ML20147C706
| ML20147C706 | |
| Person / Time | |
|---|---|
| Site: | Point Beach  |
| Issue date: | 12/31/1987 |
| From: | WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML19341D791 | List: |
| References | |
| WCAP-11667, NUDOCS 8801190326 | |
| Download: ML20147C706 (134) | |
Text
_ _ _ _ _ _
WESTINGHOUSE CLASS 3 l
POINT BEACH UNIT 2 EVALUATION FOR TUBE VIBRATION INDUCED FATIGUE DECEMBER 1987 I
t i
WORK PERFORMED UNDER SHOP ORDER MK7D-76328 t
8801190326 880111 PDR ADOCK 05000301 p
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a i
t WESTINGHOUSE ELECTRIC CORPORATION
[
POWER SYSTEMS BUSINESS UNIT P.
O.
BOX 355 PITTSBURGH,PA 15230-0355 e
t'
AMTRACT On July 15, 1987, a steam generator tube rupture event occurred at the North Anna Unit 1 plant.
The cause of the tube rupture has been determined to be high cycle fatigue.
The source of the loads associated with the fatigue mechanism is a combination of a mean stress level in the tube with a superimposed alternating stress.
The mean stress is the result of 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-band caused by flow induced vibration.
This report documents the evaluation of steam generator tubing at Point Beach Unit 2 for susceptibility to fatigue-induced cracking of the type experienced at North Anna Unit 1.
The evaluation utilizes operating conditions specific to Point Beach Unit 2 to account for the plant specific nature of the tube loading and response.
The evaluation also includes field measurements taken for Point Beach Unit 2 to establish AVB locations.
This report provides background of the event which occurred at North Anna, it presents a criterion for fatigue assessment, a summary of test data which support the analytical approach, field measurement results showing AVB positions, thermal hydraulic analysis results, and calculations to determine tube mean stress, stability ratio and tube stress distributions, and accumulated fatigue usage.
O 1
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SUMMARY
OF ABBREVI:vNOMS ASME - American Society of Mechanical Engineers ATHOS - Analysis of the Thermal Hydraulics 2f Eteam Generators AVB - Anti-Vibration Bar AVT - All Volatile Treatment ECT - Eddy Current Test EPRI - Electric Power Research Institute FFT - Fast Fourier Transform FI4VIB - FIbw induced Vibrations MEVF - Modal Effection Void Fraction OD - Outside Diameter RMS - Root Mean Square SR - Stability Ratio TSP - Tube Support Plate OF - degrees Fahrenheit hr - hour kai - measure of stress - 1000 pounds per square inch lb - pound mils - 0.001 inch MW - maga vatt psi - measure of stress - pounds per square inch psia - measure of pressure - absolute O
11
.C
TABLE OF CONTENTS SECTION 2AGI 1.0 Introduction 1-1 2.0 Summary and Conclusions.
2-1
3.0 Background
3-1 3.1 North Anna Unit 1 Tube Rupture Event 3-1 3.2 Tube Examination Results 3-2 3.3 Mechanism Assessment 3-3 4.0 Criteria for Fatigue Assessment 4-1 4.1 Stability Ratio Reduction Criteria 4-2 4.2 Local Flow Peaking Considerations.
4-7 4.3 Stress Ratio Considerations.
4-9 5.0 Supporting Test Data 5-1 5.1 Stability Ratio Parameters 5-1 5.2 Tube Damping Data.
5-6 5.3 Tube vibration Amplitudes with Single-sided AVE Support.
5-8 5.4 Tests to Determine the Effects on Fluidelastic Instability of Columnwise Variations in AVE t
Insertion Depths
. 5-10 5.5 References 5-14 6.0 Eddy Current Data and AVE Positions.
6-1 6.1 Tube Denting at Top Support Plate.
6-1 l
6.2 Tube Wall Thinning at the AVB Supports.
6-1 6.3 Eddy Current Data for AVB Positions.
6-1 6.4 AVB Insertion Depths 6-2 6.5 Unsupported Tube Summary 6-5 iii
.Y
TABLE OF CONTENTS (CONTINUED)
SECTION PJgd; 7.0 Thermal Hydraulic Analysis
........7-1 7.1 Point Beach Steam Generator operating I
Conditions
. 7-1 7.2 ATHOS Analysis Model
. 7-2 7.3 ATHOS Results.
7-4 7.4 Local Peaking Factors for Unsupported Tubes.
7-6 7.5 Relative Stability Ratio over operating History. 7-11 7.6 References 7-15 8.0 Structural and Tube Vibration Assessments.
8-1 8.1 Tube Mean Stress 8-1 8.2 Stability Ratio Distributions Based Upon ATHOS 8-2 8.3 Stress Ratio Distribution with Peaking Factor.
8-3 8.4 Cumulative Fctigue Usage 8-4 4
1-iv 8
LIST OF FIGURES FIGURE g
3-1 Approximate Mapping of Fracture Surface of Tube R9C51 S/G "C" Cold Leg, North Anna Unit 1.
3-5 3-2 Schematic Representation of Features observed During TEM Fractographic Examination of Fracture Surface of Tube R9C51, S/G "C" Cold Leg, North Anna Unit 1.
3-6 3-3 Calculated and observed Leak Rates Versus Time 3-7 4-1 Vibration Displacement vs. Stability Ratio 4-12 5
4-2 Fatigue Strength of Inconal 600 in AVT Water at 600 F. 4-13 0
4-3 Fatigua Carve for Inconel 600 in AVT Water Comparison of Mean Stress Correction Models.
4-14 4-4 Modified Fatigue Life with 10% Reduction in Stability Ratio for Maximum Stress condition 4-15 4-5 Modified Fatigue Life with 5% Reduction in Stability Ratio for Minimum Stress condition 4-16 5-1 Fluidelastic Instability Uncertainty Assessment.
5-17 Instability Constant - /3..............
5-18 5-2 InstabilityConstants,j3,obtainedforcurvedTubes 5-3 from Wind Tunnel Tests on the 0.214 Scale U-Band Model..
5-19 5-4 Damping vs. Slip Void Fraction S-20 l.
1 V
i
LIST OF FIGURIS (Continued)
FIGURE 2AgI
~
5-5 overall View of Cantilever Tube Wind Tunnel Model.
5-21 5-6 Top View of the Cantilever Tube Wind Tunnel Model.
5-22 5-7 Fluidelastic Vibration Amplitude with Non-Uniform Gaps 5-23 5-8 Typical Vibration Amplitude and Tube /AVB Impact Force Signals for Fluidelastic Vibration with Unequal Tube /AVB Gaps.
5-24 5-9 Conceptual Design of the Apparatus for Determining the Effects on Fluidelastic Instability of Columnwise Variations in AVB Insertion Depths 5-25 5-10 overall View of Wind Tunnel Test Apparatus 5-26 5-11 Side View of Wind Tunnel Apparatus with Cover Plates Removed to Show Simulated AVBs and Top Flow Screen 5-27 5-12 AVB Configurations Tested.
5-28 5-13 Typical Variation of RMS Vibration Amplitude with Flow Velocity for configuration 1 in Figure 5-12 5-29 6-1 Tubes with Dents at Tube Support Plate No. 6 Steam Generator A - Hot Leg.
6-8 6-2 Tubes with Dents at Tube Support Plate No. 6 Steam Generator A - Cold Leg 6-9 l
vi 1
l s
LIST OF FIGURIS (Continued)
FIGURE y fd; 6-3 Tubes with Dents at Tube Support Plate No. 6 Steam Generator B - Hot Leg.
6-10 I
6-4 Tubes with Dents at Tube Support Plate No. 6 6-11
)
Steam Generator B - Cold Leg 6-5 AVB Insertion Depth Configuration.
6-12 1
6-6 AVB Insertion - Point Beach Steam Generator A.
6-13 l
6-7 AVB Insertion - Point Beach Steam Generator B.
6-14 7,-l Plan View of ATHOS Model for Point Watsch Unit 2 7-23 7-2 Elevation View of ATHOS Model for Point Beach Unit 2 7-24 7-3 Hot Leg Side Plan View of ATHOS Model.
7-25 7-4 Flow Pattern on Vertical Plane of Symmetry 7-26 7-5 Flow Pattern on Horizontal Plane (Z=22) at U-Band Region 7-27 f
7-6 Flow Pattern on Top of Tubasheet 7-28 7-7 Tube Gap Velocity and Density Distributions for Tube at Rowl0/ Col 3 7-29 7-8 Tube Gap Velocity and Density Distributions for Tube at Rowl0/ Col 20 7-30 7-9 Tube Gap Velocity and Density Distributions for Tube at Rowl0/Co140 7-31 vii
.9
3737 oy yIGURES (Continued) g 7-10 Average Velocity and Density in the Plane of the U-Bends Normal to Row 10 7-32 7-11 Radial Distribution of Axial Mixture Velocity Above the Top TSP in Point Beach Unit 2 Steam Generators 7-33 7-12 Radial Distribution of Axial Mixture Velocity Above the Top TSP in a* 51 Series Steam Generator 7-34 7-13 Radial Distribution of the Ratio of Axial Mixture Velocity in Point Beach Unit 2 to that in a 51 Series Steam Generator Above the top TSP.
7-35 7-14 Schematic of AVB Insertion Configurations Tested 7-36 7-15 Point Beach Unit 2 Normalized Stability Ratio Based on High Power (>90%) Operation 7-37 8-1 Axisymmetric Tube Finite Element Model 8-9 8-2 Dented Tube Stress Distributions Pressure Load on Tube.
8-10 8-3 Dented Tube Stress Distributions Interference Load on Tube.
8-11 8-4 Danted Tube Stress Distributions combined Stress Results.
8-12 8-5 Relative Stability Ratio Using MIVF Dependent Damping. ?-13 8-6 Relative stability Ratios Using One Percent Damping.
8-14 8-7 Stress Ratio Vs. Column Number 8-15 viii i
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LIST:0F-TABLES TABLE 2.MI 4-1 Fatigue Usage per Year Resulting From Stabili':y Ratio Reduction.
. 4-11 5-1 Wind Tunnel Tests on Cantilever Tube Model
. 5-15 5-2 Fluidelastic Instability Peaking Factors for Columnwise variations in AVB Insertion Depths.
5-16 6-1 Resolution of Support Conditions for Row 10, 11, and
] .......
6-6 12 Tubes with i
6-2 Unsupported Tubes.
6-7 7-1 Point Beach Unit 2 Steam Generator Operating Conditions 7-16 7-2 Steam Generator Operating Conditions Used for ATHOS Analysis 7-17 7-3 Test Results of Air Velocity Peaking Factor.
7-18 7-4 Stability Peaking Factor Due to Local Velocity Perturbation for North Anna Unit 1 Steam Generators.
7-19 7-5 Stability Peaking Factor Due to Local Velocity Perturbation for Point Beach Unit 2 Steam Generators 7-20 7-6 Ratio of Local Peaking Factor of Point Beach Unit 2 Tubes with Respect to North Anna Unit 1 R9C51 Tube 7-21 7-7 Point Beach Unit 2 Operating History Data.
7-22 ix
-I
&t # TA3LES (C.y *?* t.nuad)
IAB. Lit P.MI 8-1 100% Power operating conditions Point Beach Unit 2 8-6 8-2 Point Beach Unit 2 Evaluation of the More Salient Unsupported U-Bends.
8-7 i
4-3 Duty cycle Description for Point Beach Unit 2 8-8 P
9 i
f 1
I
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1 f
I G
X
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i
1.0 INTRODUCTION
This report documents the evaluation of steam generator tubing at Point Beach Unit 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 1
bundle, air-tests performed to support the vibration analytical procedure, field measurements to establish AVB locations, structural and vibration analysis of selected tubes, and fatigue usage calculations to predict cumulative usage for critical tubes.
The evaluation utilizes operating conditions specific to Point Beach Unit 2 in order to account for plant specific features of the tube loading and response.
Section 2 of the report provides a summary of the Point Beach Unit 2 evaluation res~lts and overall conclusions.
Section 3 provides u
background for the tube failure which occurred at North Anna Unit 1 including results of the examination of the failed tube and a discussion of the failure mechanism.
The criteria for-predicting the fatigue life for tubes having an environment conducive to this t
type of failure are discussed in Section 4.
Section 5 provides a summary of test data which supports the analytical vibration evaluation of the candidate tubes.
A summary of field measurements used to determine AVB locations and ultimately to identify unsupported tubes is provided in Section 6.
Section 7 provides the results of a thermal hydraulic analysis to establish flow field characteristics at the top support plate which are subsequently used to assist in identifying tubes which are dynamically unstable.
The final section, Section 8, presents results of the structural and vibration asssessment.
This section determines tube mean stress, stability ratio and tube stress distributions, and accumulated fatigue usage, forming the basis for the conclusions for Point Beach Unit 2.
l 1-1
7
'l' 2.0 Summary and conclusio' s " '
~
n The Point Beach Unit 2 steam generators are evaluated for the potential of unsupported. U-band tubing with denting at the top tube support plate to a fatigue rupture of the type experienced at Row 9 Column 51 (R9C51) of Steam Generator C, North Anna Unit 1.
The initiation of the circumferential crack in the tube at the top of the top tube support plate was due to limited displacement, fluid elastic instability.
The unstable condition prevailed in the R9C51 tube from the time when the tube first 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 the uneven insertion depths of AVBs, has reduced damping because of I
denting at the top support plate, and has reduced fatigue properties because of the additional mean stress with the denting and in the presence of the all volatile treatment (AVT) chemistry of the secondary water.
The criteria established for determining tne benefit of ameliorative action was a 10% reduction in stability ratio that is expected to provide a 58% reduction in stress amplitude (to <4.0 kai) for a Row 9 tube in the North Anna Unit 1 steam generators.
This reduction is believed to reduce fatigue usage to <0.021 per year for a Row 9 tube.
This same criteria is used as one of several criteria in the evaluation of Point Beach Unit 2 tubing.
With additional effects a~ccounted for through a stress ratio criteria that permits the calculation of f atigue usage to demonstrate tube acceptability, the final criteria of cumulative fatigue usage to date plus future operation with current operating parameters can be satisfied.
The stability ratios for Point Beach Unit 2 tubing, the corresponding stress amplitude, and the resulting cumulative fatigue usage cannot be calculated directly but must be evaluated relative to the ruptured tube at Row 9 Column 51, North Anna r
i 2-1 a
Unit 1, Steam Generator C, for th reF.mN.
The %.d. U.'tect on the flow field due'to various AVB insertio.) depths is not within
~
the capability oi available evaluation techniques and must be determined by test.
In addition, an analysis and examination of the ruptured tube provided a range of initiating stress amplitudes but can only bound the possible stability ratios that correspond to these stress amplitudes.
Therefore, tbs evaluation of Point Beach Unit 2 tubing is based on relative stability ratios, relative flow peaking factors and stress ratios.
i The criteria for establishing that a tube has support from an AVB
)
and therefore eliminate it from further considerations is that at least[
- .'s This is established by analysis,of addy current (EC) a measurements.
This may be established by an
- a,s I
The AVB insertion depths are a key factor in the assessment of the i
potential for a fatigue induced tube rupture since the AVB l
positions detsrmine the local flow peaking factors.
The local flow peaking factor is a direct factor on the apparent stability ratio for uniform flow conditions where a small percentage change causes a significant change in stress amplitude.
The relative flow peaking factors for Point Beach Unit 2 tubes without direct AVB support have been determined by instability tests.
These f actors are applied to relative stability ratios determined by 3-D
]
tube bundle flow analysis and the combined relative stability ratio is used in the stress ratio determination.
i The analysis of oddy current measurements shows that virtually all of the tubes in Rows 8 to 12 are dented at the sixth (top) support plate.
It was assumed for this evaluation that all tubes are dented at the top support plate.
It also shows that none of the tubec in Rows 8 through 12 have wall thinning indications at the AVB locations.
Therefore, it is unlikely that those tubes have l
2-2 i
3
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been unstable.
Additionally,
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Virtually all row 11 and 12 tubes are supported except for a few peripheral columns.
Most row 10 and row 9 tubes are supported.
Some row 8 tubes are I
supported.
Sixteen tubes are identified as the more susceptible of the dented and unsupported tubes.
These aret Steam Generator A Steam Generator B Egg colu=n EnE column 12 2
12 2
12 91 12 91 11 2
11 2
11 3
11 91 11 4
10 4
11 91 10 5
10 3
10 90 10 4
10 5
The local flow peaking corresponding to AVB insertion depths are factored into the evaluation for each of the above tubes.
This results in the relative stability ratios and stress ratios shown below.
(All ratios are in comparison to R9C51, North Anna Unit 1, Steam Generator C.)
O 2-3
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Steam Generator A Steam Generator B Relative Relative Stability Stress Stability Stress Tube Ratio Ratio Tube Ratio Ratio R12C2 0.84 0.40 R12C2 0.84 0.48 R12001 0.84 0.40 R12C91 0.84 0.48 R11C2 0.61 0.09 R11C2 0.61 0.09 R11C3 0.86 0.60 RllC91 0.61 0.09 R11C4 0.88 0.76 R10C4 0.70 0.21 RllC91 0.61 0.09 R10C5 0.82 0.57 R10C3 0.71 0.20 R10C90 0.71 0.24 R10C4 0.70 0.21 R10C5 0.69 0.20 All of the above,'more susceptible tubes have relative s'tability ratios less than 0.9 and stress ratios less than 1.0.
Therefore, all. unsupported and dented tubes at Point Beach Unit 2 meet these two criteria.
The tube with the highest stress ratio is at Row 11 Column 4 with a ratio of 0.76.
The stress amplitude for this tube is therefore 3.04 kai.
Based on the operating history of Point Beach Unit 2, the fatigue usage to date is 0.081 and the projected 40 year usage is 0.25.
This is less than the limit of 1.0 and therefore meets the fatigue usage criteria.
Based on these evaluations, it is concluded that the Point Beach i
Unit 2 steam generator tubes are not expected to sustain a fatigue rupture at the top support plate similar to that which occurred in North Anna Unit 1.
Therefore no modifications, preventive tuba plugging or other measures to preclude such an event are believed necessary.
i i
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2-4 t
a
3.0 BACKGROUND
On July 15, 1987, a steam generator tube rupture event occurred at the North Anna Unit 1 plant.
The ruptured tube was determined to be Row 9 Column 51 in steam generator "C".
The location of the opening was found to be at the top tube support plate on the cold leg side of the tube and was circumferential in orientation with a 360 degree extent.
3.1 North Anna Unit 1 Tube Rupture Event The cause of the tube rupture has been determined to be high cycle fatigue.
The source of the loads associated with the fatigue mechanism has been determined to be a combination of a mean stress level in the tube and a superimposed alternating stress.
The mean stress has been determined to have been increased to a maximum level as the result of denting of the tube at the top tube support plate and the alterneting stress has been determined to be due to out-of-plane deflection of the tube U-band 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 chanistry environment.
The vibration mechanism has been determined to be fluidelastic, based on the magnitude of i
the alternating stress.
A significant contributor to the occurrence of excessivs vibration is the reduction in damping at the tube to tube support plate interface caused by the denting.
Also, the absence of antivibration har (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 31
l
..c.
- 0 cal.f1bv 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 AVT environment.
In summary, the praraguisite conditions derived from the evaluations were l
concluded to bei Faticue Reauirements Prerecuisite Conditions Alternating stress Tube vibration
- Dented support
- Flow excitation
- Absence of AVB Mean stress Denting in addition to applied stress Material fatigue properties AVT environment
- Lower range of properties 3.2 Tube Examination Results Fatigue was found to have initiated on the cold leg outside surf ace of Tube R9C51 immediately above the top tube support plate.
No indications of significant accompanying intergranular corrosion was observed on the fracture face or on the immediately adjacent OD. surfaces.
Multiple fatigue initiation sites were found with major sites located at 110, 1200, 1350 and 150,
0 0
Figure 3-1.
The plane of the U-bend is located at 450 with the 0
orientation system used, or approximately 90 from the geometric center of the initiation zone at Section D-D.
High cycle fatigue striation spacings approached 1 micro-inch near the origin sites, Figure 3-2.
The early crack front is believed to have broken 0 to 1400 From this point on, through-wall from approximately 100 crack growth is believed (as determined by striation spacing, striation direction, and later observations of parabolic disples 3-2 w
5 es t.c -
- ,;o1l tad ;iy equiaxed dimples) to have accelerated and t1 have chaWg'ed direction'with the resulting crack front running perpendicular to the circumferential direction.
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 ccrresponding 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 CD a short distance above the plate from operating pressure j
and tamperature, thus providing a contribution tS mean stress.
Combining.these effects with denting deflection on the tube damonstrated a high mean stress at the failure location.
Vibration analysis for the tube developed the characteristics of first mode, cantilever response of the dented tube to flow induced vibration for the uncracked tube and for the tube with an increasing crack angle, beginning at 900 to the plane of the tube and progressing around on both sides to complete separation of the tube.
i Crack propagation analysis matched cyclic deformation with the 1
stress intensities and striation spacings indicated by the 1
fracture inspection and analysis.
Leakage data and crack opening l
analysis provided the relationship between leak rate and j
circumferantial crack length.
Leakage versus time was then I
predicted from the crack growth analysis and the leakage analysis with initial stress amplitudes of 5, 7, and 9 kai.
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 l
3-3 l
1 v
v
,-,,-,-=-v-
=
, ----= - --
r- - - - ' " " - -
- o Fmiwn.
I4 'Jas show that of the two possible flow-induced vibration mechanisms, turbulence and fluidelastic instability, that fluidel'astic instability was the most probable cause.
Due to the range of expected initiation stress amplitudes (4 to 10 ksi),
the fluidelastic instability would be limited in displacement to a a
,.'cThis,1 less qa range of approximately than the distance between tubes at *.he apex, It was further confirmed that displacement prior to the rupture was limited since no indication of tube U-band (apex region) damage was evident in the eddy-current signals for adjacent tubes.
Given the probable cause of limited displacement, fluidelastic instability, a scans 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 stinility 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.
e 3-4
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D-D
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s (Q
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C-C 180' Region of Herfingbone g Pattern 4
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I*I g,
y EE A,*
g TAB F-F Coarse Texture
'e and Olepled l
Aupture
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y Indicates origins 1
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l Figurc 3-1 Approximate Mapping of Fracture Surface of Tube R9051, l
S/G "C" Cold Leg, North Anna Unit 1 1
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3-5 m
$ = 1.5/1.6 v in.
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0xide Attack j
$ s 21 v in.
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3 = 1.0/1.85 v in.
gge.
3-C Parabolic
_ 90, -
g7o.- l 1-4 Dieples
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and V
Internal hacking
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3 = 2.8/4.0 m in.
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Nearly Equi-Axed 5 = 6.1/6.9 v in.
Dimples Mots: Arrows Indicata Direction of Fracture Propagation Figure 3-2 Schematic Representation of Features observed During TIM Fractograhic Examination of Fracture Surface of Tube R9C51, S/G "C" Cold Leg, North Anna Unit 1 3-6 5
1 l
L l
l l
l l
l l
l l
l l
Caleviated and observed len rates versus time.
Observed values based on gaseous species condenser air ejector SIGNA A = 5 KS!
SIONA A = 7 KSI i
........ Siesta A = 9 KSI l l O
AP-41 o
D Xe-135 A
Ke-87 nd J
U l
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9 s
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.ok eeke an'se aske se'ee sAs se'se mes aime esos es's 8*
e TIME, MIMITES Figure 3-3 Calculated and Observed Leak Rates Versus Time 3-7 m
4.O CRITERIA FOR FATIGUf174SSESSMENT.s. Uw Evaluation against criteria to show that Point Beach Unit 2 steam generator tubing will not rupture by fatigue in the manner of North Anna Unit 1 can only be done by a relative assessment 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 ration 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 failure 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 Col 51 and a 10% reduction in stability ratio criteria was established to demonstrate that tubes left in service would have sufficiently low vibration stress to preclude future fatigue rupture events.
To accorplish the necessary relative assessment of Point Beach Unit 2 tubing to Row 9 Column 51 of North Anna Unit 1, several criteria are utilized.
First, stability ratios are calculated for Point Beach Unit 2 steam generators
- e,c
~
and ratioed,to the stability ratio for Row 9 Column 51 at North Anna Unit 1 with the same degree of refinement.
These ratios
~
of stability ratio (called relative stability ratios) for each potentially unsupported U-band in the Point Beacn Unit 2 steam generators should be 1 0'.9 (meeting the 10% reduction in stability ratio criteria). This provides the first level of screening of susceptible tubes incorporating all tube geometry and uniform flow field differences in the tube dynam1c evaluation.
It has the inherent assu=ption, however, that,
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4-1 m
e m
i l
The second criteria is to obtain as: 744 r;.tte 6 3ho ratio of stress in the Point Beach Unit 2 tube of interest to the stress in Row 9 Column 51, North Anna Unit 1, and after incorporating the requirement that the relative stability ratio to Row 9 Column 51 (R9C51) for the tube of interest is 5 0.9, require the stress ratio to be i 1.0.
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 Point Beach Unit 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 s 4.0 kai.
Finally, the cumulative fatigue usage for plant operation to date and for continued operation with the same operating parameters is eval'uated.
A fatigue usage of <1.0 is not~necessarily satisfied by meeting the stress ratio criteria since Point Beach Unit 2 has a different duty cycle than North Anna Unit 1 and the tube at issue may have a different (higher) frequency of vibration.
The t
Point Beach Unit 2 duty cycle could be more demanding and cycles could accumulate 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 amplitude history.
This should permit the calculation of current and future fatigue usage for comparison to 1.0.
t l
4.1 Stability Ratio Reduction Criteria For fluidelastic evaluation, stability ratios are determined for f
specific configurations of a tube.
These stability ratios l
represent a measure of the potential for flow-induc2d tube vibration during service.
Values greater than unity (1.0) l indicate instability (see Section 5.1).
l 4-2
.e
Motions developed by a tube in the fluidelastically unstable mode are quite large in comparison to the other known mechanisms.
The maximum nodal displacement (at the apex of the tube) is linearly related to the bending stress in the tube just above the cold leg top tube support plate.
This relationship applies to any vibration in that mode.
Thus, it is possibla for an unstable, fixed boundary condition tube to deflect an aaount in the U-bend which will produce fatigue inducing stresses.
The major features of the fluidelastic mechanian are illustrated in Figure 4-1.
This figure shows the displacement response (LOG D) of a tube as a function of increasing stability ratio (LOG SR).
A straight-line plot displayed on log-log coordinates implies a relation of the form y = A(x)n, where A is a constant, x is the independent variable, n is the exponent (or power to which x is raised), and y is the dependent variable.
Taking logs of both sides of this equation leads to the slope-intercept form of a straight-line equation in log 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
. o A c.
approximately Test results also show that the slope for the i
j fluidelastic response depends somewhat on the instability displacament(responseampg,itude).
It has been shown by tests 4 c that a slope of jis a range of values corresponding to n>c q
displacament amplitudes in the range of j,
. a, c whereas below are conservative values.
The reduction in response obtained from a stability ratio reduction can be expressed by the following equation:
O, C
~
m 4-3
.e
-c
,.c-,-
r I
t l
l where D1 and SR1 are the known values at the point correspohuing to point 1,of Figure 4-1 and D2 and SR2 are values corresponding to any point lower on this curve.
Therefore, this equation can be used to determine the reduction in displacement response for any given reduction in stability ratio.
This equation shows that there is benefit derived from even a very small percentage change in the stability ratio.
It is this reduction in displacement for a quite small reduction in stability ratio that formed the basis for demonstrating that a 10% reduction in stability ratio would be sufficient for Row 9 Column 51 to have prevented it from rupturing by fatigue.
The fatigue curve developed for the North Anna Unit 1 tube at R9C51 is from
- o, c
, Thus, G, C l
1 where, 9"a' is the equivalent stress amplitude to 7 that accounts a
for a maximum stress of 9~y, the yield strength.
The -3 signa
}
curve with mean stress effects is shown in Figure 4-2 and is 1
compared to the ASMI Code Design Tatigue curve for Inconal 600 with the maximum effect of mean stress.
The curve utilized in this evaluation is clearly well below the code curve reflecting i
4-4
the effect of an AVT environment on fatigue and the Smith-Watson-Topper technique for accounting for mean stress that applies to materials in a corrosive environment.
Two other mean stress models were investigated for the appropriateness of their use in providing a reasonable agreement with the, expected range of initiating stress amplitudes.
These were the chownin,{igure,4-3.
~
With a
, the oE The assessment of the benefit of a reduction in stability ratio begins with the relationship between stability ratio and deflection.
For a specific tube geometry, the displacement change is directly proportional to change in stress so that stress has the same relationship with stability ratio,
. o, c
~
4
.gc The slope in this equation can range from
,on a log scale depending on the amplitude of displacement.
Knowing the stress resulting from a change in stability ratio from SR1 to SR, tre 2
cycles to failura at the stress amplitude was obtained from the fatigue curve.
A fatigue usage per year was then determined assuming continuous cycling at the natural frequency of the tube.
The initial stress was determined to be in the range of 4.0 to 10.0 kai by the fractography analysis.
4-5
,.--_r
It was further developed that the maximum initiating stress amplitude was not'more than 9.5 kai.
This was
]=!cThe corresponding stress level is 5.6 kai.
The maximum stress, 9.5 kai, would "2 reduced to with a 10% reduction in stability ratio and would have a future fatigue
- o, c usage of
-,at 75% availability, Figure 4-4.
The
, e, c minimum stress, 5.6 kai, would be reduced tot Jwith a 5%
reduction in stability ratio and would have future fatigue usage
"'O C
- ,'Tigure 4-5.
In addition, if a tube were of already cracked, it could be as large as 0.125 inch in length and thru-wall and would not propagate if the stress amplitudes are reduced to s 4.0 kai.
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.
- e, ccumulative fatigue usage may then be computed to get a magnitude of alternating stress for the last cycle that results in a cumulative usage of 1.0 for the nine-year duty cycle.
The result of the iterative analysis is that the stress during the
,Qb last cycle of operation was 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 4-6 m
.conssrvatively omitted, since denting is assumed to have occurred during that.first cycle.
Based on this evaluation, the tuba fatigue crack initiation occurred over most of the operating history of North Anna Unit 1.
A similar calculation can be performed for the time history of operatiog assuming that the maximum stress for the last cycle is and that the maximum effect of mean stress is present. The resulting iteration determines that a -1.3 signa fatigue curve results in a usage of approximately 1.0.
On this basis, the effect of a 10% reduction in g,tability ratio is to reduce the str,,ess amplitude to
)andresultsinafuturefatigueusage o, c.
of other combinations of alternating stress and mean stress were evaluated with -3 signa and -2 sigma fatigue curves to demonstrate the conservatism of the 10% reduction in stability ratio.
Table 4-1 presents the results of the cases analyzed clearly demonstrating that the 10% reduction in stability ratio combined with a -3 sigma fatigue curve and with maximum mean stress effects
~
is conservative.
Any higher fatigue curve whether through mean stress, mean stress model, or probability, results in greater benefit for the same reduction in stability ratio.
And 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 L
large benefit in terms of fatigue usage for relatively small l
changes in the fatigue curve.
l 4.2 Local Flow Peaking Considerations l
l l
Local flow peaking is a factor on stability ratio that l
incorpora,tystheeffecton(
]duetonon-uniformAVBinsertiondepths.
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, 4-7 l
a swsil percentacje' increase can result in a significant change in the predicti_on of' tube response.
The development of flow peaking factors for Point Beach Unit 2 is presented in detail in Section 7.4.
The establishment of AVB positions for Point Beach Unit 2 is presented in Section 6.4.
Since the evaluation of Point Beach Unit 2 is relative to R9C51, North Anna Unit 1, the flow peaking factors are also relative, i.e. a ratio of Point Beach Unit 2 to tube R9C51 at North Anna Unit 1. The flow peaking relative instability is obtained by testing in the air test rig described in Section 5.4.
The tests
~
ofinstabilityo,g,,R9C51indicatetestpeakingfactorsintherange of
, where the peaking factor le defined as the critical velocity for R9C51 AVB pattern compared to critical velocity for a uniform AVB pattern.
As explained in Section 7.4,'
applying this test peaking factor to only the steam flow calculated in the ATHOS model results in an additional amplification of the local flow effect through increased void,gc fraction and reduc d damping.
The minimum test value of
,, is increasedto[
Applying a nominal uncertainty to the ATHOS
,analyggsresultof154,thepredictedstabilityratioforR9C51is lusingnominaldampingthatisafunctionofthemodal effdctivevoidfraction(slip).Applyingthe
~[actorgivesa
~
cerrectedstabilityratioof(
['Therefore',usingtheminimum
~
flow peaking factor and nominal damping that reflects reduced damping compared to undanted 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 fatigue rupture on the l
- a, c t
l l
4-8 l
n
,. ~,
- ~ -
1 l
?
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 failed, 4.0 ksi.
To apply this same criteria to another tube in the same or another steam generator, the differences in J u, u
=O0 4
0 i
1
~
~
i 4-9 l
0
, C, C.
l l
l i.
l
~
Having this maximum stress permits the evtluation of the maximum fatigue usage for Point Beach Unit 2 based on the time history expressed by normalized stability ratios for the duty cycle (see Section 8.4).
ii.
4-10
,.a
i Table 4-1 Fatigue Usage per Year Resulting From Stability Ratio Reduction 1
SR, %
STRESS MEAN S SS USAGE REDUCTION BASIS (l)
FATIG]()
MODEL 3 CURVE PER YEAR 5.
9 yrs to O.0207 fail (5.6) 5.
9 yrs to 0.0107 fail (7.0) 5.
9 yrs to 0.0014 fail (8.0) 10.
max. stress 0.0209 amplitude (4)
(9.5) 10.
Nax. stress 0.0053 amplitude (4)
(9.5) 10.
max. stress 0.0004 amplitude (4)
(10.3) 10.
max. stress 0.0142 amplitude (4)
(11.6) 10.
max. stress 0.0020 based on duty cycle (5)
(9.5)
(1)
This gives the basis for selection of the initiating stress amplitude and its value in ksi.
(2)
Su is the maximum stress applied with Sm"Smean + Sa*
(
(3)
S-W-T is Smith-Watson-Topper.
(4)
Cycles to failure implied by this combination of stress and fatigue properties is notably less than implied by the l
operating history.
Consequently this combination is a i
conservative, bounding estimate.
(5) [,
l 4-11 l
[
t m
aw--
,-,,r--.
,-,,e-w,-,,
0 b, r 3
~
l Figure 4-1 Vibration Displacement vs. Stability Ratio 4-12 i
,es t
I o,C s
l -
l l
l 0
l -
Figure 4-2 Fatigue Strength of Inconel 600 in AVT Water at 600 F 4-13
. ~ -
%I d
k 1
I l
l l
Figure 4-3 Fatigue curve for Inconel 600 in AVT Water Comparison of Mean Stress Correction Models I
4-14 4
n_,
.w
-y-v,,.-.
r w- -,,ww--
,s.
,_..,,,,, -,,--, - -,,m,
9 0 C.
3 Figure 4-4 Modified Fatigue Life with 10% Reduction in Stability Ratio for Maximum Stress condition
~
4-15
. ~. -
--,,---e r
ca, c i
i I
Figure 4-5 Modified Fatigue Life with 5% Reduction in Stability Ratio for Minimum Stress Condition 1
(
4-16 1
l r
,--v,
-w---
w--
-ne n w
c n
- - ~ - - -
5.0 SUPPORTING TEST DATA This section provides a mathematical description of the fluid-elastic mechanism, which was determined to be the more probable causative mechanian for the North Anna tube rupture, as discussed in Section 3.3, to highlight the physical conditions and corresponding parameters directly related to the event and associated preventative measures.
The basis for establishing the appropriate values and implications associated with these parameters are provided.
Where appropriate, test results are presented.
5.1 Stability Ratio Parameters Fluid-elastic stability ratios are performed by evaluations for specific configurations, in terms of active tube supports, of a specific tube.
These stability ration represent a measure of the potential for tube vibration due to instability during service.
Fluid-elastic stability evaluations are performed with a computer program which provides for the generation of a finite element model of the tube and tube support systan.
The finite element model provides the vehicle to describe the mass and stiffness matrices for the tube and its support systan.
This information is used to determine the modal frequencies (eigenvalues) and mode l
shapes (eigenvectors) for the linearly supported tube being l
considered.-
The methodology is comprised of the evaluation of the following equations:
Fluid-elastic stability ratio = SR = U.n/Ue for mode n, where Uc (critical velocity) and Uen (effective velocity) are determined by:
5-1 3-
_ _. _ _ _ _ _ _,.... _,,, _. _, _ _. _. - _.. ~. _., _.. _ -.. _
OC
,, ?
Y a
e S
a O
O e
M m
5-2
.7*
l Substitution of Equations (1) and (2) into the expression uhhG defines stability ratio, and cancellation of like terms, leads to an expression in fundamental terms (without the arbitrary reference mass and density para, meters).
From this resulting expression it is seen that the a, o The uncertainty in each of these parameters is addressed in a conceptual manner in Figure 5-1.
The remainder of this section (Section 5.0) provides a discussion, and, where appropriate, the experimental bases to quantitatively establish the uncertainty associated with each of these parameters.
In addition, Section 5.3 provides the experimental basis to demonstrate that tubes with Jo,c,{isimpliesthatthosetubeswith would not have to be modified because their instability response amplitude (and stress) would be small.
The very high degree of sensitivity of tube response (displacements and stresses) to changes in the velocity times square-root-density distribution is addressed in Section 4.0.
This is important in determining the degree of change that can be can attained through modifications.
Frecuency It has been demonstrated by investigators that analytically determined frequencies are quite close to their physical counterparts obtained from measurements on real structures.
Thus the uncertainty in frequencies has been shown to be qui,te small.
appropriate in the case of dented Thisisparticularly\\ubes.Therefore,uncertaintylevels
~
)
introduced by the frequency parameter are expected to be insignificant (see also "Average Flow Field" subsection below).
5-3
-___.._______.._,.____.m._._m__...,
s -
yw..
w-w--
.,,,_,,.-e,
,-w.m
Instability Constant (Beta)
The beta (stability constant) values used for stability ratio and critical velocity evaluations (see above equations) are based on an extensive data base comprised of both Westinghouse and other experimental results.
In addition, previous field experiences are considered.
Values have been measured for full length U-bend tubes in prototypical steam / water environnante.
In addition, measurements in U-bend air models have been made with both no AVB and variable AVB supports (Figure 5-3).
l To help establish the uncertainties associated with ATHOS flow velocity and density distribution predictions on stability analyses, the Model Boiler (MB-3) tests performed at Mitsubishi Heavy Industries (MMI) in Japan were modeled using ATHOS.
A beta value consistent with the ATHOS predicted flow conditions and the as determined.
These analyses
'MB-3 measured critical velocity w%v
- a,t mupported a beta value of A summary of the test bases and qualifications of the beta values used for these assessments is provided by Figure 5-2.
The lowest measuredbetafortubeswithoutAVBswasavalueof(
)'This value is used for the beta parameter in all stability ratio evaluations addressed in this Report (seu also "Average Flow Field" subsection below).
Mass Distribution The mass distribution parameter is based on known information on the tube and primary and secondary fluid physical properties. The total mass per unit length is comprised of that due to the tube, the internal (primary) fluid, and the arternal (secondary) fluid (hydrodynamic mass).
Data in Reference 5-2 suggests that at operatingvoidfractionsthe(
'3 $
5-4
.3-
,: * ~u
')_'tbe ~uamminc
. o, c Test data are available to define tube damping for ;
i tube supports, appropriate to dented tube conditions, in steam / water flow conditions.
Prototypic U-band testing has been
%c performed,1,under conditions leading to[g supports.. The datpa of(
) n Figure 5-4 provides the principal data for j
tube conditions in steam / water.
This data was obtained for cross flow over straight tubes.
Uncertainties are not defined for the data from these taats.
Detailed tube damping data used in support of the stability ratio evaluations addressed in this report are provided ir section 5.2, below.
(
Flow Field - Velocity Times Scuare-Root-Density Distribution Average and U-bend-local flow field uncertainties are addressed independently in the following.
Averace Flow Field Uncertainties in the average flow field parameters, obtained from
~
ATHOS analyses, coupled with stability constant and frequency, are essentially the same for units with dented or non-dented top support plates. If the errors associated with these uncertainties were large, similar instabilities would be expected in the t
non-dented units with resulting voar at either the top support plate or inner row AVBs.
Significant tube wear has not been observed in inner row tubes in operating steam generators.without l
,oc denting.
Thus, an uncertainty estimate of about[
Jdor the combined effects of average flow field, stability constant and i
frequency appears to be reasonable.
To further minimize the i
impact of these uncertainties,
~
l
) Thus, the uncartainties associated with the average velocity times square-root-density (combined) parameter are not expected to be significant.
l l
l 5-5 4
".hp,LLqgeU(low Field Non-uniform.AVB l'nsertion depths have been shown to have effects on stability ratios.
Flow peaking, brought about by the "channeling" effects of non-uniform AVBs, leads to a local perturbation in the velocity times square-root-density parameter at the apex of the tube where it will have the largest effect (because the apex is where the largest vibration 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.
Overall Uncertainties Assessment Based on the above discussions, and the data provided in the following sections, it is concluded that local flow peaking is likely to have contributed significantly to the instability and associated increased vibration amplitude for the failed North Anna tube.
Ratios of stresses and stability ration relative to the North Anna tube, R9C51, are utilized in this report to minimize uncertainties in the evaluations associated with instability j
constants, local flow field effects and tube damping.
5.2 Tube Damping Data The damping ratio depends on several aspects of the physical model.
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, is., single-phase or two-phase flow.
These effects are discussed below in more detail.
Reference (5-1) indicates that the damping ratio in two phase flow is a sum of contributions from structural, viscous, flow-dependant, and two-phase damping.
The structural damping i
will be equal to the measured damping in air.
However, in two-phase flow, the damping ratio increases significantly and is 5-6
- r.. e :, dspr.ndente.on the vokd.fyaction or quality.
It can be shown that thedampingcontrIbutionfromviscouseffectsareverysmall.
Damping ratios for tubes in air and in air-water flows have been measured and reported by various authors.
However, the results from air-water flow are poor representations of the actual conditions in a steam generator (steam-water flow at high pressure).
Therefore, where available, results from prototypic steam-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 and clamped tube support conditions.
Two sources of data are particularly noteworthy and a're used here.
The first is a large body of recent, as yet unpublished data from high pressure steam-water tests conducted by Mitsubishi Heavy
,KHI).
These kuNa Industries support conditions.
The second is comprised of the results from tests sponsored by the Electric Power Research Institute (EPRI) and reportad in References (5-2) and (5-3).
T1.e damping ratio results from the above tests are plotted in Figure 5-4 as a function of void fraction.
It is important to notethatthevoidfractionisdeterminedonthebasisof(
3s(v Reference (5-4)).
The upper curve in the Figure is for pinned support conditions.
i 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 5-7 m-
WESTINGHOUSE PROPRIETARY CLASS 2 location.
Therefore, the clamped tube support curve is used in the current. evaluation to include the effect of denting at the top
~
tube support plate.
The Reference 5-3 data as reported show a damping value of.5% at 1004 void fraction.
The 100% void fraction condition has no two phase damping and is considered to be affected principally by mechanical or structural damping.
Westinghouse tests of clamped clampedtubevibratioginairhasshownthatthemechanical dampingis(
rather than the.5% reported in Referenca f5-3).
Therefore the lower curve in Figure 5-4 is the a, c Reference (5-3) data with all damping values 5.3 Tube Vibration Amplitudes with Single-Sided AVB Support A series of wind tunnel tests were conducted to investigate the effects of tube /AVB eccentricity on the vibration amplitudes caused by fluidelastic vibration.
)Nrior test results obtaines 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 agreament with corresponding characteristics observed in wind tunnel and steam flow tests using U-band tube arrays.
A summary of these prior results is given in Table 5-1.
An overall view of the apparatus is shawn in, Figure 5-5.
Figure 5-6 is a top view of the apparatus.
G g
5-8
le o, c.
-o c Figure 5-7 shows the manner in which the zero-to-peak vibrat.'on amplitude, expressed a ratio normalized to
)o,c.
varies whan
- o, c.
-,o' c.
one gap remains at
, and the other gap is set to p
For increasing velocities, up to that corresponding to a stability ratio of
~ o, C.Figure 5-8 shows typical vibration amplitude and tube /AVB impact force signals corresponding to those obtained frca the tests which provided the results shown in l
5-9 a-
Figure 5-7.
[.sexpected, impacting is It is concluded from the above test results thate
-o,c j
=
i 1
5.4 Tests to Deter.aine the Effects on Fluidelastic Instability of Columnwisc Variations in AVB Insertion Depths This section summarizes a series of wind tunnel tests that were j
conducted to investigate the effects on the initiation of fluidelastic vibration of variations in AVB configurations.
Esch configuratior is defined as a specific set of insertion depths for the individual AVBc in the vicinity of an unsupported U-bend tube.
The tests were, conducted in the wind tunng using a modified version of the
, described in Section 5.3.
Figure 5-9 shows the c'.nceptual design of the apparatus.
The
. o, c 5-10 a-
7 1
)o, Figure 5-10 shows an overall o
view of the model.
Figure 5-11 shows the AVBs when the gida panel of the test section is removed.
Also shown is the top flow streoA 1
) The AVB configurations tested are shown in Figure 5-12.
Configuration 1 corresponds to tube R9C51, the failed tube at North Anna.
Configuration 4 corresponds to one of the cases in which the AVBs are inserted to a unifo n depth and no local velocity peaking effects are expected.
As shown in Figure 5-9, J. a,c, Allthetube,sexcepttheinstrumentedtubefcorrespondingto Row 10) are As discussed in Section 5.3, prior testing indicates that this situation provides a valid model.
The instrumented tube
)o. c.
]o,cas shown in Figure 5-10. Its(
direction vibrationel motion is measured using a non-contacting transducer.
5-11
.a-
) The instrumented I
tube corresponds to a Row 9 tube as shown in Figure 5-9. However, depending on the particular AVB configuration, it ccn reasonably represent a tube in Rows 8 through 12.
The AVB profile in the straight tube model is the average of Rows 8 and 12.
Ths difference in profile is quite small for these bounding rows.
.%c hot-film anamometer ocated as shown in Figure 5-9.
Figure 5-13 shows the ras vibration amplitude, as determined from PSD (power spectral density) measurements made using an FFT spectrum analyzer, versus flow velocity for Configuration 1 (which corresponds to tube R9C51 in North Anna).
Data for three repeat tests are shown and the critical velocity is identified.
The linear plot is shown since it readily displays the typical rapid increase in vibration amplitude when the critical velocity for fluidelastic vibration is exceeded.
In determining the critical velocities used in evaluating the peaking factors, log-log plots l
were used in order to establish slopes that could be associated with fluidelastic vibration.
It is believed that more accurate determinations of the critical velocities can be made from the log-log plots than from the linear plots.
l The main conclusions from the tests are
(
(
1.
Tube vibration below the critical velocity is relatively small, typical of turbulence-induced vibration, and increases rapidly when the critical velocity for the initiation of fluidelastic vibration is exceeded.
2.
Configuration 1 (R9C51 in North Anna) has the lowest critical velocity of all the configurations tested.
5-12 x
l
3.
Configuration 1 is repeatable and the configuration was rerun periodically to verify the consistency of the test apparatus.
The initial test results obtained in support of toe Point Beach-2 evaluation are summarized in Table 5-2.
The peaking factor is defined as the ratio of the critical velocity for configuration 4 divide.d by the critical velocity for any other configuration.
Configulation 4 simulates uniform AVB insertion two rows above the test tube (i.e., uniform Row 11 for a Row 9 test tube).
No significant flow peaking effects are expected for configuration 4.
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 1.
After the initial tests were completed and applied to the Point Beach evaluation an air leakage path was identified in the test apparatus. This leakage path permitted air ingress through AVB adjustment slots in the top of the test model.
The tests were then rerun with the leakage path eliminated from the test model.
The preliminary corrected test results are also provided in Table 5-2.
These results show a larger peaking factor for North Anna Tube R9C51 such that the initial test results represent a conservative application to the Point Beach evaluation.
l l
l l
l l
e 5-13
.r
5.5 References Q C.
s a
O W
p 9
e 0
0 5-14 l
2'
Table 5-1
,W ni d Tunnel Tests on cantilever Tube Model J
M O
e O
O e
9 m
8 5-15 1
b
1 l
Table 5-2
,Fluidel'astic Instability Peaking Factors for Columnwise Variation in AVB Insertion Depths r
REVISED TESTS INITIAL TESTSd WITHOUT LEAXAGE8 PEAKING RATIO TO PEAKING RATIO TO CONFIGURATION
- FACTORC R9C51 FAC"rORC R9C51 "M
""'h
b 2
3 4
5
- Configurations shown in Figure 5-12 h corresponds to Tube R9C51 in North Anna c Defined relative to uniform AVB insertion, Configuration 4 d Tests performed to support Point Beach evaluation and utilized in this report
- Tests performed after air leakage path found in initial teste was eliminated.
The leakage path occurred through AVB adjuptmant slots in the top of the test apparatus.
These results indicate that the initial test results used for the PoirN. Beach-2 evaluation are conservative for the peaking factor ratio relative to North Anna tube R9C51.
o e
5-16
)
.S
4 d
i I
%L 2
p 5
I t
t 1
f 1,
i t
-i 1
i j
i
[
t
[
4
)
I a
t 4
1 i
t i
i l
1 I
l i
r l.
F i
I Figure 5-1 Fluidelastic Instability Uncertaint'y Assessment l
i 5-17 s
w
l U-Band Test Data
- 1) MB-3 Tests
, o, b, f
/ values of
- 2) MB-2 Tests og g of[
- 3) Air Model Tests
) e, s. c.
/ of without AVBs Tendenc{for/ to increase in range of
)withinactiveAVBs (gaps at AVBs)
Tendency for [ to decrease toward a lower bound of [
]dtIh active AVBs Verification of Instability conditions
- 1) Flow conditions at critical velocity from MB-3
- 2) Measured damping for the specific tube
- 3) Calculated velocities from ATHOS 3D analysis
- 4) / determined from calculated critical values Good agreement with reported / values 5)ATHosvelocitydatawith/ of [
]and known damping should not significantly underestimate instability for regions of uniform U-band flow Figure 5-2 InstabilityConstant-f 5-18
l
)
1 i
f 1
, o, b, c e
Figure 5-3 InstabilityConstants,[,obtainedforcurvedTubes t
from Wind Tunnel Tests on the 0.214 Scale U-Band Model S-19 9
oA r.
Figure 5-4 Damping vs. Slip Void Fraction 5-20
, o, b L 3
~~
1 Figure 5-5 overall View of cantilever Tube Wind Tunnel Model 5-21 l
&f l
~
l I
i i
Figure 5-6 Top view of the Cantilever 7ube Wind Tunnel Model 5-22
__E _
J
Q> b '
t Figure 5-7 Fluidelastic Vibration Amplitude with Non-Uniform Gaps 5-23
oh,c, i
l l
Figure 5-8 Typical Vibration Amplitude and Tube /AVB Impact Forca Signals for Fluidalastic Vibration with Unequal Tube /AVB Gaps I
i 5-24
4 okL l
l l
l l
f Figure 5-9 Conceptual Design of the Apparatus for Determining the Effects of Fluidelastic Instability of Columnwise Variations in AVB Insertion Deptias 5-25
o, b, c.
I t
l l
i 1
l l
Figure 5-10 overall View of Wind Tunnel Test Apparatus 5
5-26 1
1
o, b, c 4
i a
r 4
b I
1 f
i i
i I
Figure 5-11 SideViewofWJ.i[4TunnelApparatuswithCoverPlates l
[
Removed to Show Jimulated AVBs and Top Flow Screen
{
4 I
i t
t
-27 l.
I 1
o b,3
~
Figure 5-12 AVB Configurations Tested 5-28
r o,b,c L
l
)
I Figure 5-13 Typical Variation of RMS Vibration Amplitude with Flow Velocity for Configuration 1 in Figure 5-12 l
.1
{
L 5-29
.?
6.0 EDDY CURRENT DATA AND AVB POSITIONS 6.1 Tube Denting at Top Tube Support Plate Eddy current test data from the 1987 outage were examined to assess the incidence of denting at the top tube support plate for the tubes in rows 8 through 12 of the Point Beach Unit 2 steam generators.
This examination indicated that the occurrence of denting was so frequent for these tube rows that all the tubes were assumed to be dented at the top support plate.
Figures 6-1 through G-4 summarize the denting evaluation.
6.2 Tube Wall Thinning at the AVB Supports No tube wall thinning was obssrved at the AVB/ tube intersectiens in rows 8 through 12 of either steam generator.
6.3 Eddy Current Data for AVB Positions The ECT data from the 1987 outage were reviewed to (a) determine the presence of AVBs in tube rows 8 through 12 directly from the data,and(b)toprovidadata(
. a,c To directly locate the AVBs, 4
0.L TheAVBvisible/invisibledataand(
[are summarized en the AVB insertion maps, Figures 6-6 and 6-7.
e 6-1
In some instances, the AVB characteri+ tic signals could not be confidently determined due to a noisy signal judged to result from deposits on the tubes.
In these instances, and for several columns of tubes where,,the plugging pattern prohibited determining the presence of AVBs, e, c e
These data were then used[
. o, c, 6.4 AVB Insertion Depths Figures 6-6 and 6-7 summarize the AVB insertion depths for steam generators A and B.
Previously plugged tubes, AVB visible indications,
)resultsare
~
shown on these figuras.
The AVB insertion depths were determined principally on the basis of direct observation from the eddy current data.
Cince ambiguity can occur in the interpretation of the ECT data, due to inability l
of ECT to differentiate at which side of a tube the AVB is present, other information was used to assist in establishing the location of the AVBs.
Consistency with the design of the AVB assembly, consistency between data for adjacent columns and verification by projection were utilized to determine the final depth of insertion of the AVBs.
For some of the cases of a, s i
l 6.4.1 AVB Assembly Design The design of the AVB assembly for the Model 44 Steam Generator includes a lower AVB between successive columns from column 3 through 90.
No AVBs are included between tube columns 1 and 2, 6-2
.t
2 and 3, 90 and 91, and 91 and 92.
Th? vetainer. ring, to which all of the,1,ower AVBs are welded, crosses the peripheral tube in columns 3 and 90, and projects into the space between columns 2
^
and 3, and 90 and 91.
The minimum design depth of insertion of the AVBs is to row Eddy current data indicated the presence of AVBs in columns 2 and 91.
Since no AVBs are in these columns by design, the data indications are interpreted as the retainer ring which projects between columns 2-3 and 90-91.
The retainer ring is approximately the same size as the AVBs and may be in close enough proximity to the tube to be "seen" by ECT, however, support of these tubes cannot be assured.
g :C o
6.4.2 g
0, c The adequacy of support provided by must be resolved in the cases where a potentially susceptible iube
~
is concerned, since plugging the tube may be required if adequate support cannot be shown.
Preliminary analysis indicated that row 10 tubes with peaking factors greater than the North Anna failed tube and any tube in rows 11 and 12 were potentially susceptible.
}a,s consequently, the primary focus regarding was for the tubes in rows 10 through 12.
)v. c o
ith the AVB was observed in the ECT data, Where a the L-j w, c 3e as measured.
The measured
. o.c are shown on Figures 6.6 and 6.7.
The theoretical 3.. <
6-3 4'
Table 6-1 summar.izes the potentially' susceptible tubes with
,c and the rasolution of the support conditions for these tubes.
In S/G - A, the only tube in rows 10 through 12 with 2,c
, which could not be shown to be adequately supported, was R10C44.
This tube was not susceptible based on the non-critical. peaking factor applicable to the tube.
In S/G - B, R12C91 has a j,,$iovaver,thedesigndoesnot provide for an AVB between columns 90-91 (see Section 6.4.1
-above).
This tube was assumed unsupported.
6.4.3 AVB Projection The
.'c Projection is useful where noisy ECT signals prevent direct observation of the AVBs, where testing is impossible due to plugged tubes, and in some instances to resolve ambiguities in the Ecr data.
Projection is never the method of choice where direct data for the tubes in rows 8 through 12 are available.
The projection method l
l l
l l
Q C 3
l i
6-4 l
1 Projection was effectively used to locate the AVDs in the Point Beach Unit 2 Steam Generators, primarily to confirm support of j
plugged tubes in Rows 8 through 12, and to confirm the adequacy of
.op
[
In S/G A, columns 5, 8, 9 and 45 were Verified by projection.
In S/G B, columns 5, 45, 46, 47, 48 and 90 were verified by projection.
6.5 Unsupported Tube Summary Table 6-1 summarizes the tubes for which support cannot con *idently be assured based on the depth of insertion evaluations
[
above.
y,e e
9 9
l 1
9 6-5
.Y. '
Table 6-1 Resolution of Support, Conditions for Row 10, 11 o*c and 12 Tubes with i
TUBE I4 CATION RESOLUTION OF SUPPORT CONDITION Steam Generator A R11C5 Support verified by projection.
R1108 Support verified by projection.
R11C9 Support verified by projection.
R10C16 Non-critical peaking factor; not susceptible.
R10C38 Support provided by AVB in C37-38.
This AVB must be present for 4 AV3 indications to occur in R10C37.
Non-criticali eaking factor; k
R10C41 not susceptible.
Av3 must be in C40-41 gap for 3 AVB indications to occur in R10C40.
R10C45 Assumed to be unsupported.
Non-critical peaking factor; tube is not susceptible.
Steam Generator 3 R11C5 Support verified by AVB projection.
R12C91 Assumed to be unsupported.
6-6 l
.e
Table 6-2 Unsupported Tubes Steam Generator A Row 8 all Columns Row 9 2,
3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 89, 90, 91 Row 10 2*, 3*, 4*,
5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 91*
Row 11 2*, 3*, 4*,
91*
Row 12 2*,
91*
Steam Generater B i
Row 8 1 through 10, 14, 15, 20, 23 through 59, 89, 90, 91, 92 Row 9 2 through 9, 44 through 49, 52, 53, 54, 55, 89, 90, 91 Row 10 2*, 5*, 46, 47, 91*
i l
Row 11 2*, 91*
1 Row 12 2*,
91*
- - Candidate tubes for further evaluation 6-7 1
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Figure 6-2 Tubas with Dents at Tube Support Plate No. 6 Steam Generator A - Cold Leg 4
6-9
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Figure 6-3 Tubes with Dents at Tube Support Plate No. 5 Steam Generator B - Hot Leg 6-10 l
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Figure 6-4 Tubes with Dents at Tube Support Plate No. 6 Steam Generator B - Cold Leg 6-11 l
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Multiple AYS Signals No Clear C;11 Figure 6-5 AVB Insertion Depth Confirmation 6-12
~
D0 0 0 0 0 0 0 0 0 D 00 00'00000000000 000 i.
p 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 n
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Figure 6-6 AVB Insertion - Point Beach Steam Generator A 6-13
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6-14 l
7.0 THERMAL AND HYDRAULIC ANALYSIS This section presents the results of a thermal and hydraulic analysis of the flow field on the secondary side of the staan generator using the 3-D ATHOS computer code, Reference (7-1).
The major results of the analyn s are the water / steam velocity components, density, void fraction, and primary and secondary side tube wall temperatures.
The distributiens of the tube gap velocity und density along a given tube were obtained by reducing the ATHOS results.
In the following subsections, the ATHOS model and some sample results of analysis are described.
The operating parameters utilized in the ATHOS 3-D analysis are shown in Table 7-1.
Because of the staggered anti-vibration bar insertion configurations, local flow peaking occurs at certain tubes in the U-band.
Its effect on tube gnp velocity perturbation was obtained using test data and applied to the Point Beach Unit 2 steam generators.
Normalized stability ratios ovsr 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.
l 7.1 Point Beach Steam Gensrator Operating Conditions I
The recent steam generator operating conditions for Point Beach Unit 2 provided by WEPCO are shown in Table 7-1.
The number of i
active cubes which were plugged were reported to be 134 in stean generator A and 147 in steam generator B and the numbers of active tubes which were sleeved are 1501 and 1411 in Units A and B, respectively.
The hydraulically equivalent plugged tubes for the sleeved tubes are 69.2 in Unit A and 65.0 in Unit B.
The average equivalent plugged tubes per unit is then 67.1.
In addition, it was noted that the downcomer flow resistance plate was removed in April,
~
i 7-1
.?
i 1978.
With these data the sstinghouse GENT computer code calculation.,vas p'erformed to verify the plant data and to establish a complete list of operating conditions required for the ATHOS analysis.
The GENF code determined the primary side temperatures and feedwater flow rate required to obtain the specified steam pressurs at the given power rating.
The GENT compute'd steam generator T ot is 599 F, as compared to the 0
h 0
reported value of 596 F and the computed Tcold is the same as the 0
reported value of 540 F.
The computed feedwater flow rate is also the same as the reported value of 3.25 x 106 lb/hr.
The operating conditions generated by the GENF are consistent with the plant data.
Of primary importance are the secondry side flow ratios (including circulation ratio) and steam pressure.
The operating conditions utilized in the ATHOS 3-D analysis are shown in Table 7-2.
".2 ATHOS Analysis Model e
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.%C 7-2
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i 7-3 e
7.3 ATHOS Results The results from the ATHOS analysis consist of the
~
thermal-hydraulic flow parameters necessary to describe the 3-D flow field on the secondary side of the steam generator plus tne distributions of the primary fluid and mean tube wall temperatures.
Since the velocity components computed by ATHOS are j
defined on the surfaces of a flow cell, the tube gap velocity and density distributions along a particular tube required for tuba vibration evaluation are determined by a post-processor from the ATHOS output.
The post-processor generates a data file which contains this information for all the tubes in the model and the file serves as part of the input data required for tube vibration analyses.
Because the majority of the flow cells contain more than one tube inside a cell, the tube gap velocity and density surrounding a tube are obtained by interpolation of the ATHOS calculated velocities (defined on the cell surfaces) and density (defined at the center of the cell).
The post-processor performs the necessary interpolations to determine in-plane and out-of-plane velocities at specific intervals along the length of the tubes.
Figure 7-4 shows a vector plot of the flow pattern on the vertical plane of symmetry of the steam generator (the vectors are located at the center of the flow cells shown in Figure 7-2).
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 done formed by the U-bends).
Figure 7-5 shows the resultant vectors of the radial and circumferential velocity components on the horizontal plane at 2 = 22, the fifth 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 that the axial component is about four times greater than the radial component.
Figure 7-6 shows the flow pattern (resultant of the
~
a 7-4
utelial and circumferential components) on top of the tubasheet.
Because of the thermal syphon action (resulting from the higher heat flux and vapor generation in the hot leg), a portion of the cold leg side fluid flows to the hot leg side before turning upward.
The relatively high in-flow velocity along the tubelane from the wrapper opening is also evident.
Figures 7-7, 7-8 and 7-9 show a sample of the individual tube gap velocity and density distributions along three tubes at Row 10. In each figure the gap velocity and density along the length of the tube are plotted from the hot leg tubesheet end on the left of the figure to the cold leg and 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 the numerical average of the parameter over the entire 1800 span of a U-band at a given column location.
Both velocity and density are higher at the bundle periphery than in the interior of the bundle.
The change of the average density from periphery to interior is slightly more than the average velocity.
Figure 7-11 shows the distribution of axial velocity above the top tube support plate (TSP) as a function of radius within the tube bundle.
The radial distribution at three difforent circumferential positions are shovnt IX = 1 is near the middle of the hot leg; IX = 8 is in the hot leg near the tube lane and IX = 20 is near the middle of the cold leg (see Figure 7-1).
i l
l
-gc l
. o, c i
7-5
(
l 5
[
a, c s
The not result, for the 44 series, is a small reduction in the 2
force (jaV) on the tubes in the inner rows that are of interest in the current analysis.
This effect could not be predicted from a one-dimensional analysis.
7.4 Local Peaking Factors for Unsupported Tubes l
7.4.1 AVB Insertion Contours and Local Velocity Perturbation Non-uniformity of AVB insertion depths results in a non-uniform path of flow resistance due to the presence of the AVB.
The non-uniform resistance path in turn yields local velocity parturbations.
If we consider that a uniform AVB insertion is l
associated with a nominal tube gap velocity, then perturbation due to non-uniform insertion depths can lead to an increase or decrease over this nominal velocity.
l i
(
When flow approaches the apex of an AVB from below, it tends to divert to neighboring tube gaps having no AVBs.
Flow balance is achieved in a complicated, three dimensional manner.
- However, approximate flow perturbation can be assessed using equal pressure drop considerations among flow paths.
Associated with each flow path are flow loss coefficients, which can be readily estimated.
t 7-6 l
A?
1 Locci volocity porturbations duo to non-uniform AVD insertion depths have.,been sonfirmed by an air model test.
The magnitude of velocity perturbation depends on the AVB insertion configuration.
Maps of the AVB insertion depthe for Point Beach Unit 2 and North Anna Unit 1 steam generators have been reviewed.
As discussed in Section 5.4, air nodal tests have been conducted for five types of AVB insertion configurations.
Type 1, which appears as an inverted ava (see Figure 7-14), is that associated with the ruptured R9C51 tube of North Anna Unit 1 Steam Generator C.
For the type 1 configuration, flow perturbation tends to reinforce the flow into the valley of the "V".
f l
l 7.4.2 Air Mcdel Test The purpose of the test was to determine the effect of local velocity perturbations on flow-inducud vibration.
Velocity perturbations take place locally around the apex of the U-tube where the AVB comes into contact with a tube and where flow is mainly radial (normal) to the tube.
Radial flow along the U-band is such that it has high valuo around the apex and drops to low velocity at the base of the U-bend. Although the hot leg portion r
l of the U-band experiences slightly higher velocity, the shape of the profile is the same in the hot leg and the cold leg.
In addition, density variation of the steam / water mixture is insignificant between the hot and cold leg for the inner tube rows.
Based on the above considerations, air at room temperature and atmospheric pressure is used as the working medium.
The test section used straight tubes to simulate half of the U-band rather than U-tubes.
A flow channel wall is contoured such that the tube 16ngth for flow to expand is proportional to the actual U-bend
(
length, and the normal component of flow velocity, which is I
l l
responsible for out of plane vibration, is peaking near the apex l
7-7 S
i 3
and gradually decreasing towards the flow channel wall. Perforated plates were.,placed' downstream of the test section to simulate flow resistance due to downstream tube rows not included in the test model.
As discussed in an earlier section, the air velocity peaking factor, F, can be defined as follows:
F = V*/V where V* is the critical inlet velocity for the reference case (type 4 configuration with uniform AVB insertion) at which the instrumented tube becomes unstable, and V is the corresponding critical inlet velocity for the non-uniform AVB insertion l
configuration under consideration.
i According to air test data, specific values for F1 are given in Table 7-3.
7.4.3 Local Peaking Factor for Steam / Water Mixture I
The local peaking factors from the air tests can be applied to the steam generator, steam / vater conditions either as a direct factor I
on the mixture velocity and thus a direct factor on a stability ratio, or as a factor on the steam velocity only with associated l
impacts on density, void fraction and damping.
As noted below, the application of the peaking factor to the steam velocity component is the most appropriate extrapolation from air to steam-water.
This method leads to a reduction in tube damping which anhances 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. For I
evaluation of tubes relative to stability ratio criteria, it is more conservative to minimize the peaking factor for North Anna Unit 2 tube R9C51 through direct application of the air test 78 l
l N
paaking factor.
Thio approach io theroforo used for ovaluating
~
l tube acceptability.
Under uniform AVB insertion (or aligned AVB insertion), there are 1
no local open channels for flow to escape preferentially.'
Therefore, air flow is the same as steam / water flow relative to velocity perturbations.
Under non-uniform AVB insertion the steam / water flow may differ from air, as the steam and water may separate from each other when an obstruction, such as an AVB, appears downstream.
The water would continue along the same channel while steam readily seeks a low resistance passage and thus turns into adjacent opun channels.
Two phase tests indicate a tendency for steam to preferentially follow the low pressure drop path compared to the water phase.
Moreover, steam / water separation probably behaves differently among two-phase flow regimes.
Steam / water with a void fraction as high as 854 is closer to pure steam.
As far as velocity perturbation is concerned, it is considered that only steam is free to move into the neighboring open channels.
Based on the above discussion, the Fi 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 writtsn as follows:
. o, c.
~
where D is the vapor density, Dg the yater density, Fa the g
velocity peaking factor det9rmined from air tests, j
- the nominal g
superficial vapor velocity, and jg* the superficial water velocity.
Steam quality can then be determined as follows:
- 0, G e
7-9
In cur cvolustion, tho test resulto for air peaking factor F are conservatively intirpreted as i
3., u..
}
The Lellouche-Zolotar correlation, as used in the ATHOS code, is used to determine 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 coefficients can be readily determined.
Finally, a local stabilicy peaking factor for fluidelastic vibration can be calculated as follows:
. 0, G where F, is the stability peaking factor, Fd the density scaling factor, Fy the velocity scaling factor, and Fdp the damping coefficient scaling factor.
If we use the air velocity peaking factor without translating to steam / water conditions, then
.o,'
As shown in Tables 7-4 and 7-5, stability peaking factors for the steam / water mixture are slightly highnr than air velocity peaking factors.
l l
7.4.4 Results of Local Stability Peaking Factor l
Based on the above described methodology, local stability peaking factors were calculated for tubes in rows 8 through 12 using the actual AVB insertion configurations at Point Beach Unit 2.
These factors were then divided by the stability peaking factor of the ruptured R9C51 tube of North Anna Unit 1 Steam Generator C.
Table 7-6 presents the results including the values as applied to the steam / water mixture and the corresponding values determined i
directly from the air velocity peaking factor without steam / water j
7-10 t
l l
!? '
corrcction.
Th000 roculto show that tho direct application of the air test data yiel'ds the higher relative peaking factor compared
~
~~
to R9C51.
To obtain conservatism in the peaking factor evaluation, the following conservative interpretations of the air test peaking factors are appliedt 1.
,The py king factor for North Anna tube R9C51 was ta, ken as
)whichisthelowerboundofthetestrangeof
).G In particular, the updated test results after yb
~
correction for air leakage in the test model were not utilized in the Point Beach evaluation.
The latter results (See Table 5-2) indicate signficant conservatism in the Point Beach evaluation.
2.
The peaking factor for tubes being evaluated relative to R9C51.are taken at the upper bound of the test range.
3.
Air test peaking factors less than 1.0 are applied as 1.0.
j 4.
The air test peaking factors are used directly without the steam water correction.
7.5 Relative Stability Ratio over Operating History One aspect of the evaluation of the Point Beach Unit 2 steam generators is to examine the operating history data and use it to determine the susceptibility to fatigue damage frca fluidelastic vibration resulting from the 15 years of operation.
This assessment has been completed through use of a parameter termed the normalized stability ratio.
The normalized stability ratio compares the fluidelastic stability ratio for each period of a plant's operation (fuel cycle) to a reference stability ratio based on a recent operating condition.
A plot of this ratio against operating time, therefore, provides a relative indication f
7-11
of tho offect of past cporation en tho plant'a fluidolastic stability r,atio. JThis normalized time-dependent ratio is subsequently combined with an absolute stability ratio for the reference operating point derived from detailed three-dimensional thermal / hydraulic and tube vibration calculations.
High values for the not 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 damage.
The fluidelastic stability ratio is defined as the ratio of the effective fluid velocity acting on a given tube to the critical velocity at which large amplitude fluidelastic vibration initiates:
Fluidelastic Ueffective stability Ratio, SR =
Ucritical at onset of instabilit 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 ~oased on experimental data and has been shown to be dependent upon the tube natural frequency, damping, the geometry of the tube, the tube pattern, and the fluid density, along with the appropriate correlation coefficients.
The detailed calculation of this ratio using spanvise velocity and density distributions, etc., requires three-dimensional thermal / hydraulic and tube vibration calculations which are very time consuming.
Alternately, a simplified, one-dimensional version of this ratio has been used to provide a more rapid, relative assessment technique for determining the effect of past operation on the stability ratio.
The normalized stability ratio
(
is defined by the following equation:
I 7-12
.y-
o, L i
i e
\\
In this equation "cyc x" refers to each fuel cycle and "ROP" to the recent operating condition.
While this simplified approach cannot account for three-dimensional tube bundle effects, it does consider the major operational parameters affecting the stability ratio.
Four components make up this ratio a loading term based 2
on the dynamic pressure (oV ), a tube incremental mass (m) term, the natural frequency of the tube (fn), and a damping ratio (f) 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.
[
,., c -
J The particular damping correlation which is used for all normalized stability ratio calculations is based on a dented
)o, scondition, as conditionatthetoptubesupportplate,(a[
l discussed in Section 5.2).
The [
)conditionisalsoassumed in calculating the tube natural frequency.
The referance stability ratio calculation for Point Beach Unit 2 l
was based on the following operating parameters which are for a recent operating point in cycle 13 as supplied by WEPCO I
e 7-13
.9 '
Stoco Flew 3.2SX106 lbm/hr JSteam Pres'sure 785 psia
, q, c.
A series of calculations have been completed to generate a normalized stability ratio for each of the 13 fuel cycles since the plant became operational in August 1972.
Data for this evaluation was also supplied by WEPCO and is tabulated in Table 7-7.
Included are cycle average values for full load steam pressure and primary fluid average temperature.
The equivalent number of plugged tubes are also listed along with the number of days that the plant has operated above 90% of full power.
Since tube vibration and possible fatigue damage are associated with high power operation, only these higher power operating periods are considered important to the evaluation.
The operating parameters listed in Table 7-7 were then input to the Westinghouse "GENFN couputer code to determine the overall performance of the steam generator, in particular, the circulation ratio for each fusi cycle.
Thase calculated values are also listed in the table.
The resulting normalized stability ratios are shown in Figure 7-15.
In this figure, the normalized stability ratio for each fuel cycle is plotted against cumulative operating time above l
90% power.
Note that the ratio assigned to each of these high power operating periods has been conservatively based on a full power calculation.
Figure 7-15 indicates that the normalized ratio has increased about 5% over the 13 fuel cycles.
Two factors have contributed to this increases (1) the steam pressure decreased about 35 psi over this time period and (2) the downcomer resistance plate was removed during the outage between cycles 4 and 5 which resulted in a higher circulation ratio.
The steam pressure reduction results in l'ower U-bend density, higher U-band velocity, and reduced damping as a result of higher voids in the U-bend.
Removal of the resistance plate and its associated pressure drop led to an increase in the circulation ratio which had the primary effect of increasing the flow loading on the 7-14 JP-
tubec.
Noto that Point B32ch Unit 2 h2s op3 rated cbovo tho 90%
power level,for ab'out 84% of the total operating time.
This indicates't$at the addition of any periods of lower power operation (with lower normalized stability ratios) would not have significantly affected the results discussed above.
l 7.6 References
. o C.
a
)
~
O e
i l
t G
7-15 8-l
Tcblo 7-1 Point. Beach' Unit 2 Steam Generator Operating Conditions Power 759 MWT Steam Pressure 785 psia Feedwater Flow Rate 3.25 x 106 lb/hr Feedwater Inlet 426 F 0
Tamperature Water Level 52% of Narrow Range Span Primary Inlet Temperature 596 F 0
Primary Outlet Temperature 540 F 0
l 7-16 l
l l
8 l
Table 7-2 S. team Generator Operating Conditions Used for ATHOS Analysis l
Power 759 MWT c
Primary Flow Rate 3.39 x 107 lb/hr Primary Inlet Temperature 599 F 0
t Primary Outlet Temperature 540 F 0
Feedwater Flow Rate 3.25 x 106 lb/hr Feedwater Inlet 426 F 0
Tamperature Water Level frca Tubasheet 460 inches Steam Pressure 785 psia o, c e
e e
7-17 S-
Tablo 7-3
_ Test R'esults of Air Velocity Peaking Factor g
g 9
e e
mm 9
7-18 l
l m
',,a
Table 7-4 Stability Peak'ing Factor Due to Local Velocity Perturbation For North Anna Unit 1 Steam Generators Scaling Factors for Steam / Water Air Velocity Void Stability Peaking Fraction Density Velocity Damping Peaking
- Factor, Scaling,
- Scaling, Scaling,
- Scaling, Factor, Fa Fvf Fd Fy Fdp Fs
- o, c i
NOTE
- 1. Stability peaking factor for steam / water mixture is calculated as follows:
0, c l
1 2.
Damping scaling factor is calculated using modal average
- o, s void fraction of for R9C51 tube.
7-19 l
eIok
Table 7-5 Stabili.ty-Pea ing Factor Due to Local Velocity Perturbation For Point Beach Unit 2 Steam Generators Scaling Factors for Steam / Water Air Velocity Void Stability Peaking Fraction Density Velocity Damping Peaking
- Factor, Scaling,
- Scaling, Scaling,
- Scaling, Factor, Fa Fyg Fd Fy Fdp Fs
. o, c NOTE:
- 1. Stability peaking factor for steam / water mixture is calculated as follows:
c, c Dampingscalingf,, actor,,jgcalculatedusingmodalaverage 2.
void fraction of for R9C51 tube.
O
~
i 9
7-20 1
%b
Table 7-6 R'atio of Local Peaking Factor of
._- Point Beach Unit 2 Tubes with Respect to North Anna Unit 1 R9C51 Tube Steam Generator Row No.
Column No.
Peaking Ratio o, c A
8 60 63 9
17 38 Sti 10 19 44 54 11 4
B 8
11 14 15 20 23 35 38 59 87 90 9
9
~
38 44 50 53 55 10 2
5 46 47 91
]Q c i
for North Anna Unit 1 Note:
- 1. Air velocity peaking factor is R9C51.
- o. c
- 2. stability p aking factor for steam / water mixture is
~
for North Anna Unit 1 R9C51 under current operation" conditions.
- 3. Values shown in parentheses are stability peaking factor derived from air velocity peaking directly without steam / water correction.
a 7-21 y
Table 7-7 Po' int Beach 2 Operating History Data
\\
l Full Imd Raher of Itatuur of chicaalated I
Fuel Cycle Full Emed Stasa Fluid W tems Days Ahme Full Imed l
$l343 Baniming But pnumare fysial m (Dunr1 Phzumd ** tot Stasuur cimalatim hat.it l
= o. c l
1 06-01-72 10-14-74 323.4 509.0 3
472 2
12-30-74 09-36-76 824.8 509.4 3
344 3
03-36-76 03M33 013.1 509.5 15 291 4
04-19-77 03-11-78 821.4 Sep.6 17 311 5
04-14-75 03-23-79 000.4 568.9 17 300 6
04-12-79 04-10 40 907.6 548.0 17 305 7
05-13-40 04-16-41 904.3 See.6 53 309 8
05-11 41 04-15-42 905.1 55.3 77 306 9
06-27-42 03-34-43 813.1 5e.5 87 279 10 07 96 43 Okr744 903.8 SS.6 183 416 11 11-3044 1>40-45 001.3 Sep.5 177 300 12 11-34 45 0>2746 799.6 SGB.4 187 277 13 al-2bes 10 c347 790.4 Sep.4 201 21:4 Damatname resistanos plates M &arirq autage between Cycles 4 and 5 (Agril 1978)
Ftur SS A, inchates tLees plugged plus agaivalet raaber of almeed tatsas.
l a
7-22
~
O,C i
1 J
1 1
Figure 7-1 Plan View of ATH0S Model for Point Beach Unit 2 7-23 e
- .4
5
-e.
4A 4
p.
M.
m 9 e
JA-45 4
A r
o..d aE m..
A iL 4
.m m.
m4
+s&
g j
f is. s.
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9, e e se g
. F'
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ll t
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e
=
1 I
t.
Figure 7-2 Elevation View of ATHos Model for Point Beach Unit 2 1
i 7-24 i
p 1
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f W.
e 4.b C(
1 4
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r 4
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r Figure 7-3 Not Leg side Plan View of ATH0S Model
.t i
l l
7-25 i
}
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=Y
s a, c
=
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9 (9
l l
e 1
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Figura 7-4 Flew Pattern on Vertical Plane of Symmetry 7-26 1
l r.
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w
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Figure 7-5 Flow Pattern on Morisontal Plane (Z=22) at U-Bend t
Region i
t i
7-27 i
a P
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i.
to
,r.,,
,___,-- -__..----~----.,.,._,
~--,----.----____----y-
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Figura 7-6 Flow Pattern on Top of Tubasheet 7-28
.'I
. _ _ _. _ ~. _. _ _... _ _ _ _ _
)
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e
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.. ~. -
1 i
9 QL 2
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a b
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t J
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Figure 7-7 Tube Gap Velocity and Density Distributions for Tubs
[
at Rowl0/ Col 3 1
0 t
7-29 4
}-
~r-
1 i
)
g.
s
\\
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6 f
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r 1 --
t i
r i
+
l Figure 7-8 Tube Gap Velocity and Density Distributions for Tube l*
at Rowl0/ Col 20 t
l 7-30 l
i I
e
-. ~........ - ~ ~ -
~'
4e
~
4 0>C
=
l' l
i f
?
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[i a-i i,
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r
.)
J i
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Figure 7-9 Tube Gap Velocity and Density Distributions for Tube j
at Rowi0/co140 i
i i
I 7-31 i
l l
i
.f '
. _ _ _ _ _ _ _. _. = _. _. _... _._-_._.. _._.-. _ _. - _._-
)
n f
i o, c.
i r
i
'y 4
ll s
t t
.i n
i l
1 I
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t l
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1 c
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(
i l
I l-Figure 7-10 Average velocity and Density in the Plane of the U-Bends Normal to Row 10 i
7-32 f
e
-,.,n..w.
,-a,,
,,-,,--n-
,,,=.-,. - - -,,.,.
-.e
,.. ~
a, C.
J Figure 7-11 Radial Distribution of Axial Mixture Velocity Above the Top TSP in Point Beach Unit 2 Steam Generators 7-33 3'
.s A C-Figure 7-12 Radial Distribution of Axial Mixture Velocity Above the Top TSP i,1 a 51 Series Steam Generator 7-34
.-f
,[
(
Q, C.
l l
1 Figure 7-13 Radial Distribution of the Ratio of Axial Mixture
(
i Velocity in Point Beach Unit 2 to that in a 51 4
Series Steam Generator Above the Top TSP 7-35 l
I
.4
_ _.. _ ~..
I 6
.g..
so
?
Q, C.
t i
j.
t i
1 i
t
.r i
.h i
r t
i d4 t
i-i' j
l~
t 9
I 4
t t
i.
1 i
4 a
9 6
i 1
3 r
1 i
1 Ji 2
i 4
P 4
a N
1 4
i r
l 4
4 4
Figure 7-14 Schematic of AVB Insertion configurations Tested
{
i - -
dl I
)
7-36 1
h a
e t
E L. - -
a
. s.
1.02 1.01 -
Days Above 905 Power in Each Cycle "c
283 1
3 g
13 277 F
-- o 71 s. M 0.99 -
It
?
30s 10-11 Q
8,13 1
9 1
m 5-4 3
ass.
I 0.9 7 -
0.9s -
N 291 x
W 0.95 -
3 1127
=
a94 -
- i.,
g 0.93 -
Cycle 0.92 i
0 2
4 Uhousende) twt AT/Amow Notc D. SR MAno (dan) f Figure 7-15 Point Beach Unit 2 Normalized Stability Ratio Based on High Power (> 90%) Operation a
7-37
.?
8.0 STRUCTURAL AND TUBE VIBRATION ASSESSMINTS 8.1 Tube Mean Stress This section summarizes an analysis to determine stresses in a dented tube at 1004 power.
Loads imposed on the tube correspond to steady-state pressure, differential thermal expansion between the tube and the support plate, and a thru-wall thermal gradient.
The analysis assumej the tube to be at cold shutdown.
A summary of the temperature and pressure parameters at 100% power in the vicinity of the top support plate are provided in Table 8-1.
The tube temperature corresponds to the average of the primary-side water temperature and the plate temperature.,q c the resulting tube / plate radial interference is The analysis is performed using the finite element model shown in Figure 8-1.
The model prescribes
=>QC 3
Two reference cases were run using the finite element model, the first for a primary,t,o-secondary side pressure gradient, and the second for a radial interference between the tube and plate.
The pressure case incorporates the axial load on the tube by applying a pressure loading along the top face of the model.
Plots showing the distribution of stress for the tube outer surface for the two reference cases are provided in Figures 8-2 and 8-3.
Tube stresses due to the thru-wall thermal gradient are l
calculated to be 10.3 kai using conventional analysis techniques.
l A plot showing the combined stress distribution along the tube length, incorporating appropriate scale factors for the Point Beach Unit 2 operating conditions, is provided in Figure 8-4.
The 8-1
coxitum cxici tenailo otroca 10 23.9 koi cnd cccuro cpproxinatoly 0.5 inch above th'a top surface of the support plate.
Due to the presence of denting at the top support plate, the maximum mean stress,basedonOkax"7'y,wasusedindeterminingstability ratios and fatigue usage.
8.2 Stability Ratio Distribution Based Upon ATHOS An assessment of the potential for tubes to experience fluid elastic instability in the U-band region was performed for each of the tubes in rows eight through twelve.
This was performed using FASTVIB, a Westinghouse proprietary finite element based computer code.
This code was written to predict the individual responses of an entire row of steam generator tubing exposed to a tube location dependent fluid velocity and density profile.
The program calculates tube natural frequencies and mode shapes using a linear finite element model of the tube.
The fluid elastic stability ratio U./Ue (the ratio of the effective velocity to the critical velocity) and the vibration amplitudes caused by turbulence, are calculated for a given velocity / density profile and tube support condition.
The velocity and density distributions are determined using the ATHOS computer code, as described in Section 7.3.
Also input to the code are the WICAN generated mass and stiffness matrices used to represent the tube.
(WECAN is also a Westinghouse proprietary computer code.)
Additional input to FASTVIB consists of tube support conditions, fluid elastic stability constants, turbulence constants and damping.
This process was performed for the Point Beach steam generator tubes and also for the North Anna row 9 column 51 tube (R9C51) using similarly appropriate ATHOS models.
Ration of the Point Beach 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 Point Beach Unit 2 tubes relative to the tube that burst at North Anna Unit 1.
Figure 8-5 contains the results 8-2 A
of thic proc s3 fer occh of the rows under invostigation.
Thio l
figure was, genera'ted using the following conditions for both Point Beach Unit 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.
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 ration larger then ninety percent of North Anna R9C51.
This figure indicates that all tubas in rows 8 and 9 can be considered acceptable with some tubes accaptable in row 10. Essentially all tubes in rows 11 and 12 lay above tnis line. Tubes above this line, that are not supported wi*.h AVBs, require further evaluation to determine the acceptabili?.y of the tube.
Section s.3 contains the results of the further evaluation for these tubes.
s.3 stress Ratio Distribution With Flow Peaking An evaluation was performed to determine the ratio of the Point Beach Unit 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 7-6) and bending soment factors.
Section 4.4 and 4.5 contain additional information and describe the calculational procedure used to obtain the results presented in this section.
The results contained in this section are based upon the following conditions:
4-3 x
- 1) Tube 10 fix d in tcp tubo cupp3rt plato.
- 2) Damping is void fraction dependent.
- 3) AVBs do not provide support.
i
- 4) North Anna R9C51 stability ratio is multiplied by 0.90 to decrease the acceptable stability ratio.
(Using the 0.90 factor will increase the relative stability ratio.)
- 5) The tubes are assumed to be dented.
- 6) Flow peaking factors are used.
A tube can be considered acceptable if the stress ratio is less than'1.0 when calculated using the procedure described in sections 4.4 and 4.5 and including the conditions listed above.
Using this criteria indicates that the stress acting on a given tube will not produce a fatigue event in a manner similar to the rupture that occurred in the R9C51 tube at North Anna Unit 1.
Figure 8-7 contains the stress ratio results for each of the Point Beach Unit 2 tubes in ro'ws eight through twelve.
As can be observed in the figure all of the tubes in rows 8,9,10 and 11 fill below the 1.0 acceptance line.
All of the tubes in row 12, except for column 2, lay above the 1.0 acceptance line.
The figure indicates that perturbations exist in the stress ratio curves that were not evident in the relative stability ratio plots discussed in the previous section (See Figure 8-6).
These perturbations are due to the flow peaking effects discussed previously.
8.4 Cumulative Fatigue Usage All tubes that are unsupported and have a stress ratio 5 1.0 have a maximum stress amplitude that is < 4.0 kai (from 9.5 kai) 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 8-4 1
=
tho Point Bench 2 tubing cro baccd on tho current cporcting parameters,and wi'th future operation on the same basis, the tubes will not fail by fatigue if 1) they meet the stress ratio criteria of $ 1.0 and 2) their current and future fatigue usage will total to be less than 1.0.
Table 8-2 contains a summary of the combined relative stability ratios and the stress ratios for the most critical tubes in both steam generators.
All tubes have a stress ratio less than 1.0.
Acceptability of the Point Beach Unit 2 tubing for fatigue is accomplished by demonstrating the acceptability of the tube in Table 8-2 with the highest stress ratio, 0.76 at Row 11 Column 4 of Steam Generator A.
The maximum stress with the current operating conditions is CPa = 0.76 (4.0) = 3.04 kai Based on the relative stability ratio over the operating history presented in Section 7.5, the alternating stress for each operating cycle can be determined knowing that the stress for
~
cycle x is e, c os Using conservatively (see section 4.1) establishes the maximum alternating stress for each operating cycle.
The number of cycles of vibration is obtained for each fuel cycle by multiplyingthenumberofdaystimesthegumberofcyclesperday at the frequency of the Row 11 tube, hertz.
Table 8-3 summarises the time history.
Conservatively assuming that all fuel cycles have been at 3.04 kai, the cumulative fatigue usage to date is 0.081 and the cumulative fatigue usage in 40 years (with future years at the same operating conditions as cycle 13) would be 0.250.
All of the Point Beach 2 tubes meet the fatigue usage requirement of 1.0.
8-5 d
6
Tablo 8-1 100% Power Operating Parameters o
Point Beach Unit 2 1
Primary Pressure = 2235 psi Secondary Pressure = 775 psi Pressure Gradient = 1460 psi 0
Primary side T;aperature - 579 F 0
Secondary Side Tamparature = 515 F 0
Tube Tamparature = 547 F i
e 8-6
.t'
I Table 8-2 Point Beach Uni'. 2 Evaluation of 0
the More salient Unsupported U-Bends
\\
Steam Generator A steam Generator B stability stress stability stress Tube Ratio Ratio Tube Ratio Ratio R12C2 0.84 0.48 R12C2 0.84 0.48 R12C91 0.84 0.48 R12C91 0.84 0.48 R11C2 0.61 0.09 R11C2 0.61 0.09 R11C3 0.86 0.65 R11C91 0.61 0.09 R11C4 0.88 0.76 R10C4 0.70 0.21 R11C91 0.61 0.09 R10C5 0.82 0.57 R10C3 0.71 0.24 R10C90 0.71 0.24 R10C4 0.70 0.21 R10C5 0.69 0.20 Note Ratios are in comparison to North Anna Unit 1 R9C51 A stress ratio of s 1.0 is acceptable 9
e 8-7
~
Tablo 8-3 Duty cy'cle Description for Point Beach Unit 2 Normalized Fuel stability Alternating Alternating cycles.a,o evela Ratio Stress Stress (ksi)
Days at 13 1.000 1.000 3.04 288 10,11,12 0.992 0.953 2.90 993 7,8 0.988 0.930 2.83 615 5,6 0.985 0.913 2.78 613 3,9 0.982 0.897 2.73 570 1,2,4 0.952 0.744 2.26 1127 Total cycles =
I l
8~8 R'
-. -............ -. -. -. ~.
t I
4 e,
a> c i
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t 1
i
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1-s 0
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FiTure 8-1 Axisymmetric Tube Finite Element Model P
8-9 I
l gs r
f l
5 E
1 s.
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1 1
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{
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}-
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i f
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?
l Figure 8-2 Dented Tube Stress Distributions l
Pressure Load on Tube j
I
(
i 4
8-10 l
i 4
1 i
1
-,.,,.,n....--,--.,.-,.n,
---sh s
i a
4 5
9 oa s
t l.-
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4 d
l 4
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i 6
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f f
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+
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?
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t l
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]
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Figure 4-3 Dented Tube Stress Distributions i.
Interference Imad on Tube f
i i
i i
8-11 L
i i
I t
E i
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