ratio based on dynamic pressure (pV 2 )l/2, which is one component of the relative stability ratio. A second component is the tube damping which is calculated from an experimentally-derived correlation dependent upon the void fraction. The particular correlation which is used for all relative stability ratio calculations is based on a dented condition at the top tube support plate (a clamped / clamped condition). The clamped condition is also assumed in calculating the tube natural frequency. 0210M:49/06178810
Justification for use of a simplified one-dimensional relative stability ratio is provided by making comparisons with the results obtained from more detailed
. three-dimensional flow field / tube vibration calculations. The attached Figure 7-1 presents the comparison of the results of the two calculation methods for - six other 51 and 44 Series generators which have been evaluated, to date. The l three-dimensional results are based on use of bundle f;ow fields predicted with !
the ATHOS3 computer code (Reference 7-1). Both cyadrical and Cartesian models have been used in the ATHOS3 simulations. Note that the results plotted in Figure 7-1 do not include the effects of anti-vibration bars. Their contribution is handled as part of the peaking factor evaluation (Section 8). The comparisons indicate that the ID method provides a good or modestly conservative prediction of the 3D relative stability ratios for these similar generator models. Note, in particular, that the 10 method essentially bounds the maximum 3D ratios observed for each tube row. This is so for the smaller radius tubes which are included in the comparison and which, based on past experience, are typically the tube rows of interest in the tube
. vibration / fatigue evaluations. The variation in ratios for the plants within each steam generator model reflects differences in the basic thermal / hydraulic operating conditions (Wsteam, Psteam, and circ ratio). Further, this plant-to-plant variation is maintained for each of the tube rows which are plotted. The fact that the plant-to plant variation in the ID ratios follows the 3D trends, indicates that the operating condition contribution to the relative stability ratio can be adequately accounted for by the 10 approach.
Overall, the comparison demonstrates that the ID calculation method can provide meaningful relative stability ratios in support of tube fluidelastic vibration / fatigue assessments. In particular, the one-dimensional technique can be used to adjust tube-specific stability ratios determined from detailed three-dimensional calculations for the effects of differences in thermal / hydraulic operating conditions. This 10 to 3D adjustment is justifiable as long as its applied within a group of steam generators which
. share a comon tube bundle configurstion, as in the case of the 44 and 51 Series feedring generators. In thJse situations, the overall tube bundle flow fields will be similar and the individual plant ratios will differ only as a result of the effects of variations in the basic thermal / hydraulic parameters.
0238M:49/063088 11
For the Farley evaluation, a ratio of relative stability ratics is made which will account for the effects of differences in operating conditions between the Farley units and another very similar 51 Series steam generator (termed the Reference Plant). Subsequently, this ID ratio or multiplier is applied to the
,- tube-specific stability ratios determined previously from 3D flow field (ATHOS3)/ tube vibration analyses for the Reference 51 steam generator.
7.2 Relative Stability Ratio Calculations for Farley Recent steam generator operating condition data was supplied by Alabama Power for both Farley Units 1 and 2. The data was obtained from plant operating logs for March, 1988. Table 7-1 summarizes these data along with predictions of the circulation ratio which were made for each generator using the Westinghouse GENF performance computer code. The circulation ratio is of primary importance to the stability ratio analysis since it, together with the steam flow, establishes the total bundle flow rate and average loading on the tubes. It also provides an overall indication of the voids within the tube bundle since the bundle exit quality is inversely proportional to the cire ratio (Xexit = 1/cire ratio). Based on the discussion from the previous section, it is evident that higher flow loading on the tubes leads to higher stability ratios. An increase in stability ratio can also occur with lower steam pressure; this result is associated with decreased damping which occurs when the pressure is lowered and there are more voids in the tube bundle. Given these trends, the operating conditions for the A generator in Unit 2 would be expected to have the highest predicted stability ratio. As shown in the final column in Table 7-1, the l condition for this generator does produce the highest relative stability ratio of the six generators. The components of the ID relative stability ratio (Equation 1) which were calculated for this A generator in Unit 2 are as a,b,c
. follows: -
I i 0138M:49/063088 12
Using these component ratios, the overall relativo stability ratio for a row nine tube (same as ruptured tube at North Anna), based on void dependent . damping is: a,b,c As indicated in Table 7-1, a slightly different set of operating conditions actually formed the basis for the 1D-to-30 multiplier which was applied to the existing tube-specific stability ratios /or the Reference Plant. It was necessary to define this set of conditions because the Farley plant data was not available at the time the evaluation was to be completed. The assumed conditions were based on a power level which is 0.5% above nominal full power, lower steam pressure. The resulting 10 relative along stabilitywith ratioa(slightly $'$s only about 1% higher than the maximum v calculated from the plant data. The resulting multiplier which was subsequently applied to the reference, tube specific stability ratios is: a,b,c (2) Hence, because of small differences in operating conditions, the stability ratios for the Farley generators are estimated to be about 2.4% higher than those of the Reference 51 Series generator. The application of this multiplier is considered further in Section 9.2. 7.3 3D Tube Bundle Flow Field for Reference 51 Series Steam Generator As discussed in the previous sections, the calculation of the stability ratios for Farley is based on existing ratios for a Reference 51 Series generator with I an adjustment to account for differences in the basic thermal / hydraulic operating conditions. The three-dimensional analysis of the tube bundle flow
~
field on secondary side of this Reference 51 Series generator is described in this section. Since the basic operating conditions for the Farley units are 0210M:49/061788 13
i 1 very similar to the reference plant, the flow distribution result.s included herein are also representative of the distributions in the Farley tube bundle. ATHOS Analysis Model The calculation of relative stability ratios involves comparing the stability ratio calculated for one or more tubes in a given plant to the ratio calculated for the ruptured Row 9/ Column 51 tube in the North Anna Series 51 steam generator. It makes use of ATHOS computed flow profiles for both tube bundles. Since the presence of AVBs in the U-bend region of a tube bundle could influence the overall flow field and/or the local flow parameters for a particular tube of interest, some discussion of the treatment of AV8's is Oecessary before presenting a description of the ATH0S model. The ATHOS 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 at a uniform depth of insertion via (flow cell boundary resistance factors. Practical lower limits of cell size in the iTH05 code, however, prevent a fine grid representation of the AVB V-bar l snapa which, in turn, limits the accuracy of the AVB representation. For a different plant, ATHOS calculations have been performed with and without AVBs in the model. The effects of uniform AVB insertion on stability ratios (relative to no AVBs) for tubes 1 or 2 rows below the AVBs agree well with results obtained from tbn air model tests described in Section 5. Calculated and test stability ratios for tubes 1 or 2 rows below uniformly inserted AVBs l are lower than those without AVBs in the model. In addition, calculations of stability ratios relative to North Anna R9C51 show that the relative stability ratios for tubes 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 I velocities near the peripheral tubes. However, the magnitude of this effect is lI uncertain due to the limitations in ATHOS for modeling the AVBs. Further, the global flow resistance of staggered AVB insertion would be less than that from l l l 0238M:49/063088-14
uniform insertion. Based on the sensitivity studies using ATH0S models with and without uniformly inserted AVBs, the most reliable relative stability
- ratios (for actual steam generators with non-uniform AVB insertion depths) are expected using ATH0S models excluding AVBs and including the total effects of ,- variable AVB insertion depths in the peaking factors obtained from test data]a,c. This methodology has been utilized in the Joseph Farley 1 and 2 analysis.
The ATHOS analysis model for the Reference 51 Series steam generator consists of 13,050 flow cells in a Cartesian Coordinate System having 30 divisions in the circumferential (x-axis) direction, 10 divisions in the radial (y-axis) direction and 29 divisions in the axial (z-axis) direction. In the ATHOS analysis, the steam generator is considered to be symmetrical with respect to the diametral plane of symmetry of the bundle (along the x-axis). The model therefore, consists of one-half of the hot leg and one-half of the cold leg sides of the steam generator. Figures 7-2 and 7-3 show the plan and the elevation views of the model, respectively. These two figures show the layout of the flow cells and identify locations for some of the geometric features. As shown in Figure 7-2, with a Cartesian coordinate system, the circular wrapper boundary is represented by a step-wise wall as indicated by the heavy lines. Downcomer inlet ports are located on the extreme left and right sides of the model with a solid boundary at the top (IY 15) and the plane of symmetry at the bottom. Vertical flow baffles were modeled in the bottom z slab 1 to guide the flow into the tube bundle and attain a generally radially-directed flow pattern across the tubesheet surface. All of the flow cells outside the simulated wrapper boundary above the first axial slab were blocked off by specifying extremely high flow resistances on the faces of the appropriate cells.
. Figure 7-4 reproduces the plan view of the model but with the tube layout arrangement superimposed. This figure illustrates the locations of the tubes
- in the various flow cells. The fineness of the cell mesh is evident; the 1 largest cells contain only 20 tubes while some of the smallest cells include i
. only three tubes. Note, in particular, that additional detail.was added near the bundle periphery (IY 12-15) to more closely model the inner radius tubes 0238M:49/063088-15
(rows 115) which are typically more limiting with regards to the calculated stability ratios. For this same reason,12 axial layers of cells were included j
. in the U-bend region (Figure 7-3). . ATHOS Results The results from the ATHOS analysis consist of the thermal-hydraulic flow ~
parameters necessary to describe the 3-D flow field on the secondary side of the steam generator plus the distributions of the primary fluid and mean tube wall temperatures. Since the velocity components computed by ATH0S are defined on the surfaces of a flow cell, the tube gap velocity and density distributions along a particular tube required for tube vibration evaluation are determined by a post-processor from the ATHOS output. The post processor generates a data 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 tube are obtained by
. interpolation of the ATHOS calculated velocities (defined on the cell surfaces) and density (defined at the center of the cell). The post-processor performs - the necessary interpolations to determine in-plane and out-of-plane velocities at specific intervals along the length of the tubes.
Figure 7-5 shows a vector plot of the flow pattern on the vertical plane of i symmetry of the steam generator (the vectors are located at the center of the - flow cells shown in Figure 7-3). It is seen that in the U bend region the i mixture turns radially outward, normal to the curvature of the bends toward the , region of least flow resistance (i.e., outside the dome formed by the U bends). Figure 7-6 shows the resultant vectors of the radial and circumferential velocity components on the horizontal plane at Z - 21, the sixth plane above the top tube support plate (see Figure 7-3). The radial
- , outward flow is more evident from this figure since it ignores the axial !
component. It may be noted that the radial velocity at this axial location is
- j. ,
low at the center of the bundle and increases with radius. Figure 7-5 shows that the axial compone't is about four times greater than the radial component. Figure 7-7 shows the flow pattern (resultant of the radial and i 0238H:49/063088-16
circumferential components) on top of the tubesheet. Because of the thermal syphon action (resulting from the higher heat flux and vapor generation in the
- hot leg), a portion of the cold leg side fluid flows to the hot leg side before turning upward. The relatively high in-flow velocity along the tubelane from
,,- the wrapper opening is also evident. 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 velocity and density along the length of the tube are plotted from the hot leg tubesheet end on the left of the figure to the cold leg end on the right. Figure 7-11 shows the plot of the average in-plane gap velocity normal to the tube and density profiles as a function of the column number along Row 10. The average values were taken as the numerical average of the parameter over the entire 180' span of a U-bsnd at a given column location. The average velocity'is seen to be relatively (constant with values ranging from 10.5 to 10.9 ft/sec. However, the average density varies across the bundle with lower values present in the interior of the bundle and higher values on the
- periphery)a,b,c, References 71 L. W. Keeton, A. K. Singha1, et al. "ATHOS3: A computer Program for Thermal-Hydraulic Analysis of Steam Generators", Vol .1, 2, and 3, EPRI NP-4604 CCM, July 1986.
0238M:49/063088 17
Table 7-1 TYPICAL FARLEY OPERATING CONDITIONS AND RELATIVE STABILITY RATIO PREDICTIONS Bundle 1D* Steam Steam Flow Relative Unit- Flow Pressure Circ Ratio Stability Generator 6 (osia) Enlig 6 112 lbm/hr) 11Q lbm/hr) Ratio 1-A 3.82 821 5.05 19.3 0.95 1-B 3.87 821 4.98 19.3 0.96 1-C 3.92 824 4.93 19.3 0.97 2-A 3.97 807 4.85 19.3 0.99
, 2-8 3.86 804 4.99 19.3 0.97 2-C 3.82 807 5.04 19.3 0.96 Basis for ID to-3D Relative Stability
! Ratio Multiplier 3.88 780 5.04 19.6 1.003 l l l l RSR = (SRolant x) based on analysis of a Row 9 tube *(which ruptured in N. Anna) SR N. Anna 1 0238M:49/063088 18
8,b ,C , t i L M k l 1 l i l t Figure 7-1 Comparison of Relative Stability Ratios ! Calculated From la and 3D Methods a 0238H:49/063088 19 i i
t a , b ,c r L 5 n e 4 s i i i i
- i 4
i I i i . 4 1, 5 ll ll t ! I i . i t t t ! , i l' I I l
- l l !
j. l Figure 7-2 Plan View of ATH0S Cartesian Model for i the Reference Series 51 Steam tenerator ! l I ( I l- , t i , i i I 0230M:49/063088 20 t i 4 f I i
a,b,c l 1 i ! r Figure 7-3 Elevation View of ATHos Cartesian Model for the Reference Series 51 Steam Generator 1 i 0232't: 1?/00 003 21
l 4
- l a,b.c ,
i I l l i F 1 l
. i 1
1 i 4 , l ! L L i i , i i i I
- ~
i ? I I l t l Figure 7 4 Plan View of ATH05 Cartesian Model for the $ s: q Reference Series 51 Steam Generator Indicating ; l Tube Layout l .1 ; i .I I l ! l 023SM:49/063088 22 t 1 I L
^ '
a,b.c T 1 t i i I a e ,I i [ i 1 . i i j , i t L i i 1 L 1 i , Figure 7-5 Flow Pattern on Vertical Plane of Synnetty I t J l i ! i j 023SM:49/063088 23 l 4
. t
6 a,b,e W i
)
f i f i I G i + . t 4 I [ i ,, ! I ] a Figure 7-6 Lateral Flow Pattern on a Horizontal Plane in the U-Bend Region j i '! t 023SM:4f/063088 24 j
]
i i h
O e 4 a,b,c Figure 7-7 Lateral Flow Pattern on Top of Tubesheet 023SM:49/063088 25
e t I 4 t
- l i
f t a u.c ! i a > I i I , r r j i i i i
- h 1
i + 1 E l ? i l i l : l l , 1 l } l I l Figure 7-8 Tube Gap Velocity and Density Distributions f t for Tube Row 10/ Column 3 l i i l 022Sil:49/063088 26 l I s I I
, - - _ . _ _ _ _ . , _ _ . _ _ _ _ _ _ _ . . _ . . . , _ . _ _ , . - - . . . _ . . . , . _ _ _ _ _ _ , . - , . . . _ _ , , , _ _ _ , . ____.,_,u -
a.b.c L I 1 I 4 f I + I 1 1 . 1 ! l l l > d : }. t
- l. Figure 7-9 Tube Gap Velocity and Density Distributions f for Tube Row 10/ Column to i 1 ,
i 0238M:49/063088 27
) l I
1 l t I
- - ., . . . . _ - - . , . . . . . . - . - , _ . - - , - - . . - - . - - - - - , . . - , . - - - . . . - - - - , , - - - . . . - - - - - , , - - . - - - - . = - - - . , - , , - ,
a ,d c e Figure 7-10 Tube Gap Velocity and Density Distributions for Tube Row 10/ Column 40 023S't: 49/0630SS 28
l 1 e i e a,b.c ! l i [
- t
[ I f t I m L i 9 l I l i
. i
- Figure 7-11 Average Velocity and Density in the Plane of the '
U. Bends Normal to Row 10 I 023SM:49/063088 29 t
- . . - - - - - - - - - - - - . _ . . . - . - - -I
l 8.0 PEAXING FACTOR EVALUATION ^ This section describes the overall peaking factor evaluation to define the test based peaking factors for use in the tube fatigue evaluation. The evaluation of the eddy current data to define the AVB configuration for North Anna-1 Tube R9C51 is described. This configuration is critical to the tube fatigue assessments as the peaking factors for all other tubes are utilized relative to the R9C51 peaking factor. Uncertainties associated with applying the air model test results to the tube fatigue assessments are also included in this section. Included in the uncertainty evaluation are the following contributions: o Extrapolation of air test results to two phase steam-water o Cantilever tube simulation of U-bend tubes o Test measurements and repeatability o AVB insertion depth uncertainty 8.1 North Anna-1 Configuration e 8.1.1 Backgrcund The AVB configuration of the ruptured tube in North Anna, R9C51, is the reference case for the tube fatigue evaluations for other plants. In accordance with the NRC Bulletin 88 02, the acceptability of unsupported tubes in steam generators at other plants is based on tube specific analysis relative to the North Anna R9C51 tube, including *he relative flow peaking factors. Thus, the support conditions of the R9C51 tube are fundamental to the analyses of other tubes. Because of the importance of the North Anna tube, the support conditions of this tube, which were originally based on "AVB Visible" interpretations of the eddy current test (ECT) data (Figure 8-1), were reevaluated using the projection technique developed since the North Anna event. The projection technique is particularly valuable for establishing AVB I positions when deposits on the tubes tend to siask AVB signals such as found for the North Anna 1 tubes. The results of this ovaluation are sumarized below. s 0238M:49/063088 30
8.1.2 Description of the Method ~ The basic method utilized was the projection technique in which the AVB position is determined based on measured AVB locations in larger row tubes in the same column. In this study, the projection technique was utilized in the "blind" mooe, (AVBs called strictly based on the data) as well as the reverse mode (data examined on the basis of predicted AVB positions). The objective of this application was, with the greatest confidence possible, to establish the positions of the AV8s in an 8 column range around the R9C51 tube in North Anna 1, Steam Generator C. 8.1.3 Data Interpretation The ECT traces for the U-bends in Rows 8-12 (in one case, 13) were examined for Columns 48 55. The original AVB visible calls are shown in Figure 8-1. The data were examined by an eddy current analyst experienced in reading these traces, and by a design engineer knowledgeable in the geometry of the Model 51 U berd region. The intent of this review was to determine if the presence or absence of AVBs as shown in Figure 8 1 could be confirmed using the AVP projection technique. Preliminary projected AVB positions were based on geometric data provided for a few of the tubes near R9C51. The features which were sought were evidence of data "spikes" where AVDs were predicted, offset indications (multiple spikes) where offset AVBs were predicted, single indications where single AVB intersections were predicted, etc. The data evaluation method used was a critical examination of the data, which was biased toward the presence of AVBs unless a confident call of "no AVB" could be made, and then checking the consistency of the data among the tubes in a column and against the theoretical data for the pradicted AVB positions. ( 0238M:49/063088-31
ja,c, , Figure 8 4 is the 'AVB visible" map for columns 48 through 55, based on the critical review of the date. It should be noted that the original data I interpretations 3nd the review interpretations are consistent, i 8.1.4 Projections The ( la,c ECT traces were l utilized for projecting the position of the AVBs according to the standard format of the projection method. 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, more than one, and as many as three, projection values I n23BM:49/063088-32
are shown. Hv,ltiple 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 +. lowar AVB support that tube. As many as four different projections are possible if it is assumed that the tube is supported by the upper and lower AVB's, and both upper and lower bars are staggered in elevation as shown in Figure 8-2. 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 samecolumn[ Ja,c, [ J 1 I ja,C, ! Rule 2. Two adjacent tubes in the same row ( ' > . Ja.c. Consequently, the difference in the [
)..c, l:
i l 0238M:49/063088-33
l The implementation of this is that if the position (either ieft or right) l of a projected AVB is assumed for a column, then the projections in the
. adjacent columns are also (
ja.c,
~
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, based on the projection matrix of Figure 8 5 is shown in Figure 8 6. 8.1.5 Conclusions The general AVB arrangement surrounding the ruptured tube in North Anna 1, < Steam Generator C, which was the basis for the analysis, is confirmed by a detailed critical review of the ECT data. Differences exist is the AVB 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 to the rules which were adopted for determining the position of the AVBs, as
. well as consistent with explanation of the tube failure.
- The basis of tne review was a projection technique which utilizes data from tubes one or more rows removed from the actual inserted position of the AVB to determine the position of the AVB. The intent of the review was to establish the positions of the AVBs by confirming or eliminating features of
- AVB alignments such as side to side offsets, etc. of the AVBs adjacent to the l tubes. Overall, the conclusions regarding the positions of the AVBs around i
R9C51 in North Anna 1, Steam Generator C are based on consistency among all the available data, t 8.2 Test Measurement Uncertainties
. The descriptions of the peaking factor tests and apparatus were provided in ,
Section 5.4. All practical measures were taken to reduce uncertainties.
- Nevertheitss, some still remain and should be properly accounted for. The important parameter measured during testing that has a significant impact on
- l. <
i l l j 0238M:49/063088-34
- i
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 this analysis based on past experience.
. 8.3 Test Repeatability During the peaking factor testing of AVB configuration, each test was 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 value of 5% was used in the current uncertainty analysis.
8.4 Cantilever vs U-Tube A first order estimate can be made of the validity of modeling a U bend tube by a cantilever tube in tests to determine th effects of AVB insertion depth on the initiation of fluidelastic vibration. The following assumptions are used: ac l r 7 t I 0210M:49/061588-35
r
, , a,c 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 i Row 10 tube. ( l Ja.c, The comparison between a U-bend tube and the model tube involve the consideration of an effective velocity associated with the flow perturbation , caused by the AVBs. ( i L I i l Ja.c j i 0210M:49/061588 36
[
)**C, Using these values, the ratio of the effective velocity for the cantilever measuring tube to that for the U-bend tube is about
[ Ja.c for the case treated. A similar evaluation can be made for a Row 10 tube that lies in the projection or shadow of an AVB that is inserted to a depth required to support a Row 9 tube. ( Ja,c, The net result is that the ratio of the effective velocity for the cantilever tube to that for the U bend tube is about [ Ja,c, These results indicate that, for the particular assumptions used, the ! cantilever tube model appears to be a reasonable representation of the U bend with respect to determining relative peaking factors for different AVB configurations. This evaluation also shows that, on the average, the magnitude of the systematic uncertainty associated with the use of cantilever - tube to simulate the U bend is about [ la.c, 8.5 Air vs Steam Water Mixture I 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 , l 0238M:49/063083-37 l 1
1 velocity and thus a direct factor on a stability ratio, or as a factor on the steam velocity only with associated impacts on density, void fraction and damping. This method leads to a reduction in tube damping which enhances the peaking factor compared to the direct air test value. For estimating an
. absolute stability ratio, this application of the peaking 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 air test peaking factor. This conservative approach is therefore used for evaluating tube acceptability.
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 steam 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. j Based on the above discussion, the Fj are considered to more appropriately apply to the steam phase. Thus, it follo'ss that mixture reass velocity for the tube subject to flow perturbation can be written as follows: !
- - a,C l
I where gD is the vapor density, Df the water density, Fa the velocity peaking factor determined from air tests, jg* the nominal superficial vapor l* velocity, and jf* the superficial water velocity. Steam quality can then be determined as follows: 0210M:49/061588 38 e,
a,c '
. The Le11ouche-Zolotar correlation (algebraic slip model), as used in the i ATHOS code, is applied to determine void fraction. Subsequently, mixture deasity, velocity and damping coefficients for the tube which is not supported and subject to flow perturbation is evaluated. Therefore, similar to the air velocity peaking factor, local scaling factors of mixture density and velocity and daeping coefficient can be readily determined. Finally, a local stability peaking factor for fluidelastic vibration can be calculated as follows:
- a,c where sF is the stability peaking factor, Fd the density scaling factor, Fy the velocity scaling factor, and Fdp the damping coefficient scaling
. factor. If we use the air velocity peaking factor without translating to steam /waterconditions,then
- a,C As shown in Table 8-5 stability peaking factors for the steam / water mixture are slightly higher than air velocity peaking factors. The difference between the steam / water and air peaking factors increases as the air peaking factor increases, t
For application to tube fat'gue evaluations, the ratio of the peaking factor for a specific tube to that for North Anna R9C51 is the quantity of , interest. Larger values for this ratio are conservative for the tube fatigue
, assessment. The North Anna R9C51 peaking factor is one of the highest peaking factors. As discussed in Section 8.7, a peaking factor of nearly - [ ']a,c is determined for the R9C51 tube. The differences between [
] 1 Ja.c. Typical values are shown in Table 8-2. These results show 0210M:49/061588-39
that the direct application of the air test data yields the higher relative peaking factor compared to R9C51. To obtain conservatism in the peaking factorevaluation,( i Ja,C, 4 . t Comparing the values in the first and last columns of Table 8-1, it may be noted that the stability peaking factor for : team water is ( la,c ; higher than the air velocity peaking factor. On the average, the uncertainty associated with the conservativa use of air velocity peaking factor is ! [ Ja.c, ; The conclusion that peaking fetor for steam water flow would be higher due to the dependency of damping ratio on void fraction was supported by an j alternate study. In this study, a section of steam generator tubes were ! simulated using the ATHOS code under protypic flow conditions. The objective l of this study was to examine the magnitude of the changes in void fraction and thus stability ratio as a consequence of non-uniform AVB insertion patterns. The current version of 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 i calculation of the peaking factors for a steam generator to account for the j
- preferential steam flow along the low resistance path. Consequently, the
[
- intent of this analysis is only to help bound the uncertainty on void
- fraction effects from extrapolating the air tests to steam water.
First the analysis was conducted with uniformly inserted AVB's in the ATHOS , i model. The ATHOS results were processed by the FLOVIB code to determine i l stability ratios for the specific tubes of interest. The calculation was l l repeated using a non-uniform AVB insertion pattern in the model. The results t i show that the void fraction distribution changes as a result of flow I !* perturbation. Further, the impact on stability ratio resulting from the changes in void fraction profiles was about ( la.c. This alternate l calculation provides independant corroboration of the prior discussion regarding the stability peaking factors under steam water conditions vs in air. ! \ I L 0238M:49/063088-40 l
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 ) ~, adjacent to specific tubes. The methodology used for obtaining the AVB insertion patterns from eddy current data can ascertain the AVB location only j to within approximately ( j Ja,c. The effect on peaking factor resulting from this uncertainty is addressed using test results of AV8 configurations that varied from one anotherbyupto[ Jac, ! Based on maps of AVB insertion depth of various plants, several i configurations have been tested for determining fluidelastic instability flow I
- rate by an air cantilever model. Stability peaking factors were then f
- determined from the ratio of critical flow rate for a uniform AVB insertion ;
configuration to a specific configuration. Figure 8-7 sumarizes the AVB : ,, configurations tested. l l
'. Position of AVB insertion depth is determined from Eddy Current Test (ECT)
! data. Positioning of AVB froia ECT data reading is subject to uncertainty- ! j its accuracy is probably about ( la,c. A change of an AVB l l insertion depth in a given configuration leads to a different configuration, l ) and thus a different peaking factor. A review of the tested AVB type has been made and results sumarized in Table 8 3. As can be seen, a decrease in , 1 depth of an appropriate AVB tends to decrease the peaking factor, for [ instance,a( ] la.c. Such a trend can be explained. A decrease in a specific ! 1 AVB depth will open up more channels for incoming fluid to distribute and thus less flow perturbation. However, this applies only'to those changes without inducing the reinforcement of flow perturbation from upstream to 4 downstream. ( l : ! J Un the average, the uncertainty in peaking factor resulting from small l variations in AVB insertion (of the order of 1/2 tube pitch) is found to be [ l [ la.c, i ! 1 l l l I l 0238M:49/063088 41 l
! I
8.7 Overall Peaking Factor with Uncertainty As discussed in the previous subsections, there are several aspects to be considered in applying the laboratory test data to steam generator - conditions. These considerations were reviewed one at a time in those subsections. This section will integrate the pieces into one set of - stability peaking factors. Looking forward to how these peaking factors are used in the analysis (Section P,', the relative stability ratio calculated for a given tube without the consideration of flow peaking is corrected using the ratio of the peaking factor of the specific tube to that of the North Anna R9C51 tube (Configurationla). It is to be noted that, of all the configurations tested, configuration Ib produced the highest peaking factor, followed very closely by la and two other configurations (designated 4C and Se) which are not pertinent to the Farley steam generators. This is encouraging in the sense that it tends to explain why, of all the tubes in service, the R9C51 tube was the one to experience the fatigue rupture. It is to be noted that the test results would be applied as ratios of a specific tube peaking factor to the R9C51 peaking factor. This will reduce the influence of some uncertainties since the systematic uncertainties would affect both the numerator and the denominator in the ratio of peaking factors. The major difference will be in those configurations whose peaking factors are significantly lower than that of R9C51. The approach employed here is intended to provide that conservative peaking factors are employed for such appartntly low peaking configurations. The uniform AVB configuration (2a) is selected as a reference configuration, and the peaking factors of all configurations tested are recomputed on the basis of this reference. Configuration 2a corresponds to configuration 12a in Figures 5-12 and 8-7. However, 2a applies to the original AVB configuration where 12a is for the modified AVB configuration. Similarly, 3 denotes the no AVB case in the original AVB design tests, where 13 denotes the no-AVB case for the modified AVB tests. As discussed below, some of the test uncertainties are applied to the reference case to account for its significantly low peaking relative to the R9C51 configuration. 0238M:49/063088-42
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 were discussed in more detail in the previous subsections. The magnitude of these uncertainties are listed in Table 8 4. Of these uncertainties, those due to measurement and repeatability of tests are random errors and can occur in any test. Therefore, these are treated together. The total random uncertainties are calculated by ( Ja,c. The RSS value of these is i ( ]d. Since these can occur in any test, these are to be applied to all tests. One way of doing this is to apply it to the R9C51 value, that being in the denominator of the final peaking factor ratio. Thus the peaking factor for configuration la (R9C51) is reduced by this amount to yield a value of '( Ja.cinsteadofthe( Ja.c appearing in Table 5-2. The next three uncertainties in Table 8 4 are systematic uncertainties. It could be argued that these appear in the peaking factors of both the specific t , tube under consideration and the R9C51 tube and are therefore counter balanced. However, the relative magnitude of these may be different, particularly for configurations with much lower peaking than R9C51. Therefore it was judged that the ( l Ja.c. Similarly, as noted above, the effect on peaking factor due to the uncertainty in the field AVD configuration is also included in this reference case. Thus,( . Ja,c. The peaking factor of the reference configuration 2a (Table B 5) is raised by this amount to a value of ( Jac, The change in peaking factors of configurations la and 2a resulting from the application of uncertainties as described above are shown in Column 3 of l Table 8 4. The peaking factors of all configurations are recomputed on the basis of this reference configuration (2a). These values are displayed in Column 4 of Table 8 5. i i 0238M:49/063088 43
Some of the uncertainties were applied to the reference configuration (2a) in
, 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 l* is calculated for any configuration, (in Column 4 of Table 8 5), it should be alteredto( Ja,c. Further, for some of the configurations that are conceptually similar, the more limiting (higher) value is used. For example, a peaking factor of ( Ja c is used for configu;ations 5a and Sb based on their similarity to configuration Sc.
The final stability ratio peaking factors calculated on this basis (with configuration 2a as the reference) are shown in Table 8 6. It may be noted that the peaking factors vary in the range [ ja.c the R9C51 peaking factor being ( Ja.c. Figure 8 7 snows the final peaking factors with the' pictorial representation of the AVB insertion patterns.
. Table S 7 shows the result of applying the peaking factors to specific tubes i in the Joseph Farley 1 and 2 steam generators.
The overall conclusions from the peaking fa: tor assessment are:
- 1. As noted in Table 8-4, five elements have bsen 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 I ]a,c is ! attributable to uncertainties of up to ( )4'C on determination of AVB insertion depths from field eddy current data. This relatively large uncertainty is applicable only to low peaking conditions where the AVB uncertainties can contribute to small peaking factors. The definitkn 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, AVB's were positioned within uncertainties to maximize the peaking factor. For these configurations, I
variations of AVB insertion within these uncertainties are expected to reduce the peaking factor compared to the final values of lable 8 6 and Figure 8-7. 0238M:49/063088 44
- 2. Including uncertainties directed toward conservatively decreasing the peaking factor for the North Anna tube R9C51, t,he final R9C51 peaking factor is ( Ja c relative to a no flow peaking condition such as with uniform AVB insertion depths.
- 3. The final peaking factors include peaking effects greater than the R9C51
~ tube although this is believed to be a consequence of the conservative ! uncertainty analysis and is not likely to be representative of actual peaking effects. f l l
. i i
I i i
. i I
t l 0238M:49/063088 45 i l
i Table 8 1 Stability Peaking Factor Due to Local Velocity Perturbation Scaling Factors for Stea# Water Air Velocity Void Stability ' Peaking Fraction Density Velocity Damping Peaking Factor, Scaling, Scaling, Scaling, Scaling, Factor, 4 F a Fy Fd Fy F dp Is
; , a,c i
NOTE: 1. fitability peaking factor for steam / water mixture is . j calculated as follows:
- a,c '
i
- i d
- 2. Damping scaling factor is calculated using modal I effective void fraction of [ Ja.c for R9C51 tube. l f
l j 0210M:49/061788 46
Table 8 2 COMPARISON OF AIR AND STEAM WATER PEAXING FACTOR RATIOS t Air Air Steam Steam Peaking Peaking Peaking Peaking , Factor Ratio Factor Ratio :
, a,c
~
l l
- l
. . i l l
! i
! l i
i I l ' i r I l- t f I: l i l l 0238M:49/063088-47 l {
. Table 8-3
. Effect of Local Variation of AVB Insertion A to 8 AVB Peaking Peaking Ratio Type A Type B Variation Factor A Factor 8 (B/A)
,, a,c
, a,C i
\ .
i 0210M:49/061588-48
Table 8-4 Uncertainties in Test Data and Extrapolation - Source of Uncertainty Iygg Maanitude. %
,aic
- 1. Velocity measurement Random
- 2. Test repeatability Random
- 3. Cantilever vs U tube Systematic
- 4. Air vs steam water mixture Systematic
- 5. Field AVB configuration *
. . s
- This is not an uncertainty associated with the test data.
It results from the inaccuracy in determining the true AVB position in the field using eddy current data. 0210M:49/061588-49
Table 8 5 Extrapolation of Test Results to Steam Generator Conditions t i Peaking Factor Test Data with Referenced to i confinuration Q114 Uncertainties Confia. 2a I - - , a,c , la lb i 2a 12a ' i 13 , l 14d ; 14e , 15b i 17c 17d 17e 18a ( 18b {
- i i ;
i l
- I i i 0210M
- 43/061588-50
s Table 8 6 i FINAL PEAKING FACTORS r { Confiauration Peakina Factor !
,., ., a,c l 1a i
1b , i l 2a 12a 3 1 14d 14e l 17c 17d , i 17e 18a . 18b ,
. l J L l
r i l 1 i . I C i I I i P i I l l 0210M:49/061588 51 i l I
., - _ - . _ . , , _ , _ _ , . _ . _ _ _ _ . , - -m.--g.. ,,p., _.._, , , .- , , , , ,_- . _ , . _ . . _ -_
i Table 8-7 1 Stability Peaking Factors for Specific Tubes
~
Farley 1 and 2 UNIT STEAM GENERATOR R0W NO. COLUMN NO. PEAKING FACTOR *
- . . a,c 1 A 9-11 All B 9 11 All C 9 11 All 2 A 9-11 All l
. B 9-11 All ;
C 9-11 All i i
- The peaking factor is divided by 1,47 to obtain the relative flow j peaking factor to R9C51 of North Anna 1. !
l l i i I f l 0210M:49/061588-52
22
.oooo oo ,
u 0000 OO OOOO
~
4o 90000@O 00@@@ 0000@@@ 56 55 54 53 52 51 50 49 000.00 48 47 48I 45 44 O OTs'ista @$Nisiata e FAILED WBE O PLUGGED l Figure 8-1 Original North Ant:a AYB Configuration 01 01:49/030788 49 l
Figure 8-2 Schematic of Staggered AVBs Oletti: 49/030783 50
a,e i f L I I i I t l
. r f
I l
)
l l f i l: i i Figure 8-3 Avg *Patr' in ECT Trace l I i L ) 0142M:49/030788-51 __,..,__.__________________,,_]
l
. 1 n- G , .
~
22 00@O0000 0 000 tt OOGOOOGO OOOOO ta OOGO 00@ O0000 ' OODDD@DODOOOO 8 Column OGGOGGGOOOOOO 56 55 54 53 52' 51 50 49 48 47 46 45 44
$ Plugged Tube g FacedTut:e a"
.~.*."nLT2"L*%"2122%" ".'n Q.2"2"l2"t
1 l i Figure 8-4 North Anna 1. Steam Generator C, AVB Positions critical Review 'AVB Visible
- Calls 01401:49/03078S 52 i
_ _ _ _ . . _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . . _ _ _ _...___________~.____m_ ._ __ . _ _ _ _ . _ _ _ _ _ _ l 1 l
. R13 -- ""
l u, e. l N N R,s - - ... ... ... .... R11 - - . sa 66. l.7. e.sa e,ya fn , . ea , , , s., ,,,, , ,, j p p , , , ,, Rio - - . 1. , "
~ _
O DYE
~~ g Ra--
i Ave Eve 4%(. i Se Eve $*vsSUs it s Ivs Eve l* h
- it Ivo S s l
css es4 . css esa est cso c4e c4s
*:,*Otl- . %u l u.uv ms '
a,e
,,e E ~ sm ; , w sa..
. . i
?
Figure 8-F North Anna,1. Steam ,Ge,nerator C. R9C51 AVB Matrix l 0142M:49/030788 53
22 OOO OOOO OO O O O O tt O00 0000 00 0 0 0 0 ta 0 0 0 0000 00 0 0..O.O.
-
- O OO OOOOOOOOOO
.O'O O O O O O O O D O O O 49 48 47 44 45 44 56 $$ $4 53 52 51 50
- i l
*'" i Figure 8-6 North Anna R9C51 AVB Final , ,
Positions R101M 02/f41a71A 12 - - - _ - _ - . _ - _ _ _ _ _ . - _ _ _ _ . . - - _ _ _ . _ - - _ _ _ _ _ . - - - - - - - _
TYPE OF AVB PEAKING TYPE OF AV8 PEAKING INSERTION FACTOR INSERTION FACTOR C C C C Ck t CCCCCCCO CCCCCC C CCCCC CCO C C C CCC ' CCC9 1a CC Co. coo 1.47 14e 0000.CnCO 000 1.00 OC000000 00000000 . 00000000 00000000
- CCCCCO CCCCCCC0 CCCCC0 CCCCCC Co 1b C CCC C o Co.Ce a 1.64 15b c0700c'o 0000 000 1.00 OOOOCO 00000000 00000000 00000000 CC !;; :;; ; !;; ;n3 CCCCCCC0 C :o.. ... ... ... .. u . c C ,=%: ~.
Cc 3 2a or *"*C o .0% CCN 1.00 c CCo 12a 00000000 17c OC60iOCo 1.00 00000000 00000000 oooooooo C0000000 CC CCCCCo 00000000 CC CCCC0 3 or OO 1'00 17d ": o 13 O*Ox.000 0000 c"~".: C000 C00 1.00
' 00000000 00000000 00000000 00000000 CCCCCCCO '
2 C CO C C :: C C C C 0 : CCo C C. : CCo 1.58 : C C o 4C CCCC o C. C Co 17e t 0000 000 1.00 CCC00CCo 00000000 00000000 00000000 C l.; t. 3 CC C o :: o
. .; CC C i t :: 0 Se E !!!!
C 3 FS
. O3 C 1,56 18a E ssO.'Os 8 1.02 C C 300000 00000000 C0000000 00000000
*CCc 0 C C C C C C2 0 C C C C C C: o CC eC C 0 14d p;ssss:;C e-s s8 1,00 18b EE55.6-58 1.00 00000000 00000000
, 00000000 00000000 Figure 8-7 Final Peaking Factor for Farley 1 and 2
l l I l 9.0 STRUCTURAL AND TUBE VIBRATION ASSESSMENTS 9.1 Tube Mean Stress ' - This section summari .s the analysis to determine stresses in a dented tube at 100% power. Loads imposed on the tube correspond to steady-state pressure, differential thermal expansion between the tube and the support plate, and a thru-wall thermal gradient. The analysis assumes the tube to be [ ]a,c at cold shutdown. A sumary of the temperature and pressure parameters at 100% power in the vicinity of the top support plate are provided in Table 9-1. The tube temperature corresponds to the average of the primary-side water temperature 2nd the plate tercerature. The resulting tube / plate radial interference is [ J8 . 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 [ 4 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 fora ( 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 f]r 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 calculated to be 9.6 ksi using conventional analysis techniques. The 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. 9 0238h:49/071188 53 l
The maximum axial tensile stress is 23.1 ksi and occurs approximately 0.125 inch above the top surface of the support plate. Adding, for conservatism, the surface stress due to pressure, 0.8 ksi, gives an applied mean stress of 23.9 ksi. In addition to the applied stress, residual stresses exist in the tube as a result of the manufacturing process. For mill annealed tubas with subsequent straightening and polishing, residual stresses are compressive at the tube surface, but 5-10 mils below the surface, the
~
st .s levels change to 10-15 ksi tensile, Reference 9-1. Combining the applied and residual stresses results in a cumulative mean stress of 38.9 ksi, assuming tube denting without deformation. If a tube is dented with deformation, the mean stress is limited by tube yielding. M r the case of dented tubes with deformation, the maximum effect of mean stress was incorporated by using amax " 8y in determining stability ratios and fatigue usage. 1 9.2 Stability Ratio Distribution Based Upon ATHOS 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 finite 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 U,/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 ATH05 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 FASTVIB/PLOTVIB consists of tube support conditions, fluid elastic stability constant, turbulence constants, and location dttendent flow peaking factors.
0238M:49/063088 54
This process was performed for the Joseph Farley 1 and 2 steam generator tubes and also for the North Anne "ow 9 Column 51 tube (R9C51) using similarly appropriate ATH0S mode... Ratios of the Joseph Farley 1 and 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 Joseph Farley 1 and 2 tubes relative to the ruptured tube at North Anna Unit 1.
In generating the Farley results, one-dimensional analyses are used, as discussed in Sections 7.1 and 7.2 to develop a relative stability ratio between the Farley units and another Model 51 unit for which three dimensional vibration analyses had been performed. The 1-D correction leads to a 2.5% increase in stability ratios relative ta t M.t 3-D analyzed unit. The operating conditions used in the 1-D analyse & ,ivelop the actual operating conditions (provided by Alabama Power Co.) of both Farley units. Figure 9-5 contains the results of this process for each of the rows under investigation. This figure is the result of using the following conditions
- for both Farley units 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.
Based on the AVB maps, the flow peaking test results are within the evaluated definition of no flow peaking, including the effects of AVB position uncertainty. A horizontal line is drawn at the relative stability ratio value of 0.90.
- This tuentifies the point where a ten percent reduction in stability ratio exists relative to North Anna R9C51. (Ste 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 0238M:49/063088 55
percent of North Anna R9C51. This figure indicates that relative stability
- ratios for all tubes in Rows 8, 9 and 10 and most outer tubes in Row 11 are
- less than 0.9. Essentially all inner tubes in Row 11 and all tubes in Row 12 lie above this line. ) 9.3 Stress Ratio Distribution 4 An evaluation was performed to determine the ratio of the Joseph Farley Unit 1 and 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) and bending me.ient 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) Tubes are assumed to be dented or undented (both situations were considered, but the evaluation is based on the more limiting, dented case).
A tube can be considered acceptable if the stress ratio is less than 1.0 when calculated using the procedure described in Sections 4.2 and 4.3 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.
0238M:49/063088-56
Figure 9-6 shows the results cf the stress ratio calculations for each of the Joseph Farley Unit 1 and 2 tubes in Rows 8 through 12. This figure is
- 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 conditions at Farley correspond to this latter definition of denting.
As can be observed in Figure 9-6, all tubes in Row 8 through 11 fall in the acceptance region with respect to U-bend fatigue. The two corner tubes at Columns 2 and 93 in Row 12 also lie in the acceptance region. The remaining tubes in Row 12 (as well as tubes in higher rows) lie above the SR 1.0 line but are currently supported by the AVBs, and therefore, excluded 'from further evaluation. [ 9.4 Cumulative Fatigue Usage All tubes that are unsupported and have a stress ratio 11.0 have a maximum a stress atp itude that is < 4.0 ksi (from 9.5 ksi) since a 10% reduction in the stability ratio for the North Anna Row 9 Column 51 tube was the criteria basis. The stability ratios for the Joseph Farley Units 1 and 2 tubing are based on the current operating parameters and with future operation on the same basis, the tubes will not rupture as a result of f 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 1-D adjusted analyses, all Farley 1 and 2 tubes meet the relative stress ratio criteria under the current AVB
. conditions. Table 9-2 provides a :umary of the combined relative stability ratios and the stress ratios for the highest stressed unsupported
- tubes in each of Rows 8 through 12.
0238M:49/063088 57 l
1 Acceptability of the Farley Unit 1 and 2 tubing for fatigue is accomplished by demonstrating the acceptability of the tubes with the highest stress
- ratio, 0.84, at Row 11 Columns 46 through 49. Assuming the tubes have been dented since the first cycle and continue to operate under current f
conditions, the total usage including the remaining term of the operating license would be 0.4. In the event of a future uprating of the plant, the potential for tube fatigue must be re-evaluated. Prior Fatigue Usage Currently, only Row 11 and smaller tubes in the Farely units are unsupported and subject to future fatigue usage. As discussed above, these tubes meet stress ratio criteria based on continued operation at the same stability ratio. The predicted fatigue usage for the limiting tube is about 0.01 per year or about 0.4 in 40 years. The fatigue usage prior to the modification was not calculated precisely since the old AVB positions and associated peaking factors were not determined. l l By the prior design, Row 11 tubes are expected to have had AVB support and consecuently negligible prior fatigue usage. However, AVB position evaluations for other units have indicated an occasional Row 11 tube that was not supported. Based on a sample of 2852 Row 11 tubes in similar model steam generator designs, less than 0.5% of the tubes have been determined to be unsupported. The percentage of unsupported tubes in Row 10 is somewhat higher on the order of 3.3%; however, the stress ratio for a smaller tube is progressively lower as shown in Figure 9-6. Also, based on prior analyses, only a small fraction of unsupported tubes have been judged to have flow peaking factors large enough to result in relttive stability ratios of greater than 0.9. Therefora, the probability of Row 11 and smaller Farley tubes having a significant prior fatigue usage and/or a
. large crack is very smal'.. Also, from the EC inspection, there are no indications that would suggest the presence of significant cracking in the ; susceptible region of the U bends.
l 0238M:49/063088 58 1
3 s Table 9-3 sumarizes the acceptance basis of Row 11 tubes based on the fact that Row 11 tube stress levels, expected under the current conditions,
.. would not lead to. rapid propagation of existing but undetected cracks. . If a crack does not exist now, the fatigue usage in the tubes is probably low. But if a crack were to initiate during subsequent operation, the crack growth rate would be insignificant since even a 30' (0.22 in.)
thru-wall, circumferential crack does not result in crack tip stresses that are above the threshold for crack propagation, 4.5 xsi/Tii. For reference, a 30' thru-wall crack is estimated to allow a leakage rate of 35 to 40 gallons per day (gpd). If it is postulated that a crack does exist now in some tube, the crack size would be bounded by the crack that was in the tube at A9C51, North Anna 1, before it began to leak. That crack is estimated to have taken about 12 hours to propagate from its initial thru-wall length to a length that allowed a leakage rate of 500 gpd. The most highly loaded Row 11 tube
. has a stress amplitude of $3.4 ksi. Based on a comparison to the stress amplitude that caused the rupture of R9C51, the time to reach the same level of leakage rate in Row 11 of the Farley SG's would be greater than 40 days.
l 0238M:49/063088-59
I < ( o
/
l..
\
Table 9-1 , l
- l. 100% Power Operating Parameters l Farley Units 1 and 2 <
Bounding Values for all Cycles
! i r
( l r Primary Pressure - 2250 psia Secondary pressure - 793 psia Pressure Gradient = 1457 psi Primary Side Temperature * = 577'F Secondary Side Temperature - 517'F Tube Temperature - 547'F e t ( 0238M:49/071188 60 _:_ - ~.
Table 9-2
'g Summary of Farley Evaluation of the Salient i Unsupported U-bends
.t:
l REl.ATIVE STRESS g3 LQ,LL. STABILITY RATIO (l) M (I) 8 47 and 48 0.59 0.12
- 9 38 thru 57 0.69 0.23
- 10 45 thru 50 0.80 0.45 l
11 46 thru 49 0.92 0.84 12 2 and 93 0.92 0.72 l (1) All ratios are in comparison to R9C51, North Anna 1, Steam Generator C. 1 l
;I l \
l ) ' ;T t 0238M:49/063088 61
Table 9-3 3 Disposition Criteria Relative to tube U Bend Fatigue l
,. Farley Units 1 and 2 Present Condition Pre-Mod Condition Disnosition Snii AVB Support AVB Support Accept Stable Tube No AVB Support Accept 1, 2, 3 No AVB Support Stress Ratio <1 AVB Support Accept 4 No AVB Support Accept 4 Stress Ratio >I --- Sentinel- . plug
- -- 1. lube is currently stable and has no indication of cracking.
- 2. Fatigue usage due to normal operating loads, excluding tube vibrations, is
[ 1ess than .001/ year. i l 3. If it is assumed that prior to AVB modifications the tube accumulated fatigue usage such that potential to develop a crack exists, the rate of : propagation will be very low. Leak monitoring and EC inspection during scheduled outages will provide adequate control for detection and/or an orderly shutdown. ' I
, 4. Based on the current methodology / criteria, alternating stress is less than l' 4.0 ksi due to fluidelastic vibrations. A crack, should one develop during I- operation, will not proptgate at rapid rate, thus allowing detection and/or L an ord wly shutdown. For a currently unsupported tube, the maximum future usage assuming denting and full power operation is .01/ year (at location R11Ca6).
0238H:49/063033-62
= , , - - - - - - - - - - - ,, -- , -,--,-----..,n.- --
.- ---,,-----.----,---,n,--- , - - - , .
l f i
^
, i 1. I 1 TUBE I SUPPORT PLATE I :
- - \
i -
\ .-
t ( (, Figure 9-1 Axisymmetric Tube Finite Element Model t > 0238M:49/063088-63
r DENTED TUBE STRESS DISTRIBUTIONS PRESSURE LOAD ON TUBE ' PRESSURE = 1000 PSI
, OUTSIDd SURFACE
'" i l l
. o a w.siness o Moor sTasss Iasse
'*** _e _
eeen >
= =,
\ x
. e -
2.es
\\
sees g
*M. . .a .s .. .s .e . .e .* i.
O f StassCC FDP f t8 CCN f t tt f( IN Figure 9-2 Dented Tube Stress Distributions
; Pressure Load on Tube 0238M:49/063088 64 e
DENTED TUBE STRES3 DISTRIBUTIONS
- INTERFERENCE LOAD ON TUBE 1 MIL RADIAL INTERFERENCE OUTSIDE SURFACE I I I essee -
0 Ax1AL STRESS
. O NOOP STRESS 48000 y [N N
. . e - m
\ .
e ~ 7 ~ f 9=
\> t 5
- 48006 0
.steet
- 2 ^-
1 .ieesse l l l
*129000 l
l l
- 4. .6 .2 .4 .4 .6 4 7 ,8 .9 3 OlttanCC rem top CtNitet.leC
- IN lI Figure 9-3 Dented Tube Stress Distributions 1 Interference Load on Tube l
l
- 0238H:49/063088 65 l .
i
. .. . W . > -
a m 1 SE 4 e ' a \ 8 1 COMBINED STRESSES - TOP SP - 100% POWER l 5: m l FARLEY Ut4151 #40 2 y 25 c f*/ % a m:g = : ;; = :
;ag is ::cecauseo ..
1 $ ?. 4$E 10 ( , e= \ ,j, x=r
" 2 u.
a
,;a s
I\ '[ , c*
~, m"y mm O
- s :ss u Uo . .: . ..: ' : +++
$ EM t;- -s i
m e a '
; ii
. ,+
1 -10 E r+ 1 i ( g -15 I a
-20
-25 0 0.2 0.4 0.6 0.8 1 DIST#4CE FROM TSP CCITERLIt4E - Ita O AxtAL-OUISIDE
+ LOOP-OUISIDE
2 1 _ 0 5 W O R
. X 0 ^- ..
X 0 ^- . _- X X 2 - . X ^ - .
" 0 - ..
" ^ - .. _-
x ^ -- ..
= ^ -. .
_- ,0 4 x 0 -. . x 0 -. . 1 1
-" 0 -. ,
P W -
-" 2 -. ,.
O F -" ; : , c R
* -" n : ,
c 2 a : , _" ' ' : . A R )2 n_ p ,3 0 5 R- . S q- . R A = . - _ E
. T " .- ,- ' B E
EB .
, - , M VA ,
.n '
U N p_- I T -' _- TE -" _- N0 1 M A ZP - _u UW LE p .- a , 0 2 LO D e OR . E - " s C RWE e M m .
- : s 0
.- : c
-( .
c
- " g A
L 0 6 0 A _, 0 , 1 _ : 0 9 0 y .# g , 0 W O 0 R w ,g_
. 7 0 ,
9 , I
+ -
J4 0 1 1 S - 8 7 6 5 4 3 1 0 0 0 0 0 0 0 8 W
,z = ,od e gF40 {J $ b w>E b o : c O -
R - D m
*.c s:*. g . <
- g ,, r . ' a e'+ < W5., E =cwe S 22' O*ee3ce3+r
, e ,
t
, e1:
e e e .. oEw ,o. n S n ON,.Z. .o.~OO: C.ow l11 1'1 1<
* ** * . 'A , g ,
O N taa 3 40 A m ,, ALA - STRESS RATIO ALA/NAR9C51 g (MEVF DEP ZETA W DENTING) o 2 m c - 1.9 - I m 1.8 - 1.7 - 2.6 - , e 1.'.5 - en en 1. 6 - E 1.3 - S O P 1.2 - o 4 g 1.1 -
- En 1 --
so n a.s o,g .
~
0.8 - 0.7 - 2h 2c O.6 - b O.5 - Er
.- --- '..-0::0m s
0.4 - _
- 0.3 - 1 - 000 W '' .... . .... ...
o.2 - f u..... .......: .:...: m - W y o.i - f66666;oooo-~;-a c c a c a =eesones= = =. = = =. = = =. =====S
= o . . . . ,
20 30 40 50 O 10 E
=
" COttlMN NUMBER o HOW 10 A ROW 11 X ROW 12
+ ROW 9 C D ROW 8 O
3
- - ---__ - - - - __}}