ML20151K686
| ML20151K686 | |
| Person / Time | |
|---|---|
| Site: | Prairie Island  |
| Issue date: | 03/31/1988 |
| From: | Connors H, Frick T, Hall J WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML19302D478 | List: |
| References | |
| SG-88-03-022, SG-88-3-22, WCAP-11788, NUDOCS 8804210382 | |
| Download: ML20151K686 (147) | |
Text
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WESTINGHOUSE NON PROPRIETARY CLASS 3 WCAP 11788 SG-88 03-022 PRAIRIE ISLAND UNITS 1 AND 2 EVALUATION FOR TUBE VIBRATION INDUCED FATIGUE MARCH, 1988 AUTHORS H.J. CONNORS H.M. HU I
T.M. FRICK H.O. LAGALLY J.M. HALL A Y. LEE G.W. HOPKINS P.J.PRABHV J.L. HOUTMAN R.E. SMITH
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APPROVED T.A. PITTERLE, MANAGER STLAM GENERATOR ENGINEERING WORK PERFORMED UNDER SHOP ORDER MP70-78998 WESTINGHOUSE ELECTRIC CORPORATION POWER SYSTEMS BUSINESS UNIT SERVICE TECHNOLOGY DIVISION P. O. BOX 3377 PITTSBURGH,PA 15230 0355 8804210382 880412 PDR ADOCK 05000282 O
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AS$ 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 deterstned to be high cycle fatigue. Tne source of the loads associated with the fatigue mechanism is a combination of a mean stress level in the tube with a superimposed alternatirg stress. The mean stress is the result of denting of the tube at the top tube support plate, while the alternating stress is due to out of plane deflection of the tube U bend attributed to flow induced vibration for tubes without AVB support. Local flow peaking effects at unsupported tubes j
are a significant contribution to tube vibration amplitudes.
i This report documents the evaluation of steam generator tubing at Prairie Island Units 1 and 2 for susceptibility to fatigue induced cracking of the type experienced at North Anna Unit 3.
The evaluation utilizes operating conditions specific to Prairie Island to account for the plant specific nature of the tube A
loading and response. The evaluation also includes reviews of eddy current data for Prairie Island I and 2 to establish tube denting conditions and AVB locations. This report provides background of the event which occurred at North Anna, criteria for fatigue assessment, a sumary of test data which j
support the analytical approach, field measurement results showing AVB 3
positions, thermal hydraulic analysis results, and calculations to determine tube mean stress, stability ratio and tube stress distributions, and accumulated fatigue usage. The evaluation leads to identification of tubes potentially susceptible to tube fatigue. For both Unit 1 and Unit 2, the results indicate that all tubes have acceptable fatigue usage and no corrective
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actions are required.
l-1 0139M:49/032188 2 t
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SUMMARY
OF A8BREVIATIONS i
ASME American Society of Mechanical Engineers l
Analysis of the Thernal Hydraulics of Steam Generators ATHOS AVB Anti-Vibration Bar All Volatile Treatment AVT ECT Eddy Current Test EPRI Electric Power Resaarch Institute FFT Fast Fourier Transform Flow Induced Vibrations FLOVIB MEVF Modal Effective Vold Fraction 00 Outside Diameter RMS Root Mean Square Stability Ratio SR TSP Tube Support Plate
'F degrees Fahrenheit A
hr hour ksi measure of stress - 1000 pounds per square inch Ib pound mils 0.001 inch MW mega watt psi measure of stress pounds per square inch l
measure of pressure pounds per square inch, absolute psia r
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.l 0139M:49/032188 3 it i
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l TA8LE OF CONTENTS SECTION 2A1E 1.0 Introduction........................... 11 2.0 Sumary and Concl usions...................... 21 2.1 Background......................... 21 2.2 Evaluation Criteria..................... 21 2.3 Denting Evaluation....,
............... 23 2.4 AVB Insertion Depths.................... 23 2.5 Flow Peaking Factors.................... 24 2.6 Tube Vibration Evaluation.................. 24 2.7 Overall Conclusion..................... 25 1
3.0 Background............................ 31 3.1 North Anna Unit 1 Tube Rupture Event............ 31 3.2 Tube Examinat. ion Results.................. 32 3.3 Mechanism Assessment.................... 33 4.0 Criteria for Fatigue Assessment.............
.... 41 3
4.1 Stability Ratio Reduction Criteria............. 42 4.2 Local Flow Peaking Considerations.............. 47 4.3 Stress Ratio Considerations................. 48 5.0 Supporting Test Data....................... 51 5.1 Stability Ratio Parameters................. 51 5.2 TubeDampin$onAmplitudeswith(.....jAV8 Support...
Data.......
u.......
56 5.3 Tube Vibrat 57 5.4 Tests to Determine the Effects on Fluidelastic Instability of Columnwise Variations in AV8 Insertion Depths........................... 59 6.0 Eddy Current Data and AVB Positions................ 61 6.1 Eddy Current Data.....
61 6.2 AyB Positions........................ 61 7.0 Thermal Hydraulic Analysis..........,......... 71 i
7.1 Prairie Island Steam Generator Operating Conditions..... 71 ATHOSAna1{ts........................
sis Model.................... 72 7.2 i
7.3 ATHOS Resu.
74 4
7.4 Relative Stability Ratio over Operating History....... 76 0139M:49/032188 4 itj
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TABLE OF CONTENTS (Continued) i f1Gi 81 8.0 Peaking Factor Evaluation.....................
41 8.1 North Anna 1 Configuration.................
8.2 Test Measurement Uncertainties............... 85 86 8.3 Test Repeatability.....................
86 8.4 Cantilever vs U Tube....................
88 8.5 Air vs Steam Water Mixture................
8 11 8.6 AVB Insertion Depth Uncertainty...............
8.7 Overall Peaking Factor With Uncertainty........... 8 12 9.0 Structural and Tube Vibration Assessments............. 9!
91 9.1 Tube Mean Stress......................
9.2 Stability Ratio Distributions Based Upon ATH0S....... 9.c 9.3 Stress Ratio Distribution With Peaking Factor........ 93 95 9.4 Cumulative Fr.tigue Usage..................
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1 U ST OF F16URES El.E fEl
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11 Modified AVBs Installed in Prairie Island 1 and 2 Steam Generators....................... 12 31 Approximate Mapping of fracture Surface of Tube R9C51 S/G 'C' Cold Leg, North Anna Unit 1.............. 35 32 Schematic Representative of Features Observed During TEM Fractographic Examination of Fracture Surface of Tube R9C51, S/G 'C' Cold Leg, North Anna Unit 1........ 36 33 Calculated and Observed Leak Rates Versus Time........ 37 41 Vibration Displacement vs. Stability Ratio.......... 4 12 42 Fatigue Strength of Inconel 600 in AVT Water at 600'F....
4 13 43 Fatigue Curve for Inconel 600 in AVT Water Comparison of Mean Stress Correction Models..............
4 14 44 Modified Fatigue with 10% Reduction in Stability 0
Ratio for Maximum Stress Condition.............. 4 15 45 Modified Fatigue with 5% Reduction in Stability Ratio for Minimum Stress Condition.............. 4 16 l
51 Fluidelastic Instability Uncertainty Assessment........ 5 15 52 Instability Constant A................... 5 16 53 Instability constants A, obtained for curved Tubes from Wino Tunnel Test, on the 0.214 Scale U Bend Model....... 5 17 54 Damping vs. Slip Void Fraction................ 5 18 55 overall View of Cantilever Tube Wind Tunnel Model....... 5 19 56 Top View of the Cantilever Tube Wind Tunnel Model....... 5 20 57 Fluidelastic Vibration Amplitude with Non Uniform Gaps.... 5 21 58 Typical Vibration Amplitude and Tube /AVB Impact Force
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Signals for Fluidelastic Vibration with Unequal Tube /AVB Gaps......................... 5 22 j
0139M:49/032288 6 y
i LISTOFFIGURES(Continued) flldf.
ffd 59 Conceptual Design of the Apparatus for Determining the Effects on Fluidelastic Instability of Columnwise Variations in AVB Insertion Depths.............. 5 23 5 10 Overall View of Wind Tunnel Test Apparatus.......... 5 24 5 11 Side View of Wind Tunnel Apparatus with Cover Plates Removed to Show Simulated AVBs for Field Modified Units and Top Flow Screen...................... 5 25 5 12 AYB Configurations Tested For Prairie Island......... 5 26 5 13 Typical Variation of RMS Vibration Amplitude with Flow Velocity for Configuration 1 in Figure 5 12.......... 5 27 61 Typical Eddy Current Signal for AVBs............. 68 62 AVB Positions for Prairie Island 1 S/G 11.......... 69 63 AVB Positions for Prairie Island 1. S/G 12.......... 6 10 64 AVB Positions for Prairie Island 2. S/G 21.......... 6 11 65 AVB Positions for Prairie Island 2, S/G 22.......... 6 12 O
71 Plan View of ATHOS Cartesian Model for Prairie Island..... 7 14 72 Elevation Ytew of ATHOS Cartesian Model for Prairie Island.. 7 15 73 Plan View of ATHOS Cartesian Model for Prairie Island Indicating Tube Layout.................... 7 16 74 Flow Pattern on Vertical Plane of Symetry.......... 7 17 75 Lateral Flow Pattern on a Horizontal Plane in the U Bend Region............................. 7 18 76 Lateral Flow Pattern on Top of Tubesheet........... 7 19 77 Tube Gap Velocity and Density Distributions for Tube Row'10/ Column 3........................ 7 20 78 Tube Gap Velocity and Density Distributions for Tube Row 10/ Column 20....................... 7 21 79 Tube Gao Velocity and Density Distributions for Tube Row 10/ Column 40....................... 7 22 1
j 0139H:49/032188 7 vi i!
d LIST 0FFIGURES(Continued)
FIGURE EAfd 7 10 Average Velocity and Density in the Plane of the U Bends Normal to Row 10................... 7 23 7-11 Prairie Island 1 Normalized Stability Ratio 8ased on High Power (>86%) Operation............. 7 24 81 Original North Anna AVB Configuration............. 8 25 82 Schematic of Staggered AV8s.................. 8 26 83 AVB 'Patr' in ECT Trace.................... 8 27 84 North Anna 1. Steam Generator C: AVB Positions Critical Review "AVB Visible' Calls.................. 8 28 85 North Anna 1. Steam Generator C, R9C!l[
] a.c Natrix... 8 29 a,c 86 NorthAnnaR9C51AVBFinal[
] Positions........
8 30 87 Final Peaking Factors..................... 8 31 91 Axisymetric Tube Finite Element Model............ 98 92 Dented Tube Stress Distributions Pressure Load on Tube..................... 99 93 Dented Tube Stress Distributions Interference Load on Tube................... 9 10 94 Dented Tube Stress Distributions Combined Stress Results.................... 9 11 95 Relative Stability Ratio.................... 9 12 96 Stress Ratio vs. Column Number Dented Condition....... 9 13 97 Stress Ratio vs. Column Number Undented Condition...... 9 14 1
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Ol39H:49/032188 8 vii i
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LIST OF TA8LES
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IARLI f8d 41 Fatigue Usage per Year Resulting From Stcbility Ratio Reduction........................ 4 11 51 Wind Tunnel Tests on Cantilever Tube Model.......... 5 13 52 Fluidelastic Instability Peaking Ratios for Columnwise Variations in AVB Insertion Dapths.............. 5 14 1
61 Sumary of U Bend Indications................. 66 62 Unsupported Tube Sumary................... 67 71 Prairie Island Steam Generator Operating Conditions...... 7 11 7-2 Steam Generator Operating Cor.ditions Used for ATHOS Analysis. 1 12 7-3 Prairie Island 1 Operating History Data............ 7 13 81 Stability Peaking Factor Due to Local Velocity Perturbation Scaling Factors for Steam / Water................ 8 17 82 Comparison of Air and Steam Water Peaking Factor Ratios.... 8 18
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83 Effect of Local Variation of AVB Insertion.......... 8 19 84 Lincertainties in Test Data and Extrapolation......... 8 20 85 Extrapolation of Test Results to Steam Generator Conditions For Standard AVB Configurations................ 8 21 86 Extrapolation of Test Results to Steam Generator Conditions For Standard and Replacement AVB Configurations........ 8 22 i
87 Final Peaking Factors..................... 8 23
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88 Stability Peaking Factors For Specific Tubes......... 8 24 91 100% Power Operating Parameters - Prairie Island....... 96 92 Duty Cycle Description For Prairie Island Units........ 97 e
i J-1 Ol39M:49/032188 9 Vili 1
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1.0 INTRODUCTION
This report documents the evaluation of steam generator tubing at Prairie Island Units 1 and 2 for susceptibility to fatigue induced cracking of the type experienced at North Anna Unit 1 in July, 1987. The evaluation includes three dimensional flow analysis of the tube bundle, air tests performed to support the vibration analytical procedure, field eddy current measurements to establish AVB locations, structural and vibration analysis of selected tubes, and fatigue usage calculations to predict cumulative usage for critical tubes.
The evaluation utilizes operating conditions specific to Prairie Island in order to account for plant specific features of the tube loading and response.
Furthermore, the evaluation is based on the current Prairie Island tube bundle configuration incorporating modified AVBs; a sketch of the modified AVBs is shown in Figure 1 1.
Consideration was also given to previous operation with the as built AVBs.
Section 2 of the report provides a sumary of the Prairie Island evaluation results and overall conclusions. Section 3 provides background for the tube rupture event which occurred at North Anna Unit 1 including results of the examination of the ruptured tube and a discussion of the rupture event mechanism. The criteria for predicting the fatigue usage for tubes having an environment conducive to this type of failure are discussed in Section 4.
Section 5 provides a sumary of test data which supports the analytical vibration evaluation of the candidate tubes. A sumary of field measuretrents used to determine AVB locations and ultimately to identify unsupported tubes is provided in Section 6.
Section 7 provides the.results of a themal hydraulic analysis to establish flow field characteristics at the top support plate which may be subsequently used to assist in identifying tubes which may be dynamically unstable. Section 8 describes the overall peaking factor
' evaluation to define test based peaking factors for use in the tube vibration and fatigue assessment. The final section, Section 9, presents results of the structural and vibration assessment. This section determines tube mean stress, j
stability ratio and tube stress distributions, and accumulated fatigue usage, forming the basis for the conclusions for Prairie Island.
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Figure 1-1 Modified AVls Installed in Prairie Island 1 and 2 Steaa Generators 0139M:49/030788 ll 12 4
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2.0 $Ulf%RY AND CONCLUSIONS I
The Prairie Island
- and 2 steam generators are evaluated for the susceptibility of unsupported U bend tuking with denting at the top tube support plate to a fatigue rupture of the type experienced at Row 9 Column 51 1
(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 l
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 4
due to the environment of the all velatile treatment (AYT) chemistry of the secondary water and the additional mean stress from the denting.
2.2 Evaluation Criteria i
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The criteria established to provide a fatigue usaga less than 1.0 for a finite
)
period of time (i.e., 40 years) is a 101 reduction tn stability ratio that provides at least a 58% reduction in stress amplitude (to < 4.0 ksi) for a Row i
9 tube in the North Anna 1 steem 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 40 year life. This stee criteria is being applied as l
the principal criteria in the evaluation of Prairie Island 1 and 2 tubing.
I The detemination of stability ratio is, the evaluation of a ratio of 1
velocities, the effective velocity divided by the critical velocity. A value l
greater than unity (1.0) indicates instability. The stress ratio is the I
expected stress amplitude in a Prairie Island 1 er 1 tube divided by the stress amplitude for the North Anna 1. R9C51 tube, i*
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0139M:49/032184 12 2-1 j
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Assuring a stability ratio that is equivalent to IM lower than R9C51 of North Anna 1 is required of Row 9 tubes in Prairie Island I and 2 as well as Row 10, i
Row 8, and smaller U band radius tubes than Row 8.
Prior to the antivibration bar modification (AVB), there is a very high likelihood that the Row 11 and Row i
12 tubes were supported by AVB's. This would allow a modification of the 10%
criteria to a less conservative criteria for these row tubes since prior fatigue usage is negligible and the service life expected for these tubes is 30 years without AYB support rather than 40 years. However, in spite of the low likelihood for any significant fatigue usage the 1M criteria basis has been conservatively retained for all tubes in Prairie Island I and 2.
Otsplacements i
are computed for these tubes using relative stability ratios to R9t31 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, therefor,e, 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 fatigue usage for tie Prairie Island I and 2 tubing for the reference fuel cycle analyzed.
The stability ratios for Prairie Island I and 2 tubing, the corresponding stress and a:rplitude, and the resulting cumulative fatigue usage must be evaluated relative to the ruptured tube at Row 9 Column 51, North Anna 1. Steam j
Generator C, for two reasons. The local effect on the flow field due to l
various AVB insertion depths is not within the capability of available analysis techniques and is determined by test as a ratto between two AVB configurations. In addition, an analysis and examination of the ruptured tube at North Anna 1 pr'ovided a range of initiating stress amplitudes, but could only bound the possible stability ratios that correspond to these stress amptitudes. Therefore, to minimize the influence of uncertainties, the evaluation o'f Prairie Island I and 2 tubing has been based on relative stability ratios, relative flow peaking factors, and relative stress ratios.
The criteria for establishing that a tube has support from an AVB and therefore eliminateitfromfurtherconsiderationsisthat[
[Testresultsshowthat[
]"
is sufficient to limit the vibration amplitude for fluidelastic excitation.
Ol39M:49/032188 13 2-2
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J AVBsupportatthe[
]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 Prairie Island I 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 D tube bundle flow analysis and the combined relative stability ratio used in the stress ratio determination.
2.3' Denting Evaluation The analyses of addy current (EC) measurements show a few tubes with denting induced deformation at the top support plate. A significant number of tubes show the presence of top tube support plate corrosion and magnetite in the crevice. For conservatism in the evaluation, all of the tubes in Rows 8 to 12 are postulated to be dented. The effect of denting on the fatigue usage of the tube has been conservatively saximized oy ass ning the maximum effect of mean l
stress (based on 55 ksi) in the tube fatigue usage evaluation and by incorporating reduced damping in the tube vibration evaluation.
2.4 AVB Insertion Depths Theeddycurrentdatawasreviewedto[
]to deterstne the deepest penetration of the AYBs. For the modified AVBs in the Prairie Island str generators, two legs of each AVB assembly can be identified on both the het and cold leg side of the tubing. If the bottom end 1
of an AVB assembly is near a tube, only one AYB signal is seen[
} If the single AVB l
signal is iound on one or both legs of the tube,[
[However, if both legs or an AVB assembly are j
identified on one or both legs of the tube AVB support at the [
]"
is assured.
Ol39M:49/032288 14 g
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d To locate the lowest penetration of each AVB[
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Overall, the evaluation shows that all Row 12 tubes are supported by AVIS.
Row 12 is the design depth of insertion for the modified AV8s except for a special AVB at each side of the tube bundle which penatrates to about Row 9.
The evalue' ion also shogs that the AVBs have very uniform insertion depths with l
the bottom [
] located between Rows 11 and 12. Maps of the AVB insertion depths are shown in Figures 6 2 *- 6 5, 2.5 Flow Peaking Factors 4
Tests were performed to determine the flow peaking factors for Prairie Island 1 and 2 AYB configurations relative to the North Anna R9C51 peaking factor. The modified AVB design was used in the tests for the Prairie Island value and the original AVB design was used for R9C51. Since the Prairie Island AV b 4 6 uniform AYB insertion to less than one tube pitch, the tests focused on j
sensitivity to uncertainties in determining the AYB depth of insertion. The test results were used to define an upper bound of the ratio for 'unifom AYB insertion'relativetotheR9C51configurati,ogn,. It was found that the results are enveloped by the peaking factor of[ ]cetermined for R9C51 relative to uniform AYB insertion for the original AVB design.
2.6 Tube Vibration Evaluation The calculation of relative stability ratios for Prairie Island makes use of dstalled tube bundle flow field information computed by the ATHOS steam generator thermal / hydraulic analysis code. Code output includes three-dimensional distributions of secondary side velocity, density, and void fraction, along with primary fluid and tube wall temperaturas. Distributions of these parameters have been generated for every tube in the Prhirie Island tube bundle based on a recent full power operating condition. This information was factored into the tube vibration analysis leading to the relative stability ratios.
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0139M:49/032188 15 24 l
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i Relative stability ratios of Prairie Island I and 2 (Row 8 through Row 12) tubing versus R9C51 of North Anna 1 are plotted in Figure 9 5.
These relative stability ratios do not include relatin flow peaking factors. Since the AVB pattern in both steam generators is uniform through to Row 12, the plotted stability ratighould be divided by the North Anna 1, R9C51, flow peaking factor
_ to get a comparison to 0.9, the 10% criteria. The stress ratios in Figure 9-6 include the relative flow peaking effect. This plot shows that all tubes that are unsup eted have stress ratios less than 1.0 for the reference cycle analyzed < \\ thus meet the acceptance criteria. Cumulative l
usage calculations for the.ntire duty cycle show that the 40 year fatigue usage is less than 1.0.
i 2.7 Overall Conclusion Based on the results of the tube fatigue evaluation, it is concluded that no modii; ation, preventive tube plugging, or other measure is necessary in Prairic Island I and 2 to preclude a fatigue rupture similar to the North Anna 1 event.
9 Ol39M:49/032188 16 2-5
J 3.0 GACKGROUND On July 15, 1987, a steam generator tube rupture occurred at the North Anna Unit 1.
The ruptured tube was determined to be Row 9 Column 51 in steam generator 'C'.
The location of the opening was found to be at the top tube support plate on the cold leg side of the tube and was circumferential in orientation with a 360 degree extent.
3.1 North Anna Unit 1 Tube Rupture Event The cause of the t'abe rupture has been determined to be high cycle fatigue.
The source of the loads associated with the fatigue mechanism has been determined to be a combination of a mean stress level in the tube and a superimposed alternating stress. The mean stress has been determined to have been increased to a maximum lev 31 as the result of denting of the tube at the top tube support plate and the alternating stress has been deternined to be due to out of plane deflection of the tube U bend above the top tube support caused by flow induced vibration. These loads are consistent with a lower bound fatigue curve for the tube material in an AVT water chemistry environment. The vibration mechanism has been determined to be fluid elastic, based ors 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 requisite vibration to occur. The' presence of an AVB support restricts tube motion and thus precludes the deflection amplitude required for fatigue. Inspection data shows that an AVB is not present for the Row 9 Column 51 tube but that the actual AVB installation depth exceeded the minimum requirements in all cases with data for AVBs at many other Row 9 tubes. Also contributing significantly to the level of vibration, and thus loading, is the local flow field associated with the detailed geometry of the steam generator, i.e., AVB insertion depths. In addition, the fatigue properties of the tube reflect the lower range of properties expected for an Ol39M:49/032188 17 3,)
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l AVT environment. In sumary, the prerequisite conditions derived from the l
evaluations were concluded to be:
Faticue Reauirements Prereauisite Conditions Alternating stress Tube vibration j
- Dented support
- Flow excitation
- Absence of AVB Mean stress Denting in addition to applied stress Material fatigue properties AVT environment
- Lower range of properties 3.2 Tube Examination Results Fatigue was found to have initiated on the cold leg outside surface of Tube R9C51 imediately above the top tube support plate. No indications of o
significant accompanying intergranular corrosion was observed on the fracture face or on the imediately adjacent 00 surfaces. Multiple fatigue initiation sites were found with major sites located at 110', 120', 135' and 150',
Figure 3-1.
The plane of the U bend is located at 45' with the orientation system used, or approximately 90' from the geometric center of the initiation zone at Section D D.
High cycle fatigue striation spacings approached 1 mic m inch near the origin sites, Figure 3 2. The early crack fror.t is believed to have broken through wall from approximately 100* to 140'.
From this point on, crack growth is believed (as determined by striation spacing, striation direction, and later observations of parabolic dimples followed by equiaxed dimples) to have accelerated and to have changed direction with the resulting crack front running perpendicular to the circumferential direction.
4 Ol39M:49/032188 18 3-2
3.3 Mechanism Assessment To address a fatigue mechanism and to identify the cause of the loading, any loading condition that would cause cyclic stress or steady mean stress had to be considered. The analysis of Normal, Upset and Test conditions indicated a relatively low total number of cycles involved and a 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 respont" of the dented tube to flow induced vibration for the uncracked tube and for the tube with an increasing crack angle, beginning at 90' to the plane of the tube and progressing around on both sides to complete separation of the tube.
Crack propagation analysis matched cyclic deformation with the stress intensities and striation spacings indicated by the fracture inspection and analysis. Leakage data and crack opening analysis provided the relationship a
5etween leak rate and circumferential crack length. Leakage versus time was then predicted from the crack growth analysis and the leakage analysis with initial stress amplitudes of 5, 7, and 9 ksi. The comparison to the best estimate of plant leakage (performed after the event) showed good agreement, Figure 3-3.
Based on these results, it followed that the predominant loading mechanism responsible is a flow induced, tube vibration loading mechanism. It was shown that of the two possible flow induced vibration mechanisms, turbulence and fluidelastic instability, that fluidelastic instability was the most probable cause. Due to the range of expected initiation stress amplitudes (4 to 10ksi),
the fluidelastic instability would be limited in displacement to a range of approximately[
," fhis is less than the distance between tubesattheapex,[
[f t was further confinned that displacement prior to the rupture was limited since no indication of tube U bend (apex region) damage was evident in the eddy current signals for adjacent tubes.
Ol39M:49/032188 19 3,1
s Given the probability of limited displacement, fluidelastic instability, a means of establishing the change in displacement, and corresponding change in stress amplitude, was developed for a given reduction in stability ratio (SR),
Since the rupture was a fatigue mechanism, the change in stress amplitude resulting from a reduction in stability ratio was converted to a fatigue 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.
013"':49/032188 20 3-4
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Calculated and eherved leak retas versus ties.
Chserved values ksed as gasseus species condenser etr ejector loooo <
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Figure 3-3 Calculated and Observed Leak Rates Versus Time Ol39M:49/030388 13
d 4.0 CRITERIA FOR FATIGUE ASSESSMENT Evaluation against criteria to show that Prairie Island Unit 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 uncertainties 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 tube rupture analysis of North Anna Unit 1.
For these reasons, the North Anna Unit 1 tubing evaluation was done on a relative basis to Row 9 Column 51 and a 10% reduction in stability ratio criteria was established to demonstrate that tubes left in service are expected to have sufficiently low vibration stress to preclude future fatigue rupture events.
To accomplish the necessary relative assessment of Prairie Island Unit 1 and 2 tubing to Row 9 Column 51 of North Anna Unit 1, several criteria are utilized.
First, stability ratios are calculated for Prairie Island Unit 1 and 2 steam pend ators based on flow fields predicted by 3 D thermal hydraulic models and ratioed to the stability ratio for Row 9 Column 51 at North Anna Unit 1 based t
on a flow f'11d obtained with a 3-D thermal hydraulic model with the same degree of refinement. These ratios of stability ratio (called relative stability ratios) for each potentially unsupported U bend in the Prairie Island Unit 1 and 2 steam generators should be equivalent to 10.9 of North Anna 1, R9C51 (reeting the 10% reduction in stability ratio criteria). This provides the first level of screening of susceptible tubes incorporating all tube geometry and flow field differences in the tube dynamic evaluation. It has the inherent assumption, however, that each tube has[
]."Toaccountforthese differences, flow peaking factors can be incorporated in the relative stability ratios or, as noted below, in the relative stress ratios.
Ol39M:49/032188 24 41
i l
The second criteria is to obtain stress ratios, the ratio of stress in the Prairie Island Unit 1 and 2 tube of interest to the stress in Rcw 9 Column 51, North Anna Unit 1, and, after incorporating the requirement that the relative stability ratio to Row 9 Column 51 (R9C51) for the tube of interest is equivalent to 10.9, 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 Prairie Island Unit I and 2 tube of interest to the flow peaking factor for R9C51 (flow peaking factor is defined in Section 4.2). This should provide that all tubes meeting this criteria have stress amplitudes 14.0 ksi.
Finally, the cumulative fatigue usage for plant operation to date and for continued operation with the same operating parameters is evaluated. A fatigue usage of s 1.0 is not necessarily satisfied by meeting the stress ratio criteria since the evaluation for Prairie Island Unit 1 and 2 has been performed for a reference operating cycle. The Prairie Island Unit I and 2 duty cycle was more demanding in early cycles and usage would have accumulated at a more rapid rate. Therefore, the time history of operation is evaluated on a normalized basis and used together with the stress ratio to obtain a stress L
amplitude history. This should permit the calculation of current and future fatigue usage for comparison to 1.0.
4.1 Stability Ratio Reduction Criteria For fluidelastic evaluation, stability ratios are determined for specific configurations of a tube. These stability ratios represent a measure of the potential for flow induced tubt vibration during service. Values greater than unity (1,0) indicate instability (see Section 5.1).
j 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 itnearly related to the bending stress in the tube just above the cold leg top tube support plate. This relationship appites to any vibration in that mode. Thus, it is possible for
~
an unstable, fixed boundary condition tube to deflect an amount in the U bend which will produce fatigue inducing stresses.
0139M:49/032188 25 42
The major features of the fluidelastic mechanism are illustrated in Figure 4-1.
This figure shows the displacement response (LOG D) of a tube as a function of stability ratio (LOG SR). A straight-line plot displayed on log-log coordinates implies a relation of the form y A(x)", where A is a constant, j
x is the independent variable, n is the exponent (or power to which x is j
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 j
form, log y = c + n log x, where c = log A and represents the intercept and n is the slope. In our case the independent variable x is the stability ratio SR, and the dependent variable y is tube (fluidelastic instability induced) displacement response D, and the slope n is renamed s.
From experimental results, it is known that the turbulence response curve (on log log coordinates) has a slope of approximately(,[lest results also show that the slope for the fluidelastic response depends somewhat on the instabilitydisplacege,nt(responseamplitude). It has been shown by tests that a slope of[
]is a range of values correspondina to displacement amplitudes in the range of[
], whereas below[
]are conservative values, o
The reduction in response obtained from a stability ratio reduction can be expressed by the following equation:
6e
[1]
where Di and sri are the known values at the peint corresponding to point I of Figure 4 1 and 02 and SR2 are values corresponding to any point lower on this curve. Therefore, this equation can be used to determine the reduction in displacement response for any given reduction in stability ratio.
This equation shows that there is benefit derived from even a very small percentage change in the stability ratio. It is this reduction in displacement for a quite small reduction in stability ratio that formed the basis for demonstrating that a 10% reduction in stability ratio would be sufficient to have prevented Row 9 Column 51 from rupturing by fatigue.
0139M:49/032188 26 43
J The fatigue curve developed for the North Anna Unit I tube at R9C51 is from E
\\
J. a,eThus, e,e
[2]
where, a ' is the equivalent stress amplitude to o that accounts a
a for a maximum stress of o, the yield strength. The 3 sigma curve with y
mean stress effects is shown in Figure 4-2 and is compared to the ASME Code Design Fatigue Curve for Inconel 600 with the maximum effect of mean stress.
The curve utilized in this evaluation is clearly well below the code curve reflecting the ef{ect of an AVT environment on fatigue and[
]foraccountingformeanstressthatappliestomaterialsina 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 inittagng stress amplitudes.- Thesewerethe[
]shown in Figure 4 3.
With a[
],th e E
j."
0139M:49/032188 27 44
d 1
The assessment of the benefit of a reduction in stability ratio begins with the j
relationship between stability ratio and deflection. For a specific tube geometry, the displacement change is directly proportional to change in stress so that stress has the same relationship with stability ratio,
_y (3)
The slope in this equation can range from[
] n a log scale depending on the amplitude of displacement. Knowing the stress resulting from a change in stability ratio from SRg to SR, the cycles to failure at the stress 2
amplitude was obtained from the fatigue curve. A fatigue usage per year was i
then determined assuming continuous cycling at the natural frequency of the tube. The initial stress was determined to be in the range of 4.0 to 10.0 ksi by the fractography analysis.
It was further developed that the maximum initiating' stress amplitude was not more than 9.5 ksi. Thiswasbasedon[
u J The corresponding stress level is 5.6 ksi.
The maximum stress, 9.5 ksi, would be reduc J to[
]with a 10% reduction in stability ratio and would have a future fatigue usage of[
]per year at 75% availabt.11ty, Figure 4 4.
The minimum stress, 5.6 ksi, would be reduced to
[
]Mth a 5% reduction in stability ratio and would have future fatigue usage of[
]pCer year, Figure 4 5.
E cracked, it could be as large as[
]{ inch in length and thru wall and would n addition, if a tube were already not propagate if the stress amplitudes are reduced to i 4.0 ksi.
Subsequent to the return to power evaluation for North Anna Unit 1, the time history of operation was evaluated on a normalized basis to the last cycle.
Ol39M:49/032188 28 4-5
l d
],'cumulativefatigueusage may then be computed to get a magnitude of alternating stress for the last cycle that rest:lts in a c':mulative 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 usage during the last cycle of operation was approximately
[
]for R9C51, North Anna Unit 1, Steam Generator C, and that the major portion of the fatigue usage came in the second, third and fourth cycles. The first cycle was conservatively omitted, since denting is assumed, for purposes of this analysis, to have occurred during that first cycle. Based on this evaluation, the tube fatigue crack initiation may have occurred over most of the operating history of North Anna Unit 1.
A similar calculation can be performed for the time history of operation assumingthat[
] &,C on e
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[
,].
Other combinations of alternating stress and mean stress wire evaluated with -3 sigma and 2 sigma fatigue curves to demonstrate the conservatism of the 10%
reduction in stability ratio. Table 41 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 stress, mean stress model, or probability, results in greater benefit for the same reduction in stability ratio. Further, for any of these higher curves, a smaller reduction in stability ratio than 10% would result in the same benefit. In addition, there is a large benefit in terms of fatigue usage for relatively small changes in the fatigue curve.
Ol39M:49/032188 29 4-6
i 4.2 Local Flow Peaking Considerations Local flow peaking is a factor on stability ratio that incorporates the effect on {
ue to non uniform AVB insertion depths. The flow peaking factor is applied directly to the stability ratio obtained from thermal-hydraulic analysis that does not account for these local geometry effects. Being a direct factor on stability ratio, a small percentage increase can result in a significant chtnge in the prediction of tube response.
The development of flow peaking factors for Prairie Island Unit I and 2 is presented in detati in Section 8.4.
The establishment of AVB positions is presented in Section 6.2.
Since the evaluation of Frairie Island Unit I and 2 is relative to R9C51, North Anna Unit 1, the flow peaking factors are also relative. The peaking factor is applied as a ratio of stability peaking factor of the specific tube to that of North Anna R9C51. The flow peaking relative instability is obtained by testing in the air test rig described in Section 5.4, where the peaking factor is defined as the critical velocity for R9C51 AVB pattern compared to critical velocityforayiformAVBpattern. As explained in Section 8.0, the minimum value of[
]is appropriate for R9C51 of North Anna 1.
Applying a nominal uncertainty to theyH05 analysis result of 15%, the predicted stability ratio for R9C51 is[
]using nominal damping that is a fgtion of the modal effectivevoidfractionfslip). Applying the[
] tactor gives a corrected stability ratio of[ ]. Therefore, using the minimum flow peaking factor and nominal damping that reflects reduced damping compared to undented tubes, the tube at R9C51, North Anna Unit 1 Steam Generator C is shown to be unstable by comparison to the same tube with a uniform AVB pattern. It is therefore now considered to be sufficient to address the relative susceptibility of tubes to fatigueruptureon[
] s.c Ol39M:49/032188 30 47 i
)
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[
' &,C 0139M:49/032188 31 4,g l
l i
y
~
\\
l 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 sgess (such as for non dertsd tubes), different frequency tubes from the[ ] hertz frequency of R9C51, North Anna 1, and shorter design basis service (such as 30 years).
In the case of lower mean stress, the stress amplitude that would have caused thefailureofR9C51,NorthAnna1,wouldhavebeenhigher.[
7 A lower or higher frequency tube would not reach a usage of 1.0 in the same length of time as the R9C51 tube due to the different frequency of cycling.
The usage accumulated is proportional to the frequency and, therefore, the allowable number of cycles to reach a usage of 1.0 is inversely proportional to frequency. The equivalent number of cycles to give the usage of 1.0 for a differentfrequencytube{
]u Ol39M:49/032188 32 4,9 I
J Foradifferentunsupportedtube,[
i ste Knowing the magnitude of the stress ratio allows 1) the determination of tubes that do not meet a value of s 1, and 2) the calculation of maximum stress in the acceptable tubes, g
[12]
Having this maximum stress permits the evaluation of the maximum fatigue usage for Prairie Island Unit 1 and 2 based on the time history expressed by normalized stability ratios for the duty cycle (see Section 9.3 9.4).
f I
Ol39M:49/032188 33 4-10
i Table 4-1 Fatigue Usage per Year Resulting From Stability Ratio Reduction SR, %
STRESS FATIGUE MEAN STRESS USAGE REDUCTION BASIS (I)
CURVE (2)
MODEL PER YEAR 5.
9 yrs to 0.0207 fail (5.6) 5.
9 yrs to 0.0107 fail (7.0) 5.
9 yrs to 0.0014 fail (8.0) 0.0209 10.
max.stre{g) amplitude (9.5) 0.0053 10.
max.stresg) amplitude \\
(9.5) 0.0004 10.
max.stre$g) amplitudet (10.3) 0.0142 10.
max.stre$g) amplitude \\
(11.6) 10.
max. stress 0.0020 based on dutycycle(5)
(9.5)
(1) This gives the basis for selection of the initiating stress amplitude and its val,ue in ksi.
(2) S,is the maximum stress applied with S, - Smean + 3
- a
~u
~
(3)
(4) Cycles to failure implied by this combination of stress and fatigue i
properties is notably less than implied by the operating history.
Consequently this combination is a conservative, bounding estimate.
l (5) Cycles to failure implied by the operating history requires 1.3 sigma fatigue curve at the maximum stress of 9.5 ksi.
4*Il 0139M:49/032188 34
l0 l
1
~
4 a,b,c i
i Figure 4 1 Vibration Olsplacement vs. Stability Ratio
~
0139M:49/0303BS 25 I
d i
)
\\
1 i
1 4,C i
l 1
Figure 4 2 Fatigue Strength of Inconel 600 in AVT Water at 600'F l
bl3 i
0139M:49/030388 26 i
e
3 I
_ a,e i
1 l
Figure 4 3 Fatigue curve for Inconel 400 in AYT Water Comparison of Mean Stress Correction Models Ol39M:49/030388 27 4-14
i
-e Figure 4 4 Modified Fatigue with 107, Reduction in stability Ratio for Maxiom Stress condition 4-15 Ol39M:49/030388 28 l
il l-
\\
1 1
l 1
l l
]
a,e f
~
l 1.
l 1
1 1
l 1
l l
l l
I i
1 l
l 1
l l
Figure 4 5 Modified Fatigue with 5% Reduction in $tanility Ratio for Minima Stress Condition l
1 4-16 0139M:49/030388 29 I
i 5.0 SUPPORTING TEST DATA This section provides a mathematical description of the fluid elastic mechanism, which was determined to be the most likely causative mechanism for the North Anna tube rupture, as discussed in Section 3.3, to highlight the physical conditions and ccWesponding parameters directly related to the event and associated preventative measures. The basis for establishing the appropriate values and implications associated with these parameters are provided. Where appropriate, test results are presentad.
5.1 Stability Ratio Parameters Fluid elastic stability ratios are obtained by evaluations for specific configurations, in terms of active tube supports, of a specific tube. These stability ratios represent a measure of the potential for tube vibration due to instability curing service. Fluid elastic stability evaluations are performed with a computer program which provides for the generation of a finite element model of the tube and tube support system. The finite element model provides the vehicle to define the mass and stiffness matrices for the tube and its support system. This information is used to detennine the modal frequencies (eigenvalues) and mode shapes (eigenvectors) for ths linearly supported tube being considered.
The methotology is comprised of the evaluation of the following equations:
Fluid elastic stability ratio = SR - Ven/Ve for mode n, where Uc (critical velocity) and Uen (effective velocity) are deterrined by:
2
'$f 0{(m 6 ) / (#o D))l/2 (3)
U
=
c n
e n
and; N
2 (sj/p ) Uj jn j
4 Z
o y
I.
[2]
(m /m ) (jn zj 3e 0139ti:49/032188 40 g,3
i
- where, D
tube outside diameter, inches effective velocity for mode n, inches /sec U
en number of nodal points of the finite element v.cdel N
=
mj, Uj, pj -
mass per unit length, crossflow velocity and fluid density at node j, respectively reference density and a reference mass per unit po, no length, respectively (any representative values) logarithmic decrement (damping) 6
=
n djn normalized displacement at node j in the nth mode of vioration zj average of distances between node j to j-1, and j to J+1 an experimentally correlated stability constant Substitution of Equations (1) and (2) into the expression which defines stability ratio, and cancell ation of like terms, leads to an expression in fundamental terms (without tte 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 nodal damping, tube modal frequency, and the stability constant (beta).
The uncertainty in each of these parameters is addressed in a conceptual manner in Figure 51. The remainder of this section (Section 5.0) provides a discussion, and, where appropriate, the experimental bases to quantitatively establish the uncertainty associated with each of these parameters. In
~
0139M:49/032188 41 5-2
4 addition, Section 5.3 provides the experimental basis to demonstrate that tubes
~ " This implies thatthosetubes[
]w$uldnothavetobemodified
~
because their instability response amplitude (and stress) would be small. The very high degree of sensitivity of tube response (displacements and stresses) to changes in the velocity times square root density distribution is addressed in Section 4.0.
This is important in determining the degree of change that can be attained through modifications.
Frecuency It has been demonstrated by inve,stigators 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 grticularly apprcpriate in the case of dented tubes. Therefore, uncertainty levels
)
introducedbythefrequencyparaieterareexpectedtobeinsignificant(see also ' Average Flow Field" subsection below).
Instability Constant (Betal The beta (stability constant) values used for stability ratio and critical velocity evaluations (see above equations) are based on an extensive data base comprised of both Westinghouse and other experimental results (Figure 5 2). In addition, previous field experiences are considered. Values have been measured for full length U bend tubes in prototypical steam / water environments. In addition, measurements in U bend air models have been made with both no AVB and variable AVB supports (Figure 5 3).
To help establish the uncerttinties 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 using ATHOS. A beta value consistent with the ATHOS predicted flow conditions and the MB 3 measured critical velocity was ddermined. These analyses supported a beta value of [ f 0139M:49/03218842 5-3
l 1
A sumary of the test bases and qualifications of the beta values used for these assessments is provided by F1gure 5 2.
The lowest measured beta for tubes without AVBs was a value of
, This value is used for the beta parameter in all stability ratio e' val'uations addressed in this Report (see also "Average Flow field' subsection below).
j Mass Distribution The mass distribution parameter is based on known information on the tube and primary and secondary fluid physical properties. The total mass per unit length is comprised of that due to the tube, the internal (primary) fluid, and the external (secondary) fluid (hydrodynamic mass). Data in Reference 5 2 suggeststhatatoperatingvoidfractions[
a.c Tube Da-eina ac Test data are available to define tube damping for ltube
~
~
supports, apprepriate to dented tube conditions, in steam / water flow conditions. FrotogpicUbendtestinghasbeengerformedunderconditions leading to supports. Thedataof[
]inFigure54providesthe principaldatafor[
]tubeconditionsinsteam/ water. This data was obtained for cross flow over straight tubes. Uncertainties are not defined for the data from these tests. Detailed tube damping data used in support of the stability ratio tvaluat;ons addressed in this report are provided in Section 5.2, below.
Elow Field - Velocity Times Souare Root Density Distribution Average and U bend local flow field uncertainties are addressed independently in the following.
Ol39M:49/032188 43 5-4
I j
l Avernoe Flow Field Uncertainties in the average flow field parameters, cbtained 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 a:sociated 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 steam generators without denting. Thus, an uncertainty row tubes in operating $or the combined effects of average flow field, stability estimate of about{ ]
constant and frequency appears to be reasonable. To further minimize the impact of these uncertainties, the Prairie Island Unit 1 and 2 tubes are evaluated [
f'Thus,theuncertaintiesassociatedwiththeaveragevelocitytimes 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 "channelir.g* effects of non uniform AVBs, leads to a local perturbation in the velocity times square root density parameter at the apex of the tube where it will have the largest effect (because the apex is where the largest vibration displacements occur).
Detailed local flow field data used in support of the stability ratio evaluations addressed in this report are provided in Section 5.2, below, and Section 8.0.
Overall Uncertainties Assessment 1
Based on the above discussions, and the data provided in the following sections, it is concluded that local flow peaking is likely to have contributed signifie.antly 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. U, utilized in this report to minimize uncertainties in the evaluations assot,"<d with ir. stability constants, local flow Tic 1d effects and tube damping.
Ol39M:49/032188 44 j
g e
0 5.2 Tube Damping Data The damping ratio depends on several aspects of the physical, systcr. - 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, 1.e., sir.gle phast or two phase flow. Thesa effects ace 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, ficw 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 qulity. It can ce shown that the damping contribution from viscous effects are very small.
Daeping ratios for tubes in air and in air water flows have been rmsured and reported by vhrlous autt,urs. However, the results from air water flow are poor representations of the atual conditions in a steam ge7erator (steam water flow at high pressure). Therefore, where anilable, results from prototypic steam water 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 find clamped tube support conoitions.
Two sources of data are particularly noteworthy and are used here. The first is a large body of recent, as yet unpublished data from high pressure steam water tests conducted by Mitsubishi Heavy Industries (MHI). These data i.a were gathered under tube support conditions. The second is comprised of
~
the results from tests sponsored by the Electric Power Research Institute (EPRI) r.ed reported in References (5-2) and (5 3).
The damping ratio results from the above tests are plotted in Figure 5 4 as a function of void fraction. It is important to note that tt.e void fraction is determinedonthebasisof[
~"
Ol39r:a49/032188-45 5-6 I
\\
i (Reference (54)). 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 clar. ped tube support curve is used in the current evaluation to include the effect of denting at the top tube support plate.
The Reference 5 3 data as reported show a damping value of.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 dar ing.
Westinghouse tests of clamped tug vibration in air has shown that the mechanical damping is only[
]rather than the.5% reported in Reference (53). Therefore the lower curve in Figure 5 4 is the Reference (5 3) data i
with all damping values reduced by(
5.1 Tube Vibration Astplitudes Witt [
AVB Support A series of wind tunnel tests were conducted to investigate the effects of tube /AVB eccentricity on the vibration amplitudes caused by fluidelastic vibration.
~ ' Prior test results obtained during the past year using this apparatus have demonstrated that the fluidelastic vibration characteristics observed in the tests performed with the cantilever tube apparatus are in good agreement with corresponding characteristics observed in wind tunnel And steam flow tests using U bend tube arrays. A sumary of these prior results is given in Table 51.
1 0139M:49/032188 46 5,7 l
J An overall view of the apparatus is shown in Figure 5 5.
Figure 5 6 is a top view of the apparatus.
a,c As shown in Figure 5 7, the tube vibration amplitude below a critical velocity is caused by a,e Figure 5 7 shows the manner in which the zero to peak vibration amplitude, expressed as a ratio nomalized to[
[varieswhenonegapremainsat[
]."'For increasing velocities, up to thatcorrespondingtoastabilityrattoof[
}."* Figure 58showstypicalvibrationamplitudeand tube /AV8 impact force signals corresponding to those obtained from the tests which provided the results shown in Figure 5 7.
As expected, impacting is only observedinthe[
[
Ol39M:49/032188 47 5-8
I Itisconcludedfromtheabovetestresultsthat,}
se t
5.4 Tests to Determine the Effects on Fluidelastic Instability of Columnwise Variations in AV8 Insertion Depths This section sumnarizes a series of wind tunnel tests that were conducted to investigate the effects of variations in AVB configurations on the initiation of fluidelastic vibration. Each configuration is defined as a specific set of insertion depths for the individual AVBs in the vicinity of an unsupported U bend tube.
The tests were conducted in the wind tunnel using a modified version of the cantilever tube apparatus described in Section 5.3.
Figure 5 9 shows the conceptual design of the apparatus.* Thestraightcantilevertube,[
sc fFigure511showstheAVBs, corresponding to field modified units, when the side panel of the test section Ol39M:49/032188 48 5-9 l
I is removed. Also shown is the top flow screen which is[
]a,eThe AVB configurations tested are shown in Figure 5 12.
Configuration la corresponds to tube R9C51, the failed 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.
As shown in Figure 5 9,
~
,e a
?
Allthetubesexcepttheinstrumentedtubed(correspondingtoRow10)are[
].'*AsdiscussedinSection5.3,priortestingindicates that this situation provides a valy model. The instrumented tube as shown in Figure 5 10. Its [
direction vibrational motion is measured using a non contacting transducer.
b
~UheinstrumentedtubecorrespondstoaRow10tubeasshowninFigure
- 59. However, depending on the particular AVB configuration, it can reasonably
'The AVBs shown in Figure 5 9 correspond to original AVBs. Modified model i
l AVBs corresponding to those used in field modified t.ntts, such as Prairie Island, were made using the same procedure as for the original AVBs and are shown installed in Figure 5 11'.
Ol39M:49/0321.88 49 5-10
i represent a tube in Rows 8 through 11. The AYB profile in the straight tube model is the average of Rows 8 and 11. The difference in profile is quite small for these bounding rows.
- u
]usingahotfilm anemometer located as shown in Figure 5 9.
Figure 5-13 shows the ras vibration amplitude, as detemined from PSD (power spectral density) measurements made using an FFT spectrum analyzer, versus flow velocity for Configuration la (which corresponds to tube R9C51 in North Anna).
Data for three repeat tests are shown and the critical velocity is identified.
The typical rapid increase in vibration amplitude when the critical velocity for fluidelastic vibration is exceeded is evident.
The main conelusions from the tests are:
1.
Tube vibration below the critical velocity is relatively small, typical of I
turbulence induced vibration, and increases rapidly when the critical i
velocity for the initiation of fluidelastic vibration is exceeded.
i 2.
Configuration Ib (R9C51 in North Anna) has the lowest critical velocity of all the configurations tested.
3.
Configuration Ib is repeatable and the configuration was rerun periodically to verify the consistency of the test apparatus, The initial test results obtained in support of the Prairie Island evaluation are sumarized in Table 5 2.
The peaking factor,is defined as the ratio of the I
critical velocity for Configuration 2a divided by the critical velocity for any other configuration. Configuration 12a simulates uniform AYB insertion one row abovethetesttube(i.e.,uniformRow10foraRow9testtube). No significant flow peaking effects are expected for Configuration 12a. The peaking factor indicates the relative sensitivity of each configuration to fluidelastic vibration. Also shown in Table 5 2 are the flow peaking effects for each AVB configuration relative to that for North Anna tube R9C51, Configuration la.
0139M:49/032188 50 5,3) l I
i 1
References 8,8 4
i
)
0139M:49/032188 51 5-12
]
Table 5-1 Wind Tunnel Tests on Cantilever Tube Model OBJECTIVE:
Investigate the effects of tube /AVB fitup on flow induced tube vibration.
Arrayofcantileveredtubeswithendsupports{
APPARATUS:
a.:
MEASUREMENTS: Tube vibration amplitude and tube /AVB impact forces ir preload
- forces, i
RESULTS:
ac l
i 0139M:49/032188 52 5-13 1
A i
{
Table 5 2 Fluidelsstic Instability Peaking Ratios for Coltanwise Variation in AVI Insertion Depths I
l Insertion Peaking Ratio Configuration Uta/Un o,e la i
Ib 2a 3
4c I
Sa 5b 5c 12a 14d 14e 15b 15e Note: Un is instability velocity at inlet fer type n.
t 1
l 1
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0139M:49/032188 53 5-14 1
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i Figure 5-1 Fluidelastic Instability Uncertainty Assessment 0139M:49/030388 37 5-15
4 i
l V,Jend Test Data 1)
MB 3 Tests A values of 2)
M8 2 Tests
. O,c
~ ~
3)
Air Mode 1 Tests
- of ~[wl*thoutAVBs o,,
Tendency for A to increase in range of with inactiveAVBs(gapsatAVBs) g,,
Tendency for A to decrease toward a lower bound of[ ]with active AVBs yerification of Instability conditions 1)
Flow conditions at critical velocity from MB 3 2)
M;asured damping for the specific tube 3)
Calculated velocities from ATHOS 30 analysis 4)
A determined from calculated critical values i
Good agreement with reported A values 5)
ATH0S velocity data with A cf[ [a$*d known damping should not significantly underestimate instability for regions of uniform U bend flow
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Figure 5 2 Instability Constant - A i
a 0139M:49/03?l88 55 5-16 l
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j Figure 5 3 Instability Constants. A, obtained for Curved Tubes frc:
Wind Tunnel Tests on the 0.214 Scale U Bend Model 1
1 0139M:49/0303BS 39 5 17 i
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Figure 5 4 Damping vs. Slip Void Fraction 0139M:49/030444 40 5-18
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i Figure 5 5 Overall View of Cantilever Tube Wind Tunnel liedel i
013M:49/03 tite 54 5 19 a
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4 o.c P5 pggy, s.4 Top View of the tantilever Tube vind Tunnel Wel 013 M:49/037188 59 5-20 1
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J Figure 5 7 Fluidelastic Vibration Applitude With lion Unifors Saps 0139M:49/032184 60 5-21 I
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l Figure 5 8 Typical Vibration Amplitude and Tube /AV8 !apact Force Signals for Flutdelastic Vibration with unequal Tube /AV8 taps
.t I.
1 0139M:49/032188 61 5 22 1
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i Figure 5 9 Conceptual Design of the Apparatus for Determining the Effects on Fluide1tstic Instability of Col utvise Variations in AVB Insertion Depths
]
Ol39M:49/032184 62 5 23 il
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l Figure 5 10 overall Viw of Wind Tunnel Test Apparatus 0139M:49/032188 63 5 24 f
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Figure 5-11 Side View of Wind Tunnel Apparatus With Cover plates Removed to Show Simulated AVts for Field Modified Units and Top Flow Screen i
I, 5-25 j
0139M:49/030788 64 1
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TWE OF AVS TYPE OF AVE 1
WSERTON NSERTON 0t d.C i
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Figure 5 11 AVB Configurations Tested for Prairie island Unit 1 and 2 d
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Figure 5 13 Typical Variation of MS Vibration Amplitude With 1
Flow Velocity for Configuration lain Figure 512 j
0139M:49/032148 66 5-27 i
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i1
i 6.0 EDDY CURRENT DATA AND AVB POSITIONS 6.1 Eddy Current Data d
Tube Dentina at the Tom Tube Suecort pitte l
i Eddy current data from the 1986 inspection of Unit 2 and the 1980 and 1987 inspections of Unit I were reviewed to determine the incidence of denting or corrosion at the top tube support plate for Rows 9 through 13. Several tubes were found with evidence of denting. These are susnarized in Table 61. For a sample of approximately 100 tubes in S/Gs 21 and 22 in Unit 2, 40 60% of the hot lag and cold leg top tube support plate holes were found to be corroded.
Based on this rather high incidence of corrosion, a uniform assumption of corrosion at the top 75P was made for all of the tubes in both units.
Tube Wall Thinnina at the AVB Suceerts.
The tubes in Rows 9 11 of the cteam genarators in Unit 2 which were found in the 1988 inspection to have indications of wall thinning are sumarized in Table 6 1.
J Eddy Current Data for AVB Positions The eddy current data for Rows 9 through 13 from the 1986 inspection of Unit 2 and the 1986 and 1987 inspections of Unit 1 were examined to determine the i
presence or absence of the AVBs, The presence of an AV8 is indicated by a characteristic signal as shown in Figure 6 1.
The number of these signals was reported for each of the tubes examined, and is reported on the resulting AVB position maps, Figures 6 2, 6 3, 6 4 2nd 6 5.
J 6.2 AVB Positions i
i Reelacement AVB Desian i.
ThereplacementAVBsare{
Each AVB assembly includes an upper and a lower bar together at 0139M:49/032188 67 6-1 I
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thabottom(betweenRows11and12). These AVB assembites are 1
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[* Rows 12andgreateraresupportedbytheAVBs,regardlessof their position within the tolerance range. The tip of a nominally installed lower AYB extends beyond the Row 12 centerline by[,
]k*includingan
[
jchamferattheendofeachbar). The lower bar is used as a reference, since it projects slightly farther into the bundle than the upper bar, due to the geometry of the installed AVBs in the U bends.
ThetipofanAVBinstalled[
]. "'
l Therefore, no credit is taken for support of the Row 11 tubes with two AYB indications.
AVB Proiection The depth of insertion of the replacement AVBs can be determined on the basis of[
i i
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.T 0139M:49/032188 68 62
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l Thefundamentalassumptionof(
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In each column,'
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i AVB Insertion Deaths I
i AVB positions have been established based on the ECT data which indicates the number of AVBs visible when the different tubes s?e probed. More than two AVB
' visible" calls are interpreted as sufficient evidence of tube support, since each of the 2 legs of at least one of the replacement bars are seen. However.
only two visible intersections are not necessarily adequate tube support, since each of the two AVBs visible may be the tip of the AVB assembly on opposite sides of the U bend. Thus, o
~
., u for tube support to be assured.
Figures 6 2, 6 3, 6 4 and 6 5 are the AVB maps for $/Gs 11. 12 21 and 22.
The AVB tube support conditions were established crimarily on the basis of
' direct observation data augmented by
~
Yor some of the columns.
~
Where more than 2 AYBs are visible, support of those tubes is assured. Tubes without projected values in the table are based on direct observation. For some of the columns, AYB insertions were verified by
- 1. "
4 a
The tubes which were found to be dented, and those which were previously plugged, are identified on the AVB position saps.
Ol39M:49/032188 70 64 1
Unsueeerted Tubes A sununary of the tubes which are unsupported by an AVB is jiver in T3ble 6 2.,
All Row 12 tubes in Columns 3 through 92 are adequately supported in both st9 a generators of both Units 1 and 2, consistent wi'h the design requir(Dnts of the AVB modificaiton. The Row 12 tubes in Columns 2 and 93 are unsupported, consistent with the design of the replacement AVBs.
i l
l i
0139M:49/032188 71 6;5
Table 6-1 Summary of U-Bend Indications
~
Row Column Indication Unit 1 S/G 11 9
4 Dent 0 7H 9
6 Dent 0 7H 11 5
Dent 0 7H 12 4
Dent 0 7H 13 4
Dent 0 7H S/G 12 Unit 2 S/G 21 13 3
Dent 0 7H 12 4
Dent 0 7H 13 4
Dent 0 7H 12 5
Dent 0 7H 13 42 7% 0 7H + 22.8" 13 42 11% 0 AVB 4 + 1.2" 12 44 6% 0 7H + 22.6" 12 45 11% 0 7H + 22.6" SIG_12 9
4 Dent 0 7H 11 4
Dent 0 7H 12 4
Dent 0 7H 13 4
Dent 0 7H 9
5 Dent 0 7H 11 5
Dent 0 7H 13 33 Unreportable Indication 0 7H 10 59 Dent 0 7C 9
72 Dent 9 7C 12 73 9% 0 AVB 4 + 5.7" 12 2
Dent 0 7H 13 3
Dent 0 7H NOTE: "Dent 0 7H" refers to tube support plate 7 on the hot leg side.
6-6 W
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I Table 6-2 Unsupprted Tube Sumary Unit 1 SlLll Row 9 All Columns.cyceot 91 and 92 Row 10 All Columns e.xcept 3, 4, 91 and 92 Row 11 All Columns accept 3, 4, 91 and 92 Rew 12 Columnc 2 and 93 S/G 12 Row 9 All Co?ut.ns acept 91 and 92 Row 10 All Colum.is except Si and 92 Row 11 All Coiumns except 5, 4, 91 and 92 Row 12 Colu-rs 2 and 93 Unit 2 Slk.11
- 9. w 9 All Columns exce;:t 3, 4, 91 ar.d 92 Row 10 All Columns eu ept 3, 4, 91 and 92 Row 11 All Columns except 3, 4, 91 and 92 Row 12 Columns 2 and 9.1 3/ft1:
Row 5 All Colunns except 3, 4, 91 and 92 Row 10
- All Colums ex< spt 3, 4, 91 and 92 Ro,s l\\
All Column ercept 3, 4 91-and 9.".
Row 12 Coltuis 2 and 93 1:3 d :49/032138 73 g,7
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.c a,e Figure 6-1 Typical Eddy Current Signal for AVBs 6-8 0139M:49/030488 48
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m Figure 6-2 AVB Positions For Prairie Island 1. S/G 11 Ol39M:49/0304BB 49 6-9
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e Figure 6 3 AVB Positions for Prairie Island 1, S/G 12 Ol39M:49/030488 50 640
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Figure 6-5 AV8 Positions for Prairie Island 2 $/G 22 Ol39M:49/030489 52 6-12 i
j 7.0 THERMAL AND HYDRAULIC ANALYSIS This section presents the results of a thermal and hydraulic analysis of the flow field on the secor.dary side of the steam generator using the 3 D ATHOS computercode, Reference (7-1). The major results of the analysis are the water / steam velocity components, density, void fraction, and the primary and secondary fluid and tube wall temperatures. The distributions of the tube gap velocity and density along a given tube were obtained by reducing the ATHOS results. In the following subsections, the ATHOS model and some sample results of the analysis are described.
Because of the staggered anti vibration bar insertion configurations, local flow peaking occurs at certain tubes in the U bend. Its effect on tube gap velocity perturbation was obtained using test data and applied to the Prairie Island steam generators. Normalized stability ratios over the operating history of the plant were determined based on the reported plant operating history. The results of these investigations are also presented in this section.
s 7.1 Prairie Island Steam Generator Operating Conditions Recent steam generator operating conditions from November, 1987 were supplied by Northern States Power for both Prairie Island Units 1 and 2.
Following a review of these data, the ATHOS therraal/ hydraulic simulation was based on the conditions for steam generator number 12 in Unit 1.
The conditions for this steam generator were judged to be just slightly more limiting than those of the other generators considering the effect of factors which can influence the fluidelastic stability ratio (power level, bundle flow, pressure, and water level). Table 7 1 lists the resulting operating conditions which were used in the ATHOS bu'dle flow study. Note also that the downcomer resistance plates n
were removed from both units early in operation; this is of relevance to the secondary side hydraulics calculations.
7-l 0142M:49/032188 1
b With these data calculatior s were completed using the Westinghouse GENF computer code to verify the plant data and to establish a complete list of
~
operating conditions required for the ATHOS analysis. The GENF code determines the primary side temperatures and feedwater flow rate required to obtain the specified steam pressure at the given power rating. Besides confirming these paraineters, the code calculates the circulation ratio which is of primary
~
importance since it establishes the total hundle flow rate and average loading on the tubes. The operating conditions utilized in the ATHOS 3-D analysis are shown in Table 7-2.
7.2 ATH0S 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 ar.d/or the local flow parameters for a particular tube of interest, some discussion of the treatment of AVB's is necessary before presenting a description of the ATHOS 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
," a,e 0142M:49/032188 2 72 l
1
4 I
J a,e The preceding methodology has been adopted in the Prairie Island analysis, with the exception of one modification to the ATH0S simulation. This change involves [
l
- r a,e 0142M:49/032188 3 73
]
[
se
~J) 7.3 ATH0S 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 ATHOS 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 0142M:49/032188-4 74
b l
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 7-4 shows a vector plot of the flow pattetm on the vertical plane of symetry of the steam generator (the vectors are located at the center of the flow cells shown in Figure 7-2).
It is seen that in the U bend region the 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 5 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 7-2). 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 low at the center of the bundle and increases with radius. Figure 7-4 shows th. : the axial component is about four times greater than the radial component. Figure 7 6 shows the flow pattern (resultant of the radial and 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 j
turning upward. The relatively high in flow velocity along the tubelane from the wrapper opening is also evident.
Figures 1-7, 7-8 and 7-9 show a sample of the individual tube gap velocity and density distributions along three tubes at Row 30. 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 7-10 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 tFe numerical average of the parameter over the entire 180' span of a U bend at a given column location. The average velocity is seen to be relatively a,b.c
-l 0142M:49/032188 5 75 I
d 7.4 Relative Stability Ratio Over Operating History One aspect of the evaluation of the Prairie Island steam generators is to examine the operating history data and use it to determine the susceptibility to fatigue from fluidelastic vibration resulting from the 1314 years of operation. This assessment has been completed through the use of a parameter termed the normalized stability ratio. The normalized stability ratio compares the ficidelastic stability ratio for each period of a plant's operation (fuel cycle) to a reference stability ratio based on a recent operating condition. A plot of this ratio against operating time, therefore, provides a relative indicatior, of the effect of past operation on the plant's fluidelastic stability ratio. This nonnalized time dependent ratio is subsequently combined with an absolute stability ratio for the reference operating point derived from detailed threa dimensional thermal / hydraulic and tube vibration calculations.
High values for the net stability ratio, in particular, 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 and fatigue.
.v The fluideiastic 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:
Fluidel utic Veffective Stability Ratio SR -
(1)
Ucritical at onset of instability 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.
0142M:49/032188 6 7-6
)
i 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 simplifie', one dimensional version of this ratio has been used to provide a d
more rapid, relative assessment technique for-determining the effect of past operation on the stability ratto. The normalized stability ratio is defined by the following equation:
a.e (2)
In this equation "cyc x' refers to each fuel cycle and ' ROP' to the recent operating condition. While this simplified approach cannot account for three dimensional tube bundle effects, it does consider the major operational j
parimeters affecting the stability ratio. Four components make up this ratio:
2 a loading term based on the dynamic pressure (pV ), a tube incremental mass (m) term, the natural frequency of the tube (f ), and a damping ratio n
(6) term. It should be noted that the ratio is relative, in that each component is expressed as a ratio of the value for a given fuel cycle to that of the recent operating point.
i
- a.c The particular d'amping correlation which is used for all normalized stability ratio calculations is based on a dented condition at the top tube support plate (a
{
]c*ondition,asdiscussedinSection5.2). The[
[cinditionisalso assumed in calculating the tube natural frequency.
0142M:49/032188 7 77 I
As discussed previously in Section 7.1, the reference stability ratio calculation for the Prairie Is1 And generators was based on the following operating parameters which are for a recent operating point in Unit 1:
Steam Flow 3.54 x 106 lbm/hr Steam Pressure 722 psia Circulation Ratio (Westinghouse calculation) s.e in addition to this reference condition for recent operation, it was necessary to examine the past operation of the two units and select one (or both) for use in the historical stability ratio evaluation. In making this selection, a number of factors were considered which could influence the normali:ed stability ratio / fatigue assessment: 1) the total calendar time since startup and the effective full power years of operation (EFPY), 2) the total operating timeathighpower,and3)thetime-averagestaampressureforhighpower operation.
Considering first the total operating time and the EFPY's of operation, Unit 1 began operation in December 1973, is now in its twelfth fuel cycle, and has accumulated 10.9 EFPY. Unit 2 is now in its eleventh fuel cycle since startup in December 1974 and has accumulated only slightly less full power operation, 10.6 EFPY. While the total operating time is of some relevance, from a stability ratio standpoint, only the operating periods at the highest power levels are significant. This is related to the fact that the loading on the 2
tube (pV ) drops off sharply with power reductions and, also, because the damping increases at lower power levels where the fluid has fewer volds.
Therefore, considering only those periods of high power operation (95 100%) in which the core average power was close to full power, both units were found to have operated for about 3500 days. As a result, considering total calendar time, EFPY's of operation, and the operating period at high power, both units are reasonably equivalent.
0142M:49/032188 8 7-8
i The third factor, the time average steam pressure during high power operation (95-100% of full power) is worth considering since, in general, lower steam pressures increase the cale.ulated stability ratio. Lower steam pressure results in lower U bend density, higher U bend velocity, and decreased tube damping as a result of higher voids in the U-bend. Calculating a time average pressure during the high power periods yields about 724 psia for Unit I and 732 psia for Unit 2.
This slightly lower pressure for Unit 1, along with the fact that the reference ATHOS flow field and stability ratio analyses were based on a recent operating condition in Unit 1, provides a slight advantage for basing the historical analysis on Unit l's operation. Nonetheless, all things considered, any operational differences between the two units are small, and one could just have easily selected Unit 2 and obtained approximately the same final stability ratio / fatigue usage results.
Having selected Unit I for the historical analysis, a series of calculations were completed to generate a normalized stability ratio for each of its fuel cycles. Data for this evaluation is sumarized in Table 7-3.
Included are
~
cycle average values for full load steam pressure and primary fluid temperatures. The number of plugged tubes are also listed along with the number of days that the plant has operated above 86% of full power. Since tube vibration and possible fatigue are associated with high power operation, only these higher power operating periods are considered important to the evaluation. The operating parameters listed in Table 7-3 were then input to the Westinghouse 'GENF' computer code to determine the overall performance of the steam generator, in particular, the circulation ratio for each fuel cycle.
These calculated values are also listed in the table.
The resulting normalized stability ratios are shown in Figure 7-11.
In this figure, the normalized stability ratio for each fuel cycle is plotted against cumulative o'erating time above 86% power. Note that the ratio assigned to p
each of the high power intervals listed in Table 7 3 (86 90%, 91 95%, and 96100%) and plotted in Figure 711 has been conservatively based on the highest power level in each interval. Figure 7-11 indicates that the full power normalized ratto has been a nearly constant throughout operation.
Compared to the reference Cycle 12 value, the variation has only ranged from 0142M:49/032188 9 7-9
d
-2% to +1%.
This small cycle-to-cycle variation is related to changes in steam pressure; higher pressures yield lower stability ratior and vice versa. Higher steam pressures result in higher U-bend density, lower U bend velocity, and increased damping as a result of lower voids in the U bend. The higher damping, together with decreased loading on the tubes, result in the lower normalized stability ratio which is indicated, for example, in cycle 8.
Figure 7-11 also shows that the stability ratios and operating periods at the lower power intervals are negligible compared to the full power results and could have been disregarded in the analysis.
References
~
a.c 7,3 0142M:49/032188 10 7-10 l
i e
Table 7-1 Prairie Island Steam Generator Operating Conditions Power 99.7% of 825 MWT (822.5 MWT)
Steam Pressure 722 psia Feedwater Flow Rate 3.540 x 106 lbm/hr Feedwater Inlet Temperature 425'F Water Level 44.6% 'of Narrow Range Span s
0142M:49/032188-11,
7 11
)
Table 7-2
]
Steam Generator Operating Conditions Used for ATHOS Analysis i
l Power 822.5 MWT l
Primary Flow Rate 3.74 x 107 lb/hr Primary Inlet Temperature 590'F Primary Outlet Temperature 529 'F Feedwater Flow Rate 3.54 x 106 lb/hr Feedwater Inlet 425'F Temperature Water Level from Tubesheet 502 inches Steam Pressure 722 psia Circulation Ratio 5.50 0142M:49/032188 12 7 12
Table F-3 Fralrie Island 1 Operating History Data Core Full Load
- Average Days at Each Power tevel Downcener
$ team
- Pouer Resistance Tubes
- Pressure Thot*
Tcold*
Calculated Cycle Deelnatae Lnd (31 M-1005 91-95%
M-90%
Plates tju_gged inlal Idee F1 (Oee F1 Cire. netto 1"
It-DEC-13 04-flAR-FS-13.0 396 4
IS Yes 0
782 579 332 e,c 2
03-IIAT-76 17-flAR-FF 99.9 268(302)**
8(10) 3(6) me o
F30 586 528 3
04-8847-17 26-80AR-78 M.9 289(310) 8(10) 9(F)
No 0
F30 590 525 4
19-APR-78 06-APR-79 M.8 283(334)
- 2(II) 12(F)
No 0
713 594 529 5
07-MAY-19 31-AUG-80 M.F 302(458) 5(14) 10(80) no 0-1 727 585 527 5
24-0CT-80 19-5EP-81 99.7 294(314) 13(10) 2(F)
No 1
FZF 598 536 7
24-0CT-81 15-Nov-82 99.6 283(368) 29(12)
F(8)
No 3
727 585 537 y
8 18-0EC-82 02-DEC-83 98.4 311 3
6 no 3
732 589 533 9
03-JAn-84 11-JAn-85 99.9 313 11 9
No 88-18 F20 584 530 10 10-nAR-85 04-80AR-86 M.T 281 9
8 to 27 FIF 580 528 II 09-APR-86 SF-APR-87 99.8 273 9
6 to 37-56 120 589 538 12 2F-IIAY-87 31-DEC-87 99.8 201 43 1
No 63 F20 589 538 For 56 It.
Prior to receipt of final plant data, the values la parentkels mere estimated melag the kasun average fret.tlenal distributten of days la each pausr range for Cycles 8-12.
These estimated days mere used in the historical stability retto analyele.
Cycle I operetten mee not canaldered la the historical stability retto analysis because of three factors which ullt result in a olyilficantly louer stalellity ratto cowred to Cycle 2-12 operetten:
- 1) with desacamer resistarce plates included the circulat ten rat te and bundle flow rate are significantly louer.,
- 2) the higher average steam pressure will louer the stability ratle relative to Cycle 2-12 operation and
- 3) the low core average pomer.
0142M;49/030788-13
d 2
Figure 7 1 Plan Viw of ATES Cartesian Model for Prairie Island Ol39H:49/030388 54 7,9
1 J
1 l
a.C I
l i
l
\\
Figure 7-2 Elevation Ylow of ATHos Cartesian Model for Prairie Island 013 % 49/030388 55 7 15 2
d
.i*
Figure 7-3 Plan View of ATHos Cartesian Model for Prairie Island Indicating Tube Layout Ol39M:49/0303C856 7 16 :
1 a.c i
l i
4 1
i Figure 7-4 Flow Pattern on Vertical Plane of Syumetry l
l j
0139M:49/030144 57 7-17 j
-. ~.
l PRAIRIE ISLAND 3 766mt e il 1
V
~
Figure 7 5 Lateral Flow Pattern on a 14crizontal Plane in the U Bend Region 0139M:49/030388 58 7-18
}
i d-r t
PRAIRIE ISLAND
- e6..:. i d
u
-)
-l 4
d 4
1 1
i I
l i
Figure 7 8 Lateral Flow Pattern on Top of Tubenheet j
i 0139M:49/030MS 59 i
7-19 i
i i
i r
w-,,--w-
-m--wwayem
-nwm-- ~ - -
w"w--n eyna epr-----
e-
+-"vwm*~>svm yav p-
-www----n 4--m---p w
e-w y
w-ge
-m--w--w-zmy ynse,e1+q----m---m--
w
-- w gyr
--y yw w-yw 4y--
~~
u 1
3 t*
i j
Figure 7 7 Tube Gap Velocity and Density Distributions li,
for Tube Row 10/Coltan 3 i
f 0139M:49/030388 60 7 20
d
.?
f Figure 7 8 Tube tap Velocity and Density Distributions for Tube Row 10/Coltam to i
0139M:49/03038861 7-21
.~. --..
.. ~
- 3 i
}
s 5
1
~
AC 7
k 1
Figure 7-9 Tube tap Velocity and Density 01stributtons for Tube Row 10/ Column 40
' ~
w 0139M:49/030388 62 7-22 3-
4
..s -..... -... -. -. -.. - -. --.. - -.--
e,'.
.t' m
. /
- j.
g
~
r,*
?
3
~
x s,
s b
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j
.~
y l
g.
i.
..r 1
3 s
(
f 4
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9
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~
's.
a %
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9 2
8 1
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9 1
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/ -
t
\\ s 1
figure 7 10.tverste Velocity nne Density ia tis Plane of the U Bends lloreal to Raw 10
.ls i
, 3 1'
0139M:49/030)C3 63 4
l P
5*
~
F
[..
_ _ _ _ _. __. -.. _ -.... _.. _...... - - - ;_ _. -.- --,A..
- v..~
'j
~
l l
1.02 Reference 1.01 -
p 1.00 -
4 9
10
=
=
=
U 0.99 12 3
Q.9 8 -
Cycle 8
N 0.97 -
I i
e l
y
)
n95 -
ass -
855 Par #
e as4 -
m s
oss -
=
ns2 -
f as0 -
,n,,,, /
Ost -
E O st -
nu-na7 -
nas -
nas -
nS4 e
i e
i 0.0 1,0 2.0 3.0 4.g (Thousond s) m C n/n m t m uco na c (t w s)
Figure 7-11 Prairle Island 1 Normalized Stability Ratio BasedonHl9hPower(>86%) Operation i
0139M:49/030388 64 7-24
A 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:
~
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 Backaround The AVB configuration of the ruptured tube in North Anna, R9C51, is the reference case for the tube fatigue evaluations for other plants. In accordance with the NRC Bulletin 88 02, the acceptability of unsupported tubes in steam generators at other plants is based on tube specific analysis relative to the North Anna R9C51 tube, including the relative flow peaking factors.
Thus, the support conditions of the R9C51 tube are fundamental to the analyses of other tubes. Because of the importance of the North Anna tube, the support conditions of this tube, which were originally based on 'AVB Visible" interpretationsoftheeddycurrenttest(Eg) data (Figure 81),were reevaluated using the oeveloped since the North Anna The}
~
~
event.
[."The results of this evaluation are sumarized below.
l 0142M:49/032,18825 8-1 il
Descriation of the Method
_u The basic method utilized was the technique in which the AVB
~
positionisdeterminedbasedon{~
]."Inthisstudy,the{
]Yechniquewasutilizedinthe b
~ " The objective of this application was, with the greatest confidence possibleI to establish the positions of the AVBs in an 8 column range around the R9C51 tube in North Anna 1. Steam Generator C.
Data Intereretation 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 81. The data were examined by an eddy current analyst experienced in reading these traces, and by a design engineer knowledgeable in the geometry of the Model 51 U bend region.
The intent of this review was to determine if the presence or abseng of AVBs asshowninFioure81couldbeconfirmedusingtheAVB[
] technique.
Preliminary J
0'
<u l
l 0142M:49/032188 26 8-2
3
~
AC Figure 8 4 is the 'AVB visible' map for columns 48 through 55, based on the critical review of the data. It is noted that the original data interpretatior.s and the review interpretations are consistent.
~
u E
]"
I 0142M:49/032188 27 8-3 i
I l
1
)
i AC
. Ae The logic in arranging the data is based on the following two rules:
Ac
~
~
Rule 1.
The of the same AV8 b. sed on different tubes in the
~
same column [,
]."'
.i i
1 se Rule 2.
Twoadjacenttubesinthesamerow{
[* Consequently,thedifferenceinthe{
i 1
~
j a,c 1
l 1
1 0142M:49/032188 28 8-4 i
b 1
The i plementatijn of this is that if the position (either left ogright) 3 of a JAYSisassumedforacolumn,thenthe
,in the adjacentcolumnsarealso[
} i,c The arrangement of the AVBs as shown in Figure 8 5 best satisfies the rules above and is consistent with the fatigue rupture of R9C51. The resulting AVB arrangements, based on the projection matrix of Figure 8 5 is shown in Figure 8 6.
Conclusions The general AVB arrangement surrounding the rupture 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 in 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.
S.C The basis of the review was a }
{ technique which utilizes [
['Theintentofthereviewwastoestablish the positions of the AVBs by confirming or eliminating features of AVB alignments such as side to side offsets, etc. of the AYBs adjacent to the tubes. Overall, the conclusions regarding the positions of the AVBs around R9C51 in North Anna 1. Steam Generator C are based on consistency among all the
- i available data.
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.
Nevertheless, some remain and should be properly accounted for. The important j
parameter measured during testing that has a significant impact on j
0142M:49/032188 29 8-5
b 1
l peaking factor is the air velocity. The air velocity at test section inlet was
~
measured using a
~ '* 8ased on considerable experience with
~
the use of such instruments, it is known that the magnitude of uncertainty is very small. A[ } 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 detemine the effects of AVB insertion depth on the initiation of fluidelastic vibration. The following assumptions are used:
a,e 1.
2.
3.
0142M:49/032188 30 86
\\
s u
4, For the purposes of this estimate, the geometry of the cantilever measuring tube in th,e a e test model is compared with the geometry of a prototypical Row 10 tube.
'u 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 AYBs.
1 i
l
~
u I
0142M:49/032188 31 8-7
l i
a,cUsing these values, the ratio of the effective velocity for the cantilever measuring tube to that for the U bend tube is about[ ]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.[
)#The net result is that the ratio of the effective velocity for the cantilever tube to that for the U bend tube is about[ ).
These results indicate that, for the particular assumptions used, the j
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[ }"
8.5 Air vs Steam Water Mixture w
The local peaking factors from the air tests can be applied to the steam f
generator steam / water conditions either as a direct factor on the mixture 0142M:49/032188 32 88
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 j
North Anna Unit I 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 '.;ch 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 phast tests indicate a tendency for steam to preferentially follow the low pressure drop path compared to the water phase.
Based on the above discussion, the Fg are considered to more appropriately apply to the steam phase. Thus, it follows that mixture mass velocity for the tube subject to flow perturbation can be written as follows:
(1)
(2) where p is the vapor density, pf the water density, F the a
g velocity peaking factor determined from air tests, j
- the cominal g
superficial vapor velocity, and jf* the superficial water velocity. Steas quality can then be determined as follows:
l 0142M:49/032188 33 8.
1
o (3}
.u Thep
, as used in the ATHOS g
code, is applied to deternine void fraction. Subsequently, mixture density.
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 damping coefficient can be readily determined. Finally, a local stability peaking factor for fluidelastic vibration can be calculated as follows:
-. a (4]
where F is the stability peaking fac, tor, Fd the density scaling factor, s
F the velocity scaling factor, and Fqp the damptr; coefficient scaling y
factor. If we use the air velocity peaking factor without translating to I
steam / water conditions, then i
~
is As shown in Table 81 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.
For application to tube fatigue evaluations, the ratio of the peaking factor i
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.
TheNorthAnnaR9C51peakingfactorisoneofthehighestjeakingfactors. As discussed in Section 8.7, a peaking factor of nearly@.5]is determined for the R9C51 tube. 'The differences between[
]."Typical values are shown in Table i
8 2.
These results show that the direct application of the air test data yields the higher relative peaking factor compared to R9C51. To obtain l
conservatism in the peaking factor evaluation,[
}"
l 0142M:49/032188-34 8-10
4 Comparing the values in the first and last columns of Table 81, it may be notedthatthestabilitypeakingfactorforsteamwateris[
]h5gherthan the air velocity peaking factor. On the average, the uncertainty associated J
with the conservative use of air velocity peaking factor is((*
The conclusion that the peaking factor for steam water flow would be higher due to the dependency of damping ratio on vol 6 tion was supported by an alternate study. In this study, a section of steam generator tubes were simulated using the ATHOS code under protypic flow conditions. The objective of this study was to 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 i
analysis using two fluid modeling procedure is mandatory to a calculation of the peaking factors for a steam generator to account for the preferential steam flow along the low resistance path. Consequently, the intent of this analysis is only to help bound the uncertainty on void fraction effects from extrapolating the air tests to steam water.
First the analysis was conducted with uniformly inserted AVB's in the ATHOS model. The ATHOS results were processed by the FLOVIB code to determine stability ratios for the specific tubes of interest. The calculation was repeated using a non uniform AVB insertion pattern in the model. The results show that the void fraction distribution changes as a result of flow perturbation. Further, the impact on stability ratio resulting from the changes in void fraction profiles was about[
[*Thisalternate calculation provides independent corroboration of the prior discussion regarding the stability peaking factors under steam water conditions vs in air.
8.6 AVB Insertion Depth Uncertainty The most significant uncertainty for the low peaking cor. figurations 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 0142M:49/032188 35 8-11
d to within approximately
[The
~
~
effect on peaking factor resulting from this uncertainty is addressed using testresultsofAVBconfigurationsthatvariedfromoneanotherbyupto[
}u Based on maps of AVB insertion depth of various plants, several configurations have been tested for determining fluidelastic instability flow rate by an air cantilever model. Stability peaking factors were then determined from the ratio of critical flow rate for a unifors AVB insertion configuration to a specific configuration. Figure 8 7 sumarizes the AVB configurations tested.
Position of AVB insertion depth is determined from Eddy Current Test (ECT) data. Positioning of AVB from ECT data reading is subject to uncertainty; its accuracyisprobablyabout[
." A change of an AVB insertion depth in a given configuration leads to a different configuration, and thus a different peaking factor. A review of the tested AYB type has been made and results sumarized in Table 8 3.
As can be seen, a decrease in depth of an appropriateAVBtendstodecreasethepeakingfactor,forinstance,a(
l
]."Sucha trend can be explained; a decrease in a specific AVB depth will open up more channels for incoming fluid to distribute and create less flow perturbation.
However, this applies only to those changes without inducing the reinforcement of flow perturbation from upstream to downstream.
On the average, the uncertainty in peaking factor resulting from small variations in AVB insertion (of the order of 1/2 tube pitch) is found to be
.)
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.
0142M:49/032188 36 8-12
Looking forward to how these peaking factors are used in the analysis (Section 9), the relative stability ratio calculated for a given tube without the consideration of flow peaking is corrected using the ratio of the peaking factor of the specific tube to that of the North Anna R9C51 tube (Configuration la). It is to be noted that, of all the configurations tested, configuration Ib produced the highest peaking factor, followed very closely by 4c and la.
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 apparently j
low peaking configurations, j
The uniform AVB configuration (2a) is selected as a reference canfiguration, and the peaking factors of all configurations tested are recomputed on the basis of this reference. As discussed below, some of the test uncertainties are applied to the reference case to account for its significantly low peaking relative to the R9C51 configuration.
The uncertainties in the test results and their extrapolation are those due to test measuriments, 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
~
.The RSS value of these is[ [*Since 0142M:49/032188 37 8-13
i 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 (P9C51) is reduced by this amount to yield a value of[ ]i$ stead of the[ }"
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 tube under consideration and the R9C51 tube and are therefore counter j
balanced. However, the relative magnitude of these may be different, particularly for configurations with much lower peaking than R9C51. Therefore itwasjudgedthatthe[
}."Similarly, as noted above, the effect on peaking factor due to the uncertainty in the field AV8 configuration is also included in this referance case. Thus,[
]."Thepeakingfactorofthe reference configuration 2a (Table 8 5) is raised by this amount to a value of
[
}. "
\\
The change in peaking factors of configurations la and 2a resulting from the application of uncertainties as described above are shown in Column 3 of Table 8 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.
Some of the uncertainties were applied to the referente configuration (2a) in order to apply them to all low pecking configurations conservatively. Thus, no configuration should have a lower peaking factor than this reference u
configuration. Therefore, when a peaking factor value less than[ ]is calculated for any configura+. ton, (in Column 4 of Table 8 5), it should be altered to[, }"Further, for some of the configurations that are conceptually similar, the more limiting (higher) value is used. For example, a peaking factor of[ ]N used for configurations 5a and 5b based on their similarity to configuration 5c.
e 0142M:49/03218838 8-14
d The above discussion pertained to the evaluation of peaking factors for designs with standard AVB's, including North Anna. For steam generators that h:ve replacement AVB modification installed, an additional consideration is the impact of flow peaking for this design when the depth of insertion is not uniform. Tests have been conducted to determine stability peaking factors for replacement AVB configurations. Since the overall tube fatigue analysis is performed relative to the North Anna R9C51 tube, one cannot completely dissociate from the treatme*nt and findings applied for the standard AVB design when evaluating a steam generator with replacement AVB's. The methodology utilized for the latter is identical to the prior description and the details are discussed below.
In general, the stability peaking factors for the replacement AYB design were found to be lower than those for the standard AVB's. This is true even for the uniform insertion configuration. Some of the uncertainties associated with the replacement AVB configurations were also found to be smaller. For example, the impact on peaking factor resulting from the uncertainty in djtermining AVB insertiondepthsinthesteamgeneratorwasfoundtobe(~(ontheaverage) ratherthanthe(,]Nundforthestandarddesign.
In the current analysis a conservative approach is employed by retaining the uniformly inserted configuration of the standard AVB's as the reference case and calculating the stability peaking factors of all configurations on this basis. Further, no configuration is allowed to have peaking factors less than
[ ]N1stive to this reference case. This results in the calculation of conservatively higher stability ratios for tk.a replacement AVB configurations.
Table 8 6 is similar to Table 8 5 and shows the result of applying the methodology to the replacement AVB configurations. Please note that if the uniform insertion configuration (12a) of the replacement AVB were chosen as the reference case instead of 2a, the peaking factor of North Anna R9C51 tube would beabout[
[The final stability ratio peaking factors calculated on thisbasis(withconfiguration2aasthereference)areshowninTable87.
Figure 8 7 shows the final peakir.g factors with the pictorial representation of the AVC insertion patterns, 1
0142M:49/032188 39 8-15
i i
Table 8 8 shows the result of applying the peaking factors to specific tubes in the Prairie Island (Units 1 and 2) steam generators.
The overall conclusions from the peaking factor assessment are:
1.
As noted in Table 8 4, five elements have been included in the uncertainty evaluation for the peaking factors. The uncertainty estimates were developed from both test and analysis results as described in Sections 8.2 The largest single uncertainty of ' ]U attributable to to 8.6.
uncertainties of up to on determination of AVB insertion depths from field eddy current data. This relatively large uncertainty is applicable only to low peaking conditions where the AVB uncertainties can contribute to small peaking factors. The definition of "no flow peaking" was increased to encompass the small peaking effects from AVB insertion uncertainties. For the AVB patterns leading to significant peaking factors, AVB's were positioned within uncertainties to maximize the peaking factor. For these configurations, variations of AVB insertion within these uncertainties are expected to reduce the peaking factor compared to the final values of Table 8 6 and Figure 8 7.
2.
Including uncertainties directed toward conservatively decreasing the peaking factor for the North Anna tube R9C51, the final R9C51 peaking factor is[ }r$lative 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 (such as. configuration 4c) although this is believed to be a consequence of the conservative uncertainty analysis and is not likely to be representative of actual peaking effects.
4.
For the replacement AVB configuration, although the tests showed lower peaking factors than the reference configuration, a conservttive approach was employed. The uniformly inserted configuration of the standard AVB was retainedasthereferencecasegndnoconfigurationwasallowedtohave peakingfactorslessthan[]withrespecttothisreference.
1 j
0142M:49/032188 40 B-16
~
l i
i I
i Table 8 1 I
Stability Peaking Factor Due to Local Velocity Perturbation Scaling Factors for Steam / Water j
^
Air Velocity Void Stability Peaking Fraction Density Velocity Damping Peaking
- Factor, Scaling,
- Scaling, Scaling,
- Scaling, Factor, I
F Fd F
Fqp F
a y
y s
i u
l j
)
NOTE:
1.
Stability peaking factor for steam / water mixture is calculated as follows:
6 2.
Damping scaling factor is calculated using modal oc effective void fraction of for R9C51 tube, e.
0142M:49/032188 41 8-17 I
Table 8 2 Comparison of Air and Steam water Peaking Factor Ratios Air Air Steam Steam Peaking Peaking Peaking Peaking Factor Ratio Factor Ratio
~
u 0142M:49/032188 42 8 18 l
3 l
I t
d 1
1 Table 8 3 Effect of local Variation of AVB Insertion 1
I A to e AVB Peaking Peaking Ratio j
Type A Type B Variation Ratio A Ratio B (8/A)
I i
Se i
5b Sa 4a 5e
)
5c 5a i
i 5a
$b l
5c 4a 5a 5c
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l 1
a Peaking Ratios U,/U are from Column 2 of Table 8 5 3
n l
I
- l j
l l
i 1
.I i
j ll 0142M:49/032188 43 3 19 I
l
- d l
1 I
Table 8 4
)
Uncertainties in Test Data and Extrapolation i
Source of Uncertainty lyAg Macnitude. 1 l
1.
Velocity measurement Random l
l 2.
Test repeatability Random 3.
Cantilever vs U tube Systematic 4.
Air vs steam water mixture Systematic 5.
Field AVB configuration l
i l
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.
0142M:49/032188 44 8 20 lI
I
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l l
Table 8 5 Extrapolation of Test Results to Steam Generator Conditions for Standard AV8 Configurations Peaking Factor i
Test Data with Referenced to Confiauration Data Uncertainties Confia. 2a Standard AVB Confiaurations l
At la
)
l Ib l
2a i
3 4c i
5a Bb Sc 0142M:49/032188 45 8 21
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l 4
1 Table 8 6
)
)
Extrapolation of Test Results to Steam Generator Conditions for Standard and Replacement AVB Configurations 1
Peaking Factor j
t j
Test Data with Referenced to Confiouration Q113 Uncertainties confio. 2a 4
1 Standard AVB Confiourations
~
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u la Ib la
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I 3
4c 5a
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5b Sc l
i Reelacement A,B 'enfiaurations j
i j
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J 14e
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15c i
0142M:49/032188 46 8-22 11 1
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Table 8 7 Final Peaking Factors Confiauration Peakina Facter Standard AVB Confinuratient
~
~
a.c 3,
lb 24 3
4c 54
$b 5e Reelacement AVB Confieuratient a.c 124 14d 14e 15b 15e 0142M:49/032188 47 8 23 l
l 1
i Table 8 8
)
i 3,
i Stability Peaking Factors for Specific Tubes j
i i
PRAIRIE 15 LAND UNIT 1 l
$ TEAM GENERATOR R0W N0.
COLUMN N0.
PEAKING RATIO 11 8 TO 12 ALL u
12 8 TO 12 ALL 1
l l
1 PRA!RIE !$ LAND UNIT 2 I
l STEAM GENER.ATOR R0W NO.
COLUMN NO.
PEAKING RATIO 1
i 1
l 21 8 TO 12 ALL i
i i
22 8 T0 12 ALL a
l 1
1 1
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0142M:49/032188 48 8 24 1
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@ FAILED TUBE O visiBea
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e pouaoEo Figure 8 1 Original North Anna AVB Configuration 0142M:49/030788 49 g.25 ii
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Figure 8 2 Schematic of Staggered AVBs 0142H:49/030788 50 8-26
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Column 56 55 54 53 52 51 50 49 48 47 46 45 44 g Pivgged Tube g Fa W Tube on f he T
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Fig'Jre 8 4 North Anna 1. Steam Generator C AY8 Positions Critical Review ?AVB Visible' Calls 0142M:49/030788 52 8-28
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Figure 8-5 NorthAnna1,SteamGgeratorC, R9C51 AVB Matrix 0142M:49/030762.53 8-29
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{Psitions Figure 8 6 North Anna R9C51 AVB Final 0142M:49/030788 54 8-30
I i
TYPE OF Ave PEAKING TYPE OF AVB PEAKING INSERTON FACTOR INSERTON FACTOR
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Figure 8 7 Final Peaking Factors for Prairie Island Unit 1 and 2 e
8-31 l
i 9.0 STRUCTURAL AND TUBE VIBRATION ASSESSMENTS 9.1 Tube Mean Stress This section sumarizes an 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 themal gradient. The an,a,1ysis assumes the tube to be [
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 and the plate temperature.
' e resulting tube / plate radial interference is F
i,e The analysis is perfomed using the finite element model shown in Figure 91.
The model prescrittas
].
Two reference cases were run using the finite element model, the first for a primarytosecondarysidepressuregradient,andthesecondfora[
]
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 t!,e distribution of stress for the tube outer surface for the two reference cases are provided in Figures 9 2 and 9 3.
Tube stresses due to the thru wall thermal gradient are calculated to be 9.0 ksi using conventional analysis techniques. A plot showing the combined stress distribution along the tube length, incorporating appropriate scale factors for the Prairie Island operation conditions, is provided in Figure 9 4.
The 0142M:49/032288 56 9,)
4 txial tensile stress is 22.5 ksi and occurs approximately 0.125 inch
<c above the top su face of the support plate. Adding, for conservatism, the surface stress due to pressure, 0.75 ksi, gives an applied mean stress of 23.3 ksi. In addition to the applied stress, residual stresses exist in the tube as a result of the manufacturing process. For mill annealed tubes with subsequent straightening and polishing, significant residual stresses exist in the tube.
The stresses are compressive at the tube surface, but 5 10 mils below the surface, the stress levels change to 10-15 ksi tensile, Reference 9 1.
Combining the applied and residual stresses results in a cumulative mean stress of 38.3 ksi. For those tube locations where denting was observed to occur, the maximum mean stress, based on omax
- O, was used in determining stability y
ratios and fatigue usage.
9.2 Stability Ratio Distribution Based Upon ATHOS An assessment of the potential for tubes to experience fluid elastic i
instability in the U bend region was performed for each of the tubes in rows eight through twelve. This was performed using FASTV!B, a Westinghouse proprietary finite element based computer code and PLOTVIB, a post processor to FASTVIB. These codes were written to predict the individual responses of an
+
entire row of steam generator tubing exposed to a tube location dependent fluid velocity, density and void fraction profile. The programs calculate tube natural frequencies and mode shapes using a linear finite element model of the tube. The fluid elastic stability ratio V,/Uc (the ratio of the effective velocity to the critical velocity) and the vibration amplitudes caused by turbulence, are calculated for a given velocity / density / void fraction profile and tube support condition. The velocity, density, and void fraction distributions are determined using the ATHOS computer code, as described in Section 7.2.
Also input to the codes are the WECAN generated mass and stiffntss matrices used to represent the tube. (WECAN is a Westinghouse proprietary computer code.) Additional input to FASTV!B/PLOTVIB consists of tube support conditions, fluid elastic stability constants and turbulence constants.
0142M:49/032188 57 9-2
)
This process was performed for the Prairie Island Unit 1 and 2 steam generator l
tubes and also for the North Anna Row 9 Column 51 tube (R9C51) using similarly appropriate ATHOS models. Ratios of the Prairie Island 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 Prairie Island Unit I and 2 tubes relative to the ruptured tube at North Anna Unit 1.
Figure 9 5 contains the results of this process for each of the rows under investigation. This figure was generated using the following conditions for both Prairie Island (Units 1 and 2) and North Anna Unit 1:
1)
Tube is fixed at top tube support plate.
2)
Void fraction dependent damping used.
3)
No AVB supports active.
)
4)
Flow peaking factors are not included.
A horizontal line is drawn at the relative stability ratio value of 0.90. This identifies the point where a ten percent reduction in stability ratio exists relative to North Anna R9C51. (See Section 4.3 for a discussion of the stability ratio reduction criteria.) All the tubes with ratios above this line would be considered to have stability ratios larger than ninety percent of North Anna R9C51. This figure indicates that all tubes in Row 8, one tube in Row 9 (Column 2), and one tube in Row 10 (Column 2) 1.e. below the line. All the remaining tubes in Rows 9, 10, 11 and 12 lay above this line. All tubes that are not supported by AVBs require further evaluation including flow peaking factors to determine the acceptability of the tubes. Section 9.3 contains the results of the furth4r evaluation for these tubes.
9.3 Stress Ratio Distribution With Flow Peaking An evaluation was performed to determine the ratio of the Prairie Island 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, flow peaking factors (Table 8 8) and bending moment factors. Sections 4.2 and
~
4.3 contain additional information and describe the calculational procedure 0142M:49/032188 58 9-3
)
used to obtain the results presented in this section. The results contained in I
this section are based upon the following conditions:
j
~1)
Tube is fixed in top tube support plate.
1 2)
Damping is void fraction dependent.
j
.2 3)
AVBs do not provide support.
1 f
4) 10% criteria with frequency effects used.
5)
The tubes are assumed to be dented (deformation) or undented.
6)
Flow peaking factors are used.
A tube can be considered acceptable for the reference cycle analyzed 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. Using this criteria indicates that the stress acting on a given tube will not produce a f
fatigue event in a manner similar to the rupture that occurred in the R9C51 tube at f: orth Anna Unit 1.
Figure 9 6 contains the stress ratio results for each of the Prairie Island tubes in Rows 8 through 12. This figure is applicable for tubes that are dented at the top tube support plate. As can be observed in the figure, all of the tubes.a Rows 8, 9,10 and 11 fall below the acceptance line indicating that the tubes are acceptable with respect to U bend fatigue. All of the tubes in Row 12, except for the Column 2 tube, lay above the acceptance line. This indicates that ths ;ubes are not acceptable, with respect to U bend fatigue, if the tubes are not supported by an AVB and are dented at the top tube support plate.
Figure 9 7 contains results similar to the infonnation presented in the previous figure except that the tube is assumed to be undented at the top tube 2
support plate. This figure indicates that all of the tubes in Rows 8, 9,10 and 11 also fall below the acceptance line. All of the tubes in P.ow 12, except for the tubes in Columns 2, 5, 6, 7 and 8, lay above the acceptance line. This indicates that the tubes are not considered acceptable, with respect to U bend fatigue, if the tubes are not supported by an AVB and are finnly fixed, but not dented, at the top tube support plate.
I"4 niatu.ao/n m aa.no
d 9.4 Cumulative Fatigue Usage All tubes that are unsupported and have a stress ratio s 1.0 have a maximum stress amplitude that is < 4.0 ksi (from 9.5 ksi) since a 10% reduction in the stability ratio for the North Anna Row 9 Column 51 tube was the criteria basis. The stability ratios for the P-airie Island Unit I 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 fatigue if 1) they meet the stress ratio criteria of $1.0 and 2) their current and future fatigue usage will total less than 1.0.
From Figures 9 6 and 9-7, it can be seen that all unsupported tubes (Section 6.5) have a stress ratio less than 1.0.
Acceptability of the Prairie Island Units 1 and 2 tubing for fatigue is accomplished by demonstrating th'e acceptability of the tube with the highest stress ratio, 0.73, at Row 11 Column 47. Based on the relative stability ratio over the operating history presented in Section 7.4, the alternating stress for each operating cycle can be determined. Computing stress ratios for each cycle establishes the maximum alternating stress for each operating cycle since it is equal to the stress ratio times 4.0 ksi. The number of cycles of vibration is obtained for each fuel cycle by multiplying the number of days times the number of cycles per day at the frequency of the Row 11 tube,[
[ Table 92 summarizes the duty cycle history.
The cumulative fatigue usage to date is 0.052 and the cumulative fatigue usage for the operating license period (with future years at the same operating conditions as cycle 12) would be 0.173. All of the Prairie Island Units 1 and 2 tubes, therefore, meet the fatigue usage requirement of 1.0.
Reference:
91 Westinghouse Research & Development Report 77-lD2-TUCOR R2, ' Residual Stresses in Inconel 600 Steam Generator Tubes - Part II: Straight Tubes',
Westinghouse Research Laboratories, Proprietary Class 2, D. L. Harrod, October 21, 1977.
0142M:49/032188 60,
9,5
-1 Table 91 100% Power Operating Parameters Prairie Island Primary Pretsure
- 2250 psi Secondary Pressure - 750 pst Pressure Gradient - 1500 pst Primary Side Temperature
- 567'F Secondary Side Temperature 511*F Tube Temperature
- 539'F l
0142M:49/032188 61 96 l
~
Table 9 2 Duty Cycle Description for Prairie Island Units LUMPED NORMALIZED FUEL STABILITY ALTERNATIF)
CYCLES CYCLE.
RATIO STRESS
- DAll AT 43.2 HZ 9
t,C A
1.0083 3.15 334 B
1.0021 3.04 867 C (REF) 1.0 3.00 201 0
0.9948 2.91 1384 E
0.9938 2.89 368 i
F 0.9814 2.70 322 G
0.9577 2.36 111 H
0.9494 2.24 95 I
- Based on stress ratios with frequency effects removed since frequency (43.3 hz) is used in determining cycles.
r 0142M:49/032188 62 97
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a,e
.o Figure 9-1 Axisyneetric Tube Finite Elseent Model 0142M:49/0303889 9-8 1
8,C
't e
Figure 9 2 Dented Tube Stress Distributions Pressure Load on Tube 0142M:49/030388 10 9-9
A a,C eC l
l F
l i
w Figure 9 3 Dented Tube Stress Distributions Interference Load on Tube 9-10 0142M:49/030788 65 -
j
_y Figure 9-4 Dented Tube Stress Distributtons Combined Stress Results 0142M:49/03038812 9-11
b l
4
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Figure 9 5 Relative stability Ratios 0142M:49/0303&B 13 9 12 I
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Figure 9 6 Stress Ratio vs. Column Naber - Dented Condition 0142M:49/03048813 g,j)
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Figure 9-7 Stress htlo vs. Column Number - Undented Condition 0142M:49/030488 14 9 14 m- -.,i,--
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