ML20235V917

Nonproprietary Evaluation of Degraded R1C55 Tube Located in Steam Generator a of Zion Unit 2

ML20235V917
Person / Time
Site:	Zion File:ZionSolutions icon.png
Issue date:	02/28/1989
From:	Houtman J WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP.
To:
Shared Package
ML20011C595	List: ML20235V910 ML20235V917
References
WCAP-12176, NUDOCS 8903100402
Download: ML20235V917 (84)

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{{#Wiki_filter:- - _ _ WESTINGHOUSE CIASS 3 WCAP-12176 SG-89-02-037 I f EVALUATION OF A DEGRADED R1C55 TUBE LOCATED IN STEAM GENERATOR A OF ZION UNIT 2 FEBRUARY 1989 AUTHORS: J. M. HALL R. E. SMITH ~ APPROVED (N y.4. L. HOUTMAN, ACTING MANAGER STEAM GENERATOR ENGINEERING WESTINGHOUSE ELECTRIC CORPORATION NUCLEAR SERVICE DIVISION P. O. BOX 3377 PITTSBURGH, PENNSYLVANIA 15230 \\ k[$ P ) J

TABLE OF CONTENTS List of Tables List of Figures 1.0-

Introduction 2.0 Summary and Conclusions 2.1 Tube Vibration Evaluation J

2.2 Residual Stress Conclusions i 2.3 Recommended Action I 3.0 Degraded Tube Description 4.0 Thermal Hydraulic Analysis -4.1-Zion Steam Generator' Operating Conditions l 4.2 ATHOS Analysis Model 4.3 General ATHOS Results ~ 4.4 ATHOS Results for Row 1 S.O FIV Mechanism 5.1 Stability Ratio Parameters l 5.2 Turbulence Excitation Parameters 5.3 Tube Damping Data 6.0 Tube Vibration And Stress Assessment 6.1 FASTVIB Model Description 6.2 Tube Stress At Crack Location 6.3 Evaluation of Tube With Respect To North l " Anna R9C51 6.4 Severed Tube Response L

1 l 1 l TABLE OF CONTENTS i 7,0 Residual Stress Assessment-7.1 Steady-State Thermal Stress / Support Plate Misalignment 7.2 Operating Temperature and Pressure ~ 7.3 Shear Due to Torsion 7.4 Effects of Ovality on Stress Due to Pressure 7.5 Ovalization of Tight Radius U-Bends 7.6 Residual Stresses Due to Tube Manufacture and Bending 7.7 Combined Stress Results 7.8 Analysis Summary ) 0.0 References e 1 e 2 - - _ _ _ _ _ _ __ O

List of Tables 2 Summary of The Response Of R1C55 Due To FIV 4-1 Zion Steam Generator Operating Conditions Used For ATHOS 6-1 Summary Of The Response Of RIC55 Due To FIV 7-1 Bending Moment Distribution Around The U-Bend - 100% Power Temperature Distribution - Model 51 - Row 1-7-2 Calculations For Tube Stress As A Function Of Ovality 7-3 Summary Of Tube Bending Stresses - Model 51 Row 1 Tube Applied Moment = 100 in-lbs 7-4 Summary Of Stress Contributions - Cases 1, 2, 3 7-5 Summary Of Principal Stresses - Model 51 - Row 1 Tube 7-6 Summary Of Principal Stresses - Model 51 - Row 1 Tube 7-7 Summary Of Principal Stresses - Model 51 - Row 1 Tube O 9 l* e 4 l J

List of Figures l 3-1 Eddy Current Profile Of Indication 3-2 Crack Orientation ~ 3-3 R1C55 Location On TSP 4-1 Plan View Of ATHOS Cartesian Modal For Zion 4-2 Elevation View Of ATHOS Cartesian Model For Zion 4-3 Plan View Of ATHOS Cartesian Model For Zion Indicating Tube Layout 4-4 Flow Pattern On Vertical Plane Of Symmetry 4-5 Lateral Flow Pattern On A Horizontal Plane In The U-Bend Region 4-6 Lateral Flow Pattern On Top Of Tubesheet 4-7 Tube Gap Velocity And Density Distributions For Tube Row 10/ Column 3 4-3 Tube Gap Velocity And Density Distributions For Tube Row 10/ Column 20 4-9 Tube Gap Velocity And Density Distributions For Tube Row 10/ Column 40 4-10 Average Velocity And Density In The Plane Of The U-Bends Normal To Row 10 4-11 Modal Effective Velocity For Row 1 5-1 Damping Vs. Slip Void Fraction 6-1 FASTVIB/PLOTVIB Model Of R1C55 6-2 FASTVIB Crack Orientation 6-3 Crack Modeling Nomenclature 7-1 Model 51 Tube Temperature Distribution - Normal Operation 7-2 U-Bend Moment Distribution - Operating Temperatures For Normal, Maximum Spread And Maximum Pinch Support Conditions 7-3 Ovality Effects On Pressure Induced Stresses List of Figure (Continued) 7-4 Tube Stress Distribution For Tight Radius U-Bend Under Moment Loading . 7-5 Residual. Stress Measurement - Strain Gage Location 7-6 Residual Stresses.In The Longitudinal Direction 7-7' Residual Stresses In The Hoop Direction 7-8 Residual Stress Measurements 7-8 Plot of Effective Stress Distribution For'Sequoyah -Unit 2 - Outside Surface-7-9 Plot Of Effective Stress Distribution For Sequoyah Unit 2 - Inside Surface 7-11 Plot-Of Component Stress Distributions For Zion Unit 2 - ~ Case 2 Results - Outside Surface 7-12 Plot Of Component Stress Distributions For Zion Unit 2 - Case 2 Results - Inside Surface 7-13 Plot Of Component Stress Distributions For Zion Unit 2 - Case 3 Results - Outside Surface . 7-14 Plot Of Component Stress. Distributions For Zion Unit 2 - Case 3 Results - Inside Surface a S -

1.0 INTRODUCTION

The tube located at row 1 column 55 of steam generator A at Zion Unit 2 has a circumferential indication located in the u-bend region and was leaking at a rate of up to 470 gpd. This tube has been plugged with solid plugs. Acceptability of this action is dependent upon:

1) De'monstration that the probable mechanism of cracking is not new and unique.

2) That the indicated crack in the tube will not continue to grow.

l

3) That the degraded tube will not adversely affect l

adjacent tubes. This evaluation has been performed to verify that the above criteria are satisfied. Section 3.0 contains a description of the tube degradation along with eddy current indications of the tube at the degradation site. Results of the evaluation have been summarized in Section i 2.0. Details of the FIV evaluation can be found in Section 6.0 and details of the residual stress evaluation can be found in Section 7.0. Section 4.0 contains details of the ATHOS evaluation performed to determine the expected conditions at the R1C55 location while Section 5.0 contains a discussion of the flow induced vibration methodology. e A _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

2.0

SUMMARY

AND CONCLUSIONS This section contains a summary of results obtained in the 2 evaluation along with conclusions from the analysis. 2.1 Tube Vibration Evaluation An evaluation has been performed to determine if the tube could continue to experience crack propagation due to flow induced vibrations (FIV). Two scenarios were addressed. First, the conditions at the degradation site were evaluated to determine if additional crack growth would be expected at that location. Second, the possibility of the degraded tube resulting in a North Anna R9C51 type tube crack at the top tube support plate was also addressed. The North Anna type rupture was addressed to determine that the tube would not sever at the top TSP site and contact and adversely affect an adjacent tube. An evaluation was also performed to determine the response of the tube, should the tube become totally severed at the crack location. The evaluation of the stress at the crack location has determined that the stress at the crack site (due to FIV) is small. The worst case stress near the crack has been determined to be approximately [ Ja,c. The stress at the crack tip has been determined to be less than [ Ja,c for the current crack geometry. This can be compared to the crack propagation threshold of approximately [ Ja,c,e, Substantial margin is clearly present and indicates that additional crack growth at the degradation site is not expected. An assessment was also performed to determine if the degraded tube could result in a severed tube at the top tube support plate due to increased fatigue usage. This would only be

I I possible if all the necessary conditions would become present ie: [ Ja,c,e, The scenario under consideration in this evaluation is the North Anna R9C51 type tube rupture and is discussed in more detail in Section 6.3. This type of tube rupture was addressed due to the possibility of the reduction in stiffness of the tube (due to the through wall indication) being of sufficient magnitude that a North Anna R9C51 type event could result. It was determined that this type of event would not be expected because the stress in the tube (at the TSP location due to fluid elastic excitation) is essentially zero, i.e. the tube is stable. Therefore a North Anna R9C51 type event would not be expected for the d,egraded R1C55 tube at Zion Unit 2. Finally, the response of the tube was determined if the tube should become totally severed at the current degradation site. It was established that the tube would remain stable with respect to [ Ja,c regardless of support condition. Two support conditions were addressed; [ Ja,c. Table 2-1 contains a summary of the stability ratios for the cases under consideration. Note that the response of the tube with the current amount of degradation has also been included. As can be observed in the table, the worst case stability ratio (ratio of effective velocity over critical velocity) was determined to be [ Ja,c. This indicates that the tube is stable and that the rapidly increasing displacements associated with [ ]a,c,e would not occur for the R1C55 tube. Table 2-1 also contains a summary of the maximum U-bend tube displacements associated with turbulence excitation. The maximum peak turbulent displacement is [ ]a,c with the tube in the severed condition. Therefore, the tube in the severed condition would not move through the [ Ja,c gap between tubes and contact an adjacent tube. It has also been determined that the maximum stress in the tube, with the tube in the severed condition, is insignificant (<1.0 ksi). Stresses of this -

s magnitude.will not result in accumulating fatigue usage at this location. a \\ 2.2-Residual Stress Conclusions As'a result of the analysis to determine the operating stress distribution in the R1C55 tube'at Zion, the following l conclusions can be made.

1. There are a'significant number of loading mechanisms which-H influence the operating stresses in tight radius.u-bends.

2. The resulting stress distribution is dependent to a large degree'on the residual stress pattern resulting from.the manufacturing process.

3. The presence of stress corrosion induced circumferential1y oriented cracks located on the tube intrados, similar to the degradation at Zion, is supported by existing test I

data for manufacturing residual stresses.

4. Due to the variability in manufacturing residual ftresses an exact match of the Zion degradation pattern is not possible without knowing the precise residual stress.

distribution at the location of interest. ~ 2.3 Recommended Action ~ The evaluation performed for the Zion Unit 2 R1C55 tube indicates that the probable cause of degradation of the tube located in steam generator A is primary water stress corrosion cracking. Stresses due to flow induced vibrations are not significant and it is not credible that FIV caused cracking in the tube. Plugging of the subject tube stops progression of PWSCC and FIV stresses are not large enough to result in continued propagation of the degradation of the tube. It also indicates that the tube will not experience new crack formation from fatigue while in operation with the solid plugs. Based on the evaluation performed, it is concluded that no additional action, such as plugging adjacent tubes or stabilizing the tube at R1C55, on the part of Commonwealth Edison is necessary. G = 4 9 e e 4 _ _ _

L L l TABLE 2-1

SUMMARY

OF THE RESPONSE OF RIC55 DUE TO FIV ~ l l SUPPORT COND CRACK (1) STABILITY TURBULENT (2) FREQUENCY (AT TOP TSP) RATIO DISPLACEMENT (Hz.) (Mils) l a,c j Notes: ~

1) " Severed" indicates that the tube becomes severed at the current crack location.

" Current" indicates that the tube is degraded as currently indicated in Section 3.0.

2) Turbulent displacement is the RMS displacement of the tube in the U-bend region in mils.

Maximum peak displacements could be approximately [ Ja,c times larger than the values indicated in the table. When peak displacements are compared to the distance between tubes, [ Ja,c, it is clear that contact with adjacent tubes is not expected.

3) There are no dominant U-Bend modes for this condition up to 200 Hz.

Values presented for this case are actually worst case straight leg results. Actual U-Bend values would be lower than the values listed for this case. 3.0 DEGRADED TUBE DESCRIPTION The degraded tube is located in Steam Generator A, row 1 column 55 of Zion Unit 2. It was confirmed that this tube experienced leakage of primary fluid to the secondary side of up to 470 gpd. Eddy current inspection (* see note) of the tube has revealed the probability of a circumferential through wall crack in the U-bend ragion. It was determined that the crack is located approximately 3.7 inchen above the top of the 7th (top) tube support plate on the cold leg side. The portion of the straight leg that extends above the top TSP is 3.3 inches. This means that the crack is located approximately 0.4 inches above the tangent point of the U-bend. Examination of the eddy current data, contained in Figure 3-1, has revealed that the crack is approximately 5/8 inch long. Note that a 5/8 inch crack translates to an included crack angle of approximately 82 degrees, or a half crack angle of 41 l degrees. It has also been determined that the crack is generally located on the intrados of the tube. The information available suggests that the crack is oriented as indicated in Figure 3-2. Relative to a circle inscribed around the outside of the tube perpendicular to the tube axis at the crack location, the crack is not off-set relative to the circle. This means that the crack is observed to lie totally on the circle and can be considered (for all practical purposes) to be a circumferential Crack.

• Note:

Eddy current examination of the R1C55 tube was performed by UTL. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -

Figure 3-3 contains a sketch of the tube location with respect to the plane of the tube support plates. The U-bend of the tube [ Ja,c,e. Section 4.0 discusses the ATHOS model of the steam generator in. greater detail. However, it can be noted that R1C55'is in the group of j tubes that [' Ja,c. Section 6.0 contains the FIV evaluation and the effects of various support conditions are addressed withinc that section. .i .e e i 1 l WESTINGHOUSE PROPRIETARY CLASS 2 JAN 22 '89 08:49 W SSM - 7JON STATION P.4/9 , cu e we7. c==.e. = - a po se now i ca. os ~ DSHe -- 2 l FitE9 ----- 4se kHz j SPAN *- = $36 l ROTATIDH - 292 DEC _ -g,gg g m., ~ 0.92 D i j I to. 360 ~4.91 the S .93 MX YDLTS 37.4 stKIAL PITCH 37 CIRC 91TCM 27 2 ROTATION $1$ X ROTAT10H 67,

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F01HT E. SCGr4 lei FLANT UNIT tG LEG Cn4TE ELF ILIT ZlDi Pf!-002 56 A DUTLET 91/21<69 FIGURE 3-1 EDDY CURRENT PROFILE OF INDICATION 15 - 1

WESTINGHOUSE PROPRIETARY CIASS 2-l ~ 20 Degrees A intrados - ~ 82 Degrees Y Extrados Plane of U-bend (Not To Scale) CTUBE4 e I e FIGURE 3-2 CRACK ORIENTATION

1

0. ) C, L

' ~ T l'i 1 i l l 1 \\ FIGURE 3-3 R1C55 LOCAT[ON ON TSP I -

4.0 THERMAL HYDRAULIC ANALYSIS 3. This section presents the results of a thermal and hydraulic analysis of the flow field on the secondary side of the steam generator using the 3-D ATHOS computer code, Reference (5). The major results of the analysis are the water / steam velocity l components, density, void fraction, and the primary and l secondary fluid and tube wall temperatures. The distributions l of the tube gap velocity and density along a given tube were l obtained by reducing the ATHOS results. In the following subsections, the ATHOS model and some sample results of the analysis are described. 4.1 Zion Steam Generator Operating Conditions Recent steam generator operating condition data for the Zion units were provided by Commonwealth Edison. The data reported by Commonwealth Edison for Zion 1 and 2 were recent full load operating parameters:

a. Steam pressure - 720 psig

b. Feedwater temperature and flowrates - 428 F; 14x106 0

lbs/hr 0

c. Primary inlet and outlet temperatures - Tin = 591 F, 0F Tout - 527

d. Thermal load - - 800 MWthermal/ generator With the above data, calculations were completed using the Westinghouse steam generator performance computer code, GENF, to verify the plant data and to establish a complete list of operating conditions required for the ATHOS analysis.

The GENF code determines the primary side temperatures and steam flow rate required to obtain the specified steam pressure at the. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

b given power rating. Besides confirming these parameters, the code' calculates the circulation ratio which is used to determine the total bundle flow rate and average loading on the tubes. Note that the circulation ratio calculation includes the effect of downcomer resistance plates which are present in all eight steam generators of the two Zion units. The-calculated circulation ratio along wiih the other thermal / hydraulic conditions are listed in Table 4-1. The ATHOS.3-D flow field calculation was based on these parameters. 4.2' ATHOS Analysis Model The Zion analysis is based on a [ Ja,c system for the array of flow' cells instead of the typical, and more widely used, [ Ja,c system. With a [ ]a,c system, the tube array and AVBs are arranged in a [ Ja,c configuration which is in-line with the coordinate axes. This alignment provides an enhanced representation of the tube region of interest in the bundle. The ATHos [ ]a,c system model for the Zion steam generator consists of ( 3a,c, [ In the ATHOS analysis, the steam generator is considered to be l [ l* Ja,c. Figures 4-1 and 4-2 show the plan and the elevation views of the model. These two figures show the layout of the flow cells and identify locations for some of the geometric features.

AsLshown in Figure 4-1, with the [ Ja,c as indicated by the heavy lines. [ i 1 Ja,c, j 1 Figure 4-3 reproduces the plan view of the model but with-the tube layout arrangement superimposed. This figure illustrates - the locations of the tubes in the various flow cells. The l fineness of the cell mesh is evident; the largest cells contain only [ Ja,c. Note, in particular, that additional detail was added near the [ T Ja,c to more closely model the flow conditions in the area of interest. 4.3 General ATHOS Results The results from the ATHOS analysis consist of the thermal-hydraulic flow parameters necessary to describe the 3-D flow field on the secondary side of the steam generator plus the distribution of the primary fluid and mean tube wall temperatures. Since the velocity components computed by ATHOS are defined on the surfaces of a flow cell, the tube gap l, velocity, which is the appropriately interpolated cell velocity ratioed upward to account for the flow area between the tubes, and density distributions along a particular tube required for tube vibration evaluation, are determined by a post-processor from the ATHOS output. The post-processor generates a data file - - _ _ _ _ - _ _ _ _

' gk l [ y which'contains this information for all'the tubes in'the model' and'the file serves as part.of.the input. data required:for. tube L* vibrationfanalyses.. [. ~ 1 L- ~ J l Ja,c, Figure 4-4 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 '4-2).. It.is seen that in the U-bend region'the mixture [ Ja,c. Figure 4-5 shows the resultant L, vectors of the radial and circumferential velocity components on ~ the horizontal plane at Z = 21, the sixth plane above the top n tube support plate (see Figure 4-2). The [ Ja,c. Figure 4-4 shows that the axial component is about [ Ja,c,e than the radial component. Figure 4-6 shows the lateral velocities on the top of the tubesheet. l l A Figures 4-7, 4-8 and 4-9 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 ] i length of the tube are plotted from the hot-leg tubesheet end on j the left of the figure to the cold-leg end on the right. Figure 4-10 shows the plot of the average in-plane gap velocity..

f 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-bend at a given column location. The average velocity is j - seen to be relatively constant with values ranging from [ i Ja,c. However, the average density varies across.the bundle with [ .Ja,c, 4.4 ATHOS Results For Row 1 The profile of fluid parameters change depending upon which tube is under consideration. Distributions of these-parameters along ~ row 1 can vary depending upon which column is being addressed. One parameter of consequence is the velocity of the fluid and how the fluid interacts with the vibrating tube..This interaction can be quantified by looking at the Modal Effective Velocity (MEVEL). MEVEL represents,. in a single term, the net effect of the fluid velocity (term). causing the tube to l_. experience FIV. Figure 4-11 contains a plot of MEVEL for the Zion Row 1 tubes. The mode shape over which the velocities were applied corresponds to the [ Ja,c. As can be observed in the figure, the Row 1 Column 55 tube is one of the more highly loaded tubes. - The peaks and valleys in the plot are due to the [ Ja,c, 0 e 9 l l

l, TABLE'4-1 l ~ ZION STEAM GENERATOR OPERATING CONDITIONS USED FOR-ATHOS ANALYSIS Power 812.5 MWt Primary Flow Rate 3.40 x 107 lb/hr Primary Inlet Temperature 591 F 0 Primary Outlet Temperature 527 F 0 ' Steam Flow Rate 3.49 x 106 lb/hr Feedwater Inlet Temperature 428 F 0 Steam Pressure at SG Outlet 735 psia Circulation Ratio [ ]a,c 9 - e i

s f-t' . TABLE 4-1 ZION STEAM GENERATOR' OPERATING CONDITIONS"USED FOR ATHOS ANALYSIS-s --0 8,C,9 ~ 4 d e a $ e e 9 23 -

7 1^ I I A e l -e i \\ m 4 FIGURE 4-1 PLAN VIEW OF ATHOS CARTESIAN MODEL FOR ZION. o

I 'l i f S; La L ~ i i j l l l l FIGURE 4-2 ELEVATION VIEW OF ATHOS CARTESIAN MODEL FOR ZION l I t

L 0.) C) 4 O O 4 e 4 0 a men m FIGURE 4-3 PLAN VIEW OF ATHOS CARTESIAN MODEL FOR ZION INDICATING WBE LAYOUT ]

a 1 l 1 t l l C C-- l w O3 3 r-l l l l d FIGURE 4-4 FIDW PATTERN ON VERTICAL PLANE OF SYMMETRY 3

1 1 1 - '; J ^ l ' i. l 4 '$ m entus I l \\,*i N S i l FIGURE 4-5 IATERAL FI4W PATTERN ON A HORIZONTAL PIANE IN THE U-BEND REGION,............

e d ) l O e 4 e b e FIGURE 4-6 LATERAL FLOW PATTERN ON TOP OF TUBESHEET __ _ _____ - _______ -

1 i i 9' ) ) O d 4 o O e 9 9 FIGURE 4-7 TUBE GAP VELOCITY AND DENSITY DISTRIBUTIONS FOR TUBE ROW 10/ COLUMN 3 Ojl) G FIGURE 4-8 TUBE GAP VELOCITY AND DENSITY DISTRIBUTIONS FOR TUBE ROW 10/ COLUMN 20 i,

g:7;m.. ), '. I. i 'I e (;g-- 5:: 17, ~ l' 1h l9 l 3 J 4 l r

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j.,'f, 1.< <

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m FIGURE 4-9 TUBE GAP VELOCITY AND' DENSITY DISTRIBUTIONS .FOR. TUBE ROW 10/ COLUMN 40' 1 I 1 l i m i l 1 1 l - i 0., L; o .3 4: r d ) 1 4 i FIGURE 4-10 AVERAGE VELOCITY AND DENSITY IN THE PLANE OF THE U-BENDS NORMAL TO ROW 10 ---

i 6 L) 3 t i 1 i = F FIGURE 4-11 MODAL EFFECTIVE VEIDCITY FOR ROW 1 - 34

1 i 5.0 FIV MECHANISMS This section provides a mathematical description of the 1 [ Ja,b,c,e, which was determined to be the most likely causative mechanism for the North Anna tube rupture, as discussed in Section 3.3 of Reference 11, to highlight the physical conditions and corresponding parameters directly related to the event and to describe the turbulent excitation mechanism. 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 [ h l Ja,c,e, 7 The methodology is comprised of the evaluation of the following equations: [ 3a,c,e

..tt where: .a,c,e =,.. [13

and,

[2) Where: a,c,e-4 .s + Substitution of Equations (1) and (2) into the expression which defines stability ratio, and cancellation of like terms, leads.~

to an expression in fundamental terms (without the arbitrary-reference mass and density parameters).. From this resulting expression, it is seen that the stability ratio is directly. related to the [ a ja,e,c, 5.2 Turbulence Excitation Parameters Westinghouse has performed an extensive evaluation of the [ Ja,b,c,e, 4 For the U-bend analysis the driving [ Ja,b,c,e force representations was qualified against several series of tests and verified. Included in the qualification was a direct computation of the response of a model of tested tubes and conditions. The test and analysis predicted responses compared quite favorably. The test response was measured.in prototypical two-phase test. For clarity and reference, the methodology associated with [ Ja,b,c,e analysis for tubes with linear boundary conditions is summarized below. For [ Ja,b,c,e induced excitation the modal vibration amplitude is given by: i l i a,c e a i l L. .t, i i .l and the other parameters are defined in the previous section dealing with the.{ Ja,c,e, 5.3 Tube Damping Data The damping ratio depends on several aspects of the physical system. Two primary determinants of damping are the support conditions and the flow field. It has been shown that [ Ja,c,e. These effects are discussed below in more detail. Reference 1 indicates that the damping ratio in [- j ja,c,e, 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 are used here. The first is a large body of recent, as yet unpublished data from high pressure steam-water tests conducted by Mitsubishi Heavy Industries (MHI). These data were gathered under pinned tube support conditions. The second is comprised of the results from tests sponsored by the Electric Power Research Institute (EPRI) and reporteG in References 2 and 3. The damping ratio results from the above tests are plotted in Figure 5-1 as a function of void fraction. It is important to note that [ \\ '. Ja,c,e,g. 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 3. [ ]9 Denting of the tubes at the top support plate effectively clamps the tubes at that ]l location. Therefore, the clamped tube support curve is used in the evaluation when considering the effect of denting at the top tube support plate. The Reference 3 data as reported show a damping value of 0.5% at 100% void fraction. The 100% void fraction condition has no two phase damping and is considered to be affected principally by mechanical or structural damping. Westinghouse tests of clamped tube vibration in air has shown that the mechanical damping is as low as [ ]a,c,e rather than the [ Ja,c,e. Therefore the lower curve in Figure 5-1 is the [ ja,c,e, e 9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

,m t O } + P d e e 9 m . 4 O 4 FIGURE 5-1 DAMPING VS. SLIP yOID FRACTION 1 6.0 TUDE VIBRATION AND STRESS ASSESSMENT This section contains an evaluation of the effects of flow induced vibration (FIV) of the R1C55 tube. Displacements, stress and degree of stability with respect to fluidelastic vibration are discussed in the following sections along with descriptions of the methods used. 6.1 FASTVIB Model Description Critical parameters used to describe the response of steam generator tubing were obtained using a combination of special-purpose computer programs and closed form solutions. Parameters such as turbulent displacement and stability ratio were generated using FASTVIB, a Westinghouse proprietary finite element based computer code, and PLOTVIB a post processor to FASTVIB. These codes predict the [ ja,c,e. The velocity, density and void fraction distributions are determined using the ATHOS computer code as described in section 4.0. The t WECAN generated mass and stiffness matrices used to represent the tube are also input to the code. (WECAN is also a Westinghouse proprietary computer code.) Additional input to FASTVIB/PLOTVIB consists of tube support conditions, fluid elastic stability constant and turbulence constants. _

r-1 Figure 6-1 contains a sketch of the FASTVIB/PLOTVIB model used j t' in the evaluation. The model ( e Ja,c have been modified to account for the reduced cross section (due to the crack being present) and increased tube rotation due to the opening of the crack. Note'that the actual height of the crack is not required. The model assumes that [ Ja,c,e, Therefore, the evaluation presented in this section bounds the conditions present for the R1C55 tube and results in a conservative solution. The crack was incorporated into the FASTVIB model by [ d Ja,c have resulted in an accepted methodology that can be used to model the increased rotation 4 associated with a given moment and half crack angle (GAMMA). i Figure 6-3 contains a description of the crack angle and associated nomenclature used in the following discussion with 4 representing the additional rotation due to the crack opening at the cracked secticn. For a given moment M, 4 can be found to be: .i [ Ja,C Where: o = M/ (x

• R2*t)

M = Bending Moment R = Inside Tube Radius t = Tube Wall Thickness E = Youngs Modulus GAMMA = Half Crack Angle a,c,e The crack can be modeled by [ Ja,c,e to achieve the same rotation as a tube with a crack (as described above) for a given moment M. Performing this procedure results in a constant that can be applied to the uncracked moment of inertia as indicated below:

4 [ Ja,c,e-Where: a,c,e ke 6.2 Tube Stress At Crack Location Various boundary conditions at the top tube support plate were used in the evaluation. [ ]a,e,c conditions were used in a parametric study to determine which condition would be more limiting. The evaluation determined that [ ]a,e,c conditions could result in larger stresses at the crack location if combined in a conservative manner. [ Ja,c conditions may result in the largest stress for a single mode (due to reduced damping, etc.). However the response of the tube while in the [ Ja,c condition could result in a more limiting stress if calculated in the following manner. The stress was obtained by [ Ja,c,e. This l was performed to obtain a conservative stress solution that would envelope the actual stress. [ Ja,c,e the conservative approach used in this evaluation produces a stress that is still acceptable. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

The evaluation to calculate the stress at the crack location has determined that the stress at the crack site'(due to FIV) is quite small. The worst case stress neer the crack has been ~ determined to be approximately [ Ja,c for the tube in the [ Ja,c condition. The stress for tube in the [ Ja,c condition (where only a single dominant mode is present) is smaller than the [ Ja,c valued calculated for the o [ Ja,c condition. The stress at the crack tip has been determined to be less than [ Ja,c for the current crack geometry, i.e. GAMMA (half crack angle) of [ Ja,c. This can be compared to the crack propagation threshold of approximately [ Ja,c. Substantial margin is clearly present and this indicates that additional crack growth at the degradation site is not expected. Turbulent displacements of the degraded tube have also been determined in the evaluation. Table 6-1 contains a summary of the response of the tube for various conditions. As can be observed in the table, the maximum value of turbulent displacement calculated for the tube in the current condition (GAMMA = [ Ja,c) occurs if the tube is in the [ Ja,c condition. With the tube in the [ Ja,c condition, the maximum RMS displacement is [ ]a,c, Applying a factor of [ ]a,c to obtain maximum Peak turbulent displacements results in a value of [ Ja,c. The distance between tubes is [ Ja,c. Therefore, it can be concluded that, in the current condition, contact of any adjacent tubes due to turbulent excitation is not expected. e e i j

6.3 Evaluation of Tube-With Respect To North Anna R9C51 ~ An evaluation has also been performed to determine if the degraded tube could produce a North Anna R9C51 type tube rupture. This scenario was addressed because the crack may effect the tube sufficiently (along with fixed conditions at the top tube support plate) to result in the tube responding in a-4 manner similar to the North Anna tube. Should the. tube respond in this fashion and produce a severed tube at the TSP location, then the possibility of the RIC55 tube contacting and damaging an adjacent un-plugged tube may be possible. Reference 11 contains documentation of the evaluation performed.for Zion Units 1 and 2 with respect to North Anna type U-bend fatigue. This reference should be consulted for details of the methodology and criteria developed to address this type of issue. -The major criteria that has to be met is that the [ Ja,c,g must be less than 1.0 for the tube to be acceptable for 40 years of operation. It was determined that the [ Ja,c for the degraded R1C55 tube is essentially zero and that the North Anna type tube rupture would not be expected for this particular tube. 6.4 Severed Tube Response The response of the tube was also determined assuming that the tube becomes totally severed at the current degradation site. It was determined that the tube would remain stable with respect to fluidelastic excitation regardless of support condition. Two support conditions were addressed; both [ Ja,c conditions at the top TSP were defined. Table 6-1 contains a summary of the stability ratios for the severed tube cases under consideration along with responses of the tube in the current condition. Note that the response of the tube with the current degree of degradation has also been included. As can be _

observed in the table, the worst case stability ratio (ratio of effective velocity over critical velocity) was determined to be i [ Ja,c. This indicates that the tube is stable and that the rapidly increasing displacements associated with fluidelastic excitation would not occur for the RlC55 tube.. Table 6-1 also I contains a summary of the maximum U-bend tube displacements associated with turbulence excitation. The maximum peak a-turbulent displacement was found to be [ Ja,c with the tube in the severed condition. Therefore, the tube in the severed condition is not expected to move througn the [ Ja,c between tubes and contact an adjacent tube. The maximum FIV induced stress in the tube has also been determined for the case where the tube becomes completely severed. The stress has been calculated to be much less than 1.0 ksi. Stresses of this magnitude are below the endurance limit of the material, therefore fatigue usage will not accumulate. F e w t

TABLE 6-1 1 o

SUMMARY

OF THE RES'PONSE OF'R1C55 DUE TO FIV. l' SUPPORT COND CRACK (1) STABILITY TURBULENT (2) FREQUENCY (AT TOP TSP)1 RATIO DISPLACEMENT (Hz.) (Mils)- acr o Notes:

1) " Severed" indicates that the tube becomes severed at the current crack location.

" Current" indicates that the tube is degraded as currently indicated in Section 3.0.

2) Turbulent displacement is the RMS displacement of the tube in the U-bend region in mils.

Maximu:s peak displacements could be approximately [ Ja,c times larger than the values indicated in the table. When peak displacements are compared to the distance between tubes, [ Ja,c, it is clear that I contact with adjacent tubes is not expected.

3) There are no dominant U-Bend modes for this condition up to 200 Hz.

Values presented for this case are actually worst case straight leg results. Actual U-Bend values would be lower than the values listed for this case. o __-

UT I 08 ) $P 1 a

1. 8 O

l l 6 0 muuum e FIGURE 6-1 FASTVIB/PI.DTVIB MODEL OF R1C55 - So -

e t .e 0 e T G e o FIGURE 6-2 FASTVIB CRACK ORIENTATION -_

i S o 1 (A l ) b p e. d e N-h 4 e h FIGURE 6-3 CRACK MODELING NOMENCLATURE {.

l 7.0 RESIDUAL STRESS ASSESSMENT l In response to the concern that the tube leak in R1C55 ~ represents a unique failure mechanism, this section of the report summarizes an evaluation of steady state loading conditions in the tube which can result in a stress state that i: is consistent with a stress corrosion cracking mechanism. The analysis considers stresses due to operating temperature and pressure, tolerance on tube hole position at the top support plate, hot-to-cold leg temperature variations, differential expansion of the tube and support plate, twist of the tube resulting from rolling of the tube in the tubesheet, tube ovality, and residual stresses resulting from the manufacture process. Tube stresses resulting from tube / plate interactions are determined using a finite element beam model representation of the tube. Appropriate boundary conditions are applied to the model to reflect the loading condition being evaluated. .i Stresses for the remaining load conditions are either calculated using conventional analysis techniques, or are obtained from the results of prior test programs. 7.1 Steady-state Thermal Stresses / Support Plate Misalignment Tube stresses resulting fron the hot-to-cold leg temperature distribution are calculated using a finite element beam model representation of the tube using the general purpose computer program WECAN, Reference 12. [ Ja,c The distritntion of temperature is shown in Figure 7-1. This distribution is not specific to Zion Unit 2, but is representative, since it is based on 51 Series steam generators. The resulting stresses should not vary significantly for small changes in T-hot and/or T-cold.

v V c, i. .t The-same model;is used to. evaluate misalignment between the tube-j' and support plate at the top' support plate location. 'The misalignment'is the result of a stack up'of manufacturing tolerances as well as differential thermal expansion between'the E'- es tube and plate at operating temperatures'. Manufacturing ~ tolerances. included in the evaluation include' variances on [ 3: Ja,c. A stack-up of dimensional tolerances to give the maximum possible spread of the tube legs at normal operation results in a maximum spread of ( Ja,c for each leg. Conversely, the maximum amount of tube pinch that can occur is.[ Ja,c, A summary of the resulting tube bending moments for the hot-to-cold leg temperature distribution is given in Table 7 assuming three support conditions for the tube at the top ~ support plate. The first corresponds to a tube' centered in the .i . tube support plate hole prior to coming to temperature. The second and third conditions correspond to maximum pinch and maximum spread respectively. The resulting moment distributions are summarized in Table 7-1, and are provided as a function of the distance around the U-bend from TSP centerline on the hot leg to the TSP centerline on the cold leg. A plot of.the moment distributions is provided in Figure 7-2. Note that these results do not include thru-wall thermal effects. I 7.2 Operating Temperature and Pressure Tube stresses resulting from operating temperatures (thru-wall ~ effects) and pressure are calculated using conventional analysis techniques. The primary and secondary side pressures at normal operation correspond to 2250 psia and 735 psia, respectively, -giving a pressure drop across the tube wall of 1515 psi. The thru-wall tnermal gradient is taken from Figure 7-1. The U-bend for a row 1 tube is approximately [ Ja,c above the tubesheet. The corresponding thru-wall scadient is [ Ja,c, T4 I 1 -i l The resulting pressure induced stresses'are [ J a, c. - The thermally induced stress is [ Ja,c, The stress is tensile on the outer surface of the tube and ] compressive on the inner surface. ~ tj 7.3 Shear Due to Torsion During the process of rolling the tube into the tubesheet permanent set can be introduced into the tube in the from of a torsional load. Stresses in the U-bend region of the tube due to torsion were determined using the finite element beam model discussed earlier. The amount of torsion introduced into the tube has been estimated to be on the order of ( Ja,b,c, Because the applied torque is relatively small, and because the tube is relatively flexible, the stresses in the U-bend region are on the order of ( Ja,c. At the location of. interest for the R1C55 tube, the resulting shear stress is [ Ja,c, 7.4 Effects of Ovality on Stress Due to Pressure Initial tube ovality resulting from the manufacturing process can cause hoop bending stress to occur under the application of internal pressure. A set of parametric curves, as taken from Reference 13, showing the effects of tube ovality on total (direct + bending) tube stress is shown in Figure 7-3. Using these curves as a basis, bending stresses are calculated for a 51 Series steam generator tube geometry for initial tube ovalities ranging from ( Ja,c, the maximum permissible initial ovality. A sunmary of the resulting bending stresses is provided in Table 7-2. The appropriate sign convention for the bending stress is shown in the sketch at the bottom of table. For this evaluation, the distribution of bending strert tround l h L

l the tube circumference is assumed to be [ 3a,c, 'o 7.5 ovalization of Tight Radius U-Bends v: It.has been shown in a number of experimental 1' studies that for tight. radius U-bends', bending moments applied to pipe sections .i result in ovalization. The ovalization in turn leads to the: i introduction of both hoop stresses and axial bending stresses. Expressions for calculating the hoop and axial stresses are provided in Reference 14. A summary of the stress-distribution around the tube from extrados to intrados for an applied' moment of 100 in-lb is provided in Table 7-3. These results are shown plotted in Figure 7-4. 1 Although-this effect will dissipate in the vicinity of the U-bend tangent point, the effects are considered here as the degraded region of the tube is [ Ja,c above the tangent' point. 7.6 Residual Stresses Due to Tube Manufacture and Bending Several experimental studies have shown tubes to have significant residual stresses as a result of the tube manufacture and bending process. These same studies have shown, however, that a wide variation exists in the test results as to both the magnitude and distribution of stress. These variations are in large part a function of the testing technique used, although for any given technique, the variability is still large. Results from two studies, where the resulting stress distributions support a stress corrosion cracking failure mechanism, are used for this analysis. i The first set of results is taken from a study summarized in Reference 15. This program examined tubes manufactured from 1 __ _ l

1 Inconal 600 with an outside diameter of [ Ja,c, and a wall thickness of [ Ja,c, which is consistant with the 51 Series tube geometry. The band radius of the tubes in the-study was [' Ja,c, which again.is consistent with the 51 Series tubes. The-tubes in the study are finished by cold pilgering, bright annealing under hydrogen at 1800*F, rotary vi straightening, and polishing of the external surface. Measurement of the residual hoop stress was performed by placing 3 or 4 ' strain gages on the outer surface of the tube perpendicular to the axis of the tube. Relaxat' ion of the stresses was obtained by sectioning the tube on a milling machine along two perpendicular planes at a distance 0.04 inch from the end of each gage. The longitudinal residual stress was measured by the same method using strain gages attached to. the tube at 16 points equally spaced around the tube circumference at a given angular location around the U-bend. The strain gage locations for any given angular position are shown in Figure 7-5. The circumferential residual stress distribution is provided at 45 and 90* sections around the U-bend. Although the magnitude of the stresses was found to vary, the distribution of stress is quite similar. The stress distribution [ Ja,c is not presented. For this analysis the results for the section located [ Ja,c around the U-bend is used. The hoop and axial distributions are shown in Figures 7-6 and 7-7 for the outer tube surface. Plots of the stress distribution for the inner surface are not provided, however, it is reported that the stress distribution on the inner surface of the bends looks very similar to the outer surface. TharEfare, the distribution of residual stress is assumed to be the same both on the inside and outside surfaces. The second set of residual stresses used in this analysis are taken from Reference 16. The tube geometry used in this study is also consistent with the subject tube. The tube manufacture process consists of cold drawing, followed by mill annealing, straightening and polishing. The residual stresses are obtained through a process known as strain gage sectioning (SGS). Strain gages are mounted on the inside or outside surface of the tube and a small section containing the gage is cut out of the tube. The residual stress is calculated from the strain relaxation v which occurs when the section is cut out of the tube. .l As with the first experimental study, [ Ja,c. The set of data [ Ja,c. The residual stress distributions for this study are shown in Figure 7-8. Comparing the results from the two studies confirms the variation in residual stresses between the experimental studies. Variations exist in the longitudinal stress from one study to another, and also between the inside and outside surfaces. In the first study, the inner surface stresses are reported to be generally the same as the outer surface stresses. For the second study, however, the stresses are of similar magnitude and distribution, but are of opposite sign. 7.7 Combined Stress Results With these variations in mind, several combinations of the residual stresses with the other stress contributions discussed in prior sections have been performed to demonstrate that the resulting overall stress distributions support a stress corrosion cracking mechanism. The results for three specific cases are presented. The first case presents the results of a similar analysis performed for another utility's steam generator (51 Series), where a circumferential crack was discovered in a row 1 tube. The orientation of the crack at this plant was 45* off the apex on the hot-leg side, 45' up from the intrados, with _____________ - -

a 36' principal axis direction. The second and third cases presented are specific to the R1C55 tube at Zion. The combination of loading parameters which gives the best match of the crack location and orientation for the given case is summarized'in Table 7-4. A summary of the resulting stress 3 distribution for the other plant's tube is provided in Table 7-5. Plots of the results'are shown in Figures 7-9 and 7-10 for the outside and inside surfaces, respectively. The results in Figure 7-10 show very good agreement with the crack location and orientation at other plant. Results for Cases 2 and 3 are presented in Tables 7-6 and 7-7, and in Figures 7-11 through 7-14. It should be noted for these cases that stress components are shown plotted rather than principal stresses. Because the degradation at Zion is reported to be fully circumferential, the shear stress at this location is minimal. Therefore, the stress components are coincident with the principal stress directions, and plotting the stress components gives a clearer representation of the variation in axial and hoop stress around the tube circumference. Results for the outer surface are provided for information, as the focus of interest is the stresses for the inside surface. Neither of the cases 2 or 3 provide an exact match of the degradation pattern measured at Zion. The results do, however, support a stress corrosion cracking mechanism with the longitudinal stress having the greatest magnitude, which is necessary for circumferential cracking. The case 3 distribution, shown in Figure 7-14, provides the closest match of the Zion degradation as indicated by the eddy current rotating pancake signal. The inability to get an exact match of the Zion distribution is attributable largely to the lack of knowledge of the manufacturing residual stress distribution at this location. The eddy current signals at Zion indicate a change in tube geometry at or near the tube transition point which supports the presence of residual stresses. Without knowing the actual manufacturing residual stress distribution, an exact match of the Zion degradation is not possible. 7.8 Analysis Summary The results of this analysis show that there are a significant number of loading mechanisms which influence the operating stresses in tight radius U-bends. The resulting stress distribution is dependent to n large degree on the residual stress pattern resulting from the manufacturing process. The analysis shows that the presence of stress corrosion induced circumferentially oriented cracks located on the tube intrados, as for Zion and the other plant, is supported by existing test data for manufacturing residual stresses. Due to the variability in these stresses, however, an exact match of a given degradation pattern cannot generally be achieved without knowing the precise residual stress distribution at the location of interest for the manufacturing process applicable to the tube i in question. e N o 60 -

1 i 1 l-TABLE 7-1 BENDING MOMENT DISTRIBUTION AROUND THE U-BEND l 100% POWER TEMPERATURE DISTRIBUTION 51 SERIES - ROW 1 1 i BENDING MOMENTS .IN-LB DISTANCE MAX MAX AROUND NOMINAL SPREAD PINCH NODE U-BEND ANGLE GAP 18.S MIL / LEG 21.1 MIL / LEG a,e.. 4 b 4 0 M

g4 :;.7 -.., r y s,4 ~ . -] <. y ,o 1 o gg..

W s

J, 4

s..

O m; 1 ( '., l 1..( Y j .l i t ,- L TABLE.7-2 i l W,1.<, . CALCULATIONS-FOR TUBE STRESS AS A: FUNCTION:OF OVALITYc ~ s,. .1 h j. ,','.i'

j.-

6-. -[ ,g' s ' /.<. f d 1 l s.:. +- 'i. a,c;- 7.,S.< y

. f '

,.y/4 .i- ) J 1

, 1 3

l e a O O,' 4 e e e EB 1 1 .i 62 - \\.

3 TABLE 7-3

SUMMARY

OF TUBE BENDING STRESSES 51 SERIES - ROW 1 TUBE APPLIED MOMENT = 100 IN-LB SLO-OUT SLO-MID SLO-INS STR-OUT STR-MID STR-INS ANGLE (KSI) (KSI) (KSI) (KSI) (KSI). (KSI) -acs 9 w 9 0 e P uimm> i O l ! L

TABLE 7-4

SUMMARY

OF STRESS CONTRIBUTIONS 1 CASES 1, 2, 3 i i c. OPERATING TEMPERATURES INITIAL RESIDUAL CASE HL - CL TERU-WALL OVALITY TORSION STRESSES a,c m 0 e t O 4 6 . ~

j. TABLE 7-5 l

SUMMARY

OF PRINCIPAL STRESSES 51 SERIES - ROW 1 TUBE OPERATING TEMPERATURE AND PRESSURE INCLUDES THRU-WALL GRADIENT OVALITY EFFECTS ON PRESSURE INCLUDED RESIDUAL STRESSES INCLUDED - a,c' i e O e e w-

TABLE 7-6

SUMMARY

OF PRINCIPAL STRESSES 51 SERIES - ROW 1 TUBE ) OPERATING TEMPERATURE AND PRESSURE INCLUDES THRU-WALL GRADIENT OVALITY EFFECTS ON PRESSURE INCLUDED j RESIDUAL STRESSES INCLUDED l a,c j e h w g d summi e b O.___ _ _ _

' TABLE 7-7

SUMMARY

'OF PRINCIPAL STRESSES 51 SERIES - ROW 1. TUBE'- OPERATING TEMPERATURE AND PRESSURE INCLUDES THRU-WALL GRADIENT OVALITY EFFECTS ON PRESSURE INCLUDED RESIDUAL STRESSES INCLUDED-a, c O 4 s e 9 e w M h. e _

4 .-g W t S C' - 4 4 . y L' O 0 4 e g. 4 -use = 0 eb e O 4' FIGURE 7-1 51 SERIES TUBE TEMPERATURE DISTRIBUTION NORMAL OPERATION 68 - ). :g','., '. A.. ' ' - g_ im._ m

1 -i acr 1 1 a ~ FIGURE 7-2 U-BEND MOMENT DISTRIBUTION OPERATING TEMPERATURES FOR NORMAL, MAXIMUM SPREAD AND MAXIMUM PINCH SUPPORT CONDITIONS u .L_ _ J

j +. Ph 18 18 3 l' e 73 7 assa a sa ss sa s 4.n so BI f I / / / / / jy// / /b, ?c s c1 d ,, R l 4 i / /. / / / ///// j Y b' >\\I I i / / / / //,/// /.-W2/ R II I / / / / / //////,/ < j'/;- / l ,,8 lI I / / // / //////,<,r B ll1 ) / // / ///////;,- // y f.e.oUU ,,R V I / / //f/////W/ <,/// y/ Q/YZ",'-& / /// b 2h/MW >+h B IVI - / / / l ,Rllll / // ///fA%9%66.~/) en cd-%/[ I. Ellf/#MES2%%< 25 ] ,,1f//U#AWsM88820 p

C

C

=-=;=

e;=;- I . g gE : 1.n s e m IB e-g CC_G f$ m-m

==~ _--.m t ,,,,,,,,.l,,, "a r,,a,5ma o,, 1.1 12 13 g,4 g3 13 17 18 1.9 22 2.1 e/6 ,,,3 W .O FIGURE 7-3 OVALITY EFFECTS ON PRESSURE INDUCED STRESSES 70 -

-.-.-m...------.- - - -, - - -----r----r--

---

rw,

soc, I L

= 'Q, ' E r 'O , s c 4 I ' E -14 e i e g FIGURE 7-4 TUBE STRESS DISTRIBUTION FOR TIGHT RADIUS U-BEND UNDER MOMENT LOADING p..; l

iu I a,C I-*E . O F L 0 I 9 1 e 9 e ( 4 e '9. ummus GRWRu 9 4 FIGURE 7-5 RESIDUAL STRESS MEASUREMENT - STRAIN GAGE. LOCATION 72 - 1 L-bx:. :.: = _ ___-_ __

..j +- a [.. l'; ) ',. 8 a,c' 1 'Y' 8 . O J t r ' e ; + 6 h' O O e .g 9 FIGLTRE 7 RESIDUAL STRESSES IN THE LONGITUDINAL DIRECTION (REFERENCE 15) 73 -

il

'*h'" F 4 Xw., [ I '+.{' i i ;, a s 8,C' ..W ~ muse

i. '

'I ' e 't N ^ .Q ! . e .' ? I t \\ ' 9 o' 9...

• ^

l 4 - -me enum .9-4. FIGURE 7-7 RESIDUAL STRESSES IN.THE HOOP DIRECTION (REFERENCE 15) - 74 w

k j a

8, C,8-

~ ' 's at e - 9 ,a O M e 4 .g-FIGURE 7-8 RESIDUAL STRESS MEASUREMENTS (REFERENCE 16) 8,C Y .h' t 4 l 1 o e 4 esem W FIGURE 7-9 PLOT OF EFFECTIVE STRESS DISTRIBUTION FOR ANOTHER PIANT OUTSIDE SURFACE '[ y + l .j 4 'l a,c-4 6 s e FIGURE 7-10 PLOT OF EFFECTIVE STRESS DISTRIBUTION l.. FOR ANOTHER PIANT l INSIDE SURFACE 77 - f-L

l l 8,C o e 4 e a M N M = FIGURE 7-11 PLOT OF COMPONENT STRESS DISTRIBUTIONS FOR ZION UNIT 2 - CASE 2 RESULTS OUTSIDE SURFACE. _ _ _ - _ _ _ _ -

2 \\. a,c g. 9 o 'e ai i l ~~ ~ h +. ^ FIGURE 7-12 PLOT OF COMPONENT STRESS DISTRIBUTIONS FOR ZION UNIT 2 - CASE 2 RESULTS INSIDE SURFACE -_y-_.___.. c,_, 7 b' i k-h5 8,C .y a 3 O 4 l A l l.' _ y'; I' FIGURE 7-13 PLOT OF COMPONENT STRESS DISTRIBUTIONS FOR ZION UNIT'2 - CASE 3'RESULTS OUTSIDE SURFACE

- + ? ha a', c - s. ( .9 e 1 l l e i. l n a as d.s4 s FIGURE 7-14 PLOT OF COMPONENT STRESS DISTRIBUTIONS FOR SION UNIT 2 - CASE 3 RESULTS INSIDE SURFACE . >, l w

i

8.0 REFERENCES

i i

1) Carlucci L.

N., and J. D. Brown, " Experimental Studies of damping of and Hydrodynamic Mass of a cylinder in Confined Two-Phase Flow", ASME Journal of Vibration, Acoustics, Stress and Reliability in Design, January 1893.

2) Axisa, F.

et al. " Flow Induced Vibrations of Steam Generator Tubes", EPRI-NP-4559, May, 1986.

3) Axisa F.,

et al, " Vibration of Tube Bundles Subjected to Steam-Water Cross Flow: A comparative Study of Square and Triangular Pitch Arrays", Eight SMIRT Conference in Brussels, August 1985. )

4) Lellouch G.

S. and B. A Zolotar, "A Mechanistic Model for Predicting Two-Phase Void Fraction for Water in Vertical Tubes, Channels and Rod Bundles", EPRI-NP-2246-SR, 1982. 5) L. W.

Keeton, A.-K.

Singhal, et. al., "ATHOS3: A Computer Program for Thermal-Hydraulic Analysis of Steam Generators", Vol. 1, 2, and 3, EPRI NP-4604-CCM, July 1986. 6) H. Tada, "The Effects of Shell Corrections on Stress Intensity Factors and the Crack Opening Areas of a circumferential and a Longitudinal Through-Crack in a Pipe", Section III-1 of "The Application of fracture Proof Design Methods Using Tearing Instability Theory to Nuclear Piping Postulating Circumferential Through Wall Cracks", By P. C. Paris and H. Tada, U. S. Nuclear Regulatory Commission, NUREG/CR-3464, Sept. 1983.

7) H. Tada, "The Stress Intensity Factor for a Crack Perpendicular to the Welding Bead", International Journal of Fracture, Vol. 21 pp 279-284, 1983

8) H. Tada, P.

C. Paris and G. Irwin, "The Stress Analysis of Crack Handbook", 2nd Edition, Paris Production Incorporated (and Del Research Corporation) 226 Woodbourne Drive, St. Louis, Missouri, 1985.

9) J.

L. Sanders, Jr., "Circumferential Though-Cracks in Cylindrical Shell Under Tension", Trans., ASME, Journal Applied Mechanics, Vol. 49 pp 1-3-107, 1982

10) J.

L. Sanders, Jr., "Circumferential Through-Crack in cylindrical Shell Under Combined Bending and Tension", Trans. ASME, Journal of Applied Mechanics Vol. 50 pp 221, 1983. -___.

11) [

3a,b,c,d

12) WECAN, Westinghouse Electric Computer Analysis, User's Manual, Third Edition, Revision V, 6/1/86. (Proprietary) i s

1

13) " Engineering Design", Faupel, Fisher.

14) " Experiments on'Short Radius Pipe Bends", N.. Gross, Proceedings of the Institute of Mechanical Engineering -

1952, Vol. 166.

15) [

3a,c

16) [

3a,ba c,e' S> e g e 6 e O i < }}