ML20112K075
| ML20112K075 | |
| Person / Time | |
|---|---|
| Site: | San Onofre  |
| Issue date: | 03/28/1985 |
| From: | Danfelt E AEA O'DONNELL, INC. (FORMERLY SMC O'DONNELL, INC. |
| To: | |
| Shared Package | |
| ML13309B527 | List: |
| References | |
| 1679-400-002-00, 1679-400-2, NUDOCS 8504090324 | |
| Download: ML20112K075 (58) | |
Text
_-
EVALUATION OF TUBE WEAR IN SAN ONOFRE UNITS 2 AND 3 STEAM GENERATORS Prepared for SOUTHERN CALIFORNIA EDISON COMPANY San Clemente, California March 28,1985 O'DONNELL & ASSOCIATES, INC.
ENGINEERING DESIGN & ANALYSIS SERVICES 241 CURRY HOLLOW ROAD PITTSBURGH, PENNSYLVANIA 15236 (412) 655-1200 (412) 653-6110 TWX 710-667-4857 D
A 50 61 p
EVALUATION OF TUBE WEAR IN SAN ON0FRE UNITS 2 AND 3 STEAM GENERATORS Prepared by O'DONNELL & ASSOCIATES, INC.
241 Curry Hollow Road Pittsburgh, Pennsylvania 15236.
Contributors M. L. Badlani E. L. Danfelt V. M. Elias R. G. Fasiczka E. J. Hampton B. Kasrate R. D. Kichko W. J. O'Donnell J. S. Porowski C. D. Powell A. Selz F. A. Spaniel E. L. Westermann i.
Prepared for SOUTHERN CALIFORNIA EDIS0N COMPANY San Clemente, California 92672
1679-400-002-00 EVALUATION OF TUBE WEAR IN SAN ON0FRE UNITS 2 AND 3 STEAM GENERATORS Prepared for i
SOUTHERN CALIFORNIA EDIS0N l
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EVALVATION OF TUBE WEAR IN SAN ON0FRE IilTS 2 AND 3 STEAM GENERATORS TABLE OF CONTENTS Page EXECUTIVE
SUMMARY
5 ACKNOWLEDGMENTS 6
1.0 INTR 0bOCTION 7
1.1 Purpose 7
1.2 Evaluation 7
1.3 Conclusion 8
2.0 DESIGN GE0 METRY AND PARAMETERS 9
3.0 TECHNICAL APPROACH 16 4.0 ANALYTICAL MODELS 21 4.1 Thermal Hydraulic Characteristics 21 4.2 Finite Element Analyses 22 4.2.1 U-Bend Tube Model 23 4.2.2 Batwing Strap Model 24 4.3 Linear Wear Model 24 l
4.4 Nonlinear Single Tube Wear Model 26 4.4.1 Accelerated Volumetric Wear Rates 26 l
Due to Increased Gaps 4.4.2 Reduced Thickness Wear Rate Due to 29 Increasing Wear Area 4.4.3 Theoretical Tube Wear at End of 30 Second Cycle 4.5 Wear on Staked and Plugged Tubes 34 4.6 Fatigue Evaluation of Batwings 35 5.0 RESULTS AND CONCLUSIONS 38
6.0 REFERENCES
42 APPENDIX A LIST OF TUBE-DEFECTS AT BATWING ELEVATION 6 PAGES APPENDIX B THICKNESS WEAR RATE EVALUATION 8 PAGES l
l1679-400-002-00 Page 2 of 42
EVALVATION 0F TUBE WEAR IN SAN ON0FRE UNITS 2 AND 3 STEAM GENERATORS LIST OF FIGURES Page FIGURE 1 SAN ON0FRE UNIT 2 AND UNIT 3 STEAM GENERATORS 10 FIGURE 2 CUTAWAY VIEW 0F UPPER INTERNALS 11 FIGURE 3 UPPER TUBE BUNDLE SUPPORTS 12 FIGURE 4 DETAll 0F VERTICAL SUPPORT 13 FIGURE 5 BATWING ARRANGEMENT IN CENTRAL REGION 14 FIGURE 6 CENTRAL PORTION OF LOWER BATWING ASSEMBLY 15 FIGURE 7a FLUID AXIAL VELOCITY 10 INCHES AB0VE THE 18 LAST FULL EGG CRATE (100% POWER)
FIGURE 7b FLUID DENSITY 5 INCHES AB0VE THE LAST 19 FULL EGG CRATE (100% POWER)
FIGURE 8 U-BEND TUBE MODEL 23 FIGURE 9 BATWING / TUBE MODEL 25 FIGURE 10 THE0RETICAL WEAR AT END 0F FIRST CYCLE FOR STEAM 27 GENERATORS 88 & 89 (UNIT 2)
FIGURE 11 ACCELERATED VOLUMETRIC WEAR RATE DUE TO 28 INCREASED GAPS FIGURE 12 REOUCTION IN THICKNESS WEAR RATES DUE TO 31 INCREASED WEAR AREA FIGURE 13 NET THICKNESS WEAR RATE FROM NONLINEAR MODEL 32 FIGURE 14 COMPARIS0N OF THE0RETICAL TUBE WALL WEAR AT END OF 33 SECOND CYCLE VS.-END OF FIRST CYCLE WEAR FOR SAN ONOFRE UNIT 2 STEAM GENERATORS FIGURE 15 STAKING AND PLUGGING WITH PROJECTED WEAR AT END OF 40 SECOND CYCLE FOR STEAM GENERATOR 88 1679-400-002-00 Page 3 of 42
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EVALUATION OF TVBE WEAR IN SAN ON0FRE UNITS 2 AND 3 STEAM GENERATORS EXECUTIVE
SUMMARY
An independent analysis of wear in the San Onofre Units 2 and 3 steam generator tubes was performed. The results show that the wear was caused by turbulent flow-induced vibrations of the tubes and batwings which produced forces and relative motions between the batwings and tubes. The variation of wear ovg[ the tube bundle pattern was analyzed using a dynamic finite element modelWwhich included the interactions between the batwings and multiple tubes. Differences in natural frequencies, in two-phase flow velocities and densities and in tube and batwing mode shapes and stiffnesses; produce a very definite pattern of theoretical wear distribution among the tubes which corresponds to the measured wear pattern. The reliability and accuracy of the analytical predictions was assured by using the actual average measured wear results to obtain the combined wear and vibration amplitude coefficients. The resulting theoretical wear for each tube at the end of the first cycle of operation of Unit 2 was evaluated.1 The accelerated volumetric wear rates due to the increasing gaps were 2
evaluated using a single tube nonlinear model. These accelerated volumetric wear rates are significantly mitigated as wear scar areas increase. The latter were included in the analyses and the resulting net thickness wear rates were obtained.3 The total theoretical thickness wear for all Unit 2 tubes was evaluated for the end of cycle 2.4 Additional conservatism is introduced because the single tube gap model does not take credit for the transfer of reaction loads to the other tubes as the front tubes wear.
The. measured wear on each tube at the end of the first cycle was considered along with the above theoretical wear results to establish conservative tube plugging criteria. The latter assure that all' Code and Regulatory safety margins are met, limiting all unplugged tube wall wear to 64 percent at the end of the second cycle of operation. The factor of safety of 3 on stress against bursting is satisfied with 64 percent wall wear under. normal operating conditions as required by Regulatory Guide 1.121.
Tubes were plugged according to these criteria, thus assuring that the steam generators can be operated through the second cycle"with all unplugged tube wear remaining well within the 64 percent criteria.
In addition, the inner tubes at the central cavity boundary were staked to assure their structural integrity, and preventive plugging of tubes adjacent to worn tubes was used to provide defense-in-depth.b IShown in Figure 10 "Shown in Figure 14 2Shown in Figure 11 SShown'in Figures 15 and 16 3Shown in Figure 13 1679-400-002-00 Page 5 of 42
ACKNOWLEDGEMENTS The authors wish to acknowledge the efforts of Mr.
John Mundis in providing technical support for this evaluation including a thorough understanding of the design and of various thermal, hydraulic and mechanical phenomena in the steam generator.
Messrs. Harold Ray, Dwight Nunn and Brian Katz also assisted in developing a sound technical approach to obtain reliable theoretical wear results. The cooperation of the Electric Power Research Institute and Combustion Engineering is appreciated and was useful in this independent evaluation.
1679-400-002-00 Page 6 of 42
1.0 INTRODUCTION
1.1 Purpose The purpose of this analysis was to determine the tube plugging and staking needed to assure that no operating problems would occur during the second cycle of operation of the San Onofre steam generators due to tube wear and that tube wear in all unplugged tubes will be less than 64 percent of the wall thickness.
1.2 Evaluation O'Donnell & Associates, Inc. performed an independent evaluation of l
the tube wear found in Southern California Edison's San Onofre pressurized
{
water reactor Units 2 and 3 Combustion Engineering steam generators.
Following the first cycle of operation of Unit 2, numerous worn tubes were found near the inner periphery of the tube bundles.
Inspection results showed that most of the worn tubes were in the first three rows around the central cavity, adjacent to tube separator straps.(batwings) which form part of the tube bend region support system.
The initial investigation by O'Donnell & Associates, Inc. included an analysis and evaluation of all potential causes of the observed tube wear.
The results of this investigation showed that the wear was caused by turbulent flow-induced vibrations of the tubes and batwings.
This report contains a description of the analytical model used to predict wear rates. Actual measured wear results were used to obtain reliable values for the combined flow-induced vibration amplitude and wear coefficients. Theoretical wear rates were obtained for both the first and second cycles of operation using both a linear model and a single tube nonlinear model.
1679-400-002-00 Page 7 of 42
1.3 Conclusion Conservative tube plugging and staking criteria were developed and implemented to provide assurance that no unplugged tube will approach 64 percent tube wall wear at the end of the second cycle of operation.
1679-400-002-00 Page~ 8 of 42-
2.0 DESIGN GE0 METRY AND PARAMETERS The Combustion Engineering design for the San Onofre steam generators as described in Reference 2 is shown in Figure 1.
A cutaway view of the upper portion of the steam generator is shown in Figure 2.
The vertical spans of the tubes in the tube bundle are supported by egg crate support plates.
In the upper part of the tube bundle, including the tube bend region, support is provided by vertical support grids and diagonal separator straps (batwings). The upper tube bundle support and details of the vertical support grid are shown in Figures 3 and 4, respectively.
Details of the batwing arrangement are shown in Figure 5 while the lower batwing assembly is illustrated in Figure 6.
The above figures were obtained from Combustion Engineering, Reference 2.
The area most susceptible to tube / batwing wear from flow-induced vibration is the periphery of the central cavity region. This central cavity corresponds to the tubesheet central stay cylinder, which restricts the installation of tubes in this region. Consequently, the batwing straps have long unsupported spans from the first tube contact point to the center of the bundle where they. are partially held by a cross-plate (see Figure 6). The latter center support allows swinging and rocking or twisting
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modes of vibration. These spans of flexible (90 mil thick) flat plate have low natural frequencies and tend to pick up flow energy.
The tubes are also subject to flow-induced vibrations and their motions include deflections in the plane of the batwing straps. Wear is caused by relative tangential motion between the vibrating tubes and the vibrating straps. The volumetric rate of wear on each tube is proportional to the normal force acting between the tubes and straps and the relative j
tangential' motions between them.
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1679-400-002-00 Page 9 of 42
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L 3.0 TECHNICAL APPROACH High flow rates in the steam generator create random flow-induced tube and tube separator strap (batwing) vibrations which cause wear at their interface. A systematic wear pattern was found following the first cycle of operation of Unit 2, and this pattern was consistent with the theoretical wear pattern predicted by the analyses.
As shown in Reference 1, Archard's wear relationship can be applied to reversed as well as to continuous sliding conditions. This equation is given by:
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where V = volumetric wear, in.3 K = wear coefficient, psi-1 F = normal force between surfaces, Ib U = total sliding distance, in.
Accordingly, the volumetric rate of wear is proportional to the normal forces between the batwing straps and tubes, and the relative motions between the tubes and straps. The technical approach used to evaluate the theoretical wear pattern and to predict wear during the second cycle of operation consisted of the following steps:
(a) Evaluation of dynamic characteristics of the tube and tube separator straps in terms of their natural frequencies and mode shapes.
t (b) Determination of flow-induced motions of the tubes relative to i
the batwing straps.
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1679-400-002-00 Page 16 of 42
(c) Determination of the normal relative forces acting between each l
tube and strap.
l (d) Using the interacting reaction forces obtained in (c) and the relative deflections obtained in (b), determine the theoretical wear rates for a wear coefficient K.
(e) The theoretical wear pattern is defined by the analyses of (a) through (d). The wear coefficient and flow-induced vibration coefficients were combined into a single coefficient which was established using the actual measured wear results.
(f) The accelerated wear due to the increasing gaps and the partially offsetting effects of increased wear area were evaluated using a single tube nonlinear gap model to predict wear during the second cycle of Unit 2.
The flow velocity and density distributions illustrated in Figures 7a and 7b from Reference 2 were used in this analysis of the San Onofre Units 2 and 3 steam generators.
The natural frequencies and mode shapes of.the tubes and batwing straps were obtained from finite element analyses, which were also used for determining the relative magnitudes of the tube-to-batwing interaction forces and motions. The ANSYS general purpose computer program, utilizing 0'Donnell & Associates. Inc. pre and post-processing methods, was used for performing these finite element analyses.
In order to predict absolute wear rates, material wear properties and flow-induced vibration coefficients must be quantified based on available experimental results. The steam generator itself is the best source of such data, it has the precise material and environmental conditions of 1679-400-002-00 Page 17 of 42
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interest. Although eddy current measurements include error bands, the use fof a large number of tube wear measurements to establish a combined flow and wear coefficient gives accurate best estimate results.- The best estimate values were obtained herein by minimizing the sum of the differences between the theoretical and measured wear values for all of the tubes. Root-mean-square minimizing gives very similar results.
A detailed description of the analyses performed to obtain forces and relative motions for Archard's Equation is given in the next section. The results are then used to predict wear in the subsequent cycle using linear and nonlinear models. The multi-tube / batwing linear model assumes a
- constant rate of tube wall thinning.
The single tube / batwing nonlinear model includes an evaluation of the effects of decelerating wear due to the
-increasing contact area, and accelerating wear caused by gaps increasing with the progressive depth of wear scars. The nonlinear effects were found to be quite significant.
1679-400-002-00 Page 20 of 42
4.0 ANALYTICAL MODELS 4.1 Thermal Hydraulic Characteristics Under the conditions of-high flow rates and/or high levels of turbulence, an elastic structure in contact with a flowing media will vibrate. This vibration is caused by the transfer of energy from the f?uid to the structure.
The fluid causing the vibration of concern is the secondary (shell side) fluid '(water and steam mixture) flowing past the heat exchanger tubes and their supports. The region of the heat exchanger of prime iinportance is the upper tube bundle subjected to cross flow. Because of the high level of turbulence and the high flow rate of the two-phase fluid in this region, the dominating energy transfer mechanism is random excitation due to'the flow turbulence. For this type of flow situation the turbulence is broad band.
It is comprised of a wide range of frequencies which include-the natural frequencies of the batwings and tubes. Hence, the heat exchanger tubes and their supports will be supplied with energy at their natural frequencies.
Accurate values of the thermal hydraulic variables can be obtained from suitable codes such as CALIPSOS, Reference 3, or ATHOS, Reference 4.
Combustion Engineering used the thermal hydraulic Code ATH0S to analyze the San Onofre steam generators in. Reference 2.
The axial velocity and ' flow density distribution taken from Reference 2 was used in the present analyses. For liquid flow, the vibration amplitude response to turbulent excitation is proportional to the flow velocity squared. Reference 5.
For two-phase flow, there is some evidence that the variation of the vibration
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amplitude with velocity may be closer to linear.
Velocity variations between tubes in the generator are very small and the more conservative velocity-squared relationship was used in the present analysis.
i 1679-400-002-00.
Page21 of 42
4.2. Finite Element Analyses
' Finite element analyses were performed to determine (i) the natural frequencies and mode shapes of the tubes and batwing straps, (ii) tube / strap interaction forces, and (iii) tube / strap relative motions.
The dynamic interaction between the tubes and the batwing straps was modeled using two three-dimensional finite element models - one of the U-Bend tubes and the other of the batwing straps dynamically interacting with multiple tubes. The reaction forces obtained. were normalized and used with the relative motions to evaluate the wear.
4.2.1 U-Bend Tube Model, Figure 8 'shows the three-dimensional finite element model of the U-Bend tubes fran rows 23 through 48 in the vicinity of the central cavity region.
The tubes were modeled as beams with section properties equivalent to the tube filled with water.
The finite element model of the U-Bend was used to determine the out-of-plane stiffness of each row of tubes when pushed at the location where the batwing crosses-the tube.
The tube stiffnesses were subsequently used as discrete elastic supports for the dynamic multiple tube batwing strap model.
The U-Bend model was also used to evaluate the frequency and mode shape of individual tube _ spans.
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t 1679-400-002-00 Page 22 of 42
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.4.2.2 Batwing Strap Model The natural frequencies of the batwing straps are much lower than those of the tube. - Therefore, the batwing will rest against the tube and follow the tube motion.- Figure 9 shows the finite element' model used to determine the relative force distribution between the tubes and the straps.
The o del consists of a symmetrical section of the batwing extending into the t abe bundle out to row 39.
The tubes which act as an elastic restraint for the batwing are modeled as springs of appropriate.stiffnesses. The stiffnessivalues were obtained from the U-Bend' tube model shown 'in Figure 8.
The same batwing model was used to modelLthe short and long. span straps. " Span" is used here to indicate the free span from the central-batwing support to the location where the strap enters the tube bundle.
The variations considered included batwings entering the tube bundle from row 23 to row 39. These variations in free spans were ~modeled by freeing the ends of the appropriate number of the springs used to simulate the tubes, thus effectively taking those tubes out of the model.
The displacement shape of the batwing straps was determined by modal analyses. The reaction forces at the tubes were obtained and normalized to the reaction force at the first tube in contact with the batwing straps.
The reaction forces were corrected to account for the differences in axial flow velocities and densities in the central cavity at the location of each strap free span. The velocity and density distributions were taken from Reference 2.
4.3 Linear Wear Model As discussed under the Technical Approach, the wear model used in the present work is based on Archard's -relationship given by Equation--(1).
Relative volumetric wear on each tube was obtained using the above wear equation'with forces from the coupled dynamic model of the strap and
-1679-400-002-00 Page 24' of 42
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multiple tubes discussed in the previous section. The amplitudes and frequencies were obtained from the U-bend tube model.
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Best fit wear values at the end of the first cycle of operation were obtained from the theoretical relative wear by minimizing the difference between the averaged theoretical and measured wear for Unit 2 steam generators 88 and 89. The results based on the best fit wear values are shown in Figure 10 as a percentage of wall thickness.
4.4 Nonlinear Single Tube Wear Model In order to evaluate the extent to which the thickness wear rate would be expected to deviate from a constant rate over time, an analytical model was developed to take into account the two major phenomena which cause deviations from linearity:
(i) The accelerated volumetric wear rate which occurs with increasing gaps caused by the wear itself (ii) The deceleration in thickness wear rate which occurs due to the increase in surface area being worn.
4.4.1 Accelerated Volumetric Wear Rates Due to Increased Gaps Increased gaps between the tubes and straps result in an increased volumetric wear rate because the turbulent flow forces driving the tube and batwings can produce larger root-mean-square amplitudes and forces. The change in interaction forces due to this mechanism were obtained by considering the interaction of a single tube and strap due to a difference in initial velocities. The increase in wear rate was evaluated using the increased displacements in Archard's Equation and the increase in reaction j
force. Figure 11 shows the resulting volumetric wear rate increase as a function of~the tube wall wear.
1679-400-002 Page 26 of_42
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t 4.4.2 Reduced Thickness Wear RSte D0e'to Increasing Wear Area 4
I, The complexities of the flow induced tube and strap motions and the resulting wear are such that the precise ' geometry of the wear surfaces cannot be uniquely defined. The wear pattern which minimizes the
- beneficial effects of-the increased wear area initiat'es wear at a small angle and increases the angle with progressive wear. Such a pattern is also physically realistic. A strap which,would have a free rotation slightly different from the tube it is touching tends to lie flat against the tube. As wear progresses, qhe strap fotates slightly as shown in the following illustration
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Using the wear pattern ' described above,.the rate of thickness wear can j.
be obtained for a constant volumetric wear rate. Normalizing these results to an initial thickness wear rate of unity, the reduction in thickness wear rate is shown in Figure 12. The corresponding results for wear geometries assumed in Reference 2.are also shown (see Appendix B.)
4.4.3 Theoretical Tube Wear at End of Second Cycle The models for accelerated volumetricLwear and increased wear area described above were combined in a nonlinear tube wall thickness wear rate model to predict the net amount of wear to be expected at the end of the second cycle of operation of San Onofre Unit 2.
The wear rates are of course dependent on the mass flow rates and velocities integrated over tima. The first cycle service was taken to be; Reference 2:
Mass Flow Velocity Rate LB/Sec FT/Sec 302 days 0 100% power 358 15.3 51 days-0 50% power 223 5.9 The second cycle is anticipated to be:
265 days 9 100% power 358 15.3 The 'predicticn of wear by this. nonlinear single tube model requires an iterative solution. However, the mathematical relations are well behaved and-converge. easily.
Figure 13 shows the resulting net thickness wear rate obtained from this nonlinear single tube model.
The total theoretical. wear at the end of the second cycle was also evaluated using.this nonlinear model. Figure 14' shows the resulting theoretical wear 'at the end of the second cycle as a
.1679-400-002-00 Page 30 ef=42
O'Donnell & Associates, Inc.
Pittsburah Pennsulvania THICKNESS UEAR RATE VS.
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function of.the wear in the first cycle for San Onofre Unit 2.
These results are based on the single tube nonlinear gap model which does not take credit for the transfer of reaction loads to other tubes as the front row of tubes wears. A multi-tube model with gaps corrected for wear can be used to i
' analyze such longer term wear responses.
The linear ulti-tube model
-predictions are.also included in Figure 14 for. comparison purposes.
4.5 Wear on Staked and Plugged Tubes This sbction presents an evaluation of the effects of plug'ging and staking on the subsequent' wear of the tubes. Tubes which were predicted by means of the wear model to have excessive wear at the end of the second cycle were plugged or. staked depending upon the severity of the predicted wear in accordance with the criteria presented in Section 5.0.
The original finite element model of the tubes was used to evaluate these cases:
(1)' Normal condition with filled water, (2) Tubes plugged and empty, (3) Tubes plugged and staked. These three cases were run by changing the density of the beams modeling the tubes.
No increase-in stiffness was considered for the staked tubes.
Staking entails inserting a stainless steel bar up.one side of the U-Bend. This bar is attached to a stainless wire rope which is pulled through the other end of the U-Bend. The density of the beam material used in the finite-element model was modified to account for this nonsymmetric mass distribution in the U-Bend, since the bar weighs more than the rope.
The beam properties are modified to account for the increased mass.
No credit was taken for any stiffening effects of the stainless steel bar or rope. For the three conditions considered, the normal forces between the tubes and batwings are-very nearly the same. Differences in wear rates would therefore be proportional to the' product of the frequency of vibration and the amplitude of the relative motion at the batwing.
1679-400-002-00 Page 34 of 42
l L
The results show that there is not much difference between the three cases. Hence. the wear of-_ the plugged or-staked tubes is expected to be (c
approximately the same as that for the unplugged tubes.
l'
- 4.6 Fatigue Evaluation of Batwings-Turbulent flow-induced vibrations of 'the batwings make them susceptible to high cycle fatigue, particularly at the stitch welds shown
~
below. The batwings with the longest free spans, lowest natural frequencies and subjected to the-highest turbulent flows will be the most susceptible to fatigue.
I Batwing Weld Joint 1/2" N 1/4" 1/2" t
1679-400-002-00'-
Page 35 of.42
The lack of transverse structural support at the center of the batwings will allow beating in the turbulent flow field in addition to the vibrations which occur at the natural frequencies of the batwing. The number of fatigue cycles associa',ed with the vibration and beating frequencies is large,-exceeding i cycles during the first cycle of operation at San Onofre.
In this high cycle regime, the peak stress amplitudes control the structural integrity in fatigue and the root-mean-square of the random vibration amplitudes produce negligible fatigue damage.
Accounting for potential beating of adjacent batwings, the peak amplitude of the beating motion could be twice the batwing spacing.
Stresses at the batwing welds due to such beating were obtained from a finite element model. -In this model, the beating mode shape was imposed on the batwing to obtain stresses. The resulting nominal stress amplitude at l
the batwing stitch-weld, acting on the net welded cross-section is 1,111 psi.
In addition to this raode of vibration, the batwing vibrates in the anti-symmetric mode wherein the center is pivoted.
This mode gives higher stresses at the batwing welds for smaller amplitudes of vibration. The batwings are restrained by the vibrating tubes with a nominal gap of 13 mils. A nominal stress amplitude of 2,230 psi for this mode of vibration was obtained from the finite element analysis.
The frequencies of the beating and vibrating modes of concern are not the same but their peak amplitudes will be essentially additive at the lower beating frequency which is about 1.6 Hz. The latter produces 8.5 x 7
10 cycles by the end of cycle 2 in the San Onofre units. The current ASME Code Section 111 fatigue design allowables for carbon steels with ultimate strengths below 80 ksi do not go beyond 106 cycles. The fatigue design curves for stainless steels have already been extended to include flow-induced vibrations, and current committee work is in progress for the carbon steels. The existing allowable fatigue design value at 106 cycles is 12,500 1679-400-002-00 Page 36 of'42
psi. A value of 10,000 psi is considered a conservative allowable for this application.
The-fatigue strength reduction factor for the notch effect due to the stitch-weld construction was.obtained from Reference 6, which is used
. extensively in the Naval nuclear program. The usual factors of 4 or 5 for fillet welds are too high for the particular geometry and loading conditions of interest.. A more realistic fatigue strength reduction factor, K, for f
these thin '(0.090 in, thickness) carbon steel straps subjected to bending is Kf = 1.9 from Reference 6.
1 The peak stress amplitude which controls the fatigue life of the batwing stitch-weld is therefore = 6,348 psi. This is less than the' fatigue design allowable value of 10,000 psi. Fatigue at other locations in the batwing is less limiting until there is an enormous amount of batwing wear and thinning at the first row of tubes. Stresses were evaluated at this location and batwing fatigue damage was found to be less than that at the welded section until half the total batwing thickness is worn.away. We conclude that the batwings are acceptable in fatigue through the_second cycle of operation at San Onofre.
1679-400-002-00 Page 37 of 42-
5.0 RESULTS AND CONCLUSIONS The theoretical wear for each tube at the end of the first cycle of Unit 2 is given in Figure 10. The accelerated volumetric wear rates due to the increasing gaps, evaluated using the single tube model, are shown in Figure 11. After taking credit for the increase in-scar wear area, the net thickness wear rates are shown in Figure 13.
The resulting total wall thickness wear predicted at the end of the second cycle of operation are shown.in Figure 14 These results are based on the single tube, nonlinear gap model which does not take credit for the transfer of reaction loads to other tubes as the front row of tubes-wears.
The measured wear on each tube at the end of the first cycle was considered along with the above theoretical wear results to establish conservative tube plugging criteria. The latter assure that all Code and Regulatory safety margins are met, and that no unplugged tube will approach 64 percent wa!1 thickness wear at the end of the second cycle of operation.
As required by Section III Division 1 of the ASME Code and Regulatory Guide 1.121, References 7 and 8, the factor of safety of 3 on stress against bursting is satisfied with 64 percent wear under normal operating conditions. The criteria established for plugging and staking tubes at the end of the first cycle of operation of Unit 2 are as ft llows:
1.
Tubes at the boundary of the central cavity region where theoretical wall wear is larger than 10% must be staked.
2.
Tubes with theoretical wear exceeding 10% must be-plugged.
3.
Tubes with theoretical wear exceeding 15% must be plugged and surrounded by plugged tubes.
4.
Tubes with measured wear 20% or larger must be plugged. Such tubes in high wear areas (first two rows and clusters of high wear tubes) should be surrounded by plugged tubes.
-1679-400-002-00 Page 38 of 42
5.
Staked tubes should be surrounded by plugged tubes.
The theoretical tube wall wear at the end of Cycle 2 for these criteria are given in Table 1.
TABLE I Theoretical Tube Wall Wear for San Onofre Unit 2 Steam Generator Theoretical Wear, percent of Wall Thickness End of 1st Cycle End of 2nd Cycle 5
10 10 19 15 35 20 55 25 83 The tube staking and plugging in the central region is shown in Figures 15 and 16 based on these criteria. The figures also show the theoretical tube wear at the end of the second cycle _for Unit 2 Steam Generators 88 and 89. The theoretical wear at the end of the first cycle, shown in Figure 10, was used with the nonlinear model to obtain waar at the end of the second cycle. On these figures, numbers'in circles indicate wear depth in percent of tube wall thickness and WT denotes the tube has worn through (100% wear).
Tubes.were plugged ccording to these criteria, thus assuring that the steam generators can be operated through the second cycle with all ' unplugged tube wear remaining within the 64 percent criteria. The inner tubes at the central cavity boundary were staked to assure their structural integrity and preventive plugging of the tubes adjacent to worn tubes was used to provide defense-in-depth.
1679-400-002-00 Page 39 of 42 m,_
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REFERENCES L
1.
"The Mechanism of Fretting Wear," 1. F. Stowers and E. Rabinowicz, Trans. ASME, J. Lubrication Technology p. 65 (1973).
2.
Evaluation of. Steam Generator Tube To Diagonal Tube Spacer Strip Interaction and Wear," dated March 1985, prepared for Southern California Edison Company by Combustion Engineering, Inc.
1-3.
CALIPS0S Code Report Vol. 1 EPRI NP-1391, Research Project S129-1, April 1980, by Combustion Engineering, Inc.
4 "ATH05 - A Computer Program for Thermal-Hydraulic Analysis of Steam Generators. Volume 1: Mathematical and Physical Models and Methods of Solution. Volume 2:
Programmer's Manual.- Volume 3:
User's Manual,"
Singhal, A. K., et. al., EPRI-NP-2689-CCM, October 1982.
5.
" Vibration of Heat Exchanger Tube Bundles in Liquid and Two-Phase Cross Flow," M. J. Pettigrew and D. J. Gorman in Flow-Induced Vibration Design Guidelines, edited by P. Y. Chen, PVP Vol. 52, June 1981.
6.
"The Fatigue Strength of Members Containing Cracks," by W. J.
O'Donnell and C. M. Purdy, ASME Transactions, Series B, Vol. 86, No.
2,-May 1964.
7.
ASME Boiler and Pressure Vessel Code, Section Ill, Division 1, Nuclear Power Plant Components, 1983.
8.
" Bases for Plugging Degraded PWR Steam Generator Tubes," U. S. Nuclear Regulatory Commission Regulatory Guide, Office of Standards Development, Regulatory Guide 1.121, August 1976.
1679-400-002 Page 42 of 42
l:
I
. APPENDIX A TABLE A-1 l
LIST OF TUBE DEFECTS AT-BATWING ELEVATION (UNIT 2 STEAM GENERATOR 88)
R0W COLUMN ELEVATION
% TUBE WALL e
24 70 DH 37 24 70 DH 19 27 71 DC 24 27 105 DH 63 28 104 DC 33 28 104 DH 19
~
29 73 DH 36 29 73 DC 53
'31 75 DH 40 31 75 DC 24 31 101 DH
'45 31 103 DH 35 32 76 DC 46 32 100 DH 71
}
32 100 DH 25 33 77 DH
.2 j
33 99 DH 38 33 99 DC 26 33 101 DH 42 34 76 DH 38 34 76 DC 19 34 78 DH 43 34 78 DC 53 34 98-DH 19 4
35 75 DH 19 35 77 DH 48 1679-400-002-00 Page A-1 of A-6
l TABLE A-1 (continued)
LIST OF TUBE DEFECTS AT BATWING ELEVATION l
(UNIT 2 STEAM GENERATOR 88)
R0W COLUMN ELEVATION 1 TUBE WALL 35 79 DH 39 35 97 DH 38 35 97 DC 39 36 78 DC 22 36 80 DH 31 36 80 DC 28 36 96 DH 42 37 81 DC 26 37 83 DH 42 37 93 DH 21 37 93 DC' 42 37 95 DC 35 37 95 DC 52 37 95 DH 24 37 95 DH 40 38 82 DH 55 38 82 DC 23 38 84 DC 19 38 86 DH 19 38 86 DC 19 38 86 DH 19
~
38 88 DC 24
^
38 88 DH 19 38 90 DH 28 38 92 DH 37 38 94 DC 43 39 77 DC 19 1679-400-002-00 Page A-2 of A-6
l l'
TABLE A-1 (continued) l LIST OF TUBE-DEFECTS AT BATWING ELEVATION (UNIT.2 STEAM GENERATOR 88)
R0W COLUMN ELEVATION
% TUBE WALL 39 79 DC 35 39 85 DH 22 39 87 DH 29 39 87 DC 34 39 89 DC 22 39 91 DH 46 39 91 DC 19 39 93 DH 24 3,9 95 DC 22 39 95 DH 19 40 82 DH 19 40 86 DH 31 40 92 DH 24-40 96 DC 31 41 83 DH 35 41 87 DH 19 41 93 DH 40 41 95 DC 43 43 95 DC 28 45 87 DH 23 46 92 DH 19 49 77 DH 19 49 95' DH 28 49 95 DC 19 70 58 DC 62 88 112 DC 33 108 84 DH 19 1679-400-002 Page A-3 of A-6 L
m
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I APPENDIX A TABLE A-2 LIST OF TUBE-DEFECTS AT BATWING ELEVATION (UNIT 2 STEAM GENERATOR 89)
-R0W COLUMN ELEVATION
% TUBE WALL 27 105 DH 31 28 72 DC.
23 29 73 DC 22 29 73 DH 19 29 103 DH 51 29 103 DC 19 31 101 DH 59 31 101 DC 49 32' 76 DC 40 32 76 DH 19 32 102 DH 48 33 77 DC 19 33 99 DC 32 33 99 DH 46 34 76 DC 21 34 78 DH 48 34 78 DH 28 34 78
~ DC 19 34 98 DC 48 35 79 DH 37 35 79 DC 31 35 97 DH 48 36 78 DC 38 36 80 DC 43 36 80 DH 23 36 96 DC 37 1679-400-002-00 Page A-4'of.A-6
_ _ _ _ _ _ ~.. _ =.._-_.
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h TABLE A-2 (continued)
LIST OF TUBE DEFECTS AT BATWING ELEVATION (UNIT 2 STEAM GENERATOR 89)
R0W
.C0LUMN ELEVATION
% TUBE WALL
- 37 81 DC.
48 37 81 DH 42 i
37 83 DC 54 37 83 DH 33 37 93 DC 47 37 93 DC 19 37 95 DH 32 37 95 DH 56 38 80 DC 24 s.
d 38 82 DH 61 1
38 82 DC 19 38 84 DH 69 38 84 DC 58 l
38 86 DH 48 38 88 DH 40 38 90 DH 60 38 90 DC 45 38 92 DH 47 38 92 DC 22 38 94 DH 33 38 94 DC 37 39 79 DC -
51 39 81 DC~
33 39 '
83 DC 57 39 83 DH 22 39 85 DC 39 39-87 DH 48 1679-400-002 Page A-5 of A -
l l
TABLE A-2 (continued) i LIST OF TUBE DEFECTS AT BATWING ELEVATION
~
(UNIT 2 STEAH GENERATOR 89)
R0W COLUHN ELEVATION
% TUBE WALL 39 87 DC 28 39 89 DH
.64 39 91 DH 22 39 91 DC 95 39 93 DH 19 40 80 DC 38 40 86 DH 19 40 88 DH 22 40 90 DH 19 40 94 DC 19 41 89 DH 26 41 91 DH 44 42 88 DH 41 43 91 DH 25 44 88 DH 38 45 93 DH 38 46 88 DH 23 46 94 DH 33 48 168 DC
-34 49 91 DH 24 50 90 DH 19 77 93 DC 19
'101
-105 DH 38 108 42 DH 27 127 123 DH 19 143 67 DH 19 1679-400-002-00 Page A-6 of A-6
ApFENDIX B THICKNESS WEAR RATE EVALUATION Wear between the batwings and the steam generator tubes begins with he batwings r tate into the tube as illustrated in the sketch below BATWING-l
/
f/:////////
N+s-TUBE
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The parameters d, O and I can be related mathematically as shown below:
t
~
A = wear contact length v
(between batwing and tubes) 0 0 = tube wear angle d
l d = flaw depth into tube 0 = Arctan (d/t)
For small angles make the approximation Arctan (x) = x 0=
d/t (o in radians)
For convenience, define a new depth variable, D, which is the flaw depth taken as a percent of the tube wall thickness, 1679-400-002-00 Page B-1 of B-8
0=(f)'x100%
t = tube wall thickness Also, define 0.in terms of' degrees 0 = 57.296 Ot/1001 Rearrange ' terms to solve for D.
D = (5.296 ) 0, t = tube wall thickness
= 0.048 in n
D = 36.36 10 (0indegrees) 0 Oue to the small angle approximation the flaw depth and wear angle are linearly proportional. The constant of proportionality S P is itself proportional to the contact wear length, 1.
This relationship is sketched in the plot to the right 1
The relationship between D, 0 and A can be used to assess data obtained from~ operating steam generators. Depth versus wear angle measurements for steam generator Units 88 and 89 taken from Reference 2 are shown-in Figures 8-1 and B-2. As expected these data exhibit a degree of scatter.. Also, no data is available for depths below 20%. However, as indicated above, the overall pattern of the measured data should be linear passing through the origin of the D vs. O plot. Accordingly a least souares linear fit of the data was performed for a line passing through the origin. These least squares fit lines are also shown in Figures B-1 and B-2.
The wear contact lengths obtained from the linearized results are:
1679-400-002-00 Page B-2 of B-8
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1679-400-002-00 Page B-4 of 8 i+
r Slope of Steam Generator Linear Fit A
Unit (1 Depth / Degree)
(Contact length) 88 31.33 0.86 in.
89 35.75 0.98 in.
The fully developed contact length between the tube and betwing 'is 4 inches. Therefore..t could physically take on values ranging from zero to 4 inches. The values computed above f all well within this range.
Initial wear with the batwing flat against the tube corresponds to a zero wear angle and begins with scraping and developing into an elliptically shaped wear area. The wear data shows that the' length of the wear scar is about one inch.
The derivation below shows~that the "00Al-ROT" curve in' Figure 12 applies for any constant length of wear scar, independent of wear angle.
The relationship between the contact length and the wear volume is also of interest. The wear volume in a tube can be expressed as follows, Reference 2:
V = tan (SI"* ~ *COS* * '" *)I 3
Dt
& = Arccos (1 g00r) r = tube radius = 0.375 in.
The small angle approximation can be used again tan 0 = 0 (in radians)
= Ot/1001
= 0/2083t 1679-400-002-00 Page B-5 of B-8
l Rewriting the wear volume equation:
i 083W (sine - 4cose * "3 *)
V=
9 208 "
(F(0) where F(D) = (Sin $ - (Cost S'" *)
=
D 3
After considerable manipulation the derivative of the wear volume with respects to flaw depth is obtained:
h = 2083ir' [Dc'(esine - sin 2 cose) - F(D)]
g 4
de t
+ = g = 100r/l - (1 - Ot/100r)2 Of interest is the rate of change of the flaw depth. The time rate change of the flaw depth is proportional to the derivative of the flaw depth with respect to the wear volume for a constant wear rate.
= Rate of change of flaw depth (i.e., thickness wear rate) a h = 20 31r3 [De'[4 sine - sin 24cos() - F(D)]~
The wear rate expression above indicates how the flaw depth wear rate depends on the wearing contact length A.
The wear rate is linearly proportional to the inverse of the contact length. This means that when the thickness wear rate is normalized (as is done in Figure 12), the effect of I cancels out. The reduction in thickness wear rate due to the increase in scar area is therefore identical for any rotational wear scenario.
Thus, it is safe to take credit for this thickness wear rate reduction mechanism in projecting future wear.
1679-400-002-00 Page B-6 of B-8
Other wear scenarios have been considered where the initial wear angle is nonzero Reference 2.
For these cases D varies linearly with 0 but is not proportional to it.
Such weariconfigurations assume that the batwing is cocked between tubes at the beginning of life. The D vs. O behavior of l
.such scenarios are compared with the least square fit results in Figure l
B-3.
The nonzero-initial angle wear scenarios predict a greater thickness wear rate at the beginning of life. However, they also predict a greater reduction in the thickness wear rate as wear progresses.
i For any wear scenario, the decrease in the thickness wear rate is used as a factor in predicting long-term wear. The basic correlation is that the greater the decrease in the thickness wear rate, the smaller the predicted long-term wear. For second cycle wear predictions, then the most conservative behavior is the scenario _which predicts the smallest decrease in the thickness wear rate. As Figure 12 indicates, the scenario evaluated in this Appendix demonstrates the smallest decrease in thickness wear rate and thus provides the most conservative prediction of future wear.
1 1679-400-002-00 Page B-7 of B-8
0'Donnell & Associates, Inc.
Pittsburah Pennsulvania FLAW DEPTH US. TUBE WEAR ANGLE LEGEND 100 f
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. TUBE WEAR ANGLE (DEGREES)
FIGURE B-3 FLAW DEPTH VS TUBE WEAR ANGLE