ML20217K025

Rev 1 to A-SONGS-9416-1168, Thermal Hydraulic Analysis of SCE SONGS Unit 3 SG W/Degraded Eggcrates

ML20217K025
Person / Time
Site:	San Onofre
Issue date:	10/16/1997
From:	SOUTHERN CALIFORNIA EDISON CO.
To:
Shared Package
ML20217J936	List: ML20217J931 ML20217K008 ML20217K025
References
A-SONGS-9416-11, A-SONGS-9416-1168-R1, NUDOCS 9710220363
Download: ML20217K025 (479)

Text

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ENCLOSURE 3

Thermal-Hydraulic Analysis of the Southern California Edison San Onofre Nuclear Generating Station Unit 3 Steam Generators with Degraded Eggerates A-SONGS-9416-1168 October 16,1997 ETA "Reni! Ha86 Enc PDR

3

SUMMARY

OF CONTENTS Report 37 Pages Appendices 0 Pages Attachments 475 Pages EVALUATION OF SOUTHERN CALIFORNIA EDISON SONGS UNIT 3 STEAM GENERATORS WITH DEGRADED EGGCRATES A-SONGS-9416-1168, Rev.1 l

Qt.ahty Class: QC-1 (Safety-Related)

PURPOSE: To evaluate the varicus implications en the steam generator associated with degraded eggerate tube supports for SONGS Unit 3.

This Design Analysis is complete and verified. Management authorizes the use ofits results.

PIGPARED BY: D. P. Pratt DCh DATE: 9 29 d'l VERIFICATION STATUSt COMPLETE The Safety Related design information contained in this document has been verified to be correct by means of Design Review using the Checklist in QP-3.4 of QPM-101.

Name D. P. Siska Signature ~

Date f-29'97 Independent Reviewer APPROVED BY: T. M. Taylor @$/E DATE: F M7 * '7 7

/

ABB COMBUSTION ENGINEERING CHATTANOOGA, TENNESSEE This document is tbc property of ABB/ Combustion Engineering, Chattanooga, Tennessee, and is to be used only for the purposes of the agreement wi'h ABB/CE pursuant to which it h fumished.

CSE 97 257 o . ,

A. SONGS-9416-1168. Rev.1 Page 2 of 37 RECORD OF REVISIONS

i. , ,

PARAGRAFd(S) PaEFARED- .INDEFENDENT .ArraovtD

~ NousER DATE 'INyoLVED ' BY- REYlEWER ~ BY' o ,; a -

7 0 6-4-1997 OriginalIssue D.P. Siska J.L. hds K.M. Rajan 1 82997 5.1,6.1,6.2, D.P. Pratt D.P. Siska T.M. Taylor Attachments A, B,

C, D, and E l

CSE 97 257 I

a

k A-SONGS-9416.ll68, Rev.1 Page 3 of 37 JABLE OF CONTENTS

Page 1.0 OBJECTIVE..............................................................................................................4

2.0 ASSESSMENT OF SIGNIFICANT DESIGN CHANGES................................................... 7 3.0 AN ALYTI CAL TE CHNI QUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. 8 4.0 S E LE CTION O F D ESI GN INPtTTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. . . 9

~

5.0 ASSUMPTIONS.....................................................................................................10 6.0 SUMMAny OF RESULTS 3

} 6.1 Flow Induced Vibration Analysis . ..... ..... . .................. .. .. .. . ..... .............. ...... ... 13 6.2 Sin 3 e1 Tube LOC A A nalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....... ... .. ...... .... . . . ... . . . . .. . ... .. I 8 6.3 Fui Bt..Ge LOCA Analysis (Eggerate Model) .............................................. 20

6,4 Thermal Hydraulic Analysi s . . . . . ... . . .. . . . . . .. . . .. . . . . . . . . .. . . . . . . . .. . . . . . . . .... . . . . . . ... .. .. . . .. . . 23

, 6.5 1. ao se Parts Evalu ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

6.6 Other Consideratio n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3

) 7.0 - RESULTS / CONCLUSI ONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6

8.0 REFERENCES

........................................................................................................,37 Attachment A CSE-97-254, Emluation ofFlow Induced Vibtation in the Southern Cahfornia l Edison SONGS Steam Generators with DegradedEggcrates.

Attachment B Ct,E-97-211, Emluation ofMaximum Tube Stresses During a LOCAfor Southern

Cahfornia Edison SONGS Steam Generators with Degraded Eggcrates.

1 Attachment C CSE-97-255, Emluation ofa LOCA on the Tube Bundlefor Southern Cahfornia Edison SONGS Steam Generators with DegradedEggcrates.

Attachment D CSE-97-253, Thermal-II)&aulie Analysis of the Southern Cahfornia Edison i SONGS Steam Generators with DegradedEggcrates.

Attachment E Design Analysis In-Process Approvals, Verification Plan, Design Analysis Verification Checklist, and Reviewer's Comment Form (included in QA Record

! copy only)

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A SONGS 9416 Il68 Rev. I Page 4 of 37 1.0 OBJECTIVE This report provides a summary of analyses performed by ABB Combustion Engineering to evaluate the effect of operating the San Onofre Nuclear Generating Station's Unit 3 (SONGS 3) steam generators (see Figure 1-1) with degraded eggerate tube supports.

During the pre-chemical cleaning inspection of the SONGS 3 steam generators, degradation of the peripheral eggerate tube supports was documented by visual inspections. Since the eggerates provide support to the tube bundle (i.e., the primary pressure boundary), significant degradation may result in unacceptable tube vibrations during normal operation er unacceptable tube stresses during accident conditions. The analyses contained herein document that the design basis requirements associated with the original design and fabrication of the SONGS 3 steam generators are satisfied, even with the eggerates in a degraded condition. Specifically, the attachments to this repon document the following:

Attachment A: Analysis of flow induced vibration of specific tubes during normal operation to verify there will not be unstable tube vibrations or significant wear at the tube to tube support interface. This analysis assumes two consecutive eggerates are missing while the tube is in service and three consecutive eggerates are missing while the tube is plugged and staked (stabilized). Depending on the specific tube involved, one additional eggerate may be missing and still shown to be acceptable. However, most tubes will not show acceptable results with three or four eggerates missing. It has been further assumed that all tubes that are plugged because of missing (or ineffective) eggerates will be stabilized. The analyses are similar to those documented in Reference 1 but have been updated to reflect state of the art analytical techniques. A matrix of different tubes and missing eggerate combinations were analyzed to bound worst ca::e inspection results.

Attachment B: Analysis of the LOCA and Safe Shutdown Earthquake (S"3) on a specific steam generator tube. This analysis addresses the combined LOCA and SSE loads on tubes in several ditTerent rows to verify that the draft Regulatory Guide 1.121 criterion (three times normal operating AP) is still the bounding criterion for steam generator tube plugging. That is, analysis of a 64% through-wall thinned degraded tube must be shown to have acceptable stresses during combined LOCA and SSE loadings. For those tubes that are captured by eggerate 10, this analysis assumes that eggerates 9 and 8 are ineffective. For those tubes not captured by eggerate 10, the analysis assumes that the top two eggerates providing support for that particular tube are ineffective. This analysis is similar to that documented in Reference 2.

CSE 97 257

A.SONGSo9416-1168 Rev.1 Page 5 of 37 1.0 OBJECTIVE (Continued)

Attachment C: Analysis of the effect of the combined LOCA and SSE on the overall structural integrity of the eggcrates. For this analysis, an analytical model of eggerates 0911 and 10H were constructed to determine the stresses on the ir dividual eggerate lattice bars. Only the 09H and 1011 eggerates were necessary because the effect of the accident is significantly attenuated further down in the tube bundle. Once the model was developed, individual eggerate lattice bars were remove or thinned and the redistribution ofloads was evaluated. This analysis was performed to verify that, even with significant degradation ofindividual eggerate lattice bars, the overall structural integrity of the eggerates is not adversely affected. This analysis is similar to that documented in Reference 3.

Attachment D: Thermal hydraulic analysis of the SONOS 3 steam generators using the ATHOS3 computer program. This analysis consists of two parts. Part 1 is the analysis of a clean (post-chemical cleaning) steam generator and is used as input to the flow induced vibration analysis. Part 2 contains ATHOS analyses of a fouled (pre-chemical cleaning) steam generator and are used as input to the SCE investigation of cause.

In addition to providing a summary of analyses perfonned to evaluate the effect of degraded eggerates, this report addresses those areas previously evaluated by References I through 4 that have not been specifically reanalyzed in the Attachments (e.g., the efTect of a hiain Steam Line Break). This report is shows that the degraded eggerates in the SONGS 3 steam generators do not adversely affect their ability to perform their design function and that all original design criteria are satisfied.

CSE-97-257

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AoSONGS-9416-il68. Rev. I Page 6 of 37

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A SONOS 94161168. Rev. I Page 7 of 37 2.0 ASSESSMENT OF SIGNIFIC ANT DESIGN CIIANGES The steam generator internal geometry for each of the analyses presented in the Attachments are taken from the original ASME Code Design Report described in Reference 1. The only differences are assumptions regarding the effectiveness of the eggerate supports which are addressed in the Attachments. Specifically, the flow induced vibration analyses (Attachment A) assume, depending on the particular tube, that one, two or three adjacent eggerates are ineffective.

The single tube LOCA evaluation (Attachment B) assumes eggerate 10 is effective for those tubes that are captured by that eggerate and that eggerates 8 and 9 are ineffective. For those tubes that I

are not captured by eggerate 10, it is assumed that the top two eggerates are ineffective. For the full bundle LOCA analysis (Attachment C), it is assumed that eggerate 10 is effective and, therefore, that eggerate 9 (which has higher LOCA loadings than the lower eggerates) is the sost limiting.

The operating conditions used in the thermal hydraulic analysis in Attachment D a*e taken from actual SONOS 3 Cycle 4 data (918.8 psia steam pressure) for the " clean" steam generator and l from actual Cycle 8 data (847 psia steam pressure) for the " fouled" steam generator. References for specific operating conditions or other design changes assumed m the individual analysis are documented in the Attachments.

CSD97 257 (hv

l A. SONGS >>416,1168. Rev. I l'a8e 8 of 37 I 3.0 ANALYTICAL TECHNIQUES

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A SONGS 9416 il68.Rev.1 Page 9 of 37 4.0 SELECTION OF DESIGN INPUTS The original plant design conditions are taken from Reference 1. The operating conditions listed below ha"e been taken from actual plant operating conditions (see Attachment D) to simulate conditions before and after eggerate degradatiori was documented.

4.1 Design Conditions Primary Operating Pressure: 2250 psia Primary Inlet Temperature: 611 'F Primary Outlet Temperature: 553 'F Secondary Pressure: 900 psia Feedwater Temperature: 445 'F Primary Design Pressure: 2500 psia Primary Design Temperature: 650'F Secondary Design Pressure: 1100 psia Secondary Design Temperature: 560 'F Tubesheet Differential Pressure 2250 psia 4.2 " Clean" Operating Conditions (Cycle 4 - July 1989)

Prima:y Operating Pressure: 2250 psia Primary inlet Temperature: 605.6 'F Primary Outlet Temperature: 553.2 'F Secondary Pressure: 918.8 psia '

Feedwater Temperature: 422 'F 4.3 " Fouled" Operating Conditions (Cycle 8 - October 1995)

Primary Operating Pressure: 2250 psia Primary inlet Temperature: 605.8 'F Primary Outlet Temperature: 552.2 'F Secondary Pressure: 847 psia Feedwater Temperature: 422'F Other design inputs used in a ::pecific analysis, which reflect degraded conditions, are specifically addressed in the individual Attachments.

CSE-97 257

A SONGS-94161168.Rev.1 Page 10 of 37

').O ASSUMPTIONS The assumptions used for the analyses contained herein are documented in the individuJ Attachments to this report. A summary of those assumpticas are described below.

5.1 Flow Induced Vibration Analysis (Attachment A)

1. Conservatively, no credit is taken for eggerate rotational restraint in the ANSYS modeling of steam generator tube boundary conditions.

2. The largest value of virtual mass coefficient allowed per Ref. 2 is used in the effective mass calculation. This is conservative since it lowers the natural frequency of the tubes.

l 3. Tubes in row 51 or greater need only to be modeled from the tube centerline (1/2 l model) sit ce the frequency of the vertical span , on the hot side, is not affected by tube supports on 'he cold leg side. Tubes in row 51 or less are full models which are needed to accurately calculate asymmetrical modes.

4. Additional damping, due to parallel flow induced vibrations, averages about 0.5 percent and was conservatively neglected in the calculation of tube displacements and critical velocities.(Ref.18). .

5. No credit is taken for critical velocity increases due to the influence of structural variations. Introduction of frequency differences between adjacent tubes (e.g. inactive eggerates) can increase the critical velocity for instability by as much as 4 J percent.

(See paragraph N-13316 of Ref 8).

6. Integration of flow velocities across the 90 degree tube bends adjacent to the batwing supports do not contribute significantly to the effective velocity along the venical leg because the tube bend out-of plane displacements are much smaller than the v rtical spans with inactive eggerates.

7. The most conservative instability constant for ABB-CE tube bundles (K = 3.2) is always used for calculating critical velocity acros the tube vertical legs regardless of flow orientation angle.

8. Appendix N of the ASME Code Section Ill,1995 Edition is used in this repon as a convenient one source reference for current FIV methodology. Appendix N references several authors and technical papers in presenting equations and methods recommended as appropriate for the type of analysis presented in this report. This reference is not used to develop allowables or acceptance criteria different than the applicable 1971 Edition of the Code (Ref. 8) for the original steam generator Design Report (Ref.1).

CSE-97 257 J

A SONGS-94161168 Rev.1 Page 11 of 37 5.0 ASSUMPTIONS 5.2 Single Tube LOCA Analysis (Attachment B) ,

1. De virtual mass is assumed to remain constant from tube to tube.

2. The entire friction load is assumed to act upe i the tube at the top centerline node.

! 5.3 Full Bundle LOCA Analysis (Attachment C)

1. Conservatively, the LOCA+SSE loads are applied to the eggerate support assemblies as static loads, without taking credit for the differing dynamic responses of the tubes and the eggeraa support assemblies.

2

2. Conservatively, for Numbe. i eggerate analysis, the degraded strip thickness for all strips that are identified to have 10 to 50% thickness remaining, are modeled as having only 10% thickness remaining. Similarly, all strips that are identified to have greater than 50% thickness remaining are modeled as having 50% thickness remaining.

! 3. For the load case (Case 2A) representing the hot leg LOCA which results in a net tension load on the degraded side (hot-side) of the eggerate, the slots in the 2 inch strips can be simulated by assuming 2 inch strips to be 1 inch strips.

4. The maic:ial behavior for the strips is represented by a tri-linear stress-strain curve.

i 5.4 Thermal-Hydraulic Analysis (Attachment D) i

1. '.h. Ad("i3 model includes 161 plugged tubes per one-half steam generator. The 3 plugglig locations are based on Reference 9.

2. The steam generator operating conditions are those listed in Table 4-1 (References 3

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and 10).

3. The p'imary flow rate, at 100 percent power, is assumed to remain constant at the value 6

in Trl ,le 4-1 (78.198 x 10 lbm/hr per steam generator) for Cycles 4 through 9.

4. The carry-over and carry-under values used for the ATHOS analyses are 0.25 percent of the steam flow and 0.75 percent of the downcomer flow, respectively.

5. The normal water level of 36.552 feet above the tubesheet is assumed for all cases.

6. The two-phase flow on the secondary side is homogeneous, which is one of the options of ATHOS3, The homcgeneous two-phase flow model is adequate to investigate the effects of eggerate erosion and tube outer surface and eggerate strip fouling.

CSE-97 257

A SONGS-9416-1168.Rev. I Page 12 of 37

- 5.0 ASSUMPTIONS

- 7. Tube fouling on the primary side is assumed to 1.e negligible.

8. As a result of the chemical cleaning, the Unit 3 steam generators are expected to recover approximately 70 psi of steam pressure and operate at the similar conditions as Cycle 4, prior to the observed pressure reduction phenomena.

9. For the post-chemically cleaned Cycle 9 operation, the tubes are assumed to be free of tube outside surface fouling and the eggerate strips are assumed to have a 20 percent decreased thickness, from 90 mils to 72 mils.

l CSE-97-257

A SONGS-9416-Il68, Rev. I Page 13 of 37 6.0

SUMMARY

OF RESULTS This section contains a summary of the results of the analyses performed to justify the safe operation of the SONGS 3 steam generators with degraded eggerates 6.1 Flow Induced Vibration Analysis During normal operation of the SONGS 3 steam generators, the eggerate tube supports prevent significant tube vibration that could lead to tube wear or, in the worst case, fluid-elastic instability. In CE steam generator tube bundles, the areas most susceptible to flow induced vibration are peripheral tubes just above the tubesheet and the horizontal sections of tubes in the upper bt ndle. Both of these regions have significant cross flow.

Feedwater and recirculation flow in the downcomer enters the tube bundle at the secondary face of the tubesheet and flows radially inward before it turns up as it is heated.

As a result, the peripheral tubes are subject to significant cross flow and must be evaluated for flow induced vibration. However, since the tubes are securely supported at both the tubesheet and the first eggerate, the assumptions made regarding flow induced vibration for the original ASME Code design report for the SONGS 3 steam generators (Reference 1) remain valid. Thus, reanalysis of flow induced vibration is this region of the steam generator is not necessary.

Once the secondary system flow enters the tube bundle it turns upward and is l predominantly axial flow with small radial and circumferential components. As the flow reaches the upper tube bundle it encounters the horizontal tube region and once again becomes cross flow. Flow induced vibration in this region is limited by the vertical grid supports, the batwings and, to a lesser extent, the upper eggerates (9 and 10). Since the vertical grids, batwings and eggerate 10 have not been significantly degraded, reanalysis of flow induced vibration in this region of the steam generator is not required, but has been included for information.

In the original ASME Code design report cross flow velocities in the straight tube sections and their effect on flow induced vibration were not evaluated. One reason the cross flow velocities were not evaluated was because the thermal-hydraulic analytical tools available at the time the design report was written (1976) were incapable of calculating these flows with acy degree of accuracy. As a result, the vibrational supports were conservatively designed based on previous operating experience. This design has proven effective not only at SONGS 3 but at all other CE-designed steam generators since flow induced l vibration has not been a significant problem.

The secondary system flow up the tube bundle is primarily axial but lessor components of cross flow exist. The flow induced vibration analysis, contained in Attachment A, conservatively assumes that two, or sometimes three, eggerates are ineffective. Hence, long spans of unsupported tubes have been postulated and evaluated as being acceptable.

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i 4

A SONGS 9416-1168 Rev.1 Page 14 of 37 -

6.0

SUMMARY

OF RESULTS 6.1 FlowInduced Vibration Analysis The longer the span the less energy it takes to cause lateral displacements in the tubes and sustain vibration. Accordingly, the analysis in Attachment A also addresses potential flow induced vibration resulting from these small cross flow velocities inherent in the tube bundle. In this analysis it has been assumed that the vector resultant of both the radial and

• circumferential velocity imparts energy to the tube.

Table 6.1-1 summarizes the results of the calculations of flow stability for the nineteen selected tube rows based on worst-case geometry. The results indicate that twelve tube rows have stability ratios above the limit of 1.0 when it is assumed that the top two eggerates are ineffective. Tube rows 83 and 110 were the most critical exhibiting a ,

stability ratio 1.13. When these two rows were evaluated for a single ineffective eggerate, the stability ratios dropped to 0.59 anJ 0.64 respectively. This demonstrates that the remaining tube rows will exhibit even greater margins against instability with only one inactive eggerate.

Several other tube rows exhibited stability ratios ofless than 1.0 with the top two eggerates

- inactive as shown in Table 6.1-1. However, some tube rows which wem unacceptable with the top two eggerates missing, showed acceptable stability ratios if the top eggerate was active and the next two inactive. Examples of this assumption are tu6e rows 147 and 120 widt stability ratios of 0.73 and 0.78 when the upper most eggerate was effective.

Results of the analysis for staked tubes show a Stability Ratio less than 1.0 for the case with three ineffective eggerates. The results indicate a Stability Ratio of 0.997 for the bounding case of tube row 83. Tube row 147 is also acceptable in the staked condition with four ineffective eggerates if the top two eggerates (9 and 10) are effective.

Results of the cross flow evaluation of the horizontal spans of tube rows 83,110 and 147 l '

are included in Table 6.1-1. The spans are supported by the vertical grids and batwings and are not significantly affected by the condition of the eggerates. The results indicate a stability ratio ofless than 1.0 for the worst case.

The displacements calculcted for cross flow and parallel flow (and the resultant) are shown in Table 6.1-2. The magnitude of the cross flow displacements are very small(typically 1 to 3 mils) especially for the large span lengths. The displacements due to axial flow are shown to be larger due to the lacpr axial velocities and the larger than usual spans. The combined displacements show resultants in the range of 10 mils except for the staked tubes. Dased on ABB/CE operating experience, excessive tube wear at eggerate tube supports does not occur when stability ratio's are less than 1.

CSE-97 257

A SONOS-9416 Il68 Rev. I Page 15 of 37 6.0

SUMMARY

OF RESULTS 6.1 Flow Induced Vibration Analysis The resultant displacements for staked tubes are approximately 22 mils as indicated in Table 6.2-1. This magnitude of displacement is not of concern for the staked tube and the calculated tube strestes are insignificant. Any wear associated with the staked tube is not significant because of the available wear volume of the stake.

The analysis concludes that all tubes are acceptable for FIV consideration with one eggerate being inactive. Also, Table 6.1-1 shows that many tube rows are stable with two inactive eggerates. The tube rows that exceed S.R. = 1.0 with two inactive eggerates have a maximum stability ratio of 1.13. The associated stresses are small and well below the  ;

fatigue endurance limit of the tube material. In cases where up to three eggerates are ineffective staking the tube is an acceptable repair to address FIV. It is acceptable to stake tube row 147 with four ineffective eggerates if eggerates 9 and 10 are effective.

This analysis also concludes that cross flow vibrations in the horizontal spans are not significantly affected by the condition of the eggerates.

CSE-97-257

A-SONGS-9416-Il68 Rev.1 Page 16 of 37 TABLE 6,1-1 FLUID ELASTIC INSTABILITY EVALUATION SUMMAfW FOR SONGS UNIT 3 SGs Tube Row Inactive r, Total Stability y,, y,,,gg,,,

No. Eggerates (Hz) Damping (in/sec) ' (in/sec) Ratio 3 147 10 & 9 10.9 0.0261 54.4 50.0 1.09 147 8&9 12.5 0.0255 39.1 53.4 0.73 147 7 &8 10.8 0.0261 29.6 43.8 0.68 147* 8,9,&l0 4.96 0.083 47 49.9 0.94 147* 5,6,7,& 8 3.14 0.084 21 28.0 0.75 147 " 10 & 9 56.1 0.014 216.6 493.7 0.44 145 10 & 9 11.4 0.0259 52.5 51.9 1.01 144 10 & 9 11.6 0.026 56.4 54.1 1.04 139 10 & 9 13 0.025 55.2 50.1 0.92 138 10 & 9 13.3 0.025 64.6 62.5 1.03 i 127 10 & 9 17.6 0.024 60.2 80.0 0.75 126 10 & 9 18.2 0.024 61.4 82.1 0.75 121 10 & 9 20.9 0.023 60.1 92.6 0.65 120 8&9 10.7 0.026 52.6 48.6 1.08 120 7&8 10.9 0.026 36.2 46.4 0.78 111 9&8 11 0.026 51.6 50.0 1.03 110 9&8 11.3 0.026 58.4 51.8 1.13 110 9 24.1 0.022 66.1 103.9 0.64 110 7&9 17.9 0.0237 48.2 72.6 0.66 110 ** 8&9 59.6 0.013 282.6 533.8 0.53 108 9&8 11.8 0.0257 57.9 53.8 1.08 94 9&8 16.6 0.0242 -53 73.1 0.73 93 9&8 16.9 0.0241 47.3 75.0 0.63 84 9&8 9.7 0.0265 41.4 42.5 0.97 83 8&7 8.4 0.027 42.1 37.1 1.13 83 8 18 8 0.0235 46.7 79.5 0.59 83* 6,7 & 8 3.86 0.084 37 37.1 0.997 83** 8&7 46.4 0.016 320.7 433.1 0.74 82 8&7 8.6 0.0269 41.9 37.9 1.11 70 8&7 11 0.026 48.7 48.2 1.01 49 7&6 7.9 0.0272 34 32.9 1.03 46 7&6 8.3 0.027 35.6 32.9 0.996 22 7&6 13.4 0.0252 31.5 52.7 0.60

• Indicates staked tube " Indicates critical mode for horizontal span cross flow CSE-97 257

A SONGS-94161168.Rev.1 Page 17 of 37 TABLE 6.1-2 PARALLEL AND CROSS Flow TURBULENCE DISPLACEMENTS FOR SONGS UNIT 3 SGs Tube Row Inactive A,r A6 An No. -Etscrates (mits) (mils) - (mils) 147 9,10 6.7 2.5 7.2 147 8,9 4.5 1.3 4.7 147 7,8 4.8 0.9 4.9 147* 8,9,10 19 2.6 19.2 147' 5,6,7,8 22 0.9 22.0 145 9,10 6.3 2.3 6.7 144 9,10 6 2.5 6.5 139 9,10 6.2 2.1 6.6 138 9,10 6.9 2.7 7.4 l

127 9,10 7.4 1.7 7.6 126 9,10 10 1.8 10.2 121 9,10_ 10 1.5 10.1 120 8,9 6 2.5 6.5 120 7,8 5 1.3 5.2 111 8,9 6.3 2.4 67 110 8,9 6.3 2.9 6.9 110 9 2.1 1.6 - 2.6 94 8,9 - 3.2 1.6 3.5 93 8,9 3.9 1.2 4.1 84 7,8 7.3 1.9 7.5 83 7,8 7.3 2.4 7.7 83 8 2.4 1.2 2.7 83* 6,7,8 22 2.0 22.1 70 7,8 5.5 2.3 6.0 49 6,7 10 1.8 10.2 46 6,7 4.3 1.8 4.7 22 6,7 2.9 0.6 3.0 Indicates staked tube pf Indicates parallel flow tb Indicates cross flow R Indicates resultant displacement CSE-97-257

AoSONGS-9416-ll68. Rev. I Page 18 of 37 6.0

SUMMARY

OF RESULTS 6.2 - Slagle Tube LOCA Analysis

'Ihe analysis presented in Attachment B of this report evaluates the effect of combined -

Loss of Coolant Accident (LOCA) with the Safe Shutdown Earthquake (SSE). The combined LOCA plus SSE analysis considers stresses prodeced by various phenomena.

These stresses are caused by rapid flow through the tubes, the dynamic response resulting from the impulse load occuning at the pipe break opening, SSL-induced accelerations, and differential pressure. Stresses from these loadings are combined and evaluated against the ASME Code allowables determined in accordance with Appendix F.

It should be noted that the loads associated with the LOCA plus SSE were nos part of the -

original design basis in Reference 1 for the secondary side components of the SONGS 3 steam generators because it was not required by Reference 12. The original evaluation for LOCA and SSE was performed to verify that the tube plugging criterion used by SONGS 3 of an indicated 44% (64% degradation minus 20% uacertainty) was adequate as required by draft NRC Regulatory Guide 1.121. The LOCA plus SSE evaluation was performed because it is the condition that results in the largest stresses on the tubes. The tube with 64% degradation is assumed to be uniformly thinned from OD wastage since that condition results in the highest overall stress on the tube during a LOCA.

With the assumption that eggerate number 10 is intact and provides effective support, the results presented in Attachment B show that all tubes meet the ASME Code Appendix F allowable with two adjacent eggerates ineffective,64% tube w311 degradation and no tubes plugged. For the tubes in rows 121 through 147, which pass through eggerate number 10, the most critical stress intensity of 69.68 ksi is calculated in tube row 146 with eggerates 8 and 9 assumed to be missing or ineffective. For tubes which do not pass through eggerate number 10, the highest calculated stress intensity is 77.91 and occurs in ',

tube row 120 for the case of the top two eggerates (eggerates 8 and 9 for this tube) ineffective. For the case of 1000 tubes plugged,107% flow and eggerate No. 9 ineffective, the maximum stress for the worst case tube row (Tube row 120) is 72.87 ksi and the Code faulted allowables are again met. The ASME Code Appendix F faulted condition allowable for primary membrane plus primary bending stress intensity of 1.44(.7SJ = 80.6 ksi (per Reference 2) is met in all instances.

If eggerates number 9 and 10 are assumed to be ineffective and no tubes are plugged, the tubes in rows 129 through 147 have unacceptable stress intensities with 64% wdl

' degradation. In this case the maximum tube wall degradation must be reduced to meet the allowable of 80.6 ksi.- For tubes in row 147, the maximum allowable wall degradation is 60%. In the other affected rows, maximum degradations of 61 to 63%, as -

shown in Section 7.5, are required to meet the ASME Code allowable.

__ =

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SUMMARY

OF RESULTS TABLE 6.2-1 LOCA PLUS SSE STRESSES ON SONGS 3 STEAM GENERATOR tunes mmmer

,. CODE ALLOWABLE .

7, MEFN. , c cY , ! TUBE ROW- ,,:DECRADATION BENDING STRESS. .

.- (%) . (Kst) - 39 A *

~(Kst)!

A (121 - 147) 146 64 69.68 80.6 B (116- 120) 120 64 77.91 80.6 C (85 - 115) 99 64 71.39 80.6 D (84) 84 64 59.51 80.6 E (52 - 83) 83 64 56.39 80.6 F (50 - 51) 50 64 42.18 80.6 O (24 - 49) 49 64 41.87 80.6 CSE-97 257 i

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OF RESULTS 6.3 Full Bundle LOCA Analysis (Eggerate Model)

The finite element eggerate modes for eggerate 9 and 10 were first developed to analyze the effect of the LOCA and SSE on the structural integrity of the eggerate. This analysis

, was performed to verify that the eggerate has not degraded to the point where it could break apart during an accident and cause collateral damage to the tubes. As described in

! Section 6.2, the single tube LOCA model previously demonstrated the ability of each steam generator tube (the primary pressure boundary) to retain their structural integrity.

The design analysis is performed utilizing the ANSYS finite element analysis software.

The two uppermost eggerates, that is, eggerate numbers 9 and 10 are modeled for analysis.

The models are detailed full scale models including all of the 1 inch and 2 inch strips, support rings, and the scallop bars that make up the eggerate support assemblies. The support conditions for the eggerate support assemblies at the outer edge at the baffle is duplicated by applying the appropriate support conditions representing the baffle stiffness and the support configuration. Only a 90 degree segment of the eggerate support assemblies is modeled, taking advantage of the symmetry conditions. The eggerate models are loaded by the reduced reactions to cold leg LOCA tube loads taken from the tube bundle analysis that was performed previously. Additional consideration is given to the effect of seismic SSE loads. ,

The worst time points from the LOCA analysis are analyzed for each eggerate to obtain the stress distributions in the eggerate support assemblies utilizing linear elastic theory. The initial stress runs were made considering intact eggerates with no degmded or missing strips.

In the first case, in order to prove that there would be a significant load redistribution in a support structure such as the eggerates, the eggerate models are somewhat arbitrarily modified to simulate the missing and/or degraded strip conditions at the outer periphery of the eggerates. The results indicated local areas of highly stressed strips. However, the eggerate support assemblics are highly redundant structures capable of a high degree of load redistribution. Therefore, as the structure is loaded and begins to plastically deform, the loads in the highly stressed region would be expected to experience some degree of redistribution. This load redistribution is investigated by making the highly stressed elements, or strips in the model inactive, and observing the changes in the stress distribution.

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SUMMARY

OF RESULTS 6.3 Full Bundle LOCA Analysis (Eggerate Model)

This pocedure provides an estimate of the true loading in the structure. An analysis to provide a more accurate picture of the final load and stress distribution in the eggerate structures would be an inelastic time history loading of the structures. However, this type of analysis for the whole eggerate support assembly is beyond the scope of this design analysis. A localized elastic-plastic analysis was performed for the degraded strips at the periphery of the support assembly, which is discussed below.

i In the second case, the eggerate geometry and the loads for the more critical eggerate support assembly (i.e., Number 9 eggerate) are modified to reflect the strip degradation around the periphery of the eggerate structure based on the actual results of the visual

( examination. The degraded strips are represented by elements which have only membrane l load carrying capability with clastic-plastic material properties. Both tensile and l compressive loads are evaluated. The resulting strip stress:s and strains are compared to

! the strip material allowables in order to show that the structure can withstand the LOCA plus SSE loads, even in the degraded condition, and that the displacement of the eggerate at the outer tube locations do not jeopardize the tube integrity.

The results of the first section of this analysis show the redistribution of the stresses which occurred were all below the 38,0 ksi range. Fully plastic strips were removed from the model while in reality, these strips would still carry a load compatible with their yield strength. Considering the small number of strips that were in the plastic range, an inelastic analysis of the full eggerate support structure would most likely also show a favorable redistribution ofloads.

The second section of this analysis was performed to show that the LOCA'plus SSE loads resulting from a hot leg pipe break would not cause unacceptable tensile stresses on the degraded eggerate at the outer periphery. This analysis was performed using conservative evaluations of actual eggerate strip thickness from the visual inspection. This evaluation showed a maximum membrane stress of 44.5 ksi and a maximum total strain of 3.1%

which is less than the allowable values of 55.0 ksi and 20% strain. Hence, the hot leg LOCA plus SSE condition will not affect the structural integrity of the eggerate.

For this case where most of the loading on the degraded strips at the periphery of the eggerate support structure is compressive, the resulting strip stresses are compared to the tensile strength of the strip material at temperature, and the total strain (elastic plus plastic) in the strips at the periphery of the eggerate support assembly are calculated to make sure that the resulting strains in these elements are acceptable. Additionally, the horizontal displacements at the periphery of the assembly are calculated and compared to the minimum clearances available between the peripheral tubes and the support ring, to ensure that the structural integrity of these tubes is not compromised. The results of these evaluatior.s are provided below.

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SUMMARY

OF RESULTS 6.3 Full Bundle LOCA Analysis (Eggerate Model)

Maximum Compressive Strip Stress = -51.1 ksi. H Su = 55.0 ksi.

(@ 1" strip with 10% thickness remaining)

Maximum Total (Compressive) Strain = 13.8% H Ult. Str4n = 20 %

(@ 1" strip with 10% thickness remaining)

Maximum Horizontal Displacement of Eggerate @ Outer Strips :

UY Minimum -

Row # Line # (Inch) -

' Gap (Inch) 147 8 0.011 0.132 146 13 0.015 0.160 143 22 0.020 0.163 134 37 0.058 0.174 119 52 0.072 0.196 The above results indicate that, under compressive LOCA+SSE loads resulting from a cold leg break accident, the tu5 " .ill not impact on the eggerate structure with its degraded strips at the outer periphery. Therefore, the eggerate remains stable and the structural integrity of the tubes is preserved.

In addition to the eggerate analysis, the welds between the eggerate and baffle and between the strips and eggerate rings were also analyzed and shown to meet the criteria for faulted condition allowables. This evaluation also demonstrated the ability of the vertical grids to adequately support the LOCA plus SSE loads.

)

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OF RESULTS '

6.4 Thermal-Hydraulie Analysis

I

Thermal-hydraulic analyses of the SONGS 3 steam gent.rators are performed using the l ATHOS3 Mod 01 computer program. There are two primary objectives for performing j these analyses:

• To determine the fluid dynamic conditions experienced by the peripheral tubes where l

j eggerate degradation is observed. The ATHOS3 calculated secondary side fluid

velocities, densities and dynamic viscosities as well as the primary fluid densities are used as input to the flow induced vibration analysis of the tube bundle with degraded F eggerates. These analyses are performed on a post-chemically cleaned steam generator i that is assumed to have no significant deposits but somewhat degraded eggerates. This j analysis is applicable to SONGS Unit 3 Cycle 9 operation. -I

! . Perform limited evaluations with SONGS Unit 3 Cycle 8 operating data and three

} . different tube bundle fouling assumptions in an attempt to better understand the j eggerate degradation phenomenon.

t :-

! The results of these analyses are presented in Attachment D and were used as input to the flow induced vibration evaluation in Attachment A anel in the investigation of cause

~

[ performed by Southem California Edison.

1 CSE-97-257 j.

. _ _ _ _ _ _ _ ~ ~ . . . _ _ _ _ _ . _ . _ . _ _ _ . _ _ _ . _ _ _ _ . _ _ _ _ _ _ _ _ _ _ . . _ _

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OF RESULTS '

6.5 Loose Parts Evaluation-i-

_ABB CE has evaluatect the impact of operating the SONGS 3 steam generators with

, potential loose objects from eggerate degradation and concluded that it does not represent a

significant safety hazard and there will be no significant damage to the steam generator L tubes. This conclusion is based on the following discussion.

i Potential Causes of Damage by Loose Objects I 6.5.1 i.

l ABB CE's experience in evaluating potential loose objects in the secondary side of the steam generator indicates that by the ead of the plant operating cycle the loose objects will

. find a preferred loc

tion. That is, they will find a " stable" position where a static position l~ balance exists between the size and weight of the loose objects and the local flow fields.

{ Therefore, the most likely scenario is that the loose object will remain where it is and begin j to wear the adjacent tubes once power operation is resumed, or it will migrate to another region of the steam generator. This scenario is evaluated hereht as well as the other

1. scenarios described below.

Given the geometry of the eggerate strips, the most likely size of a loose part would be appoximately one inch by two inches by 0.090 inches. His size is based on a two-inch

,- strip eroding through at the slot. However, the evaluation performed herein conservativ:ly

j. assumes the size of a potential loose object from eggerate degradation is a two-inch strip i

approximately six inches long. His value is based on the manner in which the eggerate -

l strips are welded (every third intersection), the length of the strips in the peripheral regions,

j. and the fact that there must be degradation of a minimum of at least three intersecting two-

- inch strips to release a strip of this size. A review of the inspection data indicates that -

evaluation of a six-inch strip is very unlikely thereby adding significant corservatism to this

[ evaluation.

{ Amuning a six-inch strip has degraded to an average width of 45 mils, it would weigh

!- approximately 3 ounces. This assumption appears reasonable since the degradation of the j -

strip would have to be complete (90 mits) at both ends. Additional conservatism is r - contained in this evaluation by assuming that the degraded strip is at the top of the tubesheet i where the flow rates are the highest. The actual flow rates in the area of the degraded i eggerates are significantly lower (by up to a factor of five) than at the top of the tubesheet.

L Although loose objects generally find a preferred location and stay there, it is possible that i they could dislodge (or erode into sma!!er pieces) and migrate to other areas of the steam i generator. - As a result, it is prudent to evaluate the potential consequences associated with

migration of the objects to other areas in the secondary side of the steam generator. There are L three possible scenarios which describe how loose objects have historically and

~

experimentally interacted with the steam generator tubes. These scenarios are described herein:

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i A SONGS 9416-1168, Rev.1 Page 25 of 37 6.0

SUMMARY

OF RESULTS . '

6.5 Loose Paits Evaluation A. Scenario 1 The object becomes dislodgedfrom its current location (in its current size or smaller pieces),

reenters theflowfield and randomly impacts tubes as it moves about in the steam generator.

! ABB CENO has a substantial amount of experimental data relating to this scenario from prototypical tests that simulated loose objects in the steam genemtor secondary side flow field. The first test was perfonned in 1976 and simulated a three ounce loose object (a tube guide) which was allowed to remain in the secondary flow field for an extended period of

time. The tube guide was 4.31 inches long and was made from tool steel, stainless steel and Tygon (a polymer). The tool steel in the guide was case hardened which would make it significantly harder that a degraded eggerate strip. The modeling criteria used for this test (equivalent dynamic pressure at the entrance to the tube bundle) was specifically applicable to the San Onofre steam generators.

The results of this test showed that the loose object randomly impacted the peripheral tubes as it moved about in the flow field. This test simulated two years of continuous steam generator operation and was later extrapolated to cover the entire operational life of the steam

_ generator. As the loose object impacted the tubes, its volume gradually became smaller. It was estimated that at some point the object would eventually disintegrate and simply add to the steam generator sludge inventory.

At the conclusion of the test, the tubes were removed from the model and inspected. The portions of the tubes exposed to the loose object showed evidence of uniformly distributed impacts over the entire area susceptible to impact. It was concluded from thls observation

. that the motions of the object in the flow field was random in nature. Th: tubes removed from the flow model were then examined for wear, hardness and general surface appearance.

Diameter and wall thickness measuremeuts did not indicate any measurable difference between tubes impacted by the loose object and tubes shielded from the impacts.

Exanunation of the tube wall microstructure showed a depth ofdeformation of only 1.0 to 1.5 mils. Degradation of surface hardness was limited to this depth with the remaining wall having a hardness value characteristic of the unaffected metal. Hence, it was concluded that a three ounce loose object would have no adverse effect on a steam generator over its entire operating life Further details regarding this test can be found in Reference 5.

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SUMMARY

OF RESULTS 6.5 Loose Parts Evaluation A te ;t similar to the one described above was repeated in 1980. In this test the three ounce object was replaced by a 20 ounce pipe cap moving in the downcomer flow adjacent to the tubesheet region. The downcomer flow field for this test was 12.5 ft/sec. Since this flow velocity is higher than what is calculated for SONGS 3 in the region of potential loose objects, ABB CENO has concluded the results of this test may be conservatively applied to SONGS 3.

Following this test, inspections of the tubes revealed very little differences from the pnwious test. Uniformly distributed impacts were evident on those tubes exposed to the loose object; however, no tube deformation measurement exceeded I mil in depth. In addition to inspection of the tubes, this test also used a Super 8 movie camera to record data conceming the motion of the pipe cap in the test model and to calculate the impact velocity of the cap on the tubes.

The results of this study indicated that the 12.5 ft/sec downcomer flow velocity resulted in a impact velocity of approximately 1.5 ft/sec. Any object significantly heavier than 20 ounces would probably not be entrained in the flow field but would simply remain on the tubesheet and rock back and forth in response to the downcomer flow. Additional information regarding this test may be found in Reference 6.

Based on the preceding discussion, ABB CENO has concluded that the potential loose object on the secondary face of the SONGS 3 tubesheet will not cause any damage to the heat transfer tubes from Scenario 1.

B. Scenario 2 A loose object rocks in theflowfield and repeatedly impacts a plugged tube which eventually loses its structural integrity and collapses. The collapsed (but plugged) tube in turn becomes a whip and ruptures its unplugged neighboring tube.

This scenario is the "Ginna Incident" and requires a fairly heavy object located adjacent to a plugged tube and in a flow field capable of moving or rocking the object. Only plugged tubes without through-wall defects are vulnerable to this failure mode because their internal pressure is atmospheric. An active tube has an internal pressure of 2250 psia while a plugged tube with a through-wall defect has an intemal pressure of approximately 900 psia to provide support against the repeat-d impacts by the rocking object. Specific information relating to the incident at Ginna can be found in Reference 7.

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) 6.0

SUMMARY

OF RESULTS

?

i- 6.5 Loose Parts Evaluation ,

'Ihe object inside the Ginna steam generator (later identified as an orifice plate cut during a

downcomer rwnfication) had a weight exceeding three pounds. Although there is no

threshda weight above which one must be concemed with this failure mode, ABB CE has concluded that the results from the prototype testing described in Scenario 1 indicate that j the weight of a loose object must significantly exceed the weight of potential loose objects i- that may be generated by degraded eggerates. Therefore, ABB CE has concluded that i ~ potential steam generator tube damage resulting from Scenario 2 is not a credible event.

i l C. Scenario 3 I The object remains in it's current location and continues to wear the adjacent tubes:

or, it becomes dislodgedfrom its curre@ cation. finds another " preferred" location and initiates new wear scars o.. n?ve steam generator tubes.

As objects move in the flow field they will trJgrate to a region with a lower fluid velocity l

and become stagnant or less active than in their previous position. The highest flow fields are the entrance regions to the tube lane. Once an object enters the tube~ lane it either becomes lodged in place or moves inward to a lower velocity field.

l This scenario is more difficult to evaluate since it assumes that the object is dislodged and

again finds another location to initiate tube wear. In general, the object that is wearing on -

j' the steam generator tubes is itself undergoing wear damage. Although specific values (for the object as well as the tube) are difficult to predict and quantify, some critical characteristics such as the size and velocity profile can be bounded. That is, for the object j; to become dislodged from its current location it most likely has wom down to a smaller object or has broken into two or more pieces. Smaller objects are considered to be more -

favorable since they will have less potential to cause wear than the original object. In

addition to the object being smaller, any movement of the object will be toward a lower 4

velocity field. However, since these effects are difficult to quantify, the most consen*ative approach in evaluating this scenario is to assume that the object retains its shape and weight, moves elsewhere in the system and starts a wear phenomenon similar to the original one, i

As a result of the preceding discussion, evaluations of potential damage by potential loose

~

objects will be limited to wear on the steam generator tube (Scenario 3). For consenatism L it is assumed that the loose object somehow makes it to the tubesheet where it will

{ . encounter high 1

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SUMMARY

OF RESULTS l

6.5 Loose Parts Evaluation i dynamic forces. As discussed in Section 6.1 and 6.4 (Attachments A and D), the cross flow in the region of degraded eggerates is small; hence, there would be relatively small contact i forces between the postulated loose object and the tubes. In addition, it would be difficult for a loose object generated, for example, at eggerate 5 to actually reach the tubesheet.

Thus, evaluation of potential loose objects as if they were on the tubesheet is considered conservative.

1 6.5.2 Potential Tube Damage Assessment The problem with loose objects wearing the steam generator tube wdl is the potential for a through-wall defect and associated primary to secondary leak. The allowable tube wall degradation in the straight tube region between the tubesheet and the first eggerate (the area

! oflargest dynamic forces) can be conservatively calculated using the following methodology from Reference 8.

A. Normal Operation 4

~

Calculate the stress on the tube due to differential pressure; t

2

, Axial stress ([J = (b -P) + (2Rt) = 4.3 ksi Hoop stress ([n) = (b-P) + t = 9.2 ksi Radial stress ([g) = -(Pi + P2) + 2 = -1.575 ksi Where:b = inner radius of tube = 0.327 inches P i = primary system pressure = 2.25 ksi P2= secondary system pressure = 0.90 ksi

-P = P i - P 2= 1.35 ksi

R = tube wall fd radius = 0.351 inches t = wall thickness of tube = 0.048 inches i

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SUMMARY

OF RESULTS 6.5 Loose Parts Evaluation

- Calculate the stress on the tube due to thermal expansion;

[2= F + A = 0.3 ksi Where: F = dynamic force on tube = 0.032 kips (from Reference 1) 2 A = Area of tube = 0.106 in Calculate the stress on the tube due to seismic (OBE) event (values below taken from Reference 1 for consistency);

i

[, = (F, + A)(MnC + I) = 0.9 ksi Where:F, = seismic force = 38.0 lbr 2

A = Area of tube = 0.106 in Mn = tube moment = 9.0 in-lbr C = tube outer radius = 0.375 in I = tube moment ofinertia = 0.00655 in' Calculate the stress on tube due to loads at bundle entrance;

[, = MS + 1 = 0.8 ksi Where:Mr= tube moment = 14.1 lbf C = tube outer radiue = 0.375 inches I = tube ruomcnt ofinertia = 0.00655 in' The combined axial stress on the tube is the sum of the indisidual stresses, or:

[,(total) = 4.3 + 0.3 + 0.9 + 0.8 - 6.3 ksi Since the combined axial stress is less than the bending stress for differential pressure, the stress intensity ([n - [a) is goveming and the following equation for minimum wall thickness from Reference 8 applies:

t,(min) = -P b + (S y- 0.5(P i+ P ))

_ 2 = 0.017 inches Where: t,(min) = minimum required wall thickness

-P,b,P iand P 2have been defined previously Sy= Yield strength for Inconel 600 at 600CJF CSE-97-257

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OF RESULTS -

6.5 Loose Parts Evaluation l

Thus, the allowable tube wall degradation for normal operation is:

% allowable degradation = 100(0.0480 - 0.017) + 0.0480 = 64%

B. Accident Conditions For the main steam line break (MSLB) accident the tube is analyzed for the worst case assumption that the secondary side pressure goes to zero while the primary side pressure remains at 2250 psia. This assumption is very conservative since the primary system pressure will actually decrease significantly during this event because of the uncontrolled RCS cooldown. As shown in Attachment B, a 64% degraded tube will have acceptable consequences for a LOCA. Previous evaluations (Reference 10) show that the MSLB accident is less severe than the LOCA with regard to tube wall integrity. The equations used for this analysis are based on Reference 8.

t,(min) = -Pb + (0.7S, - 0.5(P i+ P ))

2 = 0.014 inches

~

Where: S, = ultimate tensile strength ofInconel 600 at 600 CJF A required wall thickness of 0.014 inches results in an allowable tube wall degradation of 71%. This value can be compared to leak and burst tests performed by ABB/CE for tubes that were degraded by 70% (Reference 9).

During these tests, two types of tube defects were tested to simulate the type of wear ora would expect from a tube support wearing on a tube. Both simulated defects were

machined flat spots; one defect was one inch in length and one defect was 0.5 inches in length and are representative of the type of wear that could be expected from a potential loose object.

Three-quarter inch OD,0.048 inch wall Inconel 600 tubing was used to constru:t the specimens. A milling machine was used initially to achieve the desired wear condition.

For those specimans that were leak tested, the last portion of material that was removed was done so with a file while the specimen was pressurized with w3ter.

The results of the burst tests showed a minimum value of 5700 psig was required before bursting. This value is over twice the maximum pressure the steam generator tubes will experience during the most severe accident conditions. Thus, there is a high degree of confidence that tubes with as much as a 70% wall thickness degradation will still have their required pressure retaining capabilities.

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SUMMARY

OF RESULTS 6.5 Loose Parts Evaluation It should also be noted that all 18 leak rate specimens (with the exception of two statistically invalid specimens) showed leak rates less than 1.0 GPM under differential pressures ranging from iG to 1760 psid. Hence, these tests showed that a through-wall defect would not suu 'enly leak in an uncontrolled manner.

6.5.3 Ev4uation of Safety Significance Previous secticns have addressed the potential effects that loose objects may have on tne steam genera'.or tubes. As discussed earlier, the most likely event is that the objects will simply wear .he adjacent tubes and would be unlikely to ever result in a through-wall defect. For purposes ofinformation however, ABB CE has evaluated the potential effects associated with a through-wall defect and determined that this postulated scenario will also have no effect on safety. This conclusion is based on the following discussion.

A design basis Steam Generator Tube Rupture (SGTR) accident as described in Chapter 15.6 of ae San Onofre Final Safety Analysis Report (FSAR) is defined as a double-ended guillotine break of a tube that results in a primary to secondary ler.k rate. Initial leak rates for tube ruptures of this magnitude can be as high as 300 to 600 GPM. ~ABB CE has performed prototypical laboratory testing to empirically determine the leak rate from tube defects that were il mded to simulate wear defects produced by tube supports. These tests are described in detail in Reference 9 and showed that in virtually all cases a through-wall defect will result in a leak rate less than one GPM and would not suddenly leak in an uncontrolled manner. These test results have been further substantiated by the slow steady leak rate that resulted from a through-wall defect in tube 143-85. Thus, the leak rates that could result from weac defects would be more of an operational concem than a safi ty Concern.

As a result, the potential tube defects should not be considered as a possible initiating event of a SGTR accident but, rather, as a potential increase in the normal secondary system radionuclide inventory that is used as an initial condition for other Chapter 15 accident analyses. Secondary system radionuclide inventories assumed in the FSAR Chapter 15 safety analysis are based on one percent failed fuel and a continuous one GPM primary to secondary leak rate. As discussed aoove, the most severe leak rates associated with typical through-wall wear defects are less that one GPM. Since operation with one percent failed fuel is highly unlikely, actual secondary system radionuclide inventories will be much less than those assumed in the accident analysis. As a result, the radiological consequences associated with the FSAR Chapter 15 accidents will be bounded by those currently described in the FSAR.

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A SONGS-94161168 Rev. I Page 32 of 37 6.0 SUMhJARY OF RESULTS 6.5 Loose Parts Evaluation SONGS 3 also has leakage detection methods that would be capable of detecting a slow leak before it could become a safety concem. These methods are simunadzed below:

e Blowdown is sampled every 72 hours8.333333e-4 days <br />0.02 hours <br />1.190476e-4 weeks <br />2.7396e-5 months <br /> and the condenser air ejector is sampled once per week.

• Upon indication of tube leakage, chemistry leak rate determinations are increase to every 72 hours8.333333e-4 days <br />0.02 hours <br />1.190476e-4 weeks <br />2.7396e-5 months <br />.

. Upon exceeding 10 GPD leakage, chemistry leak rate determinations increase to daily.

• Upon reaching the Air Ejector Alarm Setpoint (30 GPD), Operations begins logging RE-7870 readings.

e if RE-7870 indicates leakage has increased by more than 60 GPD in any 1-hour period, they verify the reading is correct and sustained by checking blowdown. If the increase is validated, a rapid shutdown at 1% to 5% per minute is initiated.

• As necessary, portable N-16 monitors can be used as a diagnostic tool to differentiate active tube leakage from tube plug leakage.

Based on the above discussion and previous calculations, ABB CE concludes that potential loose parts resulting from degraded eggerates do not constitute a safety concem.

6.5.4 Industry Experience ABB CENO has performed various evaluations and tests to justify continued plant operation with known or suspected loose objects in a steam generator.

The most extensive and thorough analysis was performed during the initial fabdcation of the San Onofre steam generators and is detailed in Reference 5. During the steam generator tubing operation, a tube guide, which is attached to the end of the heat tmnsfer tubes to facilitate installation, became dislodged and could not be located during subsequent search efforts. It was presumed to be in the steam generator and extensive analysis and testing were performed to verify that the tube guide would not affect the safety and performance of the steam generator during its 40 year lifetime.

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SUMMARY

OF RESULTS 6.5 Loose Parts Evaluation During modification of a tube support plate at Millstone Unit II, it was postulated that plate slivers from a cutting process may not have been completely removed from the steam generator, ABB CENO performed an evaluation and concluded that the tubes would not sustain any loss of structural integrity resulting from the potential loose objects.

During sludge lancing of the Turkey Point Unit 4 steam generators, the caraern light bracket on th spray unit came offinside generator "C" The bracket was subsequently located and retrieved from the tube lane but three round head screws which attached the bracket to the camera housing could not be found. As a result, ABB CE performed an analysis to support the cont inued operation with the loose objects in the secondary side of the steam generator.

In addition to the above specific cases, ABB CE has visually identified various items (welding rods, bolts, etc.) at sites with steam generator handholes. In many cases the items could not be dislodged or removed andjustification was provided for leaving the item in the steam generator. None of these items have resulted in further known damage.

6.6 Other Considerations ,

6.6.1 Primary Pump Excitation A mechanical excitation resulting from inibalance of the pump impeller is transmitted at 19-20 Hz through the primary loop piping to the steam generator. The ma.gnitude of this vibration is expected to be less than .01 g for 20 Hz at the steam generator based on mechanical vibration data specified for similar application pumps (Reference 11). A tube in resonance with the 20 Hz pump vibration will experience a magnification of 25 for a damping ratio of 2%. The resulting load is only .25 g which is negligible. It is concluded that the pump mechanical vibrations will not produce significant stresses in tubes which are in res6 nance with the pump.

The primary pump produces a pressure pulse which is transmitted in the primary fluid of the RCS. The pressure pulse at a frequency of 95-100 Hz was considered in the SONGS III Design Report (Reference 1) by assuming the worst case of a tube at resonance frequency of the pressure pulse. The resulting stress in the tube was less than 2 ksi (negligible) in the most conservative case. The Design Report evaluation which assumed a wo st case resonance is not affected by the degraded eggerate, t

CSE-97-257

[

_. . - . . - ~ . - - -. -- . _ - ~, - - .. . - _. - ._ - - . -

A SONGS-94161168,Rev.1 Page 34 of 37 6.0

SUMMARY

OF RESULTS -

L

! 6.6' Other Considerations 6.6.2 Main Steam Line Break 1 e

Main Steam Line Break (MSLB) loads were evaluated for the SONGS tube bundle in CENC 1327 (Refemnce 10).' The largest stresses occurred in the horizontal region of the bundle in tubes supported by the vertical grid structure. These stresses resulted from the i loads produced by the large cross flow in the upper bundle during the MSLB blowdown 1 of the steam generator. Degraded eggerates at the periphery of the bundle do not affect

the vertical grid support of the most highly loaded tubes for MSLB. The maximum tube i stresses are not affected by the degradation of the eggerates at the bundle periphery.

l MSLB is a short duration event in which larger than normal axial flows occur in the tube t

bundle. The evaluations of flow induced vibrations consider the vibrations to be continuous over a long period of time, and events which occur over a few minutes, such

! as MSLB, have no significant effect on the evaluation, i

i l 6.6.3 Tube Whip During a Design Basis Tube Rupture Event

!, A design basis tube rupture accident involves a complete circumfemntfal break of a tube ruch I that the tube completely severs. SONGS 3 has not had any circumferential cracks in tubes

,- other than at the top of the tubesheet and in two tubes in the inner rows. No circumferential cracks have been detected in the peripheral region of the SONGS 3 steam generators. In addition, there has not been circumferential cracking in other CE designed steam generators

. in the peripheral region of the upper tube bundle. Since eggerates in these regions have not l_ shown any degradation and a complete guillotine break of a tube in the peripheral region of the tube bundle is not a credible event, no further evaluation is required for this event.

{

I- 6.6.4 ASME Code Applicability b

With three exceptions, all references to the ASME Code contained in this report refer to Section III of the original Construction Code which is the 1971 Edition including the

. Addenda through the Summer of 1971. The three exceptions are for the use of fatigue values -

I for Alloy 600 material, Appendix F to determine allowables for faulted conditions, and Appendix N to define the general calculative techniques for flow induced vibration. These i . evaluations use Section III of the 1995 Edition of the ASME Code, i

i I'

i 4 CSE-97 257 1

i

_ _ .. _ . _ . _ _ - _ _.__. _ _.. - ..__. _ ._ _.~m_._._.- . . . - . . _ . . _ ._. . _ _ .

A-SONGS-9416-1168, Rev.1 Page 35 of 37 -

l l 6.0 -

SUMMARY

OF RESULTS 6.6 .Other Considerations '

V In the case of Appendix F, the original Construction Code did not contain that Appendix, However, the equivalent Code allowables for faulted conditions wwe specified in the original Design SW4n for the SONGS 3 steam generators (Reference 12); Hence, there is no

change from the original Construction Code. Fatigue values for Alloy 600 material and the Appendix N analytical techniques were simply not documented at the time the unit was ;

designed; Both the fatigue values and the Appendix N methodology have since become industry standards /

6.6.5 ATHOS Computer Code The ATHOS3 Mod 01 Computer Code is a three-dimensional, two-phase, steady-state -

and transient code for :hermal-1 ydraulic analysis ofreciredadag U-tube and once-through steam generators, n was cicated by updating earlier versions of the same code for the Electric Power Research Institute'(EPRI) and has become the standard method for all three steam generator vendors to evaluate secondary side steam generator

. performance. Initial code veri 6 cation is contained in the ATHOS3 Code documentation described in Reference 13. The ATHOS3 code has been validated against small-scale experimental data and operational steam generator thermal hydraulic performance data.

See Attachment 4 for a more detailed discussion of ATHOfi ad for specific references.

ATHOS3 code is recommended by EPRI (Reference 13) for PWR steam generator thermal hydraulic analysis. -

This code has been veri 6ed and validated for safety-related use in accordance with ABB CE Quality Assurance procedures and has been used in many applications.- It was used as the basis for determining the root cause of the tube rupture at the Palo Verde Nuclear Generating Station in 1993 and to limit the eddy current inspections of the upper tube bundle at Calvert Cliffs Nuclear Plant in 1995, All the three steam generator vendors are using A'IHOS3 code to improve the design of new and replacement steam generators (e.g, CE design of Korean steam generators, Westinghouse delta steam generator at South Texas Project, BWI replacement steam generator at Ginna). More recently it was used as part of the overall evaluation of the secondary system pressure degradation at SONGS Units 2 and 3.

CSL-97-257

A SONGS-94161168, Rev. I Page 36 of 37 7.0 RESULTS/ CONCLUSIONS -

Based on the assumptions regarding the effectiveness of the eggerates from the analyses presented herein, the Southem California Edison SONGS 3 steam generators will continue to perform their design function during both normal operation and accident conditions.

d 4

a e

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1 A SONGS 9416 il68, R:v.1 Page 37 cf 37

8.0 REFERENCES

1. CENC-1298, Analytical Reportfor Southern Cahfornia Edison San Onofre Unit No. 2 Steam Generator, September 1977. -

CENC-1645, San Onofre Steam Generator Revised LOCA Tube Analysis, luly 1984.

3. CENC-1850, Evaluation ofCorrosionfor Eggcrate Tube Supports San Onofre Steam Generators, December 1988.

_4 _ CR-9417-CSE93-1126, Revision 1, Evaluation ofPotential Loose Objects on the Secondary Side ofthe San Onofre Unit 3 Steam Generators, January 1994.

5. CENC-1278, Investigation ofthe Efects ofa Tube Guide in a San Onofre Steam Generator, December 1976.

6. CENC-1381, Evaluation ofPotential Loose Parts in the Millstone IISteam Generators, August 1980.

i

7. NUREG-0916, Safety Evaluation Report Related to the Restart ofR.E. Ginna Following a Steam Generator Tube Rupture, May 1982.

8. ASME Boiler and Pressure Vessel Code,Section III,1971 Edition through Summer 1971 Addenda, Article NB 3000, Design by Analysis.

9. CENC-1698, Leak Rate and Burst Tests ofSteam Generator Tubes with Simulated Wear Conditionsfrom VerticalSupports, July 1985. ,

10. CENC-1327, San Onofre Steam Generator Pipe Break Accident Analysis lMay 1978. ,

11 Specification No. 00000-PE-110, Revision 06, GeneralSpecificationfor Reactor Vessel Assembly, September 5,1978.

12. Specification No. Ol370-PE-120, Revision 05, Project Specificationfor Steam Generctor Assemblicsfor San Onofre Unit No. 2, June 22,1977. { Note that this is the correct reference for SONGS Unit 3 steam generators. Revision 04 of the same specification

_(dated August 3,1976) was the Design Specification for the Unit 2 steam generators.}

13_ EPRI Report EPRI-NP-4604-CCML, September 1990.

CSE-97 257

ATTACHMENT E

1. Design AnalysisIn-Process Approvals (1 page).

2. - Verification Plan (1 page).

3. Design Analysis Verification Checklist (4 pages).

4. Reviewer's Conunent Form (1 page)

(Includedin QA Record copy only) i CSE-97-257

SUMMARY

OF CONTENTS Calculation _39_Pages Appendices 210 Pages Attachments __11 Pages Diskette Attached _ Yes X No l

ATTACllMENT A to A SONGS 94161168, Rev.01 EVALUATION OF FLOW INDUCED VlBRATION 4

IN THE SOUTIIERN CALIFORNIA EDISON SONGS UNIT 3 STEAM GENERATOR WITH DEGRADED EGGCRATES CSE 97 254 Quality Class: X QC-1 (Safety Related)

PURPOSE: To evaluate th: steam generator tubes for flow induced vibration with degraded eggerates.

This Design Analysis is complete and verified. Management authorizes the use ofits results.

A M [a -<"

~

PREPARED BY: 1 D. Kev DATE: IM4/h7 MENTOR: P. L Anders DATE: #M /ff VERIFICATION STATUS: COMPLETE

• Ihe Safety Related design infonnation contained in this document has been verified to be correct by means of Design Review using the Checklist in QP 3,4 of QPM 101.

Narne R. E. Johnson Signature ~ ^ Date 8! '

Independent Reviewer /

APPROVED BY: D. P. Siska 4eL- DATE: 8-29-97 ABB COMBUSTION ENGINEERING CHATTANOOG A, TENNESSEE L ,

' in .

phix document is the pnyesty of ABB/Com6ustion Engineering, Chananooga, Tennessee, and is to be used ;

f only for the purposes of the agreement with ABB/CE pursuant to which it is fumished; :

CSE 97-254

A SONGS 9416 ll68 REV 01 Page A 2 of A 39 RECORD OF REVISIONS ghik , , s .

L PAGE (s) . PREPARED; ; INDEPENDENT APPROVED NUMBER;; ;DA1E: (INVOLVED - :2BY~, g % 2BY;

< + "'

n 0 6/1/97 Odginalissue D. G. Shek N. L. Beard D. P. Siska J. D. Key 1 8/26/97 To incorporate J. D. Key R. E. Johnson D. P. Siska two additional .d/

tube tow Cases:

Revised Pages 1, 2,3,6,1J 17,27 36 & 37 Added 2 plots to Appendix A4 Added last page to Appendix A5 Added Appendix A6 Listed 2 add. files in Attachment A3 CSE-97-254 l

A SONGS 94161168 REV.01 Page A 3 of A 39 TABLE OF CONTENTS East 1.0 OBIECTIVE OF THE DESIGN ANALYSIS......................................... 4 2.0 ASSESSMENT OF SIGNIFICANT DESIGN CHANGES..................... 4 3.0 AN ALYTICAL 'E CH NIQUES .. .... .......... ....... ...................................... 5 4.0 S ELECTION OF DESIG N 1NPUTS ...................................................... 7 l '

.- 5.0 A S S UM PTl O N S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 6.0 DETAIL ED AN ALY S I S . .. . . . . ... . . . . . . . . . . . . . . . . . . .. . . . . .. . . .. .. . . .. . .. . . .. . . . . . . . . . . . . .. .. ... 9 -

6.1 Flow Dis tributio n . . . . . . .. . . . . .. . . . . ... . . . .. . . . . .. . . . . . . . . . . . . . .. . . .. . . .. .. .. . . . ... ...... . 9 6.2 Geometry and Material Properties..............................................10 6.3 _ Allowables and Acceptance Criteria .......................................... 13 6.4 M odal Analysis . .. . . . . .. .. . . . . . . .. . . . ..... . .. . . . . . . . .. . . . . . . ..... . . . . . . .. ... ..... . . . . . .. 14 6.5 Fluid Elastic Instability Analysis ................................................ 17 6.5.1 Critical Velocity ........... ................ ................................ .... 18 6.5.2 Effective Velocity............ ......... ....... .............. ................... 21 6.5.3 S t abili ty R a tio.. . .. ... .. ... . . . .. .. . ... . .. .. . . . ... .. . . .. . . . ... . .. ... . .. .. . . . .. ... 2 6 6.6 Tube Di splace men ts . . . .. ... ... .. . . .. . .. .. . . .. . . . . ... . ......... . .. ... . . . . .. . .. .. . . . .. . 2 8 6.6.1 Cros s Flow Turbule nee..................................................... 28 6.6.2 Parallel Flow Turbulence ........................................ ... ...... 30 6.6.3 V orte x S heddi n g.............. ...... ........ ....................... .... ...... 3 4 6.7 Tube S tre s se s . . .. . . . . . .. . . .. .. . . .. . . . . . . . .. . ... . ... . . . . . . . .. .. .. . . ... . . .. . . .... . . . . .. . . . 3 5 7.0 RES ULTS/ CON CLU S IONS . ...... ...... ... ... ........... ......... ......................... 3 6 7.1 S t ability R a ti o. .. . . .. . . . .. . . . .. ... . . . . . .. . . . . . . .. . .. . . .. .. . .. ... . .. . ... . . . .. .. . . . . ... .. . . .. 3 0 7.2 - Displacements and S tresses......................................................... 36 7.3 Co n c l u si o n s . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . . .. . . . . . . . .. . . . . . . . . .. . . . . . . .. . . . . . . . . . . . . . . . . . 3 7

- 8.0 RE FE RE N CE S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 8 Appendix Al Virtual Mass & V-critical Calculations for Selected Tubes...... A1-1 Appendix A2 Effective Velocity Calculations for Critical Tubes................... A2-1

.- Appendix A3 Cross & Parallel Flow Turbulence Displacement Calculations. A3-1 Appendix A4 Tube Model and ANSYS Mode Shape Plots..........................A4 1 Appendix A5 ATHOS Results Summary for FIV Input................................A5 1 Appendix A6 Calculations for Revision 1................................................... A6- 1 Attachment Al Design Analysis in-Process Approvals, Verification Plan, Design Analysis Verification Checklist, & Reviewer's Comment Form (For Q. A. Record only)

- Attachment A2 Mathcad Files & Excel Spreadsheets Attachment A3 ANSYS Input and Output Files (Diskette in Q. A. Records only)

CSE 97 254

A SONGS 9416-ll68 REV 01 Page A-4 of A-39 1.0 OB.IECTIVE OF THE DESIGN ANALYSIS This report investigates the susceptibility of selected tubes within the steam generator tube bundle to experience unacceptable flow induced vibration when provided with diminished support due to eggerate erosion. Lack of eggerate support at one or more consecutive locations can lead to much Idgher stability ratios for many tubes depending on the flow regime and region, The dynamic charactoristics of the most critical tubes are determined for use in evaluating fluid-eletic instability and turbulence due to cross flow or parallel flow.

Cunent flow vibration theory is utilized in conjunction with flow distribution analysis results and flow induced vibration test data specific to ABB/CE type tube bundles.

2.0 ASSESSMENT OF SIGNIFICANT DESIGN CII ANGES There are no significant design changes.

CSE 97 254 J

A-SONGS 9416-1168 REV 01 Page A 5 of A 39 i

3.0 ANAIXflCAL TECHNIOUES 1

l Significant eggerate erosion appears only on the hot side of the steam generator where the

- hif hest fluid velocities also exist. Therefore, only the hot side of most of the selected tube rows was modeled, which was sufficient to develop the relevant mode shapes in most cases.

However, the lower tubes required full models (hot & cold side) due to the vertical tube support grid arrangernent. The ANSYS finite element analysis program (Reference 4) was used to detemiine the natural frequencies and mode shapes. The material properties for ANSYS input are from Reference 2. The tube models with boundary constraint symbols and mode shapes are shown in Section 6.4.

Selected Tube Rows:

The tube rows selected for evaluation were based on geometry and flow regime. Figures 6.2.1 and 6.2.2 show the upper tube bundle configuration and how the various " families" of tubes pass through the various eggerates, partial eggerates and vertical grid supports.

Appendix A5 shows the ATHOS flow distribution grid with nine circumferential cells on the hot sid.: periphery of the tube bundle. The nineteen tube rows shown in Figure 6.2.2 were selected since they would envelope the other tubes in terms of frequency response (ANSYS modal analysis) and velocity profiles from ATHOS.

Boundary Conditions:

Initially, the selected tube rows were evaluated assuming the top two eggerates (for that row) were inactive. Based on those results, the two most critical tube rows (83 and 110) were analyzed for only one inactive eggerate. In addition, certain other tube rows were evaluated for other combinations of eggerate support (see Table 6.4.1). This included staked tubes with three or four inactive eggerates. At eggerates that were assumed to be active, the tube models were constrained in the x and z directions. The models were also constrained in the y and z directions at vertical support grid locations. At the diagonal batwing supports, the tube was constrained in the out of plane z-direction only. The x, y and z coordinates refer to the horizontal in plane, vertical and horizontal cut-of plane directions, respectively. At inactive eggerate locations no constraints are applied.

The master degrees of freedom are selected to accurately develop the span modal displacements.

Effective Density:

An effective density, p.tr, is used in the ANSYS input. The effective density is composed of four parts which relate to tube material, fluid inside of tube, virtual mass of fluid outside of tube and stake material (if evaluated).

CSE-97 254 4

A SONGS 9416-ll68 REV.01 Page A 6 cf A 39 3.0 ANALYTIC AL TECHNIOUES f-itical and Effective Velocity:

When tubes in a heat exchanger are subjected to a fluid cross flow, there is a thre hold velocity where the onset of fluid clastic unstable vibrations occur. This phenomena is defined I

as the critical velocity, Vca. If the cross flow velocity is not constant over a tube span, an effective velocity m'*e ts tiermined. Reference 5 presents a method for calculating the I

effective velocity, V n i The critical velocity is calculated using an instability constant which is geometry dependent l (tube pitch, diameter, flow dircuion, etc.) and is based on flow induced vibration tests I conducted by ABB CE that model the steam generator tubes and tube-support design l anrangements.

Stability Ratio:

The stability ratio, S.R., is defined as the effective velocity divided by the critical velocity:

A va'oe equal to or less than one represents the criteria for fluid clastic instability.

S.R. = V,n / Vcr Turbulence:

Tube midspan displacements due to turbulence are calculated based on the procedures and equations shown in Appendix N of the ASME Code Section III (Ref. 8). Both cross flow and axial flow are considered. The stresses due to these displacements are calculated from ANSYS modal analysis results.

Note, Appendix N of the ASME Code Section III,1995 Edition (Ref. 8)is used in this report as a convenient one source reference for current FIV methodology. Appendix N references -

several authors and technical papers in presenting equations and methods recommended as appropriate for the type of analysis presented in this report. Referenca 8 is not used to develop allowables or acceptance criteria different than the applicable 1971 Edition of the Code (Ref. 2) for the original steam generator Design Report (Ref.1).

CSE 97-254

A SONGS 9416 ll68 REV.01 Page A-7 of A 39

, 4.0 SELECTION OF DESIGN INPUTS l

I Input for the flow induced vibration analysis was obtained from the secondary side thermat-hydraulic analysis (Ref. I1) which was performed using the ATHOS computer code. Figures A5-1 and A5 2 indicate the tube row locations relative to the ATHOS cell positions (axial, radial and circumferential). The relevant ATHOS output for this analysis consisted of fluid radial and l circumferential gap velocities along the tube vertical legs (hot side) at the bundle periphery, axial l velocities, primary and secondary fluid densities and dynamic viscosity. Fluid density values were used in determining tube virtual (effective) mass for inclusion in the modal analysis of Section 6.4 and in calculating critical velocity in Section 6.5.1. Fluid gap velocities were used in the effective velocity calculations of Section 6.5.2. Fluid velocities, densities and viscosity were used in determining tube displacements from turbulence as shown in Section 6.6. Tables AS 1, AS 2, AS-3 and A5-4 in Appendix A5 summarize the resultant gap velocities. ATiiOS secondary fluid density, dynamic viscosity, and axial flow velocities as a function of ATHOS cell location and elevation above the tubesheet. Tables A5 5 and AS-6 show the cross flow velocities at the 90 degree elbow and horizontal span region for tube rows 83 and 147.

CSE-97-254

A SONGS 9416 il68 REV.01 Page A 8 of A 39 5.0 ASSUMPTIONS The assumptions included in this design analysis are:

1. Conservatively, no credit is taken for eggerate rotational restraint in the ANSYS modeling of steam generator tube boundary conditions.

2. The largest value of vinual mass coefficient allowed per Ref. 2 is used in the effective mass calculation. This is conservative since it lowers the natural frequency of the tubes.

3. Tubes in row 51 or greater need only to be modeled from the tube centerline (1/2 model) since the frequency of the vertical span , on the hot side, is not affected by tube supports on the cold leg side. Tubes in row 51 or less are full models which are needed to accurately calculate asymmetrical rnodes.

4. Additional damping, due to parallel flow induced vibrations, averages about 0.5 percent and was conservatively neglected in the calculation of tube displacements and critical velocities.(Ref.18).

5. No credit is taken for critical velocity increases due to the influence of structural variations. Introduction of frequency differences between adjacent tubes (e.g.

inactive eggerates) can increase the critical velocity for instability by as much as 40 percent. (See paragraph N 1331(g) of Ref. 8).

6. Integration of flow velocities across the 90 degree tube bends adjacent to the batwing supports do not contribute significantly to the effective velocity along the vertical leg because the out-of plane displacements in the tube bends are much smaller than those in the venical spans with inactive eggerates.

7. The most conservative instability constant for ABB-CE tube bundles (K = 3.2) is always used for calculating critical velocity across the tube vertical legs regardless of flow orientation angle.

CS E-97-254

A SONGS 9416 Il68 REV.01 Page A-9 of A 39 6.0 DETAILED ANALYSIS This section contains the evaluation of the dynamic characteristics of nineteen selected tubes in the San Onofre steam generators. (See Table 6.4.1). He tubes are assumed to have their top two supporting eggerates completely ineffective. Based on the results of this study, the two most critical tube rows (83 and 110) were evaluated assuming only one inactive eggerate.

Additionally, two staked tube rows were evaluated with three or four inactive eggerates.

The staked tubes contained 0.50 inch stainless steel cable. The stake provided significant additional damping (5.5 % per Ref. 7) and substantially more wear volume for situations in

which an unplugged tube would exhibit an unsatisfactory stability ratio.

In summary, the tube rows and support conditions chosen for this study (Table 6.4.1) emvelope the acceptable number and location of ineffective eggerate supports for the most l

critical tube rows.

1 6.1 Flow Distribution l

l l The kinetic energy of fluid on the shell side of the steam generator is the source of excitation which produces flow induced tube vibration. The flow characteristics in the San Onofre Steam Generator Unit 3 tube bundle are evaluated by the ATHOS computer code and presented in Reference 11. The flow data is summarized in Tables AS-1 through AS-3 with ATHOS reference celllocations shown in Figures AS 1 and A5-2 of Appendix AS, CS E-97-254

A SONGS 9416 ll68 REV.01 Page A-10 of A 39 6.0 DETAILED ANALYSIS i

6.2 Geometry and Material Properties The steam generator tube bundle is described in Reference 1 and is comprised of 0.75 inch diameter Inconel 600 tubes with 0.048 inch wall thickness which are supported by grid type "eggerate" tube supports in the axial flow region. In the fluid exit region the tube pattern is a 1.75 inch by 1.732 inch rotated square while the vertical leg region has a 1.0 inch

+:iangular pitch. The upper bundle is supported by horizontal egg crates in the vertical portion of the tubes, and the diagonal strips and vertical grids support the bend and horizontal tube region. 'Ihe supports are arranged in the tube bundle as shown in Figures -

6.2.1 and 6.2.2. The selected tube rows are shown in relation to the partial support plates and ve.tical support grids. These tubes envelope the various constraint and flow regime combinations.

Material properties were obtained from Reference 2 and are listed below:

Inconel:

E = 29.2 x 10' psi at T = 600 deg. F. (Modulus of elasticity) v = 0.3 (Poisson's ratio) p = 0.305 lb/in8 ( density)

Tube Stake:

• p = 0.192 lb/in' (density)

CSE-97-254

A SONGS 9416-ll68 REV.01 Itge A ll of A-39 6.0 DETAII ED ANALYSIS 6.2 Geometry (continued)

Figure 6.2.1 Steam Generator Tube Support Arrangement 3 , e RC10**t.0W P DEMC1ot

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ELEVATION CSE-97 254

_ .. _. _ _ ._ _._. - _ _ ..__ _. .____m . _ - . _ _ . _ . _ - - ._ _ . _ .. _ . - _ _ _ ..

A SONGS 94161168 REV,01 Page A 12 of A 39 J

A 6.0 DETAILED. ANALYSIS 6.2 Geometry (continued) 3 Figure 6.2.2 Upper Tube Bundle Support Details with Selected Tube Rows

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CSE 97 254 1

,, , - - ~ . . . . , -:,.,,-.-eeg , -c - , , -..- , , , - . . - . . . - - - . - - - . , , - , ,,,n~. n.,

A-SONGS 9416-ll68 REV.01 Page A-13 Cf A 39 l

6.3 Allowables and Acceptance Criteria l The following allowables are used in this analysis.

1. The str.bility ratio of a tube (defined as the effective velocity divided by the critical l velocity,i.e. S.R. = V.a/Vca) is limited to 1.

1 l

2. The tube stresses due to flow induced vibration are limited to the fatigue endurance limit of 13.6 ksi at 10" cycles from Reference 2 (1989 Edition).

i CSE-97-254

A SONGS 9416 ll68 REV.01 Page A-14 of A-39 6.0 DETAILED ANALYSIS 6.4 Modal Analysis An ANSYS modal analysis of all the selected tubes was performed in order to detemiine the relevant frequencies and mode shapes. The tube row number, inactive eggerate identification and relevant frequency are summarized in Table 6.4.1. The lowest mode with maximum displacement in the out-of plane (z-direction) was selected (usually mode 1 or 2).

This was because the orbital motion characteristic of fluidelastic instability cannot occur.

unless the tube can respond in the out-of-plane direction as well as in plane. The resulting frequencies for the vertical legs with two inactive eggerates were usually in the 8 to 22 Hz range. These frequencies were used in determining the effective and critical velocities i shown later.

l Although the primary concern for tube vibration from degraded eggerates was the vertical tube spans, tube vibration analysis was also performed for the horizontal spans of tube rows 83,110 and 147. The horizontal spans are above the diagonal tube support and are not significantly affected by eggerate degradation. The evaluation of the horizontal spans used the same methodology used for the vertical spans and is included here for information.

Tube wall thinning was not considered in the modal analysis since it will not contribute to a significant change in the tube natural frequency. Thinning is most likely very localized and will not appreciably affect the stiffness or mass distribution of the tube.

The boundary conditions used in the ANSYS models were as described in Section 3.0. The boundary condition symbols are displayed in the mode shape plots shown Li Appendix A4.

An effective density, p., which is used in the ANSYS input, is composed of four parts which relate to tube material, stake material (if included), fluid inside of the tube, and the virtual mass of fluid outside of the tube,is calculated as follows:

p, = (1/(Ai)) x (pixAi + pgxAi + C.xpaxA.) w/o stake p, = (1/(Ai)) x (pixAi + p, x A,+ C xp,xA.) w/ stake C. = Vinual mass coefficient (3.1, vertical tubes, triangular pitch. Figure 14; 1.7, horizontal spans, Figure 16, Reference 3)

A. = Cmss sectional area of tube wall ,in:

A, = Cross sectional area of inside of tube, in' A = A + Ai .in' A. = Cross sectional area of stake ,in2

. pg = Density of primary fluid (variable w/ elevation. Ib/in')

pi = Density of tube material (0.305 lb/in', inconel 600 tubing at design condition) pa = Density of secondary fluid (variable w/ elevation. Ib(m', values usually taken at region of maximum displacement) p, = Density of stake material ' .m ab/in'. Stamless Steel material at design condition)

The vinual mass calculations for all selected tubes are sho;,a in Appendix A1.

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1 A SONGS-9416-ll68 REV.01 l Page A 15 of A 39 6.0 DETAILED ANALYSIS 6.4 Mad =1 Analysis (continued)

A typical tube model and mode shape plot is shown below (tube 147 with eggerates 10 & 9 inactive). Plots for all tube rows are displayed in Appendix A4. A modal analysis summary is shown 13. Table 6.4.1.

i

$ k7 MENT 0.93

=1 46 4dS.

?

e6 Row 147 with two uppermost eggerates inactive CSE-97-254

A SONGS 94161168 REV.01 Page A 16 of A 39 6.0 DETAILED ANALYSIS l 6.4 Modal Analysis (continued)

The accuracy of analytical models for predicting tube frequencies has been venfied by ABB CE in several test programs using ANSYS (Ref. 4) A typical example is Ref,15 which presents a comparison of the measured flow-induced vibration frequencies with calculated values. Table 5.8, of tids document, compares the first 7 modes with c.ach calculated mode having a range of frequencies. Since tubes in a bundle are coupled by surrounding fluid, it was necessary to consider a vinual mass factor variation to establish a maximum and minimum frequency. A reasonably good correlation was obtained for all modes with the largest deviation showing the analysis under predicting the first mode frequency by about 10 percent for most of the instrumented tubes.

The effect of partial support from degraded (one or more lattice bars missing) eggerates was not addressed in this report. It was conservatively assumed that the eggerate provided no support at locations of partial degradation. Thus, the resulting calculated frequencies are lower than what would be predicted with intermittent suppor t.

CSE-97-254

A SONOS 94161168 REV.01 Page A-17 of A-39 6.0 DETAILED ANALYSIS 6.4 MMal Analysis (continued)

Table 6.4.1 Modal Analvs s Summary Tube Row lanctive f.

No. Eggerates Glz) 147 10 & 9 10.9 147 8&9 12.5 147 7 &8 10.8 117' 8.9,&10 4.%

147' 5,6.7,& 8 3.14 147** 10 & 9 56.1 145 10 & 9 11.4 144 10 & 9 11.6 139 10 & 9 13 138 10 & 9 13.3 127 10 & 9 17.6 126 10 & 9 18.2 121 10 & 9 20.9 120 8&9 10.7 120 7&8 10.9 til 9&8 11 110 9&8 11.3 110 7&9 17.9 110 " 8&9 59.6 110 9 24.1 -

108 9&8 11.8 94 9&8 16.6 93 9&8 16.9 b4 9&8 9.7 83 8 18.8 83 8&7 8.4 82 8&7 8.6 83* 6,7 & 8 3.86 83 " _8&7 46.5 70 - 8&7 11 49 7&6 7.9 46 7&6 8.3 22 -7&6 13.4

• indicates staked tube

" critical mode for bend region CSE 97-254 9

A SONGS 94161168 REV.01 Page A 18 of Ao39 6.0 DETAILED ANALYSIS 6.5 Ruid Fl== tic Instability Annivsis 6.5.1- Critical Velocity When tubes in a heat exchanger are subjected to a fluid cross flow, there is a threshold-velocity below which fluid-clastic unstable vibrations de not occur. This velocity is defined as the critical velocity, Vca, and is given by the following equation in Reference 5:

Vcx = f. x K x d x ((M. x 6.)/(p. x d'))"

where:

f. = Natural frequency of the Nth mode of vibration (Hz)

K = Threshold instability constant (Dimensionless) d = Tube O.D. (in.)

M. = Reference mass of tube per unit length (lb/in) 6,= Logarithmic decrement = 2 x x x (

% = Damping ratio of tube in fluid (ABB/CE test data)

p. = Reference fluid density (lb/in')

The above parameters are obtained from the tube geomeuy and from test data. nc threshold instability' constant, K, used in this analysis is 3.2 for cross flow on the tube venicallegs and 7.1 for the tube horizontal spans. He K values were obtained from flow-induced vibration tests of ABB/ Combustion Engineering (ABB/CE) tube bundles and tube supports.( See Reference 10).

A comprehensive flow test program was conducted by ABB/CE to evaluate the vibration behavior of various tube bundle arrangements when subjected to liquid cross flow and two-phase flow (References 6 and 10). The 1.0" triangular pattern with 0.75" O.D. tubes was one of those evaluated as well as the rotated square pitch pattern of the upper bend region.

The tube bundles were driven to instability and critical velocities were detennined as well as tube response to flows of various orientations.

The damping values were based on CE test data per Ref.10; they are consioered to be conservative for water and two phase flow. The curve shown on Figure 10 of Ref.10 is a lower bound for 95 percent of the measured data. Additional data that validates the conservativeness of the damping used in this analysis is contained in Ref.14. It provides results for damping in heat exchanger tube bundles subjected to two phase cross-flow.

Void fraction (V.F.) is shown to be the dominant pararneter with damping varying from 3 to 4 percent for V.F,'s in the 60 to 90 percent range. The region being analyzed for SO'sGS Unit 3 S.G.'s also has V.F.'s in this range and the maximum value of damping used in the flow induced vibration analysis of 2.7 percent for unstaked tubes is less than the values of Ref.14.

CSE-97-254 a

AoSONGS 9416-ll68 REV.01 Page A 19 of A-39 6.0 DETAILED AblALYSIS 6.5 Fluid Woic Instability 6.5.1 Critical Velocity -

The critical velocity calculations for all selected tubes are shown in Appendix A1. The lowest mode in the out-of plane (z) direction was determined to be the most severe in determining stability ratio. Double span modes had frequencies about four times higher and negated any increase in effective velocity relative to the calculation of stability ratio hence these modes were non-controlling. An example calculation is shown on the following page for tube row 147 with eggerates 10 & 9 inactive.

CSE-97-254 I

J

A SONGS 94161168 REV,01 l Page A 20 of A 39 l

l l

6.0 DETAILED ANALYSIS 6.5 Ruid Einctic Inceshility Annivsis 6.5.1 Critical Velocity l Sample Critical Velocity Calentation (Tube Row 147. EC's 9 & 10 inactiyc)

Input Paranrters:

D := 0.75 in (Tube Dia.)

K := 3.2 (Instability Constant, per Ref.10 for tri. pitch CI:. bundles) f := 10.93 Hz (Tube Natural Frequency, ANSYS result for row 147 out of plane, max. disp. between EC's 9 & 10, Mode #1) mo  := 0.0462 h (Tube virtual mass per unit length) in p := 6.415 (Avg. secondary fluid density, row 147, between EC's 9 & 10, hot side) 3 ft

( := 0.0261 (Damping per Ref.10) 8o := 2 n _ (Log decrement)

Critical Row Velocity

'mo 6o Vcr : K f D- 2

,pD V cr ' 50.0seeA CSE-97 254

A SONOS 9416 ll68 REV.01 Page A-21 of A 39 6.0 DETAILED ANALYSIS 6.5 Fluid Elastic Instability Analysis 6.5.2 Effective Velocity If the cross-flow velocity is not constant over a tube span, an effective velacity must be determined. Reference 5 presents a method for calculating the effective velocity, V,s. The general equation is:

V2,,, Jgggx)fg,,) x y2gx) x 4 2(x) dx f(ht(x)/Mo) x c2(x) dx where:

p = Density of secondary fluid (ib/in')

M = Effective mass of tube (ib/in)

$ = Modal displacement (dimensionless) 2 V = Resultant cross flow gap velocity (in/sec) = (Vr + Vo )u Vr = radial velocity from ATHOS

~

Ve = circumferential velocity from ATHOS M = Reference mass of tube (Ib/in) p, = Reference fluid density (Ib/in')

All parameters vary with distance along the tube, x. However, to simplify the process, the densities were assumed constant. The density values were taken in the region of maximum displacement for the relevant mode shape.

The cross flow velocity profile is taken from ATHOS results (Ref. I1) and summarized in Appendix A5. A resultant velocity is used to calculate the effective velocity with radial and circumferential components combined by the SRSS method.

Effective velocity calculations for all critical tubes are contained in Appendix A2. An example calculation, for tube row 147 with eggerates 10 & 9 ineffective using Mathcad, is presented on the following sheets.

Mathcad is not required to be a verified and validated computer program because it provides adequate information for the Independent Reviewer to follow the calculative process.

CSE 97-254

A SONGS 9416.I168 REV.01

, Page A 22 of A 39 I

6.0 DETA11.ED ANALYSIS I I

6.5 Fluid Flattic Instability Analysis 6.5.2 Effective Velocity Effective Veiocity Calculation for Circumferential Sector 1 Tube Row 147 i (Vertical Spans from EC#5 to tube tangent point) top two eggerates inactive

xc

Spanwise coordinates (from ANSYS model) .

l disp: Normalized Displacements perpendicular to span (z dir) from ANSYS output for i Mode No.1, frequency = 10.93 Hz UZ.

Node No. xc disp Node No. xc disp

1 171.25 0 32 279.08 0.05135 2 174.85 -0.00231 33 282.15 0.11497 i 3 178.45 -0.00448 34 285.23 0.18829 4 182.05 -0.00636 35 288.3 0.26876 3

5 185.65 -0.00781 36 291.38 0.3539 j 6 189.25 -0.00869 37 294.45 0.44127 7 192.85 -0.00887 38 297.53 0.52855 8 196.45 -0.00821 39 300.6 0.61352 i

9 200.05 -0.0066 40 303.68 0.69411 10 203.65 -0.0039 41 306.75 0.7684

11 207.25 0 ,

42 309.83 0.83466 12 211.05 0.00542 43 312.9 0.89137

( 13 214.85 0.01156 44 315.98 0.93721 14 218.65 0.01769 45 319.05 0.9711 15 222.45 0.02306 46 322.13 0.99222 16 226.25 0.02695 47 325.2 1 17 230.05 0.02866 48 328.28 0.99412 18 233.85 0.02748 49 331.35 0.97452 19 237.65 0.02275 50 334.43 0.94143 20 241.45 0.01381 51 337.5 ' O.8953 21 245.25 0 52 90..; 0.83r, ';

22 248.33 -0.01487 53 .Lt2.T 177tl5 23 251.4 -0.03144 54 346.31 0.69 5, 24- 254.48 -0.04782 55 349.52 9.60675 25 257.55 -0.0621 56 352.52 0.51347 26 260.63 -0.07241 57 355.52 0.41472 27- 263.7 -0.0769 58 358.53 0.31216 28 266.78 -0.07372 59 361.53 0.2076 29 269.85 -0.06104 60 364.54 0.1029 30 272.93 -0.03706 61 367.54 0

. 31 276 ', 62 370.62 -0.10197 4

CSE-97-254

A SONGS 9416 il68 REV.01 Page A.23 of A 39 6.0 DETAH ED ANALYSIS 6.5 Fluid Flattic Instability Analysis 6.5.2 Effective Velocity (Cont'd)

Fluid Cross Flow Velocity from ATHOS Circumferential Sector 1, xv = elevation above tubesheet (in), velo = radial, circumferential and result gap cross flow velocities.

velo:= 4(velorad) (veloc ir) velo veio velo, alo velo velo.

xy rad. cire. result xv rad. cire. result 0 -115.36 0.45 115.36 245.25 -28.54 2.67 28.66 j 7.5 -115.36 0.45 115.36 245.35 29.5 3.28 29.68 7.6 110.5 0.34 110.5 255.5 29.5 3.28 29.68 15 -110.5 0.34 110.5 255.6 12.48 2.8 12.79 15.1 -6.94 -0.09 6.94 265.75 12.48 2.8 12.79 27.25 -6.94 0.09 6.94 265.85 -40.26 2.19 40.32 27.35 -4.1 -0.53 4.13 276 -40.26 2.19 40.32 44.75 -4.1 -0.53 4.13 T/ 6.1 41.97 4.16 42.18 44.85 -2.71 -1.29 3 286.25 41.97 4.16 42.18 62.25 -2.71 -1.29 3 286.35 15.79 5.15 16.61 62.35 -4.19 -0.66 4.24 296.5 15.79 5.15 16.61 80.25 -4.19 -0.66 -4.24 296.6 -49.74 7 50.23 80.35 5.9 -2.37 6.36 306.75 -49.74 -7 50.23 98.25 5.9 -2.37 6.36 306.85 49.29 10.18 50.33 98.35 22.41 1.08 22.44 317 49.29 10.18 50.33 117.25 22.41 1.08 22.44 317.1 20.04 12.22 23.47 117.35 3.17 3.48 4.71 327.25 20.04 12.22 23.47 136.25 3.17 3.48 4.71 327.35 -53.35 16.5 55.84 136.35 1.46 4.22 4.47 337.5 -53.35 16.5 55.84 153.75 1.46 4.22 4.47 337.6 77.67 4.19 77.78 153.85 -23 5.5 23.65 349.56 77.67 4.19 77.78 171.25 -23 5.5 23.65 349.66 53.93 -6.34 54.3 171.35 22.91 4.74 23.4 361.63 53.93 6.34 54.3 189.25 22.91 4.74 23.4 361.73 336.9 -3.13 336.91 189.35 7.58 3.22 8.24 370.59 336.9 3.13 336.91 207.25 7.58 3.22 8.24 207.35 3.51 3.31 4.82 226.25 3.51 3.31 4.82 226.35 -28.54 2.67 28.66 CSE-97 254 j

A-SONGS 94161168.REV.01 Page A 24 of A-39 6.0 DETAILED ANALYSIS 6.5 Finid Flactic Inctability Analysis 6.5.2 Effective Velocity (Cont'd)

Tube Row 147 (Vertical Spant from EC#5 to tube tangent nointi top two eggerates inactive Cross Flow Gap Velocity Profile Mode Shape Mode 1 (10.93 hz) l 3g  :.~ -- - - _

360$ '

1 l

340 l~~,,**-~*-

~~] $40 j 320 $, "~~~~

320I r i o 3, :; _. _ _L _._._L ,, ,

3

+**"

280 -

~ ~ "

e-2s09

)

260 '

260 240 . j" 240-

'~ ~

220 "--*

' 09 4

o gg i mn.4 . o.4 -_<

.m 3'0 0 so teo 240 320 400 i, ..v l

3 v.iocny (in/=>

CSE-97-254

i i A SONGS-9416-1168 REV,01 Page A 25 of A 39 '

6.0 DETAILED ANALYSIS '

6.5 Fluid Finctic Instability Analysis 6.5.2 Effective Velocity (Cont'd)

Tube Row 147 (Vertical Spans from EC#5 to tube tangent point) top two eggerates inactyi Normalded displacement ($) as a function of spanwise x-coordinate (Mathcad cubic spline interpolation function) is shown below. (Note, "espline" and "interp"are MATHCAD functions which fit a cubic spline to the nodal displacements.) .

vs :=cspline(xc disp) $( x) := interp(vs , xc. disp , x)

Velocity (v) as a fuaction of spanwise x coordinate is shown below. (Note,"linterp"is a MATHCAD function which fits a piece wise linear curve to the velocity distribution.)'

v(x) :=linterp(xv, velo,x)

Integrallimits; a := xg b := xe a = 171.25 m b = 370.62 Assuming no spanwise variation in tube virtual mass or secondary fluid density, the effective velocity equation reduces to the 'ollowing:

'b v( x)2,,( x)2dx Vd := g Vg =54.4 in/sec

$(x)* dx 3 <

a CSE-97-254 4

5

.y--vr.- y-- =-.-...c1---er-m--., -i--+-- .-----w c- <.,,%,--i y- w- - . . - , -,- . . . . . r----- --*a s- v--- -ev---rv*1-we-m:-*-~~?

A SONGS 94161168 REV 01

Page A 26 of A 39 i 6.0 DETAILED ANALYSIS 6.5 - Fluid Fl==6 In=*=hility Analysis i -

6.5.3 Stabilltv Dario i _

, The effective and critical velocities are used to calculate the stabihty ratio (S.R.).

!. S.R. - V.,/ V,

A stability ratio of 1.0 represents the ABB/CE design criteria for fluid clastic instability. Also,-

! based on ABB/CE operating experience, excessive tub wear is not expected for SR < 1. A ,

j stability ratio slightly higher than 1 would require further evaluation since it wculd exceed the '

j. design cri eria but still does not represent an immediate concern for the integrity of the tube 3

bundle because of the conservative dJ ddon of the critical velocity (Section 6.5.1).

i

[

Table 6.5.1 gives a summary of the Stability Ratios for all selected tube rows. '

i-i i

i-t 5

4

)-

1 k J-e v

t l CSE-97-254

- - , , - _ , :e .m , , _ . _ ....,<---4 - , _-._,..,._,,,,--w.-- y..-, ., .,y, . _ , , , , . , ,,c ,-m#,-g_m_...m.y...,,,- ,w,-ar,z._..._. m,-. +

. __ _... . _ _ _ _ . . _ __ _ _ . _ . _ _ _ ~_ - -

A SONGS 9416-1168 REV,01 3

Page A 27 of A 39 6.0 DETAILED ANALYSIS l 6.5 Fluid ma* 1anahility Analysis

6.5.3 Stabihty Ratio

) Table 6J.1 Fluid Elastic lastability Evaluation Summary

Tube Row lanctive f. Total  % Vm Stability No. Esscrates 01z) Damping (in/sec) (in/sec) Ratio j 147 10 & 9 10.9 0.0261 54.4 50.0 1.09

. 147 8&9 12.5 0.0255 39.1 53.4 0.73 l 147 7 &8 10.8 0.0261 29.6- 43.8 0.68

)- 147' 8.9.&l0 4.96 0.083 47 49.9 0.94 147* 5.6,7.& 8 3.14 0.084 I 21 28.0 0.75 1

147 " 10 & 9 56.1 0.014 216.6 493.7 0.44

145 10 & 9 11.4 0.0259 52.5 51.9 1.01 l 144 10 & 9 11.6 0.026 56.4 54.1 1.04

} 139 10 & 9 13 0.025 55.2 60.1 0.92 l 138 10 & 9 13.3 0.025 64.6 62.5 1.03 1 127 10 & 9 17.6 0.024 60.2 80.0 0.75

!' 126 10 & 9 18.2 0.024 61.4 82.1 0.75 I

121 10 & 9 20.9 0.023 60.1 92.6 0.65 120 8&9 10.7 0.026 52.6 48.6 1.08 l 120 7&8 10.9 0.026 36.2 46.4 0.78 111 9&8 11 0.026 51.6 50.0 1.03 .

3 110 9&8 . I1.3 0.026 58.4 51.8 1.13

j. 110 9 24.1 0.022 66.1 103.9 0.64

) 110 7&9 17.9 0.0237 48.2 72.6 0.66 l

110 " 8&9 59.6 0.013 282.6 533.8 0.53

108 9&8 11.8 0.0257 57.9 53.8 1.08 e

94 9&8 16.6 0.0242 53 73.1 0.73 93 9&8 16.9 0.0241 47.3 75.0 0.63 84 9&8 9.7 0.0265 41.4 42.5 0.97 1 83 8&7 8.4 0.027 42.1 37.1- 1.13 83 8 18.8 0.0235 46.7 79.5 0.59 83* 6,7 & 8 3.86 0.084 37 37.1 0.997 83 " 8&7 46.4 0.016 320.7 433.1 0.74 82 8&7 8.6 0.0269 41.9 37.9 1.11

-70 8&7 .1I 0.026 48.7 48.2 1.01 1= 49 7&6 7.9 0.0272 34 32.9 1.03 46 7&6 8.3 0.027 35.6 32.9 0.996 i 22 7&6 13.4 0.0252 31.5 52.7 0.60

• Indicates staked tube " Indicates critical mode for horizontal span cross flow

}

CSE-97-254

-p 3. ere - p , e- m %.w-+,_. ..-.,.w,.y ..,m--..r-eg-af--**-* - w m

• w % +t -r w - = 'm *e +v*'me~+---et- wy- - -

'-77-*

A-SONGS 9416-ll68 REV.01 i

Page A 28 of A-39 6.0 DETAILED ANALYSIS ,

i 6,6 Tube Disolacements 6.6.1 Cross Flow Turbulence

] Tube midspan displacements due to cross flow turbulence are calculated according to the procedures and equations shown in N 1343.2 of the ASME Code Section III (Ref. 8) and

. .WRC Bulletin 372 (Ref.13). The displacement calculations for au selected t bes are shown in Appendix A3 and summarized in the table on the following sheet. An example calculation is shown below for tube row 147 with eggerates 10 & 9 ineffective.

p := 6.41 Ibf (Sec. fluid density) ft3 d . 0.75 in (Tube O.D.)

m := .0461 Ibf- (Effective mass of tube per unit length) in fn := 10.9 Hz (Natural frequency of applicable mode) 4 := 0.035 (Critical damping ratio)

• ~

V

= 4.53: (Fluid cross flow velocity)

WC Cr

= 0.023 h (Ref. 8, Appendix N, Fig. N-1343-1)

L := 91.5 in (Tube span)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981), Ref.16)

' lx I a = 0.236 (Joint acceptance)

J a :" g 2

a  :. 0.5 h p d V Cr 3 -3 in a A rms = 2.5 10 3 2

,64 n f n m,g (Note: The rms disp. calculated above is redefined on the following page as Att ,.)

CSE-97 254

A' SONGS 9416-il68 REV.01 Page A 29 of A 39 6.0 - DETAILED ANALYSIS 6.6 Tube Disolacements (continued) 6.6.1 Cross Flow Turbulence (continued)

The follo#ng table summarizes the tube displacement calculation for cross flow turbulence, Table 6.6.1 ~

Summary of Displacements due to Cross-flow Turbulence Tube Row Geometry r, ( p, m L Ver Atb no. Inactive EC (Hz.) _.

Ib./ft3 Ob/in.) (in.) (ft/sec) (mils) 147 9,10 10.9 0.0261 6.41- 0.0462 91.5 4.53- 2.5 147- 8, 9 12.5 0.0255 7.17 0.0468 92.3 3.26 1.3 l 147 7, 8 10.8 0.0261 8.16 0.0475 99.5 2.47 0.9 _

L 147* 8,9,10- 4.96 0.083 8.16 0.0755 123 3.92 2.6 l

147* 5,6,7,8 3.14 0.084 9.06 0.0772 170.5 1.75 0.9 145 9,10 11.4 0.0259 6.41 0.0462 90.3 4.38 2.3 144 9,10 11.6 0.026 6.09 i 0.0459 89.3 4.7 2.5 139 9,10 13 0.025 6.09 0.0459 85 4.6 2.1 138 9,10 13.3 0.025 5.82 0.0457 84 5.38 2.7 127 9,10 17.6 0.024 5.82 0.0457 74.6 5.02 1.7 126 9,10 18.2 0.024 6.05 0.0452 73.6 5.12 1.8 121 9,10 20.9 0.023 6.05 0.0452 69.3 5.01 1.5 120 8, 9 10.7 0.026- 6.5 0.0461 99 4.38 2.5 120 7, 8 10.9 0.026 7.38 0.0464 101 3.02 1.3 111 8,9 11 0.026 6.5 0.0461 91.3 4.3 2.4 110 8,9 11.3 0.026 6.3 0.0456 90.3 4.87 2.9 110 9 24.1 0.022 5.89 0.0452 59.6 5.51 1.6 94 8,9 16.6 0.0242 6.3 0.0456 76.4 4.42 1.6 93 8,9 16.9 0.0241 6.27 0.046 75.5 3.94 1.2 84 7, 8 9.7 0.0265 7.2 0.0467 105 3.45 1.9 83 7,8 8.4 0.027 7.2 0.0467 104 3.51 2.4 83 8 18.8 0.0235 6.74 0.0464 66.8 3.89 1.2 83* 6,7.8 3.86 0.084 7.66 0.0761 140 3.08 2.0 ,

70 7, 8 11 0.026 7.01. 0.0466 93.4 4.06 2.3 49 6, 7 7 0.0272 8.18 0.0475 110.5 " 83

.. 1.8 46 6, 7 8.3 0.0'27 7.64 0.047 108.4 2.97- 1.8 22 6,7 13.4 0.0252 8.68 0.0478 87.4 2.63 0.6

• Indicates staked tube CSE-97-254 i

m _ U

A SONGS 9416-1168 REV.01 Page A 30 of A 39 6.0 DETAILED ANALYSIS 6.6 Tube Displacements (continued) 6.6.2 Parallel Flow Turbulence Tube midspan displacements due to cross parallel flow turbulence are calculated according to the procedures and equations shown in N-1345 of Reference 8. The displacement calculations for all selected tubes are shown in Appendix A3 and summarized in the table on the following sheet. An example calculation is shown below for tube row 147 with eggerates 10 & 9 ineffective.

V := 14.59 (Velocity of two phase mixture between EC's 9 & 10) seC p s := 6.41 lbf (Density of two-phase mixture between EC's 9 & 10) fd d := 0.75 in (Tube OD) t := 0.048 in (Tube thickness) i d h := 0.72 in (Tube Hydraulic diameter) l j m t:= 0.0461 lbf-(Total tube Virtual Mass) in f n := 10.93 Hz (Tube first mode frequency w/two EC's missing)

L := 91.5 in (Span length, Dist, between EC#8 & BW)

F ent := 3.1 (Hydrodynamic added mass factor for surrounding fluid) 2 2 A o := d d  := d - 2 t A o = 0.4 in m ma a := F eniP s' A o =0.00508 -

in Ibf (Added Mass of Sec. Fluid)

I mt =0.0461 bf -

(Total Virtual Mass) in CSE-97-254 l

A SONGS-9416-1168 REV.01 Page A-31 of A 39 6.0 DETAILED ANALYSIS 6.6 Tube Displacements (continued) 6.6.2 Parallel Flow Turbulents ma

@ := =0.1 (Range 0.00026 to 0.62) OK mt L

e := - e = 122 (Range 26.8 to 58.7) d 1:=64 1-(d - d *#)(Tube moment ofinertia) 6 l- E := 29.2 10 psi (Tube modulus of Elasticity)

Im a l V2 l'*

E u := u = 0.133 3 E1 2

u = 0.018 Range 0.0021 to 0.8) OK (Noise factor)

K n := 5 lbf vd := 2.8210'5 -

(dynamic viscosity) ftsee

-I 2 v := v = 4.4 10 sec ft (kinematic viscosity)

Ps Vd 5 Re := R e = 2.1 10 (Reynolds No. Range 2.6E4 to 7E5) OK v

D := 2 n f n n = 68.7 rad seC Im t 4\*

• __ .1 E 2 ot:= h k E 1 j cx = 3.8 a = 14.4 (Range 2.10 to 20.8) OK 2

l5 10'#K n \u'e'R e ld h S  := d- -

(N-1345, Eq. 97)

1. 2

( a / 1+u (dj 1 + 4-nm = M 40 4 (Note, this disp. is redefined on the following Page as: 6p r)

CSE-97-254

A SONGS-9416-1168 REV.01 Page A-32 of A-39 6.0 DETAII ED ANALYSIS 6.6 Tube Disolacements (continued) 6.6.2 Parallel Flow Turbulence Table 6.6.2 - Parallel Flow Evaluation Summary Tube Row Inactive y ,,3 ,, r, viscosity Span Q No. Eggerates 4 2 (ft/sec) (Hz) (10 ft /sec) (in.) (mils) 147 10 & 9 14.58 10.9 4.4 91.5 6.7 147 8&9 12.67 12.5 4.23 92.3 4.5 147 7 &8 10.67 10.8 4.02 99.5 4.8 147* 8,9,&l0 14.58 4.96 3.45 123 19 147* 5.6,7,& 8 10.17 3.14 3.82 170.5 22 145 10 & 9 14.58 11.4 4.26 90.3 6.3 144 10 & 9 15 11.6 4.49 89.3 6 139 10 & 9 15,0 13 4.52 85 6.2 138 10 & 9 15.3 13.3 4.6 84 6.9 127 10 & 9 15.3 17.6 4.71 74.6 7.4 126 10 & 9 17.4 18.2 4.46 73.6 10 121 10 & 9 17.3 20.9 4.46 69.3 10 120 8&9 13.92 10.7 4.26 99 6 120 7&8 11.6 10.9 3.85 101 5 l 111 9&8 13.9 11 4.15 91.3 6.3 I 110 9&8 14.58 11.3 4.47 90 3 6.3 110 9 16.4 24.1 4.56 59.6 2.1 94 9&8 14.58 16.6 4.47 76.4 3.2 93 9&8 16.5 16.9 4.54 75.5 3.9 84 7&8 13.08 9.7 4.2 105 7.3 83 7&8 13.08 8.4 4.2 104 7.3 83 8 14.3 18.8 4.29 66.8 2.4 83* 6,7 & 8 13.3 3.86 3.88 140 22 70 8&7 12.6 11 4.22 93A 5.5 49 7&6 11.67 7.9 3.02 110.5 10 46 7&6 11.2 8.3 4.18 108.4 4.3 22 7&6 9.5 13.4 3.97 87.4 2.9 CSE-97-254

A SONGS-9416-1168 REV,01 Page A-33 of A-39 6,0 DETAILED ANALYSIS 6,6 Tube Displacements (continued) 6.6.2 Parallel Flow Turbulence The displacements due to cross flow and parallel flow turbulence are combined by the SRSS method. The resultant displacements (Sa) are presented below.

Table 6.6.3. Resultant Dis placements due to Parallel and Cross Flow Turbulence Tube Row Inactive 0" Spf Atb no. eggerates (mits) (mils) (mils) 147 9,10 6.7 2.5 7.2 147 8,9 4.5 1.3 4.7 147 7,8 4.8 0.9 4.9 147' 8,9,10 19 2.6 19.2 147* 5,6,7,8 22 0.9 22.0 145 9,10 6.3 2.3 6.7 144 9,10 6 2.5 6.5 139 9,10 6.2 2.1 6.6 138 9,10 6.9 - 2.7 7.4 127 9,10 7.4 1.7 7.6 126 9,10 10 1.8 10.2 121 9,10 10 1.5 10.1 120 8,9 6 2.5 6.5 120 7,8 5 1.3 5.2 111 8,9 6.3 2.4 6.7 110 8,9 6.3 2.9 6.9 110 9 2.1 1.6 2.6 94 8,9 3.2 1.6 3.5 93 8,9 3.9 1.2 4.1 84 7,8 7.3 1.9 7.5 83 7,8 7.3 2.4 7.7 83 8 2.4 1.2 2.7 83* 6,7,3 22 2.0 22.1 70 7,8 5.5 2.3 6.0 49 6,7 10 1.8 10.2 46 6,7 4.3 1.8 4.7 22 6.7 2.9 0.6 3.0

• Indicates staked tube

• pf Indicates parallel flow tb Indicates cross flow R Indicates resultant displacement CSE-97-254

A SONGS-9416-1168 REV,01 Foge A 34 of A 6.0 DETAILED ANALYSIS 6.6 Tube Displacements (continued) 6.6.3 Vortex Sheddine Vortex shedding manifests itself in a classic resonance situation when the vonex shedding frequency coincides with a tubespan natural frequency. He forcing function must introduce more energy into the system than cra be dissipated through damping or a stable ,

level of vibration will be established. Results from the vibration test program described in Reference 6 revealed that the ABB/CE tightly packed triangular pitch arrays in the axial flow and fluid exit regions were not susceptible to vortex shedding resonance. This is because the turbulence swamps out the vortex shedding. In addition Reference 8 indicates in paragraph N-1322(d) that vortex shedding is not a concem in two-phase flow. The presence of axial flow will also disrupt the formation of vortex streets. Therefore there is no need for any funher evaluation of vortex shedding for this analysis.

j CSE-97-254

4 A-SONGS 9416-1168 REV.01 Page A-35 of A-39 6.0 DETAH.ED ANALYSIS 6.7 Tube Stresses due to Turbulence The maximum bending stresses in the tubes due to cross flow and parallel flow turbulence are calculated with the resultant displacements shown in the preceding section and with the modal stresses from the ANSYS modal analysis. The modes conesponding to the frequency used to calculate the turbulent displacements are used to calculate the stresses in the tubes. Since the mode shapes are normalized to a unit displacement, the stress due to turbulence is the product of the resultant displacement and the modal stress The resulting stresses are shown in Table 6.7-1 below:

Table 6,7-1. Maximum Bending Stresses due to Parallel and Cross Flow Turbulence Row Resultant Modal Bending Actual u bacm.e Displacement Stress Bending

. ggera es Sa (mils) (psi) Stress (psi)

! 147 9.10 7.2 17213 122 147 ,: 4.66 18383 86 147 7.8 4.88 16940 83 147* 8,9.10 19.15 10178 195 147* 5.6,7.8 22.01 7121 157 145 9.10 6.64 17809 118

.144 9,10 6.5 18131 117 139 0,10 6.6 19782 128 138 9,10 7.4 20168 148 127 9,10 7.57 24918 189 126 9,10 10.14 25413 258 121 9,10 10.08 28915 291 120 8,9 6.43 15445 99 120 7,8 5.17 15899 82 111 8.9 6.67 16128 108 110 8.9 6.82 1M06 112 110 9 2.6 36225 94 94 8,9 3.49 23288 81 93 8.9 4.05 23876 97

~

84 7.8 7.5 14624 110 83 7.8 7.62 13291 101 83 8 2.7 28590 77 83* 6.7.8 8381 185 22.07 _ _

70 7.8 5.89 16346 96 49 6,7 10.14 12585 128 46 6.7 4.59 13162 60 22 6.7 2.96 19303 57

• Indicates staked tube.

' CSE-97-254

A-SONGS-9416-1168 REV. 01 Page A-36 of A-39 7.0 RFRULTS/ CONCLUSIONS

- 7.1 Stability Ratio Table 6.5.1 summarizes the results of the calculations of flow stability for the selected tube rows. The results indicate that twelve tube rows have stability ratios above the limit of 1.0

. when it is assumed that the top two eggerates are ineffective. Tube rows 83 and 110 were the most critical exhibiting a stability ratio 1.13. When these two rows were evaluated for a single ineffective eggerate, the stability ratios dropped to 0.59 and 0.64 respectively. 'Ihis shows that the remaining tube rows will exhibit even greater margins againstm' stability with only one inactive eggerate.

Several other tube rows exhibited stability ratios of less than 1.0 with the top two eggerates inactive as shown in Table 6.5.1. However, some tube rows which were unacceptable with the top two eggerates missing, showed acceptable stability ratios if the top eggerate was active and the next two inactive. Examples of this are tube rows 147 and 120 with stability j ratios of 0.73 and 0.78 when the upper most eggerate was effective.

Results of the analysis for staked tubes show a Stability Ratio less than 1.0 for the case with three inetTective eggerates. The results indicate a Stability Ratio of 0.95 for the bounding c-case of tube row 83. Tube row 147 is also acceptable in the staked condition with four ineffective eggerates if the top two eggerates (9 and 10) are effective.

Results of the cross flow evaluation of the horizontal spans of tube rows 83,110 and 147 are included in Table 6.5.1 for information since the original steam generator design report (Ref.1) also evaluated this region. The spans are supported by the vertical grids and batwings and are not significantly affected by the condition of the eggerates. Resulting frequencies were in the same range (46 to 59 Hz) as for the original analysis (49 Hz) but.

with somewhat higher stability ratios. This was primarily due to current refinements in the flow distribution analysis (ATHOS) and FIV methodology. The results indicate a stability ratio ofless than 1.0 for the worst case.

7.2 Disolacements and Stresses The displacements calculated for cross flow and parallel flow turbulence are shown in Table 6.6.3. The magnitude of the cross flow displacements are very small (typically 1 or 2 mils) especially for the large span lengths. The displacements due to axial flow are shown to be larger due to the larger axial velocities and the larger than usual spans. The combined displacements show resultants in the range of 10 mils except for the staked tubes. Based on ABB/CE operating experience, excessive tube wear at eggerate tube supports does not occur when stability ratios are less than 1. Reference 17 predicted wear rates for tubes in degraded eggcrates and concluded that the tube wear would be negligible for the magnitude of midspan Yom displacements determined in this analysis.

CSE-97-254 i

A-SONGS-9416-1168 REV. 01 -

Page A-37 of A-39 7.0 RESULTS/ CONCLUSIONS 7.2 Displacements and Stresses (continued)

The resultant displacements for staked tubes are 22 mils as indicated in Table 6.6.3. 'Ihis magnitude 'f displacement is not of concem for the staked tube and the calculated tube stresses are insignificant. Any wear associated with the staked tube is not significant because of the wear volume of the stake.

The tube stresses based on the vibration displacements are shown in Table 6.7.1. These stresses are small and well below the fatigue endurance limit of the tube material.

7.3 Conclusions l

l The analysis concludes that all tubes are acceptable for FIV with one eggerate inactive.

Also, Table 6.5.1 shows that many tube rows are stable with two inactive eggerates. The tube rows that exceed S.R. = 1.0 with two inactive eggerates have a maximum stability ratio of1.13.

In cases whc: three eggerates are ineffective staking the tube is an acceptable repair to address FIV. L is acceptable to stake tuoe row 147 with four ineffective eggerates if eggerates 9 and 10 are effective.

It is concluded that stability ratios in the horizontal spans are not significantly affected by the condition of the eggerates CSE-97-254 1

b

A-SONGS-9416-lio8 REV. 01 Page A-38 of A-39

8.0 REFERENCES

1. CENC-1298, Analytical Report for Southem Cahfomia Edison, San Onofre Unit No. 3 Steam Generators, Combustion Engineering, September 1977.

2. ASME Boiler and Pressure Vessel Code, Section IU for Nuclear Power Plant Components, 1971 edition, with addenda thru Summer 1971.

3. " Design Guide for Calculating Hydrodynamic Mass Part I: Circular Cylindrical Structures",

Chen, S.S. and Chung, Ho, June 1976, Argonne National Laborttory (REF-96-013).

4. ANSYS Finite Element Computer Code, Rev. 5.3, by ANSYS Inc.

5. "Fluidelastic Vibration of Heat Exchanger Tube Arrays", Connors, H.J., Jr.,1977, ASME-Publication 77-DET-90 (REF 96-014).

6. " Vibration in Nuclear Heat Exchangers Due to Liquid and Two-Phase Flow", Heilker, WJ., .

and Vincent, R.Q., April 1981, Engineering for Power, Vol.103 No. 2 (REF-96-015).

7. " Tube Stake Damping Test Report", Interoffice Correspondence AEL-88-326,11/21/88, from

! D.E. Hart to P.L. Anderson. (REF-96-012)

8. Appendix N, ASME Boiler and Pressure Vessel Code,1995 edition.

9. Mathcad 6.0, by Mathsoft, Inc., Cambridge, MA.

10." Flow Induced Vibration Analysis in Support of the Design of the Yongwang Units 3 and 4 Steam Generators", Heilker, WJ. and Beard, N.L., Proceedings of the Intemational Symposium on Pressure Vessels Technology, Nuclear Codes and Standards, April 19-21, 1989, Seoul, Korea (REF-96-017).

11.CSE-97-253," Thermal-Hydraulic Analysis of the Southem Califomia Edison SONGS Steam j

Generator with Degraded Eggerates", J. Thakkar, August 1997,

12. ABB/CE Drawing: E-234-724 Rev. 01, " Baffle and Tube Support Assembly," April 1975.

ABB/CE Drawing: E234-726 Rev. 01," Tube to Tube Sheet Assembly," January 1975.

13.WRC 372, Welding Research Council Bulletin, " Guidelines for Flow-Induced Vibration Prevention in Heat Exchangers, May 1992.

14. Pressure Vessel Research Committee 1988-1989 Annu.d Report, Damping of Tube Bundles in Two-Phase Flow, M. J. Pettigrew, Principal Investigator, AECL.

15. CENC-1939, " Final Test Report, Flow Induced Vibration Test Yonggwang Units 3 & 4 Steam Generator Economizer and Lower Tube Bundle Region," ABB-CE Nuclear Power, July 1991,

16. Flow-Induced Vibration, Robert D. Blevins, Second Edition, Van Nostrand Reinhold, New York,1990.

17. Letter dated June 1,1997, Robert D. Blevins, PhD. to Nabil El-Akily, SCE,

Subject:

._ Wear of SONGS Unit 3 Steam Generator Perpherial Tubes.

CSE-97-254

' A-SONGS-9416-1168 REV.01 Page A 39 of A-39 8.0 - REFERENCES i

-18. Letter dated A'sy 19,1997, Robert D, Blevins,PhD., to Nabil El Akily, SCE,

Subject:

Parallel Flow Lduced Stability and Damping with Application to SONGS Unit 3.

l 4

4 CSE-97-254

4 A-SONGS-9416-1168, Rev. 00 Appendix Al Page Al of Al-50 i: AFPENDIX A1. VIRTUAL MASS & CRITICAL VELOCITY FOR SELECTED TUBES CSE-97-IS8

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A2 of Al-50 San Onofre 2 & 3 Tube - Virtual Mass Calculation Tube Rows 147 & 145 Vertical Le.r Region - EC's 9 & 10 inactive:

p t := 0.305 Ibf Tube Density (I-600) D = 0.75 in Tube Dia, m

t := 0.048 in Tube Thickness p p := 45.463 ibf Avg. Pri. Fluid Density A

P = 1.0 in Triangular Pitch p s := 6.41 lbf Secondary Fluid Density g3 (vert. leg region, row 147, between EC's 9 & 10) l 2 2 A*t D - (D - 2 t)2' A o := E.D A; := E-(D - 2 t)2 4- 4 4 2

A t= 0.1059 in A o=0.442 in 2 A; = 0.336 in 2

Hydrodynamic Mass Coefficient (7):

(Note: In the text of the report this factor is defined as C.)

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (Ibf/in): Wy W y := At'Pt + PpA + F p s'A -2 o W y= 17.839 lb sec (For Vcritical)

Virtual Density (lbfTm3 ): p y Wv p

y := A py = 0.4365 lbf (for ANSYS input) t m CSE 97-158 j

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A3 of Al-50 Tube Virtual Ma== Cale dation Tube Row 147 - vertical les region - ECs 8 & 9 inactive. with 10 active:

lbf Pt := 0.305 3 m Tube Density (I-600) D := 0.75 in Tube Dia.

p p := 45.275 lbf Avg. Pri. Fluid Density t := 0.048 in Tube Thickness ft P := 1.0 in Triangular Pitch p s := 7.171 lbf Secondary Fluid Density '

g3 (vert, leg region, row 147, between EC's 8 & 9)

A t:= E D2 - (D - 2 t)2' A o := E D 2 A j := E-(D - 2 t)2 4 4 4 l 2 A t= 0.1059 in A o= 0.442 in2 A i= 0.336 in2 Hydrodynamic Mass Coefficient (F):

F = 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (IbfTm): W y W y := At'Pt + PpA + F p s A o W y=0.0468 lbf -

' (For Veritical) in Virtual Density (IbfTm3 ): p, Wv p

y := A py = 0.4418 lbf (f r ANSYS input) t m i.

CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A4 of Al-50 Tube Virtual Mass Calculation Tube Row 147-vertical les renion-EC's 7 & 8 inactive. 9 & 10 active: .s p t := 0.305 Ibf Tube Density (I-600) D := 0.75 in Tube Dia.

m t := 0.048 in Tube Thickness

-p p := 45.067 Ibf Avg. Pri. Fluid Density A

P := 1.0 in Triangular Pitch I Secondary Fluid Density p 3 := 8.164 bf l 3 3 (vert. leg region, row 147, between EC's 7 & 8) 2 2 A*t '

.D - (D - 2 t)2' A o :=4 E D A; := E-(D - 2 t)2 4 4 2

A t= 0.1059 in A o= 0.442 in2 A ; = 0.336 in 2

$ydrodynamic Mass Coefficient (F):

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (Ibf/in): W,

-W y := At'Pt

• P pA; + F p s A o W y= 0.0475 Ibf -

_(For Vcritical) m VirtualDensity (IbfTm3 ): p y Wv p y := py = 0.4489 Ibf (for ANSYS input)

At m

CSE-97-158

---

J

A-SONGS-9416-1168, Rtv. 00 Appendix Al Page AS of Al-50 Tube Virtual Mass Calculation Vertical Len Region-Tube Row 147 Staked Tube With Three Top EC's 8.9.&l0 Inactivg p t := 0.305 lbf Tube Density (I-600) D := 0.75 in Tube Dia.

m t := 0.048 in Tube Thickness p stk := 0.192 ibf Stake Density m p : 1,0.in Triangular Pitch p s := 6.91 lbf Secondary Fluid Density g 3 (vert. leg region, row 147, between EC's 8 & 10) 2 2 A"t '

.D - (D - 2 t)2' A o := D D stk := 0.5 in 2

A t= 0.1059 in A o= 0.442 in2 Astk := D stk A stk = 0.196 in 2

Hydrodynamic Mass Coefficient m:

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass Obflint (Wd

.W y := A t'P t+ P stk' A stk + F p s A o W y = 0.0755 -@ (For Veritical)

In Virtual Density Obf/inl): p, Wv py := py = 0.7129 lbf (for ANSYS input)

At m

CSE-97-158

A-SONGS-9416.I168, Rev. 00

- Appendix Al Page A6 of Al-50 Tube Virtual M= Calculation Venical Leg Region-Tube Row 147 Staked Tube With ECs 9.&l0 active & 5-8 inactive p t := 0.305 Ibf Tube Density (I-600) D := 0.75 in Tube Dia.

m t := 0.048 in Tube Thickness p stk := 0.192 Ibf Stake Density m p := 1,0.in Triangular Pitch p s := 9.063.$I Secondary Fluid Density ft 3 (ven. leg region, row 147, between EC's 5 & 8) l 2 2 At '

- D - (D - 2 t)2' A o=

D D stk := 0,5 in A t= 0.1059 in 2 A , = 0.442 in 2

A stk := D stk 2

A stk =0.196 in Hydrodynamic Mass Coefficient (F):

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (lbf7in): (Wy3 W y := A t'Pt* P stk' Astk + F p s A o W y =0.0772 h (For Veritical)

-m Virtual Density (lbf/inl): py Wv p y := py = 0.729 Ibf (for ANSYS input) t m CSE 97158

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A7 of Al-50.

Tube Virtual M=== Calcad= tion Tube Rows 144 & 139 with EC'L9 & 10 inactive pt := 0.305 Ibf Tube Density (I-600) D := 0.75 in Tube Dia. '

m t := 0.048 in Tube Thickness p p := 45.45 lbf- Avg. Pri. Fluid Density A

P := 1.0 in Triangular Pitch i

p s := 6.09 lbf Secondary Fluid Density

! g 3 (vert. leg region, row 144, between EC's 9 & 10)

A g:= E ,D2 - (D - 2 t)2' A o := E D 2

A;:= E-(D - 2 t)2 4 4 4 2 2 A t= 0.1059 in A o= 0.442 in A =0.336 in 2 Hydrodynamic Mass Coefficient (F):

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (IbfTm): Wy ,

W y, := At'Pt+ P p' A +i F p s' A o W y= 0.0772 Ibf -

(For Veritical) m Virtual Density (IbfTm3 ): py Wv p v_ent

• 4t P v = 0.729 lbf (for ANSYS input) m CSE-97-158

- A-SONGS-9416-1168, Rev. 00 Appendix Al Page A8 of Al-50 Tube Virtual Mass Calculation Tube Rows 138 & 12" 'C's 9 & 10 Inactive:

p t := 0.305 lbf Tube Density (I-600)

D := 0.75 in Tube Dia, m

Avg. Pri. Fluid Density t := 0.048 in Tube Thickness p p := 45.43 A P := 1.0 in Triangular Pitch p 5 := 5.824 lbf Secondary Fluid Density g3 (vert, leg region, row 138, between EC's 10 & 9)

A t:= E D2- (D - 2 t)2' A o := E D 2 A := E-(D - 2 t)2 4 4 4 2

A t= 0.1059 in A o= 0.442 in2 A; = 0.336 in 2

l Hydrod namic Mass Coefficient (F): ,

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (lbf7in): Wy W y := At'Pt ? PpA; + F p s A o W y_= 0.0457 Ibf -

(For Veritical) m Virtual Density (Ibffm3 ): p, Wv p y := py = 0.432,3lbf (for ANSYS input)

At m

CSE 97-158

f A-SONGS-9416-1168, Rev. 00 Appendix Al Page A9 of Al-50 Tube Virtual Mass Calculation

, Tube Rows 126 & 121 - EC's 9 & 10 Inactive:

p t := 0.305 lbf Tube Density (I-600) D := 0.75 in Tube Dia, m

t := 0.048 in Tube Thickness p p := 42.664 lbf Avg. Pri. Fluid Density A

P := 1.0 in Triangular Pitch p s := 5.824 Ibf Secondary Fluid Density 3 (vert leg region, row 126, between EC's 10 & 9) g 2 2 A*t '

.D - (D - 2 t)2' A o ::4E D A; := E-(D - 2 t)2 4 4 A t= 0.1059 in 2 A o= 0.442 in 2 2 A ; = 0.336 in .

Hydrodynamic Mass Coefficient (F):

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (IbfTm): Wy W y :: A t'Pt+ P A p j + F p s'A o W y= 0.0452 Ibf (For Veritical) m Virtual Density (lbfTm3 ): py Wv p y := A py = 0.427 lbf (f r ANSYS input) t m CSE-97158

A-SONGS-9416-1168, Rev 00 Appendix Al Page A10 of Al Tube Vhtual Mass Calculation Tube Rows 120 & 111 - EC's 8 & 9 Inetive p t := 0.305 Ibf Tube Density (I-600) D := 0.75 in - Tube Dia.

m t := 0.048 in Tube Thickness pp  := 44.646 Ibf Avg. Pri. Fluid Density 0 P := 1.0 in Triangular Pitch p s := 6.498 lbf Secondary Fluid Density 3 (vert, leg region, row 120, between EC's 8 & 9) g A t:= 1 D2- (D - 2 t)2' A o:=ED 2 A; := E-(D - 2 t)2 4 4 4 A t= 0.1059 in 2 A o= 0.442 in 2 A g = 0.336 in 2

Hydrodynamic Mass Coefficient (F):

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

VirtualMass (lbflin): Wy W y := At'Pt + PpA + F p s A o W y=0.0461 Ibf --

(For Veritical) m Virtual Density (lbffm3 ): p, Wv p v_ent

• A py 0.427 lbf (for ANSYS input) t m CSE-97158

A-SONGS-9416.I168, Rev. 00 Appendix Al Page Al1 ofAl-50 Tube Virtual Mass Calculation Tube Row 120 - EC 9 active. 8 & 7 inactive:

p t := 0.305 lbf Tube Density (I-600) D := 0.75 in Tube Dia.

m t := 0.048 in Tube Thickness pp  := 42.624 Ibf Avg. Pri. Fluid Density A

P := 1.0 in Triangular Pitch p s := 7.382 lbf Secondary Fluid Density g3 (vert. leg region, row 120, between EC's 7 4: 8) 2 2 A"t '

.D - (D - 2 t)2' A o := E D A;:= E-(D - 2 t)2 4 4 4 A t= 0.1059 in 2 A o= 0.442 in A i,= 0.336 in 2

Hydrodynamic Mass Coefficient (F):

F := 3.1 (factor for venical leg region, Ref. 3, Fig.14)

Virtual Mass (lbffm): Wy W y := At'Pt

• P p'A +i F p s A Ibf o W y= 0.0464 r (For Veritical) m Virtual Density (lbf/in3 ): py Wv p v_ent

• A py 0.427 lbf (f r ANSYS input) t m CSE-97-158

A-SONGSJ416-1168, Rev,00 Appendix Al Page A12 of Al-50 Tube Virtual Mass Calculation l

Tube Rows 94.108. & 110 - EC's 8 & 9 inactive:

p t := 0.305 lbf Tube Density (I-600)

D := 0.75 in . Tube Dia.

m t := 0,048 in Tube Thickness pp := 42.642- Avg. Pri. Fluid Density e

P := 1.0 in Triangular Pitch p s := 6.3 lbf Secondary Fluid Density g3 (vert leg region, row 126, between EC's 9 & 8) 2 2 l A"t '

. D - (D - 2 t)2' A o := D A := -(D - 2 t)2 A t= 0.1059 in 2 .

A n= 0.442 in2 A j = 0.336 in 2

Hydrodynamic Mass Coefficient (F):

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (ibffm): Wy

-W y := At'Pt + PpA + F p s'A o W v= 0.0456 lbf-(For Veritical) m Virtual Density (IbfTm3 ): py Wv py := py 0.4305 lbf- (for ANSYS input)

At m

s CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A13 ofAl-50 Tube Virtual Mass Calculation -

Tube Row 93 - EC's 8 & 9 inactive:

pt := 0.305 lbf Tube Density (I-600)

D := 0.75 in Tube Dia.

m Avg. Pri. Fluid Density t := 0.048 in Tube Thickness p p := 45.127-ft l P := 1.0 in Triangular Pitch p s := 6.271 lbf Secondary Fluid Density g 3 (vert. leg region, row 93, between EC's 9 & 8) 2 At 2" '

.D - (D - 2 t)2 g o ;,3 D 2 A; := E-(D - 2 t)2 4 4 4 A t= 0.1059 in 2 A o= 0.442 in2 A = 0.336 in 2 Hydrodynamic Mass CoefHeient (F):

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Vinual Mass (Ibf7in): Wy W y := At*Pt + Pp'A +i F p s A o W y= 0.046 Ibf -

(For Vcritical) m Virtual Density (lbffm3 ): py Wv p v_ent

• A py =0.4305 lbf (for ANSYS input) t m CSE-97-IS8

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A14 of Al-50 Tube Virtual Mass Calculation Tube Rows 81. 83. & 84 - EC's 7 & 8 inactive:

pt := 0.305 lbf Tube Density (I-600) D .= 0.75 in Tube Dia.

in t := 0.048 in Tube Thickness p p := 44.928 Ibf Avg. Pri. Fluid Density A P := .1. 0 in Triangular Pitch p s .- 7.2 lbf Secondary Fluid Density g 3 (vert. leg region, rows 83 & 84, between EC's 9 & 8)

A2 t 5' 2

D - (D - 2 t)2 A o := E D 2 A; := E-(D - 2 t)2 4- 4 4 2

A t= 0.1059 in A o= 0.442 in 2 A i= 0.336 in 2

Ilydrodynamic Mass Coefficient (F). k F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (Ibf7in): Wy W y := At*Pt + Pp' A i+ F p s'A o W y= 0.047 Ibf (For Veritical) ,

Virtual Density (Ibf71n3 ): py Wv p

y := A py = 0.4414 lbf (f r ANSYS input) t in CSE-97-IS8

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A15 of Al-50 Tube Virtual Mass Calculation Vertical Lee Reaion-Tube Row 83 Staked Tube With Three Top EC's 6.7.&8 Inactive p t := 0.305 Ibf Tube Densi y (I-600) D := 0.75 in Tube Dia.

m

= . 8 Tube Thickness p stk := 0.192 Stake Density m

P := 1.0 in Triangular Pitch lbf Secondary Fluid Density p s := 7.67 3 (vert, leg region, row 83, between EC's 6 & 8) ft 2 2 A*t '

D - (D - 2 t)2' A o := D D stk := 0.5 in 2

A t= 0.1059 in A o= 0.442 in 2 A stk := D stk A stk =0.196 in 2

Hydrodynamic Mass Coefficient (F):

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (Ibf71n): Wy W y := A t'P t+ P stk A stk + F p s A o W y =0.0761 k (For Veritical) m Virtual Density (Ibf/in3): py TV v

p v_ent ;" A py 0.4414 lbf (f r ANSYS input) t m CSE-W-158

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A16 of Al-50 Tube Virtual Mass Calculation Tube Row 70 - EC's 7 & 8 inactive:

p t := 0.305 lbf Tube Density (I-600) D := 0.75 in Tube Dia.

m t := 0.048 in Tube Thickness p p := 44.859 lbf Avg. Pri. Fluid Density A

P = 1.0 in Triangular Pitch p s := 7.006.bf Seconda. y Fluid Density ft 3 (vert. leg region, row 70, between EC's 7 & 8) 2 2 A t:= -

D - (D - 2 t)2' A o := E D A j := E-(D - 2 t)2 4 4 4 2 2 2

- At= 0.1059 in A o= 0.442 in A; = 0.336 in Hydrodynamic Mass Coefficient (F):

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (lbfTm): Wy W y := A p t + PpA + F p s' A o g

W y= 0.0466 - (For Veritical) m Virtual Density (IbfTm3 ): p y

\V v p py = 0.4398 Ibf (for ANSYS input) y := A t m

st-97-158

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A17 ofAl-50 Tube Virtual Mass Calculation -

Vertical Lee Remion-Tube Row 49 Tube Row 49 - EC's 6 & 7 inactive:

p t := 0.305 lbf Tube Density (I-600) D := 0.75 in Tube Dia.

m t := 0.048 in Tube Thickness

pp

= 44.651 Ibf Avg. Pri. Fluid Density A P := 1.0 in Triangular Pitch p s := 8.181 lbf Secondary Fluid Density g 3 (vert. leg region, row 49, between EC's 6 & 7)

A t:= 1 D2 - (D - 2 t)2' A o=ED 2 A := E-(D - 2 t)2 4 4 4 A t= 0.1059 in 2 A o= 0.442 in 2 A = 0.336 in 2

I Hydrodynamic Mass Ccefficient (F):

F := 3.1 (factor for vertical leg region, .tef. 3, Fig.14)

Virtual Mass (Ibf/in): Wy W y := At'Pt + Pp'A + i F p s'# o W y= 0.0475 lbf -

(For Veritical)

In Virtual Density (lbflin3 ): py WV p y := A py = 0.4482 lbf- (for ANSYS input) t m-CSE-97-158

l A SONGS 9416-1168, Rev. 00 Appendix Al Page A18 of Al-50 l Inhelhinallians C4kaladea Tube Row 46 - EC's 6 & 7 inactive:

p t := 0.305glbf Tube Density (1-600) D := 0.75 in Tube Dia.

In l t := 0.048 in Tube Thickness

! p p := 44.596 lbf Avg. Pri. Fluid Density A

P := 1.0 in Triangular Pitch p s := 7.637 lbf Secondary Fluid Density 3

3 (vert leg region, row 46, between EC's 6 & 7) 2 2

-A t "

.D - (D - 2 t)* A o :=4 E.D 4

A i:= 34(D - 2 t)2 4

2 2 t = 0.1059'in A o=0.442 in* A i= 0.336 in Hydrodynamic Mass CoefEcient (F):

F := 3.1 (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (Ibf/in): W, W y = At'Pt + Pp'A i+ F p, A o W y= 0.047 Ibf --

(For Veritical) m VirtualDensity (lbf7in3 ): p y Wv p y: py = 0l444? lbf (f r ANSYSinput)

At m CSE 97158

A -SONGS 9416.I168, Rev. 00 Appendix Al Page A19 of Al 50 Tube Yhtual Maas CaletdaliRR Iube Row 22 - EC's 6 & 7 inmetive:

p t := 0.305 lbf Tube Density (I-604 D := 015 in Tube Dia.

In t := 0.048 in Tube Thickness p p := 44.52 Ibf Avg. Pri. Fluid Density A

P := 1.0 in Triangular Pitch p s := 8.684 lbf Sectadary Fluid Density g-3 (vert, leg region, row 22, between EC's 6 & 7) 2 2 A t:= D - (D - 2 t)2 A o=3D A g := E-(D - 2 t)2 4 4 4 A t=0.1059 in2 A o= 0.442 in 2 A g = 0.336 in 2

Hydrodynamic Mass Coefficient (F):

l F := 3.1 _ (factor for vertical leg region, Ref. 3, Fig.14)

Virtual Mass (lbfTm): Wy r

W y := At'Pt + Pp'A i+ F p , A o W y= 0.0478 Ibf -

(For Veritical) m Virtual Density (Ibf7in3 ): py p y: p y = 0.4518 - (for ANSYS input)

At m CSE-97158

A-SONGS 9416-ll68, Rev. 00 Appendix Al Page A20 of Al 50 Critical Velocity Calculations h

CSE 97158 m . . ~

i

' A SONGS 9416-1168, Rev. 00 Appendix Al Page A21 of Al 50 Critical Flow Velocity for Tube Row 147 - Vertieni Lee -hot side EC's 9 & 10 tametive Inout Parameters:

D:=0.7$in (Tube Dia.)

K:=3.2 (Instability Constant, per Ref.10, for triangular pi- h CE bundles) f:= 10.93 Hz (Tube Natural Frequency, ANSYS result for row 147 out-of-plane, max, disp. between EC's 9 & 10, Mode #1) m o := 0.0462 -

Ibf (Tube virtual mass per unit length) in p := 6.41 Ibf (Avg. secondary fluid density, row 147, between EC's 9 & 10, hot side) g3 .

( := 0.0261 (Damping per Ref.10) 6 o:=2x-( (Log decrement) m o o Critical Flow Velocity V cr := K f D-3 pD V cr = 4.165 1 V e g'= 54.4 I sec V cr " 49 99 * ,

see see V eg SR := SR = 1.088 > 1.00 V cr '"""*""

CSE 97158 a

l A-SONGSo94161168, Rev. 00 Appendix Al Page A22 of Al 50 Cr4*le=1 Plow Vataalty for Tube Row 147 - Ver+1eal T hot eMa EC #10 active. EC's 9 & 8 lametive innut Paramers:

D := 0.75 in (Tube Dia.)

K := 3.2 (Instability Con; tant, per Ref.10, for triangular pitch CE bundles) f:= 12.5 Hz (Tube Natural Frequency, ANSYS result for row 147 out-of-plane, i max. disp. between EC's 9 & 8) m o := 0.0462 lbf (Tube virtual mass per unit length) in ,

p = 7.17 Ibf (Avg. secondary fluid density, between EC's 9 & 8)

A

. ( := 0.0255 (Damping from Ref.10) 6 o := 2 n G t

m o o Critical Flow Velocity V cr := K f D- 2 3 PD V cr = 53.43 I V cr " 4 45 *seC -- V eft

• 39 l' Sec SCC -

SR := SR = 0.732 < 1.0 '

V cr *********

CSE-97 IS8 P-a..me- ~- . . . - . . - ..-.,,v_.,_ ,,-.-9_..._.-y.w,,._w,,..,, , , , , , , , < , , , , , , , , , , - . -.g_... . _, , _y-r., -,

I A SONGSo94161168 Rev. 00 0

l Appendix Al Page A23 of Al-50 l

1 1 Critical Mow Velocity for Tube Row 147 - Vertical Lee -bot side EC's 10 & 9 active. CC's 8 & 7 inactive input Parameters:

D := 0.75 in (Tube Dia.)

K = 3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f.= 10.81 Hz (Tube Natural Frequency, ANSYS result for row 147 out-of plane, max. disp. between EC's 8 & 7) m o := 0.0462 Ibf -

(Tube virtual mass per unit length) m p .= 8.164 ibf (Avg. secondary fluid density, between EC's 8 & 7) 3 ft G := 0.0261 (Damping per Ref.10) 6 o:=2xG (Log decrement) m6o o Critical Flow Velocity:

V cr := K f D- ,

3 p D*

V cr = 3.65 1 V cr = 43.81 I V eg:= 29.6

• sec see see V ett SR:= SR = 0.676 <l.0 V er ""*""" '

CSE 97158

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A24 of A150 l

Critical Flow Vdocity for Row 147 Stak4 Tubes - Ver*kM Ise

-bot side EC's 8. 9. & 10 Inactive Inout Parameters:

D := 0.75 in (Tube Dia.)

K := 3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f:= 4.96 Hz (Tube Natural Frequency, ANSYS result for row 147 out-of-plane, max. disp. between EC's 8 & 10, Mode #1) m o := 0.0755 --

tn lbf (Tube virtual mass per unit leng.h) p := 6.91 Ibf (Avg. secondary fluid density, row 147, between EC's 8 & 10, hot side) ft 3

( := 0.0283 (Damping, per Heilker, Beard, Park paper, Ref.10)

G stk := 0.055 (Damping due to stake, Ref. 7)

( := ( + ( stk ( = 0,083 6 o:=2x-( (Log decrement) m5oo Critical Flow Velocity:

V cr := .K f D-s pD 3 V cr = 49.89 - V cr = 4.16 1 V efr:=

see see 47sec0 A Y eff SR:= SR = 0.942 < l.0 V cr **********

CSE 97 IS8

A-SONGS-9416-ll68, Rev. 00 Appendix Al Page A25 of Al 50 Critical Row Valaelty for Tube Row 145 - Verele=1 Im -bot sMa EC's 9 & 10 l==*tive Innut Parameters:

D := 0.75 in (Tube Dia.)

-K:=3.2 -_ (Instability Constant, per Ref.10, for triangular pitch CE bundles) 1 f:= ll.39 Hz (Tube Natural Frequency, ANSYS result for row 145 out-of-plane, max. disp. between EC's 9 & 10, Mode #1) -

m o := 0.0462 --

lbf (Tube virtual mass per unit length) m p := 6.41 Ibf (Avg. secondary fluid density, row 145, between EC's 9 & 10, hot side) fl _

( := 0.0259 (Damping per Ref.10) 6 o := 2.x-( (Log decrement) mo o Critical Flow Velocity:

V cr := K f D-3 pD V cr = $1.89 b V cr= .4.321 V,fr:=52.5I see see see V eg SR .= SR = 1.012 > 1.0 V cr CSE-97158

__---a

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A26 of Al-30 l

Critical Mow Velocity for Tube Row 144 - Venical Lee -hot side EC's 9 & 10 inactive Input Parameters:

D := 0.75 in (Tube Dia.)

K:=3.2 (Instability Constant, per Ref.10, for tri, pitch CE bundles) f:= 11.64 Hz (Tube Natural Frequency, ANSYS result for row 144 out-of-plane, max. disp. between EC's 9 & 10, Mode #1) m o := 0.0459 -

lbf (Tube vinual mass per unit length) m p := 6.09 ibf (Avg. secondary fluid density, row 83, between EC's 9 & 10, hot side) 3 ft

( := 0.0258 (Damping from Ref.10)

S o:=2x-( (Log decrement) m o o Critical Flow Velocity: V cr := K f D-3 pD V cr = 54.12 - y cr = 4.51 1 sec V eft:= 56.4 I see V eft SR:= SR = 1.042 > 1.0 V cr ...........

CSE-97158

7 A-SONGS-9416-1168, Rev. 00 Appendix Al Page A27 of Al-50 e

Critical Mow Velocity for Tube Row 139 - Vereleal i m -hot side l

, EC's 9 & 10 laictig I Input Parameters:

D := 0.75 in (Tube Dia.)

K := 3.2 (Instability Constant, per Ref.10, for tri. pitch CE bundles) f:= 13.02 Hz (Tube Natural Frequency, ANSYS result for row 139 out of-plane, max. disp. between EC's 9 & 10, Mode #1) m o := 0.0459 -

lbf (Tube virtual mass per unit length) m p := 6.09 ibf (Avg. secondary fluid density, row 139, between EC's 9 & 10, hot Side) d'

( := 0.0254 (Damping from Ref.10) 8 o =2.x-( (Log decrement) m6o o Critical Flow Velocity: V cr =KfD-3 pD V cr = 60.07 I V cr r= 5.01 1 V eg:= 55.2 I SeC Sec Sec SR := SR = 0.919 < 1.0 V cr ***********

CSE.97158

A-SONGS 9416-1168, Rev. 00 ,

Appendix Al Page A28 of Al 50 I I

Critical Flow Velocity for Tube Row 138 - Vertical Lee -hot side Ep's 9 & 10 immetive Inout ParamdtrI

\

D := 0.75 in (Tube Dia.)

K:=3.2 (Instability Constant, per Ref.10, for tri. pitch CE bundles) f:= 13.3 Hz (Tube Natural Frequency, ANSYS result for row 147 out-of-plane, max. disp. between EC's 9 & 10, Mode #1) m o := 0.0457 -

lbf (Tube vinual mass per unit length) m p := 5.824 Ibf (Avg. secondary fluid density, row 83, between EC's 9 & 10, hot side) tt

( := 0.0253 (Damping per Ref.10) 6 o:=2x-( (Log decrement) mSo o Critical Flow Velocity.; Y cr := K f D-4 pD V cr = 62.48 I V cr = 5.21 1 V eg:= 64.6 I sec sec see V efy -

SR := SR = 1.034 > 1,0 V cr ............

CSE 97-158

-- -. - _ . - . - . - _ - .. - .._ - .- - . - - . - - . - _ .. ~ . . - . _ - .. - - .

4 1

A-SONGS-9416-1161 m. ,

Appendix Al Page A29 ofAl-i k

Critical Mew Velocity for Tube Row 127 - Ver+1eal I mr -hot side EC's 9 & 10 inactive Input Parameters: r D := 0.75 in (Tube Dia.)

- K:=3.2 (Instability Constant, per Ref.10, for tri pitch CE bundles)

, f:= 17.56 Hz (Tube Natural Frequency, ANSYS result for row 127 out-of-plane,

max. disp. between EC's 9 & 10, Mode #1) m o := C 0457.lbf --

(Tube virtual mass per unit length) m p := 5.824 ibf (Avg. secondary fluid density, row 127, between EC's 9 & 10, hot side) fl

( := 0.0238 (Damping per Ref.10) ,

6 e := 2 x-( (Log decrement) mo o Critical Flow Velocity:

V cr :: K f D-3 pD V cr = 80.02 I V cr = 6.67.1 V eg:= 60.2 I sec sec see V ,gy SR := SR = 0.752 < l.0 V cr ***********

CSE 97-158

-w. - . . . . . . , _ , . -,___..-...m.m... - , , - - , - - - , , _ , , . - - - .

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A30 of Al-50 l

Critical Mow Velocity for Tube Row 126 - Ver* leal Lee -hot side EC's 9 & 10 i==etive lap _u!.PKameters:

1 D := 0.75 in (Tube Dia.)

i K := 3.2 (Instability Constant, per Ref.10, for triangilar pitch CE bundles) f s 18.15 Hz (Tube Natural Frequency, ANSYS result for row 147 out-of-plane, max. disp. between EC's 9 & 10, Mode #1) m o = 0.0452 lbf -

(Tube virtual mass per unit length) m p ;= 5.824 ibf (Avg. secondary fluid density, row 83, between EC's 9 & 10, hot side) 3 ft

( := 0.0237 (Damping per Ref.10) 5 o:=2x-( (Log decrement) mOO Critical Flow Velocity :

V cr := K f D- ,

3 p D' V cr = 82.08 I V cr = 6.84 1 V ,gy:= 61.4.1 uc nc ac

.V eft SR:= SR = 0.748 < l.0 V cr ***********

CSE 97-158

i l

A SONGS-9416-1168, Rev. 00 l Appendix Al Page A31 of Al-50 Critical Mow Velocity for Tube Row 121 - Vertical Lee -hot side EC's 9 & 10 i==ctive l

Innut Parameters:

D .= 0.75 in (Tube Dia.)

K := 3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f:= 20.87 Hz (Tube Natural Frequency, ANSYS result for now 121 out-of-plane, max. disp. between EC's 9 & 10, Mode #1) m o := 0.0452 -

Ibf (Tube virtual mass per unit length) in p := 5.824 Ibf (Avg. secondary fluid density, row 121, betwwa EC's 9 & 10, hot side) fY

( := 0.0228 (Damping per Ref.10) 8 o:=2x-( (Log decrement) m6 n n Critical Flow Velodly; V cr := K f D-s pD V cr = 92.57 I V cr = 7.71 1 V eft:= 60,1 I see see sec V egy SR = SR = 0.649 < 1.0 V cr CSE-97158 l

J

A-SONGS-9416-1168, Rev. 00 ,

Appendix Al Page A32 ofAl-50 Critical Flow Velocity for Tube Row 120 - Vertical Lee -hot eMe EC's 8 & 9 i==ctive Input Parameters:

D := 0.75 in (Tube Dia.)

K := 3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f:= 10.69 Hz (Tube Natural Frequency, ANSYS result for row 120 out-of-plane,

max. disp. between EC's 8 & 9, Mode #1) mo

= 0.0461 m Ibf (Tube virtual mass per unit length) ibf p := 6.4983 (Avg. secondary fluid density, row 83, between EC's 7 & 8, hot side) ft 4

( := 0.0262 (Damping per Ref.10) 5 o:=2x.( (Log decrement) i mS o o Critical Flow Velocity:

V cr := K f D' 3 pD 2 V cr = 48.6 - V cr = 4.05 .1 V eg:= 52.6 -

SCC SCC Sec Vg e SR := SR = 1.082 > 1.0 Y cr ,,........

CSE 97158

. - . . , _ - . _ .~ _ _ . _ . _ _ _.- __ ..

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A33 of Al-50 Critical Flow Velocity for Tube Row 120 - Ve+=1 Lee -hot side i

EC #9 active. EC's 8 & 7 Inactive f

Inout Parameters:

l D := 0.75 in (Tube Dia.)

l K := 3.2 (Instability Constant, per Ref.10, for trian gular pitch CE bundles) f:= 10.87 Hz (Tube Natural Frequency, ANSYS result for row 120 out-of. plane, max, disp between EC's 8 & 7) mo  := 0.0464 m lbf (Tube virtual mass per unit length) p := 7.382 ibf (Avg. secondary fluid density, row 83, between EC's 7 & 8, hot side) ft

( := 0.0261 (Damping per Ref.10) -

6 o:= 2 x C (Log decrement) mSo o Critical Flow Velocity :

V cr := K f D-3 pD V cr =46.42 b V egy:= 56.2 I see see SR:= SR = 0.78 < l.0 V cr **********

CSE 97158

A-SONGS-941601168, Rev. 00 Appendix Al Page A34 cf Al 50 l

l Critical Flow Velocity for Tube Row 111 - Vertical Lee -hot side EC's 8 & 9 i==ctive innut Parameters:

D := 0.75 in (Tube Dia.)

K := 3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f:= ll.04 Hz (Tube Natural Frequency, ANSYS result for row 111 out-of-plane, max. disp. between EC's 8 & 9, Mode #1) m o := 0.0461 lbf -

(Tube virtual mass per unit length) m p := 6.498 Ibf (Avg. secondary fluid density, row 111, between EC's 7 & 8, hot side) 3 ft

( := 0.0260 (Damping per Ref.10) 6 o := 2 x-( (Log decrement) m o o Critical Flow Velocity :

V cr := K f D-3 pD V er = 50 I V eg = 51.6 I see see V eg SR:= SR = 1.032 > 1.0 Y cr CSE-97158

c A SONGS-9416-ll68, Rev. 00 Appendix Al Page A35 ofAl-50 Cn4*le=1 Mew Velocity for Tabe Rew 110 - Ver* leal Y -hot side EC's 8 A 9 inactive Input Parameters:

D := 0.75 in (Tube Dia.)

K := 3.2 (Instability Constant, per Ref. 20, for triangular pitch CE bundles) f;* ll.34 Hz (Tube Natural Frequency, ANSYS result for row 110 out-of-plane, max. disp. between EC's 8 & 9, Mode #1) mo  := 0.0456 Ibf (Tube virtual mass per unit length) in p := 6.3 Ibf (Avg. secondary fluid density, row 83, between EC's 7 & 8, hot side) 3 ft (is 0.0259 (Damping per Ref.10) 6 o:=2nG (Log decrement) j m6 o n Critical Flow Velocity :

V cr := K f D-3 pD V cr = 51,77 I V ,g := 58.4 *-

sec see SR !=

Vy SR =...1 128..>.10 .

CSE-97158

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A36 of Al-50 Critical Mow Velocity for Tube Row 108 - Vertleal Lee -hot side EC's 8 & 9 l==etive

! Inout Parameters:

l D := 0.75 in (Tube Dia.)

K:=3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f:= 11.84 Hz (Tube Natural Frequency, ANSYS result for row 110 out of plane, max. disp. between EC's 8 & 9, Mode #1) m o := 0.0456 m lbf (Tube virtual mass per unit length) p := 6.3 lbf (Avg. secondary fluid density, row 83, between EC's 7 & 8, hot side) 3 A

( := 0.0257 (Damping per Ref.10)

(Log decrement) 6 o=2z-(

mOO Critical Flow Velocity :

V cr := K f D-3 pD V cr =53.84 I Vge := 57.9-SeC seC Vge SR := SR = 1.075 > 1.0 V cr ..............

CSE-97158

_ __ __ _ n

A SONGS-9416-1168, Rev. 00 Appendix Al Page A37 of A150 3

Critical Flow Velocity for Tube Row 94 - Vertical Lee -hot side EC's 8 & 9 Inactive p

v 5

'1 Innut Parameters; D = 0.75 in (Tube Dia.) .

K:=3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f = 16.56 Hz (Tube Natural Frequency, ANSYS result for row 94 out of plane, max. disp. between EC's 8 & 9, Mode #1) m o = 0.0456 lbf (Tube virtual mass per unit length) in l

l p = 6.3 Ibf (Avg. secondary fluid density, row 94, betw m EC's 7 & 8, hot side) f\

( .= 0.0242 (Damping per Ref.10) 6 o:=2n-( (Log decrement) m6 o o Critical Flow Velocity :

V cr := K f D-3 pD V cr = 73.08.I V see eft =53.0I see V egy SR:* SR = 0.725 < l.0 V cr " * " " * " "

CSE-97 158

A SONGS 9416-1168, Rev. 00 Appendix Al Page A38 of Al-50 L ,

Critical Flow Velocity for Tube Row 93 - Vertical Lee -hot side gg .

Ef's 8 & 9 inactive 7

n InimLPNanieters:

- D := 0.75 in (Tube Dia.)

K = 3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f = 16.92 IIz (Tube Natural Frequency, ANSYS result for row 93 out-of plane, max. disp. between EC's 8 & 9, Mode #1) m o = 0.046 lbf (Tube vinual mass per unit length) p a 6.271 lbf (Avg. secondary fluid density, row 93, between EC's 8 & 9, hot side) ft

( := 0.0241 (Damping per Ref.10) -

6 o =2n-( (Log decrement) m6 o o Critical Flow Velocity : V cr aKfD-3 pD Y cr = 75.01 I V eg := 47.3.5 seC seC V eg SR = SR = 0.631 < l.0 V cr *"*"***""

l CSE-97 IS8 l l

' A0 SONGS-9416-1168, Rev 00 Appendix Al Page A39 of Al-50 l

l Cdtscal Flow Velocity for Tube Row 84 - Vertical Lee -hot nide EC's 8 & 7 i==etiv<t, Input Parameters:

D := 0.75 in (Tube Dia.)

K := 3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f:= 9.73 Hz (Tube Natural Frequency, ANSYS result for row 84 out-of-plane, max. disp. between EC's 8 & 7, Mode #2) m o := 0.0467 lbf (Tube virtual mass per unit length) in p := 7.2 Ibf (Avg. secondary fluid density, row 84, between EC's 8 & 7, hot side) ff

( := 0.0265 (Damping per Ref.10) 8o:=2xG (Log decrement) m6 o o Critical Flow Velocity :

V cr := K f D-3 pD V cr =42.53 I V eg:= 41.4 I uc m:

V ett SR := SR = 0.973 < l.0 V cr "************

CSE 97158 1

A-SONGS-94161168, Rev. 00 Appendix Al Page A40 ofAl-50 i

e Critical Mew Velocity for Tube Row 83 - Vertical Lee -hot side EC's 7 & 8 laaetive

Input Parameters

D := 0.75 in (Tube Dia.)

K = 3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f := 8.4 Hz (Tube Natural Frequency, ANSYS result for row 83 out-of-plane, max. disp. between EC's 7 & 8, Mode #1) m o := 0.0467 m lbf (Tube virtual mass per unit length) p := 7.2 Ibf (Avg. secondary fluid density, row 83, between EC's 7 & 8, hot side) fd

( 2 0.027 (Damping per Ref.10) 6 o:=2n.( (Log decrement) m o 5, Critical Flow Velocity :

_V cr := K f D-3 pD V cr = 37.07 I V eg := 42 I see see SR:= SR = 1.133 > 1.0 V cr ***************

CSE-97-158

1 A-SONGS 9416-1168, Rev 00 l Appendix Al Page A41 of Al-50 '

Critical Mow Velocity for Tube Row 82 - Vertical Len -hot side l

EC's 7 & 8 t==ctive Input Parameters:

D := 0.75 in (Tube Dia.)

K := 3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f:= 8.6 Hz (Tube Natural Frequency, ANSYS result for row 83 out-of-plane, max. disp. between EC's 7 & 8, Mode #1) m o := 0.0467 --

lbf (Tube virtual mass per unit length) m p := 7.2 ibf (Avg. secondary fluid density, row 83, between EC's 7 & 8, hot side) ff

( := 0.0269 (Damping per Ref.10) 6 o:=2x-( (Log decrement) mo o Critical Flow Velocity :

V cr := K f D-3 pD V cr = 37.88 I V eg := 41.9 I see see SR:= SR = 1.106 > 1.0 V cr ...............

CSE-97158

~. _- __ ___ _ _ . . _ _ _ - - . _ . _ _ _ _ . , _ . _ _ _ _ - _ _ - . - _ _ _ .__

l A-SONGS-9416-1168, Rev. 00 Appendix Al Page A42 ofAl-50 i

l Critical Flow Velocity for Row 83 Senk4 Tubes - Vertical Lee

-hot side - EC's 6. 7. & 8 Inmetive Inout Parameters:

D := 0.75 in (Tube Dia.)

K := 1.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f:= 3.86 Hz (Tube Natural Frequency, ANSYS result for :ow 147 out-of plane, max. disp. between EC's 9 & 7, Mode #1) m o := 0.0761 -

lbf (Tube virtual mass per unit length) m p := 7.66 Ibf (Avg. secondary fluid density, row 147, between EC's 6, & 8, hot side) 3 A .

( := 0.0287 (Damping, per Heilker, Beard, Park paper, Ref.10)

( stk '= 0.055 (Damping due to stake, Ref. 7)

( = ( + ( stk ( = 0.084 4

6 o := 2 z ( (Log decrement) m6 n n Critical Flow Velocity :

V cr := K f D-3 PD V cr = 37.11

• V cr = 3.09 1 V gy e := 37-seC see seC SR := SR = 0.997 < l.00 V cr ***********

CSE-97158

A SONGS-9416-1168, Rev. 00 Appendix Al Page A43 of Al Critical Mow Velocity for Tube Row 70 - Vertkal La -hot side EC's 8 & 7 Inactive 1

Inout Parameters:

D := 0.75 in (Tube Dia.)

K:=3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f:= 10.97 Hz (Tube Natural Frequency, ANSYS result for row 70 out-of plane, max. disp. between EC's 8 & 7, Mode #2) m o := 0.0466 m Ibf (Tube virtual mass per unit 'ength) p := 7.006 ibf (Avg. secondary fluid density, row 70, between EC's 8 & 7, hot side) ft 3

( := 0.0261 (Damping per Ref.10) 6o:=2x-( (Log decrement) mSo o Critical Flow Velocity :

V cr := K f D-n pD V cr = 48.19 - V eg:= 48.7 I see see V eg-SR:= SR = 1.01 > 1.0 V cr '

4 CSE 97158

A-SONGS 9416-1168, Rev. 00 Appendix Al Page A44 of Al-50 Critical Flow Velocity for Tube Row 49 - Verticalh Hot & Cold Lens Modeled - EC's 6 & 7 inactive i

l Input Parameters:

l I

D := 0.75 in (Tube Dia.)

l K := 3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f:= 7.86 Hz (Tube Natural Frequency, ANSYS result for row 49 out-of-plane, max. disp. between EC's 6 & 7, Mode #1 for full model )

m o := 0.0475 m Ibf (Tube virtual mass per unit length) p := 8.181 Ibf (Avg. secondary fluid density, row 49, between EC's 6 & 7, hot side) 3 ft

( := 0.0272 (Damping per'Ref.10) t 6o:=2x-( (Log decrement) j m6 no Critical Flow Velocity : -

V cr = K f D-3 pD V cr = 32.94 I V efy = 34.0 A Sec Sec Vg e SR := SR = 1.032 > 1.00 V cr *************

CSE 97 tS8 0

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A45 of Al-50 Q4tical Flow Velocity for Tube Row 46 - Vertical lan-Fat & Cold sides modeled - EC's 6 & 7 lanctive Inout Parameters:

l D := 0.75 in (Tube Dia.)

l K:=3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) l f:= 8.32 Hz (Tube Natural Frequency, ANSYS result for row 46 out-of-plaae, i max. disp. between EC's 6 & 7, Mode #1) m o := 0.047 -

lbf (Tube virtual mass per unit length) m p := 7.637 ibf (Avg. secondary fluid density, row 46, between EC's 6 & 7, hot side) ft

( := 0.0270 (Damping per Ref.10)

I 5 o:=2x-( (Log decrement) m5 o o Critical Flow Velocity :

V cr := K f D-3 pD V cr = 35.76 *b V eg = 35.6 I see see V eg SR:= SR = 0.996 < l.0 V cr ***********

CSE 97-158 e o

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A46 of Al-50 Critical How Velocity for Tube Row 22 - Vertical Lens -

Hot & Cold Sides Modeled - EC's 6 & 7 inactive Input Parameters:

D := 0.75 in (Tube Dia.)

K:=3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f '= 13.41 Hz (Tube Natural Frequency, ANSYS result for row 22 out-of-plane, max. disp. between EC's 6 & 7, Mode #1) m o := 0.0478 m lbf (Tube virtual mass per unit length) p := 8.684 Ibf (Avg. secondary fluid density, row 22, between EC's 6 & 7, hot side) f0

( := 0.0252 (Damping per Ref.10) 6 c:=2x-( (Log decrement';

m6 o o Critical Flow Velocity :

V cr := K f D. ,

3 p D' V cr = 52.66 I V efy:= 31.5 I sec see SR := SR = 0.598 < l.00 V cr *********

CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A47 of Al-50 Critical Mow Velocity for Tube Row 147 - Vertical Lee -hot side EC's 10 & 9 active. EC's 5.6.7.8. inactive--StahM tube Inout Parameters:

D := 0.75 in - (Tube Dia.)

K:=3.2 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f:= 3.14 Hz (Tube Natural Frequency, ANSYS result for row 147 out-of-plane, max. disp. between EC's 8 & 7)

! m o := 0.0772

• lbf (Tube virtual mass per unit length) l p := 9.063 lbf (Avg. secondary fluid density, between EC's 8 & 7) fY

( stk := 0.055 (damping due stake in tube, CE Test)

( := 0.0289 (Damping from Ref.10) 5 ;* 5 + 5 stk

( = 0.084 6 o := 2 x-( (Log decrement)

CriticalFlow Velocity:

V cr := K f D-s pD 2 V cr =27.989 in V eg := 21.0 *-

sec SR:= SR = 0.75 < l.0 V cr ***********

CSE 97-158 l

A-SONGS-9416-1168, Rev. 00

. Appendix Al Page A48 of Al-50 Critical mo Velocity fer Tube Row 147 - Bend Rerion -

Cross-hw - EC's 9 & 10 inggy,g Input Parameters:

D := 0,75 in (Tube Dia.)

K:=7.1 (Instability Constant, per Ref.10, for triangular pitch CE bundles) f := 56.1 Hz (Tube Natural Frequenc!. ANSYS result for row 147 out-of-plane, max. disp. between EC': 9 & 10, Mode #1) m o := 0.043 -

Ibf (Tube vinual mass per unit length) m p := 4.255 Ibf 7 (Avg secondary .uid density, row 147, between EC's 9 & 10, hot side) 3 ft C := 0.014 (Damping per Ref.10) 5 o:=2x-( (Log decrement)

L m5o o Critical Flow Velocity V cr := K f D-3 pD V cr =493.664 I V cr " 41 14

• V eg:= 216.5 I sec see see

-V ety SR := SR = 0.439 < 1.00 V cr ************

CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix Al Page A49 of Al-50 Critical Flow Velocity for Tube Row 83 - Bend Rerion -

Cross-Mow - EC's 7 & 8 inactive Input Parametern D := 0.75 in (Tube Dia.)

K := 7.1 (Instability Constant per Ref.10 for tri. pitch CE bundles) i f:= 46.4 Hz (Tube Natural Frequency, ANSYS result for row 147 out-of-plane, ,

max. disp. between EC's 7 & 8) m o := 0.043 m lbf (Tube virtual mass per unit length)

p

= 4.322 lbf (Avg. secondary fluid density, row 147, between EC's 9 & 10, hot side) g3

( := 0.016 (Damping, per Heilker, Beard, Park paper) 6 o:=2x-( (Log decrement) mOO Critical Flow Velocity V cr := K f D-3 pD V cr =433.102 I V cr = 36.09 - V egy:= 320.7 I seC sec sec V eg- -

SR := SR = 0.74 < l.00 V cr **************

CSE-97-158

A-SONGS-9416-1168, Rey, 00 Appendix Al Page A50 of Al-50 Critical Mow Velocity for Tube Row 110 - Vertical Lee -hot side EC 9 inactive Inout Parameters:

D := 0.75 in (Tube Dia.)

l K := 3.2 (Instability Constant, per Ref. 20, for triangular pitch CE bundles) f:= 24.1 Hz (Tube Natural Frequency, ANSYS result for row 110 out-of-plane, max. disp. between EC's 8 & 10, Mode #1) m o := 0.0452 -

lbf (Tube virtual mass per unit length) m p := 5.89 lbf (Avg. secondary fluid density, row 83, between EC's 8 & 10, hot side) 3

{ ft

( := 0.0218 (Damping per Ref.10) 6o:=2x-( (Log decrement) m5 n n Critical Flow Velgt V cr := K f D-t 3 pD V cr = 103.94 - V eg:= 66.1 b see sec SR:= SR = 0.636 > 1.0 V cr **************

CSE-97-158

A-SONGS-9416-1168, Rev. 00

^~

ABB-CENO ,

9 APPENDIX A2 EFFECTIVE VELOCITY CALCULATIONS FOR CRITICAL TUBES l

f CSE-97-158

~

ABB-CENO Appendix A2 Page A2 2 to A2-5 F.ffective Velocity Calt dation for Circumferentini Sector 1 Tube Row 147 (Venical Sonne from EC#5 tc tube taneent nointi eggerates 8 and 9 inactive xc: Spanwise coordinates (from ANSYS model) disp: Nonnalized Displacements perpendicular to span (z-dir) from ANSYS output for Mode No. 2, frequency = 12.5 Hz UZ.

Fluid Cross Flow Velocity (ATHOS results), Coordinate and Disp. Vectors are shown below:

Node No. n :=0 62- 1 n, := n + p g,

'171.25' ' 171.25 1' .0 0 -11536 0.45 '

174.85 174.85 2 .01 7.5 -11536 0.45 178.45 178.45 3 .01936 7.6 -110.5 0.34 182.05 182.05 4 .02746 15 -110.5 034 185.65 185.65 5 .0337 15.1 -6.94 -0.09 "A ' D) " 189.25 6 .03746 189.25 27.25 -6.94 -0.09 192.85 192.85 7 .03818 27.35 - 4.1 -0.53 196.45 196.45 8 .03531 44.75 - 4.1 -0.53 200.05 200.05 9 .02832 44.85 -2.71 -129 203.65 203.65 10 .01671 62.25 -2.71 -1.29 l 207.25 207.25 11 .0 62.35 -4.19 -0.66 211.05 211.05 12 .02316 80.25 -4.19 -0.66 214.85 214.85 13 -

.04934 8035 5.9 -237 218.65 218.65 14 .07538 98.25 5.9 -237 222.45 222.45 15 .09813 9835 22.41 1.08 226.25 226.25 16 .11455 117.25 22.41 1.08 230.05 230.05 17 .12162 11735 .

3.17 3.48 233.85 233.85 18 .11646 136.25 3.17 3.48 237.65 237.65 19 .09626 13635 1.46 4.22 241.45 241.45 20 .05832 153.75 1.46 422 24525 245.25 21 .0 153.85 -23.0 5.5 24833 24833 22 .06329 171.25 -23.0 5.5 251.4 251.4 23 .13859 17135 22.91 4.74 254.48 254.48 24 .22289 189.25 22.91 4.74 257.55 257.55 25 31321 18935 7.58 3.22 260.63 260.63 26 .4067 207.25 7.58 322 263.7 263.7 27 .50056 20735 3.51 331 266.78 266.78 28 .59218 226.25 3.51 331 269.85 269.85 29 .6791 22635 -28.54 2.67 272.93 272.93 30 '

.75906 245.25 -28.54 2.67 276 276 31 .83006 24535 29.5 3.28 279.08 279.08 32 .89035 255.5 29.5 3.28 282.15 282.15 33 .93847 255.6 12.48 2.8 285.23 285.23 34 .97328 265.75 12.48 2.8

. . . . noe 2 oc o., o,,o, . . . , . . .

CSE-97-158

A SONGS-9418-1188, Rev. 00

- , ABMEW ,,,,,,, ,,,,, W A2, g y g uA24 29138 29138 36 1.0 276.0 -40.26 2.19 294.45 294.45 37 .9913 276.1 41.97 4.16 297.53 297.53 38 .96807 286.25 41.97 4.16 300.6 300.6 39 .93085 286.35 15.79 5.15 303.68 303.68 40 .88056 296.5 15.79 5.15 306.75 306.75 - 41 .8184 296.6 -49.74 7.0 309J3 309.83 42 .74592 306.75 49.74 7.0 312.9 312.9 43 .66492 306.85 49.29 10.18 315.98 315.98 44 .57747 I17.C 49.29 10.18 319.05 319.05 45 .48589 317.1 20.04 12.22 322.13 322.13 46 39268 327.25 20.04 12.22 325.2 325.2 47 30052 32735 -5335 16.5 328.28 328.28 48 .21221 337.5 -5335 16.5 331.35 33135 49 .13069 337.6 77.67 4.19 334.43 334.43 50 .05894 349.56 77.67 4.19 337.5 337.5 51 .0 349.66 53.93 -634 340.5 340.5 52 .04284 361.63 53.93 -634 343.51 343.51 53 .07202 361.73 336.9 -3.13

! 346.51 54 346.51 .08905 ,370.59, , 336.9 - 3.13 ,

349.52 349.52 55 .09546 -

352.52 352.52 56 .09281 355.52 355.52 57 . 08267 358.53 358.53 58 .06667 361.53 361.53 59 04645 364.54 364.54 60 .02367 367.54 367.54 61 .0

, 370.62, ,370.62 62 .02368 ,

+=J(we>)*+ (we>)*

CSE-97-158 I.mm .

A SONGS-94181168, Rev. 00 ABS-CENO ' Appendix A2 Page A24to A2 St N-liH displacement ($) as a function of spanwise x-coordinate (cubic spline interpolation function)is shown below:

vs :=cspline(xe, disp)

$(x) :=interp(vs,xc. disp,x)

Velocity (v) as a function of spanwise x-coorriinate:

v(x) :=linterp(xv, velo,x)

Integmllimits; a := xc, b := xc a = 171.15 b = 370.62 Assunsg no spanwise variation in tube virtual mass or secondary fluid density, the effective velocity equation reduces to the following:

• b v(x)* $(x)* dx Vg :=

• b V g = 39.1 in/sec

$(x)2dx

$ e&

s

{

CSE-97-158

A SONGS-9418-11C2, Rev. 00 ABB-CENO . Appendix A2 Page A2-fto A2-j x :sxco .xe,+ 1 xg,3 i:n0.1 last(xc)

Cron Flow Gap Velocity Profile (in/sec) Mode 2 (12.5 HB Mode Shn=

380 380 -

370.33 <r 360' :

352J -

1  :

343.33 -

- I r.

. J 34o . ,

334.17

.s .

325 -

' 3209 315.83 -

306.67 297.5 -

3co n .

288.33 ,,,,,

279.17 280 ,e 1 -

pg

1. s -a m, .

-+- , .

"I3 ii.

260 "<

251.67 242.5 .

240 .

233.33 .

224.17 215 ,.

205.83 196.67 *"

187.5 ,

178.33 180 5 169.17 -

s I" 0 200 400 *

.;; 0 1 'l v(x).0 Wx).0 CSE-97-158

A SONGS-9418-1168 Rev. 00 ABS-CENO .. Appendix A2 Page A2-(to A2-51 Effective Velocity Calculation for Tube No. In Circumferentin! Sector 1 Tube Row 147 Staked (Vertical Snans from EC#5 to tube taneent noint) erecrates #8. 9 and 10 inactive xc: Spanwise coordinates (from ANSYS model) disp: Normalima Displacements perpendicular to span (z-dir) from ANSYS output for Mode No.1, frequency = 4.% Hz Fluid Cross Flow Velocity (ATHOS results), Coordinate and Disp. Vectors are shown below:

Node No. n := 0 62 - 1 n *:=n+ 1 VW. Cod.'

pga fd.

'171.25' 171.25 1 .0 0 ' 11536 0.45 '

174.85 174.85 2 .00527 7.5 -11536 0.45 178.45 178.45 3 .01022 7.6 -110.5 034 182.05 182.05 4 .01452 15 -110.5 034 185.65 185.65 5 .01786 15.1 -6.94 -0.09 189.25 **

• D)

• 189.25 6 .01991 27.25 -6.94 -0.09 192.85 192.85 7 .02036 2735 - 4.1 -0.53 196.45 196.45 8 .01891 44.75 - 4.1 -0.53

200.05 200.05 9 .01523 44.85 -2.71 -1.29 203.65 203.65 10 .00903 62.25 -2.71 -1.29 207.25 207.25 11 .0 62.35 -4.19 -0.66 211.05 211.05 . 12 .01263 80.25 -4.19 -0.66 214.85 214.85 13 .02702 8035 5.9 -237 218.65 218.65 14 .04144 98.25 5.9 -237 222.45 222.45 15 .05416 9835 22.41 1.08 226,25 226.25 16 .06349 117.25 22.41 1.08 230.05 230.05 17 .06771 117.35 3.17 3.48 233.85 233.85 18 .06514 136.25 3.17 3.48 237.65 237.65 19 .05411 13635 1.46 4.22 241.45 241.45 20 .03294 153.75 1.46 4.22 245.25 245.25 21 .0 153.85 -23.0 5.5 24833 24833 22 .03614 171.25 -23.0 5.5 251.4 251.4 23 .07992 '17135 22.91 4.74 254.48 254.48 24 .13022 189.25 22.91 4.74 257.55 257.55 25 .18589 18935 7.58 3.22 260.63 260.63 26 .24583 207.25 7.58 3.22 263.7 263.7 27 3 0892 20735 3.51 331 266.78 266.78 28 37409 226.25 3.51 331 269.85 269.85 29 ,

44028 22635 - 28.54 2.67 272.93 272.93 30 .50648 245.25 - 28.54 2.67 276 276 31 .5717 24535 29.5 3.28 279.08 279.08 32 .63501 255.5 29.5 3.28 282.15 282.15 33 .69552 255.6 12.48 2.8 285.23 285.23 34 .7524 265.75 12.48 2.8 CSE-97-15S

_ _ - - - - - - i

~

A-SONGS-94181188 Rev.00 ABS-CENO Appemix A2-Page A2-773 A21 288 3 288 3 35 .80449 265.85 -40.26 2.19 - l 29138 29138 36 J5229 2764 -40.26 2.19 294.45 294.45 37 A9397 276.1 41.97 4.16 297.53 297.53 38 .92937 286.25 41.97 4.16 300.6 300.6 - 39 .95802 286.35 15.79 5.15 303.68 303.68 40 .97953 296.5 15.79 5.15 306.75 306.75 41 .9936 296.6 -49.74 7A 309.83 309.83 42 14 306.75 -49.74 7A 312.9 312.9 43 .9986 49.29: 10.18 396J5 315.98 315.98 44 .98937 3174 49.29 10.18 319.05 319.05 45 .97233 317.1 20.04' 12.22 322.13 322.13 46 .94764 327.25 20.04 12.22 325.2 325.2 47 .91551 32735 -53.35 16.5 328.28 328.28 48 .87625 337.5 -5335 16.5 .

331.35 33135 49 .83023 337.6 77.67 - 4.19 334.43 334,43 50 .77793 349.56 77.67 4.19 337.5 337.5 51 .71987 349.66 53.93 -634 340.5 340.5 52 .65819 361.63 53.93 -634 343.51 343.51 53 .59222 361.73 336.9 -3.13 346.51 346.51 54 .52264 ,370.59, , 336.9 - 3.13 ,

349.52 349.52 - 55 .45018 -

352.52 352.52 56 3756 355.52 355.52 57 .29971 358.53 358.53 58 .22333 361.53 361.53 . 59 .14734.

364.54 364.54 60 .0726 367.54 367.54 61 .0 370.62, ,370.62. 62, ,.07149,

+=J(s>)* (s>)5 CSE-97-158

ABS-CENO Appendbc A2 Page A2 9to A2-Normalived displacement ($) as a function of spanwise x-coordinate (cubic spline interpolation function)is shown below:

vs := cspline(xc, disp)

$(x) :=intwp(va,xc. disp,x)

Velocity (v) as a function of spanwise x-coorriinate:

L v(x) :=linterp(xv, velo,x)

Integrallimits:

a := xe n

b := xeg ,) a = 171.25 b =370.62 Assuming no spanwise variation in tube virtual mass or secondary fluid density, the effective velocity equation reduces to the following:

^

l "b

v(x)* $(x)* dx V g :=

• b , V g = 47 in/sec

$(x)* dx n .a s

CSE-97-158

A-SONGS-9418-1168, Rev. 00 ABB-CENO / Appendix A2 Page A2- to A2-f x := xc o ,ze,+ 1. xg,3 i:=0,: lan(xc)

Crora Flow Gap Velocity Profile (in/sec) Mode 1 (4.96 HM Mode Shane 380 380 -

360 l 360$'r

.4 340 gar.

o 320 5 320$ r 300 r.

l - 300 -;

l

• I M ~

280$ r i  : "

=i -

-+-

260 l 2604- -

d g ',= .

D M

m. .

200

. 200 - -

1 160 0 200 400 ' '

1 ~0 1 M x),o CSE-97-158

A-SONGS-9418-1168, Rev. 00 ABB-CENO Appendix A2 Page A2 to A2 5 F&ctive Velocity Calculation for Circumferential Sector 1 To be Row 147 StakM IO (Vertical Somns from EC#5 to tube taneent noint) eccerates #5. 6. 7. and 8 inactive xe: Spanwise coordinates , disp: NormalirM (z-dir) from ANS YS output for Mode 2, fn = 3.14 Hz)

. . v6Lo. coat. ooao cg..

. 9825 . 98.25 1

.0 0 ,11536 0A5 102.05 102.05 2 7.5 -11536 0.45

.01437 105.85 105.85 3 7.6 -110.5 034

.02787 109.65 109.65 4 15 -110.5 034

.0*962 113.45 113.45 5 15.1 - 6.94 -0.09

.04874 117.25 augm(xcM " 117.25 6

.05437 G7.25 - 6.94 -0.09 121.05 121.05 7 2735 - 4.1 -0.53

.05564 +

124.85 124.85 8 44.75 - 4.1 -0.53

.0517 128.65 128.65 9 44.85 -2.71 -1.29

.04167 132A5 132.45 10 62.25 -2.71 -1.29

.02472 136.25 13625 11 6235 -4.19 -0.66

.0 139.75 13935 12 8025 -4.19 -0.66

.03017 143.25 143.25 13 8035 5.9 -237

.06682 l 14635 146.75 14 98.25 5.9 -237

.10911 15025 15025 15 9835 22A1 1.08

.15621 153.75 153J5 16 117.25 22.41 1.08

,20731 157.25 157.25 17 11735 3.17

.26158 ,3.48 160.75 16035 18 13625 3.17 3.48 31824 164.25 164.7.5 19 13635 1.46 4.22 37649 167.75 167.75 20 153J5 1.46 4.22

.43556 171.25 171.25 21 153 85 -23.0 5.5

.49472 174.85 174.85 22 171.25 -23.0 5.5

.55491 178.45 178.45 23 17135 22.91 4.74

.61369 182.05 182.05 24 189.25 22.91 4.74

.67035 185.65 185.65 25 322 J2422 18935 7.58 189.25 189.25 26 207.25 7. 18 3.22

.77469 192.85 192.85 27 20735 3.51 331 82119 196.45 xv := velo :=

196.45 28 .8632 226.25 3.51 331 200.05 200.05 29 22635 -28.54 2.67

.90025 203.65 203.65 30 245.25 -28.54 2.67

.93195 207.25 207.25 31 24535 29.5 3.28

.95796 211.05 211.05 32 29.5

,97gg3 255.5 3 28 214.85 214.85 33 12A8

,993 255.6 2.8 218.65 218.65 34 265.75 12.48 2.8 1.0 222.45 222A5 35 265.85 -40.26 2.19

, ,99986 22625 226.25 36 276.0 -40.26 2.19

.99258 230.05 230.05 37 276.1 41.97 4.16

.97826 233.85 233.85 38 28625 41.97 4.16

.95706 237.65 237.65 39 28635 1539 5.15

.92925 241.45 masan - - - - ** "* *"

CSE-97-158

MEN

-3 333 ,, W.A2,Page,A2-lito A2 5 245.25 245.25 41 296.6 49.74 7.0

.8552 24833 24833 42  %* , ggg9g 306.75 -49.74 7.0 ~

251.4 251.4 43 ,7794 306J5 49.29 10 18 254.48 354,48 44

,737 317.0 49.29 10.18 257.55 257.55 41' .69205 317.1 20.04 12.22 260.63 260.63 46 327.25 20.04 12.22

.64495 263.7 263.7 47 - 327.35 -53.35 16.5 39609 266.78 266.78 48

• 337.5 -5335 16.5

.54591 269.85 269.85 49 b 337.6 77.67 4.19

.49485 272.93 272.93 $0 349.56 77.67 4.19

,44y 276 276 51 349.66 53.93 -634 39203 279.08 279.08 52 34126 361.63 53.93 -634 282.15 282.15 53 361.73 336.9 -3.13

.29159 285.23 285.23 54 370.59, 336.9 -3.13 ,

.24358 2883 2883 55

.19775 29138 29138 56 .15465 294.45 294.45 57 .11486 297.53 297.53 58 .07893 300.6 300.6 59 ,04743 303.68 303.68 60 . .02093 306.75 306.75 61 ,o 309.83 309.83 62 .,oi495 312.9 312.9 63 .02453 -

315.98 315.98 64 02949 319.05 319.05 65 g (goco>)2 ( <t>)2

.03062 322.13 322.13 66 .02867 325 2 325.2 67

.02443 32828 32828 68 .01867 33135 33135 69 .01216 334.43 334.43 70 . 00568 337.5 337.5 71 ,o 340.5 340.5 72 .00414 343.51 343.51 73 .00694 346.51~ 346.51 74 .00855 349.52 349.52 75 .00913 352.52 352.52 76 ,oogg4 355.52 355.52 77 .00785 358.53 358.53 78 .0063 361.53 361.53 79 .00437 364.54 364.54 80 .00222 367.54 367.54 81 ,o

,370.62, , 370.62 82 .0022 '

CSE-97-158

ADG4ENO Appendr A2 Page A2eo A2>

NormmHwa displacement ($) as a function of spanwise x-coordinate (cubic spline interpolation function)is shown below:

vs := csphne(xc. disp)

$(x) :=imerp(vs,ze, disp,x)

L Velocity (v) as a function of spanwise x-coordinate:

l v(x) := hmerp(xy, velo,x)

Integrallimits:

t := xe, b := xeg a = 98.25 b = 370.62

~

Assumirg no spanwise variation in tube virtual mass or secondary fluid density, the effective velocity equation reduces to the following: .

• b v(x)* $(x)* dx Vd ;* '

• b Y d = 21 in/sec

$(x)2dx s a ,

CSE-97-158

A-SONGS-94181168. Rev. C ABS-CENO - @n A2 Page A2-oto A:

x := xe,, xe,+ 1. g,3 1:=0,1 last(xc)

Cmas Flow Gap Velocity Pmfile (in/sec) Mode 2 (3.14 Hz) Mode Shane 3.o 3s0 -

360 :

E5

, m <

340 j - 340 3':

320 {, 320 ;

D 300

" 3001 280 2804 -

o,

(

260 ;

. 2601 240 ,'

x .

240i;

~

"I

• ::10 220$ e i i o

200 200 --

180 , .

_ 180 --

160 ".

- 160 -?

140 340 r 80 0 200 400 Z a

13 0 1 M n).O CSE-97-151

A SONGS-9418-9168 Rev.0(

ABB-CENO Appendix A2 Page A2 eto A2 EMeetive Valacity Calenti tion for Tube No. In Circumferentini Sector 1 Tube Row 147 Elbow xc: Spanwise coorrlia*> (from ANSYS model) disp: Normalized Displacements perpendicular to span (z-dir) from ANSYS output for Mode No. 7, frequency = 56.1 Hz Fluid Cross Flow Velocity (ATHOS results), Coordinate and Disp. Vectors as shown below:

c := x 20 g :=c dl = 3.927 i := 023 n3 := 61 + i n := reverse (n) 360 Node No.

. . 'O 84' , , y,4 z,,

84.288 0 pg, gg, . .

g3 81.208 .22691 '

0 41.17 77.281 .56764 8.03 26.67 73.354 .85924 8.03 + .1 26.67 69'427 1.0

• • ( *

• D) " 20 79 15.94 45.92 65.5 .92886 15.94 + .1 45.92 62.583 .78161

.5 6L70 59.667 .6151 22.75 + .1 61.70 56.75 .43923 28,99 75 3 l 53.833 .2673 50.917 28.99 + .1 M

.11512 48.0 35.12 86 5

.0

• • 48 7 disp := 35.12 + .1 86.59 44.0 .07607 40.0 41.36 W5

. 07963 41.36 + .1 95.15 36.0 .04301 .,

32.0 #7'0 0 .-

28.0 .02108 47.6 r .1 W 53.85 105M 24.0 .02225 53.85 + .1 105.19 20.0 .01219 59.4 116.25 16.0 0 59.4 + .1 11625 12.0 .0066 8.0 59.4 + d M 73

. 00762 4 59.4 + d1 + .1 199.73

.00479 ~

• - 59.4 + 2 d1 286.53 0 . '

.0 '

59.4+ 2 d! + .1 286.53 59.4+ 3 d1 241.62

, 59.4 + 3.d1 + .1 241.62 59.4t46 163.67 xcureverse(xc) disp := reverse (disp) 59.4 e 4.dl + .1 ,163.67 84.288 ,

CSE-97-158

A SONGS-9418-1168, Rev. 00 ABS-CENO #. .

Appendx A2 Page A2-p A2-fi Normalized displacement ($) as a function of spanwise x-coordinate (cubic spline interpolation fnWw.)is shown below:

vs := cspline(xc, disp)

$(x) :=interp(vs,xc. disp,x) g Velocity (v) as a function of spanwise x-coordinate:

v(x):=linterp(xv volo,x)

Integrallimits:

a := xc o

b := xc a=0 b = 84.288 Assuming no spanwise variation in tube virtual mass or secondary fluid density, the effective velocity equation reduces to the following:

• b

! v(x)* $(x)* dx Vd*  !

b

, .y d = 216.5 in/sec

$(x)* dx n a CSE-97-158

ABB-CENO Appendix A2 Page A2gte A2-5 x := xe,,xe,+ 1. xc ,3 1:=0,1 last(xc)

Cross Flow Gan Velocity Pmfile (in/sec) Mode 7 (56.1 Hz) Mode Shane 90 90--

d.

70 ,

70--

60 -

, 60 ,,

50 50-i

u. \

h

~

t 30 g 3o. .

/

20 20- -

~l ,

2"

,s 10-0 100 200 300 13 g  !

3 v(x).0 1

CSE-97-158

A. SONGS-94181168, Rev. 00 ABB-CENO '

Appendix A2 Page A2- to A2-5

/7 F.ffective Velocity Calculation for Circumferentini Sector 4 Tube Row 120 Nenical Sonne from EC#4 to tube taneent point) too two eggerates inar-tive xc: Spanwise coordinntre (from ANSYS model) disp: Nomalized Disp 1=~ments perpendicular to span (z-dir) from ANSYS output for l Mode No. 2, frequency = 10.69 Hz.

Fluid Cross Flow Velocity (ATHOS results), Coorriinate and Disp. Vectors are shown below:

Node No. n := 0 64- 1 m* := n+ 1

'136.25' ' 136.25 1' .0 L'

W M ,t A t.

AA0 Cd.

139.75 o '-11533 0.06 '

139.75 2 .00223

+

143.25 7.5 -11533 0.06 143.25 3 .00433 146J5 7.6 -110.41 -0.08 146.75 4 .00614 150.25 15 -110.41 -0.08 150.25 5 .00755 153J5 supn@,n) = 15335 6 15.1 -6.92 -1.59

.0084 157.25 27.25 -6.92 -1.59 157.25 7 . 00858 160.75 2735 -439 -335 16035 8 . 00795 164.25 4435 -439 -3.85 164.25 9 .00639 167.75 44.85 -332 -7.04 167.75 10 , .00378 171.25 62.25 -332 -7.04 171.25 11 .0 17435 6235 - 7.2 -9.74

, 174.85 12 .00511 178.45 80.25 - 7.2 -9J4 178.45 13 .01088 182.05 8035 23.64 7.72 182.05 14 .01664 185.65 98.25 23.64 7J2 185.65 15 .02168 189.25 9835 5.2 1223 189.25 16 .02534 192.85 117.25 5.2 12.23 192.85 17 .02696 196.45 11735 3.66 15.26 196.45 18 .02586 200.05 136.25 3.66 15.26 200.05 19 .02142 203.65 13635 -22J5 16.63 203.65 20 .01301 207.25 153.75 -22J5 16.63 207.25 21 .0 211.05 153.85 25.95 22.71 211.05 22 .01889 214.85 171.25 25.95 2231 214.85 23 . 0408 218.65 17135 8.05 16.17 218.65 24 .06296 222.45 189.25 8.05 16.17 222.45 25 .08262 226,25 18935 5.07 13.52 226.25 26 .09707 230.05 207.25 5.07 13.52 230.05 27 .10365 23335 20735 -30.49 11.8 23335 28 .09975 "

237.65 226.25 -30.49 11.8 237.65 29 .08283 241.45 22635 -30.49 14.74 241.45 30 .05039 245.25 245.25 -30.49 1434 245.25 31 .0 24833 24535 33.14 12.77 24833 32 .05509 251.4 255.5 33.14 1237 251.4 33 .12111 254.48 255.6 14.06 11.49 254.48 34 .19568 257.55 m" " - ~ ~ *

• 265.75 14.06 11.49 CSE-97-158

Rev. 00

. ,,, ABB-CENO

- . . . . . - A. SONGS-9418-1168, Appendix A2 Page A2  % A2-4

.e.t o*3 260.63 265.85 -4431 14 11 260.63 36 36107 263.7 276.0 -4431 14 11 2633 37 44735 276.1 47.57 17.88 266.78 266.78 38 .53312 286.25 47.57 17.88 269.85 269.85 39 .61635 272.93 28635 1838 22.86 272.93 40 .69514 276 2963 18.78 22.86 276 41 36775 279.08 296.6 53J6 35.87 279.08 42 .8326 282.15 306.75 5336 35.87 282.15 43 .88832 285.23 306.85 61.41 28.24 285.23 44 .93375 2883 317.0 61.41 2834 288 3 45 .96793 29138 317.1 27.02 36.49 291.38 46 .99017 294.45 327.25 27.02 36.49 294.45 47 1.0 297.53 32735 -1935 77.22 297.53 48 .9972 300.6 337.5 -1935 77.22 300.6 49 .98182 303.68 337.6 5233 59.15 303.68 50 .95414 306J5 349.56 5233 59.15 30635 51 .91469 349.66 0.0 0.0 309.85 309.85 52 .86385 361.63 0.0 0.0 312.94 312.94 53 .8029 361J3 0.0 0.0 316.04 316.04 54 33308 319.14

,370.59, , 0.0 0.0 319.14 55 -

.65585 322.24 322.24 56 .57288 32533 325 33- 57 .48598 328,43 328.43 58 39712 331.53 331.53 59 3 0841 334.63 334.63 60 .22203 337.72 33732 61 .14027 340.82 -340.82 62 .06547 343.92 343.92 63 .0 -

,346.99, ,345.99 64 ,.05406 veio = [v,3oef + [y,3,of s

CSE-97-158

AoSONGS-9418-1168, Rey, OC ABB-CENO . Appendix A2 Page A2. to A2

/t Normali=1 displacement ($) as a function of spanwise x-coordinam (cubic spline interpolation function)is shown below:

vs := cspline(xc, disp)

$(x):=interp(vs.sc disp,x)

L Velocity (v) as a function of spanwise x-coordinate:

v(x) :=linterp(xv, velo,x)

Integrallimits:

a := xc b := xc a = 136.25 b = 346.99 o

l Assuming no spanwise variation in tube virtual mass or secondary fluid density, ,

th6 effective velocity equation reduces to the following:

• b v(x)* $(x)* dx Vd" 'b V g = 52.6 in/sec

$(x)3dx 3 .a

, s s

CSE-97-158

A-SONGS-9418-1168, Rev. 00 ABB-CENO . Appendix A2 Page A2- to A2; to x := xc,,ze,+ 1. xg,) 1:=0,1 last(xe)

Cross Flow Gan Velocity Profi;e (in/sec) Mode 2 ( 10.69 Hz) Mode Shane m ...

m.-

350 m  : mi.

m  : _

L  :

320 : 320; -

310

~

290 : ~  :

280 -

• J0 ,.r 270 -

l 250 "

i i 1 g 20 -

240 h.

=+- ,-

230 210 2m

, 2m-190 .

180 ". ggo q.

170 ,

150 "

~

140

~ 140 - -

130 ,

0 50 100 13 n- 0 k

• ( x).O K x).0 CSE-97-158

ABB-CENO . Appendix A2 Page A2- to A2 3 21 Emetive Valaelty PalenIndon for Cirenenferendal Sector 5 Tube Row HD (Vertical Sonnt from EC#4 to tube tanvent point) too two ececrates inactive I

xc: Spanwise coordinates (from ANSYS model) disp: Normalized Displacements perpendicular to span (z-dir) from ANSYS output for Mode No.1, frequency = 11.34 Hz.

Fluid Cross Flow Velocity (ATHOS results), Coordinate and Disp. Vectors are shown below:

Node No. n := 0 61- 1 m :=n+.1

.0

' VE4.CxW. 4@. &E.

136.25 - 136.25 1' ,'

.00241 0 -115.71 -1.13 '

139.75 139.75 2 7.5 -115.71 -1.13 143.25 143.25 3 .00466 7.6 -110.87 -1.09 146.75 146.75 4 .00662 15 -110.87 -1,09 150.25 150.25 5 .00813 agnent(xc.n) = 153.75 6 15.1 -6.78 -2.24 153.75 .00904 27.25 -6.78 -2.24 157.25 157.25 7 .00923 27.35 -436 -4,97 160.75 160.75 8 .00855 44.75 -436 -4.97 164.25 164.25 9 .00687 44.85 -331 -837 167.75 167.75 10 .00406 62.25 331 -837 171.25 171.25 11 .0 174.85 .00549 6235 -73 -11,74 174.85 12 '

178.45 80.25 -73 11 74 178.45 13 .01169 8035 23.87 8.72 182.05 182.05 14 .01785 98.25 23.87 8.72 185.65 185.65 15 .02326 9835 5.63 15.83 189.25 189.25 16 .02718 117.25 5.63 15.83 192.85 192.85 17 .02889 11735 432 19.74 196.45 196.45 18 .02771 136,25 4.32 19.74 200.05 200.05 19 .02295 203.65 136.35 -2235 21.27 203.65 20 .01393 207.25 153.75 -2235 21.27 207.25 21 .0 153.85 2637 28.83 211.05 211.05 22 .02021 171.25 2637 28.83 2i4.85 214.85 23 .04363 17135 8.11 19.82 218.65 218.65 24 . 0673 189.25 8.11 19.82

"?' 45 222.45 25 .08828 18935 5.42 16.83 226.25 226.25 26 .10367 207.25 5.42 16.83 230.05 230.05 27 .11065 20735 -30.62 14.47 233.85 233 85 28 .10644 xy :=

226.25 -30 62 14 47 237.65 237.65 29 .03834 22635 -30.62 18.52 241.45 241.45 30 '

.05372 xc 245.25 245.25 -30.62 18.52 245.25 31 disp := .0 24535 34.78 15.7 24833 24833 32 .05865 255.5 34.78 15.7 251.4 251.4 33 .1288 255.6 14.77 14.69 254.48 254.48 34 .20779 265.75 14.77 14.69 757.55 ,c, e c 3, ,7pgi CSE-97-158

A-SONGS-9415-11683 R(u. 00

_, , , ABS-CENO . Appendix A2 Page A2;ato A2-;

260.63 38188 265.85 -4532 19.02 260.63 36 6.0 4 5.32 19m 263.7 263.7 - 37 .47195 266.78 266.78 33 .56083 269.85 265.85 39 .64628 272.93 .72623 635 M3 2W 272.93 40 276 276 41 79877 279.08 .86221

.6 -m3-ml 279.08 42

- 3 1 282.15 282.15 43 .91508 285.23 .95613 t 70R -8m 285.23 44 2883 2883 45 .9844 317.1 30.13 1532 29138 29138 46 .99916 294.45 294.45 47 1.0 297.53 .98675 1m .5 297.53 48 300.6 .95953 300.6 49

.6 14.81 1 4 .14 303.68 303.68 50 .91876 306.75 306.75 51 .86509 0.0 0.0 309.91 309,91 52 .79752 6L63 0.0 0.0 313.07 313.07 53 .7186 6133 0.0 0.0 316.22 316.22 54 .62984 9, 0.0 Oh .

31938 31938 55 .53298 -

322.54 322.54 56 .4299.5 325.7 325.7 57 32286 328.86 328.86 58 .21393 332.01 332.01 59 .10551 335.17 335.17 60 .0 338.24 ,338.24 61 .09801 velo := (velo *) + (velo *)

CSE-97-158

A-SONGS-9E18-1168, Rev. 00 ABB-CENO .

Appendix A2 Page A2{G A2a Normalimd displacement ($) as a function of spanwise x-coorriinam (cubic spline interpoladon fuuction)is shown below:

vs := csphne(xc. disp)

$(x):=interp(vs,xc disp,x)

L Velocity (v) as a function of spanwise x-coordinate:

v(x):=linterp(xv velo,x)

Integrillimits:

a := xco b := xc a = 136.25 b = 338.24 Assuming no spanwise variation in tub: virtual mass or secondity fluid density, the effective velocity equation reduces to the following:

b v(x)2,9(,)2dx y d*

• b-y d = 58.4 in/sec

$(x),dx

$ .a s

CSE-97-158

A SONGS-M181168, Rev. O ABB-CENO . --

Appendix A2 Page A2go A2 x := xe,,ac,+ 1. g3 i := 0.1. lam (sc)

Cman hw Gan Velochy Profile (in%c) Mada 1 (11.24 Hri Mrvie Shane MO. Mot:

. 1 320 -

320 = -

- k N

2so  : 2:04 .

e 1

260 260 3

+

1 220 -

220 a:

m 4 >

I D

1

- ~

D D

D s

4-k o 50 100 150 .

.;; i M 0 1 xa).0 Wt).0 CSE-97-15E i

1

A-SONGS 94181168. Rev. 00 N .

Appendk A2 Page A2p A2 5

, Effective Valeelty Calculation for Cirrumsferential Sector 5 Tube Row 110 (Ve+=1 Enana from EC#4 to tube tannent noint) with ennerate #9 inactive xc: Spanwise coordinates (from ANSYS model) disp: Normalized Displacements perpendicular to span (z-dir) from ANSYS output for Mode No. 2, frequency = 24.1 Hz.

Fluid Cross Flow Velocity (ATHOS results), Coordinate and Disp. Vectors are shown below:

Node No. n : 0. 61 - 1 n, := n + 1 136.25, 136.25 1' .0 8 % 3 4.'

N'M 0 '.115.71 1.13 '

139.75 139.75 2 .00202 143.25 7.5 .I15.71 1.13 143.25 3 .00391 146.75 .00551 7.6 110.87 .l.09 146.75 4 150.25 .00672 15 .I10.87 1.09 150.25 5 153.75 augment (xc.n) = 15.1 6.78 2.24 153.75 6 .0074 27.25 6.78 2.24 157.25 157.25 7 .00747 27.35 4.36 4.97 160.75 160.M 8 .00682 164.25 44.75 4.36 4.97 164.25 9 .0054 167.75 44'83 3 33 *8 37 167.75 10 .00314 62.25 331 8.37 171.25 171.25 11 .0 174.85 6235 7.3 11.74 174.85 12 .00411 -

80.25 7.3 11.74 178.45 178.45 13 .00863 182.05 8035 23.87 8.72 182.05 14 .01301 98.25 23.87 8.72 185.65 185.65 15 .01673 189.25 9835 5.63 15.83 189.25 16 .01928 117.25 5.63 15.83 192.85 192.85 17 .0202 196.45 117.35 432 19.74 196.45 18 .01909 200.05 136.25 4.32 19.74 200.05 19 . 01556 203.65 .00929 13635 2235 21.27 203.65 20 207.25 .0 153.75 2235 21.27 207.25 21 211.05 153.85 26.37 28.83 211.05 22 .01305 214.85 171.25 2637 28.83 214.85 23 .0278 218.65 17135 8.11 19.82 218.65 24 .0423 189.25 8.11 19.82 222.45 222.45 25 .0547 189.35 5.42 16.83 226.25 226.25 26 .06327 207.25 5.42 16.83 230.05 230.05 27 .06643 233.85 20735 30.62 14.47 233.85 28 .0628 xy :n ve o s 237.65 226.25 30.62 14.47 237.65 29 .05117 241.45 22635 30.62 18.52 241.45 30 .03053 xes 245.25 245.25 30.62 18.52 245.25 31 disp := .0 24535 34.78 15.7 24833 24833 32 .03189 255.5 34.78 15.7 251.4 251.4 33 . 06675 255.6 14.77 14.69 254 48 254.48 34 .10058 257 55 s c., c c ,e ,i794g 265.75 14.77 14.69 CSE.97158

, , J

A40NGS-9418.1168,3"to Bev. 00 A219

. . . . .. Ass cENO AppmutuA2 Pa0eA2 260.63 260.63 36 .14967 265.85 4532 19.02 263.7 .15754 6.0 45.32 19.02 263.7 37 ,

266.78 6.1 19 61 266.73 3g .14965 269.85 269.85 39 .12278 II'0I 272.93 286.35 19.83 29.64 272.93 40 . 07386 276 276 41 .0 2W 279.08 296.6 52.13 62.81 279.08 42 .10014 282.15 306.75 52.13 62.81 282.15 43 .21976 285.23 .5 0.61 8.02 285.23 44 .35072 288.3 31 .0 70.61 8.02 2883 45 .48515 317.1 30.13 15.32 291.38 291,,4 A6 .61562 294.45 .73531 0.13 1532 294.45 47 297.53 297.53 48 83819 300.6 . .75 300.6 49 .91912 303.68 337.6 14.81 148.14 303.68 50 .97404 306.75 306.75 51 1.0 309.91 309,91 52 99475

' ~

313.07 61.63 0.0 0.0 313.07 53 .9567 316.22 .3 0.0 0.0 316.22 54 .88675 l '

319.38 319.38 55 78714 '

322.54 322.54 56 .66133 325.7 325.7 57 .5139 328.86 328.86 58 .35032 332.01 332.01 59 .17679 335.17 335.17 60 .0 338.24 , 338.24 61, ,.16945, wio :-d(wlo*)'+ (wlo*)'

CSE-97-158 9

A-80NGS 94181188, Rev. 00 ABS-CENO Appendk A2 Pape A2- O A2-5 0

Normali=d displacamant (4) as a function of spanwise x-coordinate (cubic spline interpolation i

ibaction)is shown below:

v :sospline(xe, disp)

+(x) := insap(ve,xe, disp,x) l Velocity (v) as a function of spanwise x-coordinate:

v(x) := linterp(xv, velo,x)

Integrallirnits:

a :s xc, b := xc a = 136.25 b = 338.24 Assunung no spanwise vanation in tube virtual mass or secondary fluid density, the effective velocity equation reduces to the following:

'b v(x)2.$(x)' 6c v g := .-

b v g = 66.1 in/sec

$(x)*dx 3 .a CSE-97-158

A-SONGS-M18-1160. Rev. 00 ABSCENO. Appendk A2 Page A2- b A2 28 i x:=w,,w,+1. g 3 i :: 0,l.,!sst(xes Cross Flow Gan Velocity Profile (m/sec) Mode 2 (24.1 Hz) Mode Shaa.

m. W:

h d

a da m ~

m .' - -

~

D k k

% g M -

Mg r 4>

240 s 2#5 E """"

mi D

-t- .

-+-

20 ==j 4 220 ,

1>

M ~

g. m m I e

(>

IM , 3 gat D

.p 0 $0 IM !$0 y ".;

O

< s).o '

g,3,,

CSE-97-158 I

ABB-CENO Appendix A2 Page A2 O A2-24 E&celu Valader rniculation for Circumferential S.cenr 5 Tube Rnw 10R (Vertical Snant from EC#4 to tube taneent nointi too two erecrutes inactive xc: Spanwise coordinates (from ANSYS model) disp: Normm11mi Displacements perpendicular to span (z-dir) from ANSYS output for Mode No. 2, frequency = 11.84 Hz.

Fluid Cross Flow Velocity (ATHOS results), Coordinate and Disp. Vectors are shown below:

mde No_ n := 0 61 - 1 n, := n + 1 Hlog MM Ano. cit.

'136.25' ' 136.25 1' .0 o' '.115.71 1.13 '

139.75 139J5 2 - 2 252 7.5 -115.71 -1.13 l 143.25 143.25 3 . 00487 7.6 -110.87 1.09 146.75 14635 4 .00692 15 -110.87 1.09 150.25 150.25 5 .00849 15.1 -638 -2.24 153.75 aupnmq u.n) = 15335 6 .00945 27.25 -638 2.24 157.25 157.25 7 .00964 27.35 -436 4.97 16035 16035 8 ' 8 893 4435 -436 -4.97 164.25 164.25 9 .00717 44.85 -331 837 167.75 167.75 10 .00424 62.25 -3.31 837 171.25 171.25 11 .0 62.35 - 7.3 -11.74 174.85 174.85 12 .00572 80.25 -7.3 . -1134 178.45 178A5 13 .01218 8035 23.87 8.72 182.N 182.05 14 .0186 98.25 23.87 8.72 185.65 185.65 15 .02423 9835 5.63 15.83 189.25 189.25 16 .0283 117.25 5.63 15.83 192.85 192.85 17 .03007 11735 432 1934 196.45 196.45 Ig .02883 136.25 432 1934 200.05 200.05 19 .02387 13635 -2235 21.27 203.65 203.65 20 .01448 153J5 -2235 21.27 207.25 207.25 21 .0 153.85 2637 28.83 211.05 211.05 22 . 02099 171.25 2637 28.83 214.85 214.85 23 .04531 17135 8.11 19.82 218.65 218.65 24 .06987 1g9.25 8.11 19.82 222.45 222.45 25 . 09162 18935 5.42 16.83 226.25 226.25 26 .10755 207.25 5.42 16.83 230.05 230.05 27 . 11475 20735 - 30.62 14.47 233.85 .11033 233.85 28 226.25 - 30.62 14.47 237.65 237.65 29 .09153 22635 - 30.62 18.52 241.45 241.45 30 .05563 245.25 - 30.62 18.52 xca 245.25 245.25 31 disp := .0 24535 3438 153 24833 24833 32 .06068 255.5 3438 13J 251.4 251.4 33 .13316 255.6 14.77 14.69 254.48 254.48 34 .2146 26535 14.77 14.69 CSE-97158

ABS-CENO ..

ApM A2 Pape y'O A2 j 257J5 257.55 35 .30222 265.85 45.32 19A2 260.63 260.63 36 39333 2764 45J2 1942 263.7 263.7 37 .4853 276.1 5036 19.61 266.78 266.78 33 J7562 286.25 5036 19.61 269.85 269J5 39 .66196 286.35 19,83 29.64 272.93 272.93 40 .74212 296J 19J3 29.64 276.0 276 41 31414 296.6 52.13 - 62J1 279.08 279.08 42 A7627 306.75 52.13 62J1 282.15 282.15 43 .92702 306A5 70.61 8A2 285.23 285.23 44 .96513 3174 70.61 8A2 288.3 288.3 45 NM 317.1 30.13 15.32 291.3d 291.38 4b 1e 327.25 30.13 15.32 294.45 294.45 47 99374 327.35 12.08 99.75 297J3 297.53 43 .97684 337.5 1238 99.75 300.6 300.6 49 94337 337.6 14.81 148.14 303.68 303.68 50 .89647 349.56 14.81 148,14 l 306.75 306.75 51 .83638 349.66 0.0 0.0 309.71 309.71 52 .76723 361.63 0.0 0.0 312.68 312.68 53 .68826 361.73 0.0 0.0 315.64 315.64 54 .6009 ,370.59, ,

0.0 0.0 ,

318.6 318.6 55 .50676 321.57 321.57 56 .40759 324.53 324.53 57 .30529 327.49 327.49 5g .20186 330.46 330.46 59 .09939 333.42 333.42 60 .0 336.49 ,336.49 61, .. 09795, i

CSE-97-158 a , , , , -

A SONGS-94181968, Rev. 00 ABB-CENO 4 Appendix A2 Page A2' D A2 j 31 Normallred displacement ($) as a function of spanwise x-coordinate (cubic spline interpolation function)is shown below:

vs := cspline(xc. disp)

$(x) :=inte:p(vs.xe, disp,x) t Velocity (v) as a function of spanwise x-coordinate:

v(x) :=linte@(xv, velo,x)

Integrallimits:

a := xt, b := xc,g,3 a = 136.25 b = 336.49 Assuming no spanwise variation in tube virtual mass or secondary fluid density, the effective velocity equation reduces to the following:

'b v(x)2,9(g)2dx V d* 'b y d = 57.9 in/sec

$(x)* da n .a CSE-97-158 i

a

A: SONGS-94181168, Rev. 00 ABS-CENO Apperx2x A2 Page A2 t3 A21 31 x := xe,,xe,+ 1. g ,3 1:s0,1. lam (sc)

Crams Flow Gan Velocity PrnM1e (in/ead . Mode 2 (11.84 Hz) Mnde Shane g u0 -

y 4

L 320a3 320

, ~~ <,

j .

uo : 2:00 260 260 240 240 a

"i

=+-

220 .

20 P

200 300' 100 [ 180$

160 160=

140 140= -

120 0 50 100 150 'l O 1 Ms),0 CSE-97-158

ABB-CENO Appendix A2 Page A2 0 A2>5 i 35 Emetive Valar4tv ralentation for Circurnferentini Sector 6 Tutw Row R3 (Venical Snant from EC#3 to tube tancent nointi too two evocrates inactive xc: Spanwise coordinates (from ANSYS model) l l

disp: Normalized Displacements perpendicular to span (z-dir) from ANSYS output for Mode No.1, frequency = 8.43 Hz.

Fluid Cross Flow Velocity (ATHOS results), Coordinate and Disp. Vectors are shown below:

gg y, a := 0. 63 n, := n + 1 yrs.c43e. AAD. CA4

' 98.25 ' ' 98.25 1'

• 0

.0 '- 115.18 0.26 '

102.05 102.05 2 .00201 7.5 -115.18 0.26 105.85 105.85 3 . 0039 7.6 110.28 -0.03 109.65 109.65 4 . 00554 15 110.28 0.03 113A5 113.45 5 . 0068 15.1 -6.89 1.79 117.25 augment (xc.n) = 117.25 6 .00758 27.25 6.89 -1.79 121.05 121.05 7 . 00774 27.35 -4.56 -5.76 124.85 124.85 8 . 00717 44.75 -4.56 -5.76 128.65 128.65 9 . 00577 44.85 -3.53 -939 132.45 132.45 10 62.25 3.53 939

. 00341 136.25 136.25 11 .0 62.35 -7.29 -13.24 139.75 139.75 12 80.25 -7.29 - 13.24

.00409 ,

143.25 143.25 13 .00864 8035 9.67 6.72 ,

146.75 146.75 14 98.15 9.67 6.72

.01313 150.25 150.25 15 9835 24.78 19.45

.01705 153.75 153.75 16 117.25 24.78 19.45

.01989 157.25 157.25 17 117.35 6.4 25.05

.02112 160.75 160.75 18 136.25 6.4 25.05

.02024 164.25 164.25 19 13635 533 2632

.01676 167.75 167.75 20 153.75 533 2632

.01018 171.25 171.25 21 153.85 -21.59 35.45

.0 174.85 174.85 22 171.25 21.59 35.45

.01436 178.45 178.45 23 171.35 26.62 23.1

.03096 182.05 182.05 24 189.25 26.62 23.1

. 04775 185.65 185.65 25 189.35 8.14 19.84

. 06267 189.25 1g9.25 26 207.25 8.14 19.84

. 07367 192.85 192.85 27 5.43 16.9

. 07874 207.35 196.45 196.45 28 5.43 16.9

.07588 226.25 200.05 200.05 29 22635 -30.86 22.27

. 0631 203.65 203.65 30 245.25 -30.86 22.27

. 03845 207.25 207.25 31 24535 35.68 17.96

.0 211.05 211.05 32 255.5 35.68 17.96

.05688 214.85 disp :=

214.85 33 .12796 255.6 15.87 1837 218.65 218.65 34 265.75 15.87 1837

.20991 CSE 97158

. OC ABS-CENO A. SONGS-94181168,p3 Apperktx A2 Page A2 .

m.43 222.45 35 .29949 265.85 44.69 29.34 226.25 226.25 36 .39349 276.0 44.69 29.34 230.05 230.05 37 .48885 276.1 55.63 5.99 233.85 233.85 38 .58263 286.25 55.63 5.99 237.65 237.65 39 .6721 286.35 22.25 4.74 241.45 241.45 40 .75471 296.5 22.25 4.74 245.25 245.25 41 J2819 296.6 17.68 57.94 24833 248.33 42 J7958 306.75 -17.68 57.94 251.4 251.4 43 .92275 306.85 6 41.96 32.56 254.48 254.48 44 .95694 317.0 41.96 32.56 257.55 257.55 45 .9815 317.1 0.0 0.0 260.63 260.63 46 .99596 327.25 0.0 0.0 263.7 263.7 47 1.0 327.35 0.0 0.0 ,

266.78 266.78 48 .99346 337J 0.0 0.0 269.85 269.85 49 .97632 337.6 0.0 0.0 272.93 272.93 50 .94875 349.56 0.0 0.0 276 276 51 .91106 349.66 0.0 0.0 278.96 278.96 52 .8655g 361.63 0.0 0.0 281.93 281.93 53 .81167 361.73 0.0 0.0 i 284.89 284.89 54 .74997 ,370.59, ,

0.0 0.0 287.85 287.05 55 '

.68125 290.81 290.81 56 .60638 293.78 293.78 57 .52633 296.74 296.74 58 44213 299.7 299.7 59 .35491 302.66 302.66 60 .26585 305.63 305.63 61 .17616 308.59 308.59 62 .08712 311J5 311.55 63 '

. .0

,314.62 , 314.62 64 ;

[.08709 ve!o := (velo *) + (velo *)

CSE.97158

A SONGS-94181188 Rw. 0(

ABB-CENO , Appendix A2 Page A2 O A2 38 i

Normalized displacement ($) as a function of apanwise x-coordinase (cubic spline interpoladon function)is shown below:

vs := cspline(se, disp)

$(x):=laterp(vs,xc. disp x) l Velocity (v) as a function of spanwise x-coordinate:

l v(x) :=lintorp(xv, velo,x)

Integrallimits:

a := xc b := xc a = 98.25 b = 314.62 o m Assuming no spanwise variation in tube virtual mass or secondary fluid density, the effective velocity equation reduces to the following:

'b v(x)' $(x)* dx V g :=

• b V g = 42.1 in/sec

$(x)2A q .a e

CSE-97-158

A SONGS 9490>9268 Hev.oc ABB-CENO Appendix A2 Page A2- O A2-x :o xen ,xe,+ 1. xc ,3 1:30,1. last(xc)

Qggi, Sow Gap Velocity Profile (in/sec) Mode 1 (8.4 Hz) Mode Shane 320 320 -

f 310 .

3w -

500 - -

290 ; L 240 l 2804 r 270 D -

D q>

260 260' 250 l 240 ',

240i}

230 <

• • 0 $

220 -:-

210 .' .

I a

~~~ a j.

200 g L-acg

-+- - ac( ,

190 -

I' 180 ,

gge G 170 l 160 ,

160d' -

150 140

, 140- -

130 .

120 , 12, ..

110 -

Im '. __

3.;

90 s

80 0 20 40 60 80 13 n, 'g v( s),0 4( t).0 CSE-97158 )

l 1

__b

A. SONGS-94181168. Rev. 00 ABB-CENO . Appendix A2 Page A2> to A2-Il Effective V.Inclev ralenistion for Circumferential Sector 6 Tube Row R3 Nertical Snant from EC#3 to tube taneent nohit) crecrate no. 8 inactive xc: Spanwise coordinales (from ANSYS model) disp: Normalized Displacements perpendicular to span (z-dir) from ANSYS output for Mode No. 2, frequency = 18.75 Hz.

Fluid Cross Flow Velocity (ATHOS results), Coordinate and Disp. Vectors are shown below:

Node No. n := 0. 63 o8 :=n+ 1 g, gg, g

' 98.25 ' 1' '

~0

~ 98.2.* .0 '.115.18 0.26 '

102.05 102.05 2 .00161 7.5 115.18 0.26 105.85 105.85 3 .00311 7.6 -110.28 -0.03 109.65 109.65 4 .00439 15 -110.28 -0.03 113.45 113.45 5 .00535 15.1 -6.89 -1.79 117.25 algment(xc.n) = 117.25 6

.00591 27.25 -6.89 -139 121.05 121.05 7 .00597 27.35 4.56 -536 124.85 124.85 8 .00547 44.75 -4.56 -536 128.65 128.65 9 .00434 44.85 3.53 939 132.45 132.45 10 .00253 62.25 -3.53 -939 136.25 136.25 11 .0 6235 7.29 -13.24 139.75 13935 12

~

. 00295 80.25 -7.29 -13.24 143.25 143.25 13 . 00618 3035 9.67 6.72 14635 14635 14 . 00931 98.25 9.67 6.72 150.25 150.25 15 . 01198 9835 2438 19.45 153J5 15335 16 .01385 117.25 24.78 19.45 157.25 157.25 17 . 01457 11735 6.4 25.05 16035 16035 18 . 013g4 136.25 6.4 25.05 164.25 164.25 19 . 01135 13635 533 2632 167J5 167J5 20 . 00683 15335 533 2632 171.25 171.25 21 .0 153.85 21.59 35.45 174.85 174.85 22 .00946 171.25 -21.59 35.45 178.45 178,45 23 .02024 17135 26.62 23.1 182.05 182.05 24 .03099 189.25 26.62 23.1 185.65 185.65 25 .04036 18935 8.14 19.84 189.25 gg9.25 26 ,m707 207.25 8.14 19.84 192.85 '

192.85 27 ,04989 20735 5.43 16.9 196.45 196.45 28 .N765 226.25 5.43 16.9 200.05 200.05 29 .03926 226.35 -30.86 22.27 203.65 203.65 30 .0237 245.25 30.86 22.27 207.25 207.25 31 .0 24535 35.68 17.96 211.05 211.05 32 . 03398 255.5 35.68 17.96 214.85 214.85 33  %* . 07295 255.6 15.87 1837 218.65 218.65 34

... .. .11185 265.75 15.87 1837 CSE 97158 1

A> SONGS-94181168. Rev. 00 ABS-CENO Apoondix A2 Page A2N A2 9 mM 222.45 35 '

.14576 265.85 . 44.69 2934 226.25 226.25 36 . 16996 276.0 44.69 2934 230.05 230.05 37 .17999 276.1 55.63 5.99 233.85 233.85 38 . 17169 286.25 55.63 5.99 237.65 237.65 39 .14123 28635 22.25 4.74 241.45 241.45 40 . 0851 296.5 22.25 4.74 245.25 245.25 41 .0 296.6 17.68 57.94 248.33 24833 42 .09122 306.75 17.68 57.94 251.4 251.4 43 .1977 306.85 41.% 32.56 254.48 254.48 44 J1375 317.0 41.96 32.56 257.55 257.55 45 .43386 317.1 0.0 0.0 260.63 260.63 46 .55272 327.25 0.0 0.0 263.7 263.7 47 .66541 327.3$ 0.0 0.0 266.78 256.78 48 .7674 337.5 0.0 0.0 i 269.85 269.85 49

' .85471 337.6 0.0 0.0 272.93 272.93 50 .92392 349.56 0.0 0.0 276 276 51 .9723 349.66 0.0 0.0 278.96 278.96 52 .99733 361.63 0.0 0.0 281.93 281.93 53 1.0 361.73 0.0 0.0 284.89 284.89 54 ,979g4 ,370.59, 0.0 0.0 ,

287.85 ,

287.85 55 .93705 290.81 290.81 56 .87247 293.78 293.78 57 *

.78759 296.74 296.74 58 .68446 299.7 299.7- 59 .56567 302.66 302.66 60 .43427 305.63 305.63 61 .29363 308.59 308.59 62 .14762 311.55 311.55 63 .0

,314.62

,314.62 64, ,.15087, velo := (velo *)*+ (velo *)

CSE-97158 i j

A1 SONGS 94181168, Rev. 00 ABB-CENO Appendix A2 Page A2gto A2 j l

Normalized displacement ($) as a function of spanwise x<oordinate (cubic spline interpolation function)is shown below:

vs := cspline(xc. disp)

$(x) :=interp(vs,xc. disp,x)

Velocity (v) as a function of spanwise x-coordinate:

v(x) :alinterp(xv, velo,x)

Integrallimits:

a := xe, b := xc a = 98.25 b = 314.62 Assuming no spanwise variation in tube virtual mass or secondary fluid density, the effective velocity equation reduces to the following:

'b v(x)* $(x)* dx V g :=

• b Vg = 46.7 in/sec

$(x)*dx 1 *a CSE-97-158

. A SONGS M181168 Rev.00 !

ABB-CENO . Appendix A2 Page A2 O A24 l fo Cross Flow Gan Velocity Pmfile (in/see) Mode 2 ( lE.75 Hz) Mode Shan, 320 320 -

l  %~

310 . ,

290 .

4b 280 -

2809r o

270 .

1

• l 250 240 l 24 --

230

. W 220 l - ..

210 '

x , ,

x .

200 M nej .,i. 200 -

ggg 190 -

4}

180 -

180k 170 ,

4

~

150 .

$W o

130 [

220  : - 20 l,.

!!0 ,'

100 , -

• g 90 "o 20 40 to 80 1., n, '

)

v( x),o Kx).O CSE-97-158

A SONGS 9418-1168. Rev. OC ABB-CENO ' Appenoix A2 Page A20 G A2-41 Effective Valar4tv Palesdatinn for Circurnferential Sectar 6 Tuhe Row R3 Simkod Nertical Snann from EC#3 to tube tanoent noint) with top 3 erecmtes inactive GC#6. 7. & 81 xc: Spanwise coordinates (from ANSYS model) disp: NormaliW Displacements perpendicular to span (z-dir) from ANSYS output for Mode No.1, frequency = 3.85 Hz.

Fluid Cross Flow Velocity (ATHOS results), Coordinate and Disp. Vectors kre shown below:

Node No. n :=0. 64- 1 n*:=n+ 1 98.25

, . ca U D- M.

98.25 1 .0 g' o :w'. -115.18 0.26 102.05 102.05 2 .0M45 105.85 7.5 115.18 0.26 10525 3 .00863 109.65 7.6 -110.28 -0.03 109.65 4 01226 113.45 15 -110.28 -0.03 113A5 5 .01W 117.25 aupace,n) = 117.25 6 15.1 -6.89 -1.79

.016a

) 121.05 27.25 6.89 -139 121.05 7 .01721 124.85 27.35 4.56 -536 l 124.85 8 .01598 I

128.65 4435 -4.56 -536 128.65 9 .01288 132.45 44.85 -3.53 -939 132A5 10 .00764 136.25 62.25 -3.53 -939 136.25 11 .0 13935 6235 -7.29 -13.24 139.75 12 .00918 143.25 -

80.25 -7.29 -13.24 143.25 13 .01944 14635 8035 9.67 632 14635 14 .02961 150.25 98.25 9.67 6.72 150.25 15 . 0385 9g35 24.78 19.45 15335 15335 16 . .M496 117.25 157.25 24.78 19.45 157.25 17 . .M781 160.75 11735 6.4 25.05 16035 18 .0459 164.25 136.25 6.4 25.05 164.25 19 .03806 16735 13635 533 2632 167.75 20 . 02314 171.25 15335 533 2632 171.25 21 .0 174.85 153.85 -21.59 35A5 17425 22 .03324 178.45 171.25 -21.59 35.45 178.45 23 .07513 122.05 17135 26.62 23.1 182.05 24 .12442 185.65 189.25 26.62 23.1 185.65 25 .17983 189.25 139.35 8.14 19 84 189.25 26 .24013 192.85 207.25 8.14 19 84 192.85 27 JM09 1%AS 20735 5.43 16.9 196A5 28 37051 ""

200.05 226.25 5.43 16.9 200.05 29 .43822 203.65 '

22635 -3026 22.27 203.65 30 .50609 207.25 245.25 -30.86 22.27 207.25 31 .57303 211.05 24535 35.68 17.96 211.05 32 .64153 214.85 255.5 35.68 17.96 214.85 33 30669 218.65 255.6 1537 1837

' 218.65 34 .76745 222.45 e' d * $8 265.75 15.87 1837 CSE-97-158

A. SONGS-94181168, Rev. 0(

ABB-CENO . .. .

_ .. ~ .aua3 Appendix A2 Page A2g3 A2 226.25 265.85 -44.69 2934 226.25 36 .87191 276.0 -44.69 2934 230.05 230.05 37 .91396 276.1 55.63 5.99 233.85 233.85 38 .94828 286.25 55.63 5.99 237.65 237.65 39 .97414 286.35 22.25 4.74 241.45 241.45 40 .99168 296.5 21.25 434 245.25 245.25 41 1.0 24833 296.6 -17.68 57.94 24833 42 1.0 306J5 -17.68 57.94 251.4 251.4 43 .99392 3p6.85 41.96 32.56 254.48 254.48 44 .98179 317.0 41.96 32.56 257.55 257.55 45 .96366 OD 317.1 0.0 260.63 260.63 46 .93967 0.0 0.0 327.25 263.7 263J 47 .90999 327.35 0.0 0.0 266J8 266.78 48 .87483 337.5 0.0 0.0 269.85 269.85 49 .83447 337.6 0.0 0.0

! 272.93 272.93 50 .78924 0.0 349.56 0.0 276 276 51 .73949 349.66 0.0 0.0 278.96 278.96 52 .68768 361.63 0.0 0.0 281.93 281.93 53 .63246 36133 0.0 0.0 284.89 284.89 54 .57425 0.0 0.3

,370.59, 287.85 287.85 55

.51353 290.81 290.81 56 .45079 293J8 29338 57 .38652 296.74 296.74 58 32127 299.7 299.7 59 .25559 302.66 302.66 60 .190CM 305.63 305.63 61 .1252 308J9 30839 62 .06166 311.55 311.55 63 .0

,314.62 314.62 64 . 06139 g, co>)2 g)2 s

CSE 97-1SB

A SONGS-94181188. Rev. OC ABS-CENO Appendix A2 Page A2 G A2 f3 Normalized diepLemt ($) as a funcdon of spanwise x-coordinate (cubic spline interpolation function)is shown below:

vs := cspline(ac, disp)

$(x) :=interp(vs,ac, disp,x)

Velocity (v) as a f.inction of spanwise x-coordinate:

v(x) :=lintorp(xv,volo,x)

Integrallimits:

a := xc b := xe g a = 98.25 b = 314.62 o

Assuming no spanwise variadon in tube virtual mass or secondary fluid density, -

the effective velocity equation reduces to the following:

'b v(x)*.((x)* dx V g :=

• b V g = 37 in/sec

$(x)* ds 3 .a s

CSE-97158

A SONGS-94181168 Rev.

3 OC ABB-CENO ,

• Appendtx A2 Page A2- G A2-ft x := xe,,xe,+ 1 g,3 i :=0,1.le(me)

Cmas Flow Gap Velocity Profile (in/sec) ' mode 1 (3.85 Hz) Mode Shane 320 320 *

F 310 , ,

300 -

300 --

D d>

W ,

2:0 ! 2:06 o

270 D

260 2M^

~

250 o

240 ,

240p l 230 <

220 [

20 -

" 210 '

o

=_ -

.} .

200

, 200 --

"i l

190 -

180 ,

180$

170 < >

1* .

- Is0 l 150 .

140 140- -

130 .

4 120 l 1204 -

110 100 - -

100i-M s

0 20 40 eo so 1, n,

< x),o

(

I CSE-97-158

A SONGS 94181168, Rev. 00 ABB-CENO ,

Appendix A2 Page A2gto A2fg Effactive Velocity Calculaflon for Tuhe Row R3 Elbow and Horimnial Snan Crocc Flow l xc: Spanwise coordinates (from ANSYS model) disp: Normali7ed Displacements perpendicular to span (z-dir) from ANSYS output for Mode No. 6, frequency = 46.39 Hz xv: Flow developed length horizontal coordinates from bundle centerline to diagonal strip velo: Cross flow gap velocities. irn/sec (ATHOS results) e :=x 20

] 6 := c 22.5 d = 3.927 i := 0.15 n, := 63 + i n := reverse (n) 360 Velocity Normal Node No- Velo. Profile Coor. Tube Centerline 0.0 0 236.88' 0 78' 0 4.0 4 0.27225 236.88 77 10.5 0.63038 216.57 8 76 10.5 + .1

.0 0.89831 216.57 12 75 213 1 288.25 l

16 74 21.5+.1

.8.92 augment (xc.n) " 0.89752 33,3 288.25 18.92 73 0.7393 288.24 21.83 72 33.5+.1 velo := 288.24 xes 24.75 71 0.57241 n.: 33.5 + dl SSP .- . 365.21 27.67 27.67 70 0.40446 33.5 + dl + .1 0.2453 365.21 30.58 69 33.5 t 2.d!

0.10635 387.39 33.5 68 33.5 + 2 6 + .1

^ 37.43 67 0 33.5+ 3 dl 387.39 41.35 41.35 66 -0.07715 I98 II 33.5 + 3.dl t .1 45.28 -0.08878 198 II 45.28 65 33.5 + 4 dl I 49.21 64 -0.05574 52.29 ,

.I98 II .

, 52.29 63, 0 ,

node 63 is at diagonal strip (xc = 49.21 + 3.08= 52.29) 69 =m(6sp)

Cross Flow Gap Velocity Profile Mode Shape (Mode 6,46.4 bz) 400

-T 1

l p l y 52.29 j 52.29 3 300 .l OJ - -

$ i c I T

> 4

, 200 0 ---- -------------

b 0 20 40 T O '

av. Cantertae to Duganal Sgpost(m) Nodal Coundaneses (in)

CSE-97158

A> SONGS-94181168, Rev 00 ABB-CENO Appendix A2 Page A2gto A2-1 Normalized displacement ($) as a function of spanwise x-coordinate (cubic spline interpolation function)is shown below:

vs :s espline(xc. disp) l

$(x):=interp(vs xe, disp,x)

Velocity (v) as a funedon of spanwise x-coordinate:

v(x) :=linterp(xy, velo,x)

Integrallimits:

a := xc, b := xc u a=0 b = 52.29 Assuming no spanwise variadon in tube virtual mass or secondary fluid density, the effeedve velocity equadon reduces to the following:

'b v(x)2,,c,)2dx vg :=

• b V g = 320.7 in/sec

$(x)2dx 1 ea CSE 97158

-a

A SONGS-9418-1168. Rev. 00 ABB-CENO , Appendtx A2 Page A2 to A2-.

47 Emceive V.tadtv Cale.d=* tan for Circumferentl=1 Secenr 6 Tube R2 (Vertical Snant from EC#3 to tube tanoent nointi ton two concrates innctive xc: Spanwise coordinates (from ANSYS model) disp: Normalimi Displacements perpendic f.ar to span (z-dir) from ANSYS output for Mode No.1, frequency = 8.6 Hz.

Fluid Cross Flow Velocity (ATHOS results), Coordinate and Disp. Vectors are shown below:

Nede No. n := 0. 64- 1 n, := n+ 1 t!EL. Q1N. AAO' Ut

• 18.25 ' 98.25 1' ' ' ' '

.0 0 ' 115.18 0.26 '

102.05 102.05 2 . 00205 7.5 -115.18 0.26 105.85 105.85 3 . 00397 7.6 -110.28 0.03 109.65 109.65 4 . 00564 15 -11018 -0.03 113.45 113.45 5 . 00693 15.1 -6.89 -1J9 117.25 augment (xc.n)

• 117.25 6 . 00771 27.25 -6.89 -139 121.05 121.05 7 . 00786 2735 -4.56 -536 124.85 124.85 8 . 0073 4435 -4.56 -5J6 128.65 128.65 9 . 00587 44.85 -3.53 -939 132.45 132.45 10 .00347 62.25 -3.53 -939 136.25 136.25 11 .0 6235 -7.29 -13.24 139.75 13935 12 .00416 80.25 -7.29 -13.24 143.25 143.25 13 ,00g79 8035 9.67 6.72 146.75 146J5 14 .01336 98.25 9.67 6.72 150.25 150.25 15 .01735 9835 2438 19.45 153.75 15335 16 .02023 117.25 2438 19.45 157.25 157.25 17 .02148 11735 6.4 25.05 160J5 16035 18 .02059 136.25 6.4 25.05 164.25 164.25 19 .01704 13635 533 2632 167.75 167.75 20 .01035 15335 533 2632 171.25 171.25 21 .o 153.85 -21.59 35.45 174.85 174.85 22 .0146 171.25 -21.59 35.45 178.45 178.45 23 .03148 17135 26.62 23.1 182.05 182.05 24 . 04854 189.25 26.62 23.1 185.65 185.65 25 . 0637 18935 8.14 19.84 189.25 189.25 26 .07488 207.25 8.14 19.84 192.85 192.85 27 . 08003 207.35 5.43 16.9 196.45 #

196.45 28 . 07711 226.25 5.43 16.9 200.05 200.05 29 - .06412 22635 30.86 22.27 203.65 203.65 30 .03907 245.25 -30.86 22.27 207.25 207.25 31 .0 24535 35.68 17.%

211.05 211.05 32 .05778 255.5 35.68 17.96 214.85 214.85 33 N* . 12993 255.6 15.87 1837 218.65 218.65 34 mm 265J5 15.87 1837 CSE-97-158

A> SONGS-94181168 Rev. 00 222.45 a.-eEno 222.45 35 ,30379 265J5 mn no.ngn ,

.44.69 29.34 226.25 226.25 36 39g88 276.0 -44.69 2934 230.05 230.05 37 .49516 276.1 55.63 5.99 23335 233.85 38 286.25

.58964 55.63 5.99 237.65 237.65 39 .67952 286.35 22.25 4.74 241.45 241.45 40 .7622 296.5 22.25 4.74 245.25 245.25 41 .83537 296.6 -17.68 57.94 248.33 248.33 42 .88621 306.75 -17.68 57.94 251.4 251.4 43 .92858 306.b5 41.96 32.56 254.48 254.48 44 .96168 317.0 41.96 32.56 257.55 257.55 45 ,9849 317.1 0.0 0.0 260.63 260.63 46 327.25

.99777 0.0 0.0 263.7 263.7 47 1.0 327.35 0.0 0.0 266.78 266.78 48 .99144 337.5 0.0 0.0 269.85 269.85 49 .97212 337.6 0.0 0.0 272.93 272.93 50 349.56

.94224 0.0 0.0 276.0 276 51 .90213 349.66 0.0 0.0 278.89 278.89 52 .85558 361.63 0.0 0.0 281.78 281.78 53 0.0

.801 361.73 0.0 284.67 284.67 54 0.0 0.0

.73902 370.59, ,

287.56 287.56 55 .67042 290.45 290.45 56 .59602 29334 29334 57 .51677 29623 29623 58 .43368 299.12 299.12 59 34782 302.01 302.01 60 .26034 304.9 304.9 61 .17239 307.79 307.79 62 .0852 310.68 310.68 63 .0 -

,313.74 ,313.74 64 ,.08719 e , g <1>)2

, g >)2 CSE-97-158

A SONGS-94181168, Rev. 00 ABS-CENO Appendu A2 Page A2- to A2 j 19 Normalized del = ment ($) as a function of spanwise x-covitasase (cubic spline interpolatioa function)is shown below:

1 v :=cspline(xe, disp)

L

$(x) :=intsp(vs,u, disp,x) l L Velocity (v) as a function of spanwise x-coordinate:

v(x) :=linterp(xy, velo,x) 1 I

Integrallimits:

a := xc b := xc a = 98.25 b = 313.74 o

Assuming no spanwise variadon in tube virtual mass or secondary fluid density, the effective velocity equation reduces to the following:

• b v(x)2,9(g)2dx V g :=

• b y g .41,9 in/sec

$(x), dx 9 *4 i

e b

CSE-97-158

6M2HIXD2 5-11w. Hw. W ABS-CENO Appendix A2 Page A2 O A2q So x :s me,,se,+ 1 g, i :a 0,1. last(ac) crnu Flow Gan Velocity Profile (in/= 1 Mode 1 ( R.60 Hz) Mrvi, Shane 320 320 -

" ~

' l 1 310 ,

y 3co .

300a..e m  ; I, -

i 280 280 l .

} no l 260 - 260 d; 250 .

240 ,

2409 230 220 [

220k -

210 , -

~ ,

s a j, -

200 --

200 9

-+-  % "

" -+-

190 - -

180 .

180' h 170 ,

160 ,

1604 '

150 i.o ido , .

130 .

120 -  %

120a'.

110 -

,0 l '

i 30 -

0 20 40 80 - a g .~ g g v( s).0 4( x).0 CSE-97158

AoSONGS 94181168. Rev. 0( '

ABB-CENO Appendix A2 Page A2 G A2 SI Eggdye Velocity Calculation for Circumfersatial hetnr 7 Tube Row 49 Full Model (Vertical Spant fmm EC#2 to tube taneent eninti ton two erecrates inactive xc: Spanwise coontinatec (from ANSYS model) disp: NormmH=i Displacements perpendicular to span (z-dir) from ANSYS output for  ;

Mode No.1, frequency = 7.86 Hz.  !

Fluid Cross Flow Velocity (ATHOS results), Coordinate and Disp. Vectors are shown below:  !

Node No. n := 0 64- 1 n, := n + 1 62 25 62.25 yrt . cop, .UA CM. .

1

.0 On - 115.05 433 65.85 65.85 2 .00173 7.5 -115.05 433 69.45 69.45 3 . 00335 7.6 -110.23 3.14 73.05 73.05 4 . 00476 15 -110.23 3.14 76.65 76.65 5 .00585 15.1 -7.01 0.19 80.25 magment(xc.n) " 80.25 6 .(0652 27.25 -7.01 0.19 83.85 83.85 7

. 00666 27.35 -4.68 -6.29 87.45 87.45 8 . 00618 44.75 -4.68 -6.29 91.05 91.05 9 .ON97 44.85 -3.46 -10.41 94.65 94.65 10 .00295 62.25 -3.46 -10.41 98.25 98.25 11 .0 6235 -6.24 -14.98 4

102.05 102.05 12 .0 0:11 80.25 -6.24 -14.98 ~

105.85 105.85 13

.00g79 8035 1.84 6.09 109.65 109.65 14 .0134g 98.25 6.09 1.84 113.45 113.45 15 9835 2634 24.71

.0176 117.25 117.25 16 .02061 117.25 2634 24.71 121.05 121.05 17 .02197 11735 73 33.52 124.85 124.85 18 .02111 136.25 73 33.52 128.65 128.65 19 .01752 13635 6.62 32.65 132.45 132.45 20 153.75 6.62 32.65

.01066 4

136.25 136.25 21 - 20.57 4438

.0 153.85 l' ' 75 139.75 22 .01331 171.25 -20.57 4438 1

143.25 23 .02845 17135 27.1 26.52 1*- 3 146.75 24 189.25 27.1 26.52

.04362 150.25 150.25 25 .057 18935 836 23.51 ,

153.75 153.75 26 207.25 836 23.51

.0668 157.25 157.25 27 .07122 *0735 6.17 19.52 150.75 160.75 28 . 0685 %f6.25 6.17 19.52 164.25 164.25 29 -30.42 27.19

.05688 22635 167.75 167.75 30 '

245.25 -30.42 27.19

.03462 171.25 171.25 31 24535 16.74

.0 38.15 174.85 174.85 32 255.5 38.15 16.74

.04969 178.45 178.45 33 N* .11172 255.6 16.87 19.25 182.05 181.05 34 265.75 16.87 19.25

.18355 185.65 sec 4c sc - - - - are ae aa ar ea a CSE-97158

ABS-CENO Ap;nmdix aom -

~.<w A2~Page A2- t3 A2, 189.25 l 52.

189.25 36 .V465 276A 40.76 53.0 192J5 192.85 37 .4330s 276.1 65.49 -58.57 196.45 196A5. 38 .51k4 286.25 65.49 58.57 c

200.05 200.05 39 .60417 28635 OA 0.0 203.65 203.65 40 .68461 296.5 04 04 -

207.25 207.25 41 .75908 2%.6 02 OA 211.0.~ 211.05 42 J2931 306.75 0.0 04 214.85 214.85 43 .88922 306.85 04 04 218.65 218.65 44 .9373 3th 0.0 04 222.45 222A5 45 .97233 317.1 0.0 0.0 226.25 226.25 46

,99343 327.25 O.0 0.0 230.G; 230.05 47 1.0 32735 04 0.0 233.85 233.85 48 .99173 337.5 0.0 0.0 237.65 237.65 49 .96884 337.6 0.0 0.0 241.45 241.45 50 .93155 349.56 0.0 0.0 245.25 245.25 51 .88063 349.66 0.0 0.0 ,

2483 2483 52 .83063 361.63 0.0 0.0 l 25134 25134 53 .77316 361.73 0.0 0.0 25439 25439 54 .70899 370.59, 0.0 0.0 ,

257.44 257.44 55 .63897 260.48 260.48 56 .56409 263.53 263.53 57 .48539 266.58 266.58 58 .40399 269.62 269.62 59 32109 272.57 272.67 60 .23794 275J1 275.71 61 .15582 278J6 278.76 62 .07606 281.81 281.81 63 .0 -

,284.87 , 284.87 64, ,. 0716 ,

e>)2 )2 t

CSE-97-158

&%ioK@C31Lk11(dJ Hrw.00 '

ABS-CENO -

Appendix A2 Page A2 0 A2-3 Nm m=1i=d displacement ($) as a function of spanwise x-coordinase (cubic spline interpolation function)is shown below:

vs := cspline(xc. disp)

$(x) :=interp(vs,xc. disp,x)

L Velocity (v) as a function of spanwise x-coordinate:

v(x) :=linterp(xv, velo,x)

Integrallimitt:

a := xe n

b := xc a = 62.25 b = 284.87 l

Assuming no spanwise variation in tube virtual mass or recondary fluid density, the effective velocity equation reduces to the following:

b v(x)* $(x)* dx

.a V d ;*

'b , V g = 34 in/Sec

$(x)* ds 3 .a s

CSE-97-158

ABSCENO. Appendx A2 Page A2 to A2, x :2 xc o ,xe,+ 1 - g) i :s 0,1.last(xc)

Cross Flow Gap Velocity PrnMle (m/sec)

Mode 10.86 Hz) Mode Shane NO 300 -

290

r 2s0 - 2:0, 270 -

260 ; 260d5-M .

Wk 230 .

220 ll20 --

210  %

200 200 --

190 - -

. t

~

180 l 180 -1

% ac 170

• j.

160 [

150 .

140 , ,

130 ,

120

. 1204 '

110 100 "-

1005-90 ,

r .

g

. 40a =

70 - * -

60 ..

0 50 100 ' -- '

M ^ 0 1 v( x).0 K ),0 CSE-97-158

A-SONGS-9416-1168, Rev 00 Appendix A3 Page A3-1 of A3-50 i

APPENDIX A3. DISPLACEMENTS DUE TO TURBULENT

. PARALLEL & CROSS FLOWS -

l o

CSE-97158

f A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-2 of A3-50 Tube Die = hee =ents Due To Turbulence mot Les Vertical Sean Cross Mow) 4 Tube Row 147 ec's 9 & 10 inactive:

(Methodology: Article N-1340 of ASME Code SectionIII, Appendix N.)

p := 6.41 Ibf (Sec. fluid density) d := 0.75 in (Tube O.D.)

g3 Freq. (fn) vs Random Excitation m := .0461 lbf -

Effective mass of tube Coefficient (Cr). Fin. N-1343-1.

m per unit length) expressed as equation.

fn := 10.9 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode) l

( := 0.035 (Critical damping ratio)

Cr(fn):= exP(a n f + b)-[sec if n 40<f s70 4

V := 4.53- (Fluid cross flow velocity) 0.025[sec otherwise see Cr := 0.025hc (Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L := 91.5 in . (Span width between verticallegs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

r-Lc J a" I= a 0.236 (Joint acceptance) 0.5 h p d V2 Cr -3 .

A rms = 2.4817 10 t

Arms '  !

I a m 3

64 x f n m2,g A

rms = .......

2.5 mils CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-3 of A3-50 Tube Disniacements Due To Turbulence (Hot Lee Vertical Soan Cross How)

Tube Row 147 ec's 8 & 9 inactive - 10 active (Methodology: Article N-1340 of ASME Code SectionIII, Appendix N.)

p := 7.17 lbf (Sec. fluid density) d = 0.75 in (Tube O.D.)

ft

' Freq. (fn) vs Random Excitation m := .0468 Ibf --

(Effective mass of tube Coefficient (Cr). Fin. N-1343-1.

m per unit length) spgssed as equation.

fn := 12.5 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode)

( := 0.029 (Critical damping ratio)

Cr(f n) := exP(an f + b) ke if 40<f n s70 V := 3.261 (Flaid cross flow velocity) 0.025hc otherwise sec Cr := 0.025-[sec(Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L := 92.3 in (Span width between EC 10 & 7)

Le := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

Le J , := J a= 0.235 (Joint acceptance) 0.5 h p d V2 Cr ~3 .

A rms;* I a O rms = 1.2613 10 m 3

64x f n mE?

CSE-97-158 I

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-4 of A3-50 Tube Disniacements Due To Turbulence (Hot Lee - Vertical Sean - Cross-Flow)

Jube Row 147 ec's 7 & 8 inactive with 9 & 10 active (Methodology: Article N-1340 of ASME Code Section III, Appendix N.)

p := 8.164 lbf (Sec. fluid density) 3 d := 0.75 in (Tube O.D.) ,

ft

' Freq. (fn) vs Random Excitation m := .0475 lbf -

(Effective mass of tube Coefficient (Cr). Fin. N-1343-1.

m per unit length) expressed as equation.

f n:= 10.8 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode)

(Critical damping ratio)

(:= 0.0261 Cr(f n) := exP(;fn + b) hc if 40<f ns70 V := 2.47 b (Fluid cross flow velocity) 0.025h otherwise see Cr := 0.025 kc (Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L := 99.5 in (Span width between verticallegs)

Le:=6.8d (Correlation length, Ref. Blevins, et al. (1981))

r--

'Lc J , := J a= 0.226 (Joint acceptance) 0.5 h p d V2 Cr A  := 'J a A rms = 1.0269 10'3 in 64 2 f n m&

CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-5 of A3-50 Tube Disolacements Due To Turbulence (Hot Lee - Vertical Soan - Cross-Mow)

Tube Row 147 - Staked Tube - EC's 8.9. & 10 inactive (Methodology: Article N-1340 of AShE Code Section III, Appendix N.)

l p = 8.160 bf (Sec. fluid density) 3 d := 0.75 in (Tube O.D.)

ft Freq. (fn) vs Random Excitation m := .0755 lbf -

(Effective mass of tube Coefficient (Cr1 Fin. N-1343-1.

m per unit length) expressed as eauation.

fn := 4.96 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode)

( .= 0.083 (Critical damping ratio)

Cr(f n) := exp(anf + b) h if 40<f ns70 V := 3.92.1 (Fluid cross flow velocity) 0.025 kc otherwise see Cr := 0.025 hc (Ref. AShE Code Section III, Appendix N, Fig. N-1343-1)

L ': 123.0-in (Span width between vertical legs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

r--

Lc J ,:= -

J a= 0.204 (Joint acceptance) 0.5 h p d-V2 Cr -3 a  := 'I a A rms = 2.6356 10 in 64- fn m(

CSE-97-158

A-SONGS-9416-Il68, Rev. 00 Appendix A3 Page A3-6 ofA3-50 Tube Disolacements Due To Turbulence (Hot Lee - Vertical Snan - Cross-Flow)

Tube Row 147 - Staked Tube - EC's 5 thru 8 inactive. 9 & 10 active (Methodology: Article N-1340 of ASME Code Section III, Appendix N.)

p := 9.06 lbf (Sec. fluid density) 3 d := 0.75 in (Tube O.D.)

ft Freq. (fn) vs Random Excitation m := .0772 lbf -

(Effective mass of tube Coefficient (Cr1 Fin. N-1343-1.

m per unit length) exoressed as eauation.

, f n:= 3.14 Hz (Natural frequency ~

a := -0.0317763 b := - 2.4062 of applicable mode)

(:= 0.084 (Critical damping ratio)

Cr(f n) := exP(an f + b)-[sec ifn 40<f 570 t

V := 1.75= (Fluid cross flow velocity) 0.025 4sec otherwise see Cr := 0.025 kc (Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L .= 170.5 in (Span width between venicallegs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

Le J a ;" -

I=a 0.173 (Joint acceptance) 0.5 h p d V2 Cr ~4 Arms * 'I a A xms = 9.5602 10 in r

3 2 64 x f n m ,4 CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-7 of A3-50 Tube Disniacements Due To Turbulence (Hot Lee - Vertical Soan - Cross-Mow)

Tube Row 145 - EC's 9 & 10 inactive (Methodology: Article N-1340 of ASME Code Section III, Appendix N.)

p := 6.41 lbf (Sec. fluid density) 3 d := 0.75 in (Tube O.D.)

ft Frea. (fn) vs Random Excitation

! m := .0461 lbf --

(Effective mass of tube Coefficient (Cr1 Fie. N-1343-1.

I

• per unit length) exoressed as ecuation.

f n:= 11.4 Hz (Natural frequency a := -0.0317763 b := - 2.4062 of applicable mode)

(:= 0.0259 (Critical damping ratio)

Cr(f n) := eXP(a n f + b) hc-if 40<f n 570 V := 4.38 A (Fluid cross flow velocity)

- 0.025 sec otherwise seC Cr := 0.025 he (Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L := 90.3 in (Span width between verticallegs)

Le := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

r-

'Lc J a*

I=a 0.238 (Joint acceptance) 3 L 0.5 h p d V2 Cr -3 Arms * 'I a A rms = 2.5382 10 m

3 64 x f n mE?

CSE-97-IS8

A-SONGS-9416-1168, Rev 00 Appendix A3 Page A3-8 ofA3-50 Tube Disolacemerts Due To Turbulence (Hot Lee - Vertical Sean - Cross-Mow)

Tube Row 144 - EC's 9 & 10 inactive (Methodology: Article N-1340 of AShG Code SectionIII, AppendixN.)

l p := 6.09 lbf (Sec. fluid density) 3 d := 0.75 in (Tube O.D.)

l ft i

Frea. (fin vs Random Excitation m.=.0460lbf -

(Effective mass of tube CoefEcient (Crt Fic. N-1343-1.

m per unit length) exnressed as equation.

f n:= 11.6 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode)

% = 0.026 (Critical damping ratio)

Cr(fn ):: exp(a nf + b)-[sec if 40<fn s70 V := 4.701 (Fluid cross flow velocity) 0.025 kc otherwise see Cr := 0.025 kc (Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L := 89.3 in (Span width between verticallegs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

Le J J a= 0.239 (Joint acceptance) a=iL-0.5 h p d V2 Cr Arms ;"

A rms = 2.721 10'3 m

=J

a 642 fn'M'k CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-9 of A3-50 Tube Dimlac.cments Due To Turbulence ggi Lee Va-ical Snan - Cross-Mow)

Tube Row 139 - EC's 9 & 10 inactive (Methodology: Article N-1340 of ASME Code SectionIII, AppendixN.) ,

L p := 6.09 Ibf (Sec fluid density) 3 d := 0.75 in - (Tube O.D.)

ft Frea. (fn) vs Random Excitation m := .0460 lbf -

(Effective mass of tube Coefficient (Cr). Fin N-1343-1.

" -per unit length) exoressed as eauntion.

I n:= 13.0 Hz (Natural frequency a := -0.0317763 b := -2,4062 of applicable mode) eXP(anf + b)- c if 40<f ns70

( := 0.025 (Critical damping ratio)

Cr(f):

n V := 4.601 (Fluid cross flow velocity) 0.025 hc otherwise seC Cr := 0.025 kc (Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L := 85.0 in (Span width between verticallegs)

Le := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

Lc J a" gI a = 0.245 (Joint acceptance)

O.5 h p d V2 Cr ~3 Arms

• A rms = 2.2964 10 in

=3 r a 64 x* f n mE(

CSE-97-IS8

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-10 of A3-50 Tube Disniacements Due To Turbulence (Hot Lee - Vertical Snan - Cross-Flow) l Tube Row 138 - EC's 9 & 10 inactive (Methodology: Article N-1340 of ASME l Code Section III, Appendix N.)

p := 5.82 Ibf (Sec. fluid density) d := 0.75 in (Tube O.D.)

a3 Freq. (fn) vs Random Excitation m := . 0457 lbf (Effective mass of tube Coefficient (Cr). Fin. N-1343-1.

m per unit length) expressed as eauntion.

f n:= 13.3 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode)

(:= 0.025 (Critical damping ratw) Cr(fn) ;" exP(an f + b)-[sec ifn 40<f 570 V := 5.38 - - (Fluid cross flow velocity) 0.025-[sec otherwise seC Cr := 0.025-[sec(Ref. ASME Code Section III, Appendix N, Fig N-1343-1)

L := 84.0 in - (Span width between vertical legs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

r-

'Lc J a*

I=a 0.246 (Joint acceptance) 0.5 h p d V2 Cr -3 Am := A rms = 2.9374 10 in

'I a

2 64.x'.f,3.m .g CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-11 of A3-50 Tube Disolacements Due To Turbulence mot Lee - Vertical Soan - Cross-Mow)

Tube Row 127 - EC's 9 & 10 inactive (Methodology: Article N-1340 of AShE

Code SectionIII, Appendix N.)

p := 5.82 Ibf (Sec, fluid density) d := 0.75 in (Tube O.D.)

g3 Freo. (fn) vs Random Excitation

, m := .0457 lbf -

(Effective mass of tube Coefficient (Cr1 Fin. N-1343-1.

l m per unit length) .e_;spiessed as equation.

fn := 17.6 Hz (Natural frequency

a. .s317763 b := -2.4062 of applicable mode)

( := 0.024 (Cdtical damping ratio)

Cr(f n) := exP(a n f t b) kc if 40<f n s70 V := 5.02 - (Fluid cross flow velocity) 0.025 kc otherwise see Cr := 0.025 hc (Ref. AShE Code Section IU, Appendix N, Fig. N-1343-1)

L := 74.6 in (Span width between verticallegs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

r-

'Lc J a" -

I=a 0.261 (Joint acceptance) 2 A, = 0.5 h p d V Cr Ia A rms = 1.8195 10

~3 in

[64 n .f g .m k CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-12 of A3-50 Tube Disolacements Due To Turbulence (Hot Lee - Vertical Sean - Cross-Flow)

Tube Row 126- EC's 9 & 10 inactive (Methodology: Article N-1340 of AShE Code Section M, Appendix N.)

p := 6.05 Ibf (Sec. fluid density) 3 d := 0.75 in (Tube O.D.)

ft Frea (in)vs RandoriExcitation m := .0452 lbf -

(Effective mass of tube Coefficient (Crt Fie. N-1343-1.

m per unit length) exoressed as equO f n:= 18.2 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode)

( := 0.024 (Critical damping ratio)

Cr(f):=

n exP(an f + b) h if 40<f n s70 V := 5.121 (Fluid cross flow velocity) 0.025 h otherwise sec Cr := 0.025 hc- (Ref. AShE Code Section E, Appendix N, Fig. N-1343-1)

L := 73.6 in (Span width between bw and eggerate)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

Lc J

a*gI a = 0.263 (Joint acceptance) 0.5 h p d V2 Cr -3 A A rms" I a rms = 1.9045 10 m 64 x f n 3 m2,g l

CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-13 of A3-50 Tube Disolacements Due To Tubulence (Hot Lee - Vertical Soan - Cross-Mow)

Tube Row 121 - EC's 9 & 10 inactive

! (Methodology: Article N-1340 of AShE Code Section III, Appendix N.)

l p := 6.05 lbf (Sec. fluid density) d := 0.75 in (TubeO.L.)

l fd Frea. (fn) vs Random Excitation m := .0452 Ibf -

(Effective mass of tube Coefficient (Cr). Fin. N-1343-1.

5 per unit length) exoressed as ecuation.

fn := 20.9 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode)

( := 0.023 (Critical damping ratio)

Cr(f n) := exP(an f + b) ke if 40<f n s70 Y := 5.01- (Fluid cross flow velocity) 0.025 he otherwise see Cr := 0.025 hc (Ref. AShE Code Section III, Appendix N, Fig. N-1343-1)

L := 69.3 ir. (Span width between verticallegs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

r-Le J a* -

I=a 0.271 (Joint acceptance) 0.5 h p d V2 Cr -3 A rms " 'I a O rms = 1.56 10 m

3 2 4

64 2 f n m ,C CSE-97-158

\

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-14 of A3-50 Ight Disolacements Due To Turbulence

@pfLLee - Vertical Soan - Cross-Mow)

Tube Row 120 - EC's 9 & 8 inactive (Methodology: Article N-1340 of AShE Code Section III, Appendix N.)

p := 6.50 Ibf (Sec. fluid density) d := 0.75 in (Tube O.D.)

ft 3 Frea (fn) vs Random Excitation m := .0461 lbf (Effective mass of tube Coefficient (Cr). Fie. N-1343-1.

m per unit length) exoressed as eauation.

f n:= 10.7 Hz (Nature.1 frequency -

a := -0.0317763 b := -2.406'2 of applicable mode)

(:= 0.026 (Critical damping ratio)

Cr(fn) = eXP(a n f + b).h if 40<f n 570 V := 4.38 d (Fluid cross flow velocity) 0.025 hc otherwise seC Cr .= 0.025 h (Ref. AShE Code Section III, Appendix N, Fig. N-1343-1)

L := 99.0 in (Span width between verticallegs)

Le := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

m Lc a = 0.227 J (Joint acceptance) a ;" y I 0.5 h p d V2 Cr ~3 A rms;* 'I a A rms = 2.6981 10 in 7

64 x f n m2,4 CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-15 ofA3-50 Tube Disolacements Due To Turbulence (Hot Lee - Vertical Soan - Cross-Flow)

Tube Row 120 - EC's 7 & 8 inactive (Methodology: Article N-1340 of ASME Code Section III, Appendix N.)

p := 7.38 Ibf (Sec. fluid density) 3 d := 0.75 in (Tube O.D.)

ft lbf Frea. (fn) vs Random Excitation m = .0464 -- (Effective mass oftube CoefBeient (Crt Fin. N-1343-1.

m per unit length) exoressed as eauation.

I fn := 10.9-Hz (Natural frequency a := -0.0317763 b := - 2.4062 of applicable mode)

(Critical damping ratio)

( := 0.026 Cr(fn):= exp(anf + b).h if 40<f n570 V := 3.021 (Fluid cross flow velocity) 0.025-[sec otherwise see Cr := 0.025 he (Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L := 101.0 in (Span width between vertical legs) '

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

r--

Le J

a "g 3 a = 0.225 (Joint acceptance) r

^ 0.5 42 p d V2 Cr ~3 Arms * 'I a A rms = 1.3933 10 in 64 n f n m4 CSE-97-IS8 l

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-16 of A3 50 Tube Displacements Due To Turbulence '

filot I ee - Vertical Sean - Cross-Mow)

Tube Row 111 - EC's 7 & 8 inactive '

(Methodology: Article N-1340 of ASME Code Section III, Appendix N.)

p := 6.50 lbf (Sec. fluid density)

3 d := 0.75 in (Tube O.D.)

ft Freq. (fn) vs Random Excitation m := .0461 lbf (Effective mass oftube Coefficient (Cr1 Fin. N-1343-L m

per unit length) exoressed as equation.

f n:= 11.0 Hz (Natural frequency a := -0.0317763 b := - 2.4062 of applicable mode) 4 := 0.026 (Critical damping ratio)

Cr(f n) := exP(an f + b) hc if 40<f n s70 V := 4.30 S- (Fluid cross flow velocity) 0.025 kc othenvise see Cr := 0.025 hc (Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L := 91.3 in (Span width between verticallegs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

Le Ja I=a 0.236 (Joint acceptance) 0.5 h p d V2 Cr ~3 A ms *

'J a A rms = 2.5978 10 *in q 64 x f n m&

CSE-97-158 s

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-17 of A3-50 Tube Disolacements Due To Turbulence (Hot Lee - Vertical Sean - Cross-Flow) e Tube Row 110 - EC's 9 & 8 inactive (Methodology: Article N-1340 of ASME Code Section IH, Appendix N.)

p := 6.30 Ibf (Sec. fluid density) d := 0.75 in (Tube O.D.)

g3 '

Frea. (fn) vs Random Excitation m := .0456 lbf -

(Effective mass of tube Coefficient (Cr1 Fig. N-1343-1.

• per unit length) exnressed as eauation.

fn := 11.3 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode)

( := 0.026 (Critical damping ratio)

Cr(fn ): eXP(a n f + b).h if 40<f n s70 V = 4.87- (Fluid cros.s flow velocity) 0.025ke otherwise see Cr := 0.025hc (Ref. ASME Code Section IH, Appendix N, Fig. N-1343-1)

L := 91.3 in (Span width between verticallegs)

Lc = 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

Le I a = 0.236 J

a "g (Joint rcceptance) 0.5 h p-d V2 Cr -3 Arms * 'I a A rms = 3.136 10 m

3 64 2 f n m2,4 CSE-97-158 1

-J

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-18 of A3-50 Tube Displacements Due To Turbulence l

(Hot Lee - Vertical Sean - G oss-Flow)

Tube Row 110 - EC 9 inactive (Methodology: ArticleN-1340 ofASME Code Section m, Appendix N.) ,

p := 5.89 Ibf (Sec. fluid density) 3 d := 0.75 in (Tube O.D.)

ft Freq. (fn) vs Random Excitation m := .0452 lbf (Effective mass of tube Coefficient (Cr1 Fie. N-1343-1 m

per unit length) exoressed as equation.

f n:= 24.1 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode)

(:= 0.0218 (Critical dam;.'ng ratio)

Cr(f n) := exP(an f + b) h if 40<f n s70 V := 5.511 (Fluid cross flow velocity) 0.025 h otherwise Sec Cr := 0.025 h (Ref. AShE Code St.ction m, Appendix N, Fig. N-1343-1)

L := 59.6 in (Span width between vertical legs)

Lc := 6.8 d- (Correlation length, Ref. Blevins, et al. (1981))

Lc J a ;* -

I=a 0.293 (Joint acceptance) 0.5 h p d V2 Cr ~3 Arms ;* 'I a A rms = 1.6432 10 m

3 64 2 f n m2,4 CSE-97-158 j

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-19 of A3-50 Tube Disolacements Due To Turbulence mot Lee - Vertical Soan - Cross-Mow)

Tube Row 93 - EC's 9 & 8 inactive (Methodology: Article N-1340 of ASME Code Section E, AppendixN.)

p := 6.27 Ibf (Sec. fluid density) d := 0.75 in (Tube O.D.)

i ft

' Freq. (fn) vs Random Excitation m := .0460 Ibf -

(Effective mass of tube CoefEcient (Cr). Fin N-1343-1.

m per unit length) exoressed as equation.

fn * .16.9 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode)

(:= 0.0241 (Critical damping ratio)

Cr(f n) := exp(a nf + b)-[sec if 40<fn 570 V := 3.94- (Fluid cross flow velocity) 0.025 h otherwise see Cr := 0.025 h (Ref. ASME Code Section E, Appendix N, Fig. N-1343-1)

L := 75.5 in (Span width between verticallegs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

Lc J a* -

J a= 0.26 (Joint acceptance) 0.5 h p d V2 Cr -3 Arms * =I a A rms = 1.2646 10 in 3

64 x f n mE&

,- CSE-97158 a

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-20 of A3-50 Tube Displacements Due To Turbulence (Hot Lee - Vertical Soan - Cross-Flow)

Iube Row 84 - EC's 7 & 8 inactive (Methodology: Article N-1340 of ASME Code Section III, Appendix N.)

p

= 7.2 lbf (Sec. fluid density) 3 d := 0.75 in (Tube O.D.) .

l ft Freq. (fn) vs Random Excitation m := .0467 lbf -

(Effective mass of tube Coefficient (Crt Fig. N-1343-1.

m per unit length) exoressed as equation.

fn := 9.7 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode)

( := 0.0265 (Critical damping ratio)

Cr(f n) := exP(an f + b) h if 40<f n s70 V := 3.451 (Fluid cross flow velocity) 0.025 h otherwise see Cr := 0.025 hc (Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L := 105.0 in (Span width between vertical legs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

r-Lc I=a 0.22 (Joint acceptance)

Ja

{

0.5 h p d V2 Cr -3 A  := 'I a A rms = 2.0396 10 in 4 64 2 fn*b CSE-97-158

A-SONGS-9416-1168, Rev. 00 A;,pendix A3 Page A3-21 of A3-50 Tube Disniacements Due To Turb=le=ce (Hot Lee - Vertical Sean - Cross-Flow)

Tube Row 83 - EC's 7 & 8 i==ctive:

(Methodology: Article N-1340 of ASME Code SectionIII, AppendixN.)

p := 7.2 Ibf (Sec. fluid density)

, d := 0.75 in (Tube O.D.) -

ft l Freq. (fn) vs Random Excitation

! m := .0467 lbf -

(Effective mass of tube Coefficient (Cr1 Fin. N-1343-1.

m per unit length) exoressed as eauatbn.

f n:= 8.34 Hz (Natural frequency a := - 0.0317763 b := -2.4062 of applicable mode)

& := 2.7 % . (Damping ratio, percent of Cr(fn) :=

critical) exP(a n f + b)-[sec if n 40<f 570 V := 3.51= (Fluid cross flow velocity) 0.025-[sec otherwise SCC 0

Cr(8.4) = 0.025 sec ,5 Cr := .025-[sec(Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L := 104.0 in (Span width between vertical legs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

r-Le J ,:= J a= 0.221 _(Joint acceptance) 2 3 :_ 0.5 h p d V Cr=I ~3 A rms = 2.6361 10 in a A rms = 2.6 mils 642 fn 'M 'k CSE-97-IS8

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-22 of A3-50 Tube Disolacements Due To Turbulence mot Lee - Vertical Soan - Cross-Mowl Tube Row 83 - EC 8 inactive:

(Methodology: Article N-1340 of ASME Code Section III, Appendix N.) .

! p := 6.737 Ibf (Sec. fluid density) 3 d := 0.75 in (Tube O.D.)

ft Freo. (fh) vs Random Excitation m := .0464 lbf -

(Effective mass of tube CoefficiS (Cr). Fin. N-1343-1.

m per unit length) exoressed as eauntion.

_ f n:= 18.75 Hz (Natural frequency a := -0.0317763 b := -2.4062 of applicable mode)

( := 2.35 % (Damping ratio, percent of Cr(fn) '=

critical) exP(a n f + b) h if 40<f n s70 V := 3.89-- (Fluid cross flow velocity) 0.025hc otherwise sec

-0 Cr(8.4) = 0.025 sec .5 Cr := .025 hc (Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L := 66.8 in (Span width between verticallegs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et ai ,1981))

Lc J -

I= a 0.276 (Joint acceptance) a*iL 0.5 h p d V2 Cr ~3 .

Arms

• I a A rms = 1.2098 10 m 3 2 4

64 n f n m ,4 CSE 97-158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-23 of A3-50 Tube Displacements due To Turbulence (Hot Lee - Vertical Sean - Cross-Flow)

Tube Row 83 - Staked Tube EC's 6. 7 & 8 inactive (Methodology: Article N-1340 of AShE Code Section III, Appendix N.)

p := 7.66 Ibf (See, fluid density) 3 d := 0.75 in (Tube O.D.)

ft Frea. (fn) vs Random Excitation

! m := .0761 lbf -

(Effective mass of tube Coefficient (Cr1 Fie. N-1343-1.

I m per unit length) expressed as equation.

f n:= 3.86 Hz (Naturalfrequency -

a := -0.0317763 b := -?. 4062 of applicable mode)

Cr(f n) := exp(a nf + b) h if 40<f ns70

(:= 0.084 (Critical damping ratio)

V := 3.08- (Fluid cross flow velocity) 0.025 h otherwise SCC Cr .= 0.025 h (Ref. AShE Code Section III, Appendix N, Fig. N-1343-1)

L := 140.0-in (Span width between vertical legs)

Le := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

r-LC J I=a 0.191 (Joint acceptance) a*yL-0.5 h p d V2 Cr -3 Arms" 'J a A rms = 2.0565 10 in 3

64 x f n m2,4 CSE-97-158

l l

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-24 ofA3-50 Tube Disolacements Due To Turbulence (Hot Lee - Vertical Snan - Cross-Mow)

Tube Row 70 - EC's 7 & 8 inactive (Methodology: ArticleN-1340 ofAShE Code Section m, Appendix N.)

p := 7.01 Ibf (Sec. fluid density) 3 d := 0.75 in (Tube O.D.)

ft Freq. (fn) vs Random Excitation m := .0457 lbf -

(Effective mass of tube Coefficient (Cr1 Fie. N-1343-1.

• per unit length) exuressed as equation.

fn :- 11.0 Hz (Natural frequency a := -0.0317763 b':= -2.4062 of applicable mode)

( := 0.026 (Critical damping ratio)

Cr(fn ):: exP(an f + b) h if 40<f n 570 V := 4.061 (Fluid cross flow velocity) 0.025 kc otherwise sec Cr := 0.025 hc (Ref. AShE Code Section m, Appendix N, Fig. N-1343-1)

L := 93.4 in (Span width between verticallegs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

Lc J a* -

I a= 0.234 (Joint acceptance) 0.5 h p d V2 Cr ~3 .

Arms * 'I a A rms = 2.491 10 m 3

4 64 x f n mE(

CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-25 of A3-50 Tube Disolacements Due To Turbulence (Hot Lee - Vedical Sean - Cross-Mow)

Tube Row 49 - EC's 6 & 7 inactive (Methodology: Article N-1340 of ASME Code SectionIII, AppendixN.)

p := 8.18 Ibf (Sec. fluid density) 3 d := 0.75 in (Tube O.D.)

ft Frea. (fn) vs Random Excitation l m := .0475 lbf -

(Effective mass of tube Coefficient (Cr). Fie. N-1343-1.

5 l per unit length) exoressed as eauation.

i

! f n:= 7.9 Hz (Natural frequency l a := -0.0317763 b := -2.4362 of applicable mode)

(Critical damping ratio)

% := 0.027 Cr(f n) := exp(a nf + b) he if 40<f ns70 V := 2.831 (Fluid cross flow velocity) 0.025 h otherwise see Cr := 0.025 hc (Ref. ASME Code Section III, Appendix N, Fig. N-1343-1)

L := 110.5 in (Span width between verticallegs)

Le := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

r-Lc J a ;* -

I=a 0.215 (Joint acceptance)

,L 0.5 h p d V2 Cr -3 Arms " 'I a A rms = 2.0142 10 m

3 2 642 f n m ,(

CSE-97158

N A SONGS 94161168, Rev. 00 1

Appendix A3 Page A3 26 of A.3 50 I

)

Tube Disniacements Due To Turbulence mot Lee - Vertical Sean - Cross-Mow)

T.ukgjow 49 - EC's 6 & 7 i==cth>e (Methodology: Article N 1340 of ASME Code Section E, Appendix N.)

~

p;=4,18lbf (Sec fluid density) d := 0.75 in (Tube O.D.)

3 ft Freq. (fn) vs Random Excitation m := .0475;--lbf (Effective mass of tube Coccicient (Cr). Fig. N-1343-1.

m per unit length) expressed as eauntion.

i f n:= 7.9 Hz (Natural frequency i a := -0.0317763 b := -2.4062 of applicable mode)

(:=0.027 (Critical damping ratio)

Cr(fn) = exP(a nf + o) see if 40<fn s70

)

V := 2.831 (Fluid cross flow velocity)

,,e 0.025-[sec othenvise Cr := 0.025-[sec (Ref. ASME Code Section E, Appendit N, Fig. N-1343-1)

L := 110.5 in (Span width between venical legs)

Lc := 6.8 d (Correlation length, Ref. Blevins, et al. (1981))

Lc

J a ;* -

I=a 0.215 (Joint acceptance) 2 A,:= 0.5 h p d V JCr a A

rms = 2.0142 10

~3 in 64 X f n m4 CSE 97158

A SONGS-94161168, Rev,00 Appendix A3 Page A3-27 of A3 50 Tube Disniacements Due To Turbu!ence (Hot Lee - Vertical Sean - Cross-Flow)

Tube Row 22 - EC's 6 & 7 lanctjyg (Methodology: Article N-1340 of AShE Code Section III, Appendix N.)

p := 8.68 Ibf (Sec. fluid density) d := 0.75 in (Tube O.D.)

fd Frea (fni vs Random Excitation m := .0478 Ibf (Effective mass of tube Coefficient (Cr) Fin. N-1343-1.

In per unit length) exoressed as equation.

f,, := 13.4 Hz -(Natural frequency a := -0.0317763 b := -2.4062 of spplicable mode)

( := 0.025 (Critical damping ratio)

Cr(fn):* exP(a n f + b) h if 40<f n s70 V := 2.631 (Fluid cross flow velocity) 0.025-[sec otherwise sec r

Cr := 0.025 h (Ref. ASME Code Section III, Appendi: N, Fig. N-1343-1)

L := 187.4 in (Span width between bw & first active EC)

Lc := 6,8 d (Correlation length, Ref. Blevins, et al. (1981))

r-Lc J ,:= J , = 0.165 (Joint acceptance) 0.Sh p d V2 Cr Ay, : = .J , A rms = 6.6262 10 *in q64 3 f n mk(

CSE 97158 l

. - - - . - . - . . . . . . _ . - - - - - - - - . ~ . . - - - - - - - - . - - - - -

i A-SONGS 94161168. Rev. 00 '

Appendix A3 Page A128 of A3 50 i

b f

6

.I 1

k f

3 ,

T l PARALLEL FLOW INDUCED DISPLACEMENTS i

1 P

i CSE-97158 9-ur.,=.ewr-.y.. .,eg. ,y-p---w pm9 -.m. , y -.ye vg vg n s ,wy r,. .,g g q ,,p999g, 9y y y - ,,-,,7 79 ,,, ,,,,9,.,, 9,,_,, w,p r, .-.7,-.%,,w -y.,,- , ,-,*.er yw u.

A .3ONGS 941ti-1168, Rev. 00 Appendix A3 Page A3 29 of A3 50 Parallel Flow Evalunden E== Onofre 3

Reference:

ASME Co6e Santian III Annandiv N. Ar*leta N-1345. Fan =+1on 97 (for displacement due to axial flow)

Row 147, Two EC's ( 9 & 10) Inactive:

l V := 14.58 A (Velocity of two-phase mixture berew.. EC's 9 & 10) l * ,

p , := 6.41 Ibf (Density of two-phase mixture between EC's 9 & 10)

A d := 0.75 in (Tube OD) t := 0.048 in (Tube thickness) d h := 0.72 in (Tubs Hydraulic diameter) mt := 0.0462 m lbf- (Tatal tube VirtualMass) f n = 10.9 Hz (Tube first mode frequency w/two EC's nussing)

L := 91.5 in (Span length, Dist. between EC#8 & BW)

F ent := 3.1 (Hydrodynamic added mass factor for surrounding fluid) 2 A o := _d A o=0.442 in 2 d g := d - 2 t m , '= F .7t e PsAo m , = 0.00508 Ibf . (Added Mass of Sec, Fluid) m mt =0.0462m h (TotalVirtualMass).

CSE-97158

^

A SONGS-9416.I168, Rev. 00 Appendix A3 Page A3-30 of A3-50 EAtallel Flow Evaluation - San Onofre 3 - cont'd.

$:= S = 0.11 (Range 0.00049 to 0.62) OK mt L

e := - t = 122 (Range 26.8 to 58.7) i d 4 4 I :=

-(d - d $ )_ (Tube moment ofl'nertia) 6 E := 29.210 psi (Tube modulus ofElasticity) a

,y2 L2 I

ua u = 0.133 3 EI 2

u = 0.018 (Range 0.0021 to 0.8) OK K n:=5 (Noise factor)  ;

lbf v d ;= 2.82210'5 --

(dynamic viscosity)

A sec v :=

-I 2 v = 4.4 10 acc R (kinematic viscosity)

Ps 5

R , := V d R , = 2.07 10 (Reynolds No. Range 2.6E4 to 7ES) OK v

CSE.97158 -

I

A-SONGS 9416-ll68, Rev. 00 Appendix A3 Page A3-31 ofA3 50 l

l Parallel Flow Evaln= tion - San Onofre 3 - cont'd.

l 0 := 2 s f n Q = 68.5 +b sec l

(mt

-L 4\'

a = 3.787 a := 40- ( IE1 )

a = 14.341 (Range 2.10 to 20.8) OK 2

t l510'# KnI u .6,,1.8 R ,0.25 /dh '

S 6 max := d- (N-1345, Eq. 97)

( a 4

/ 1+u 2 (d/ 1+4.p

~3 6

max = 6.747 10 in CSE 97 lS8

A 50NGS 9416-ll68, Rev. 00 Appendix A3 Page A3-32 of A3 50 Tube Displacements Due to Parallel Flow Staked Tube Row 147- EC's ( 9. & 10) active and 5.6.7.8. Inactive:

Reference:

ASME Code Section III. Aopendix N. Article N 1345. EquatiQnj!

V := 10.17 A (Velocity c,f two-phase mixture between EC's 9 & 8) see p s := 9.063 Ibf (Density of two phase mixture between EC's 9 & 8) ft d := 0.75 in (Tube OD) t = 0.048 in (Tube thickness) d h := 0.72 in (Tube' Hydraulic diameter) l I

m t := 0.0755 --

lbf (Total tube Virtual Mass) m fn = 3.14 Hz (Tube first mode frequency)

L := 170.5 in (Span length, Dist. between EC#6 & 9)

F ent := 3.1 (Hydrodynamic added mass factor for surrounding fluid) 2 A o := d A o= 0.442 in 2 d ; := d - 2 t m a := F mt'P s' A o m , = 0.00718 Ibf (Added Mass of Sec. Fluid) m m t = 0.0755 -

m lbf (Total VirtualMass)

CSE 97158

l. . . . . -

l 4

A SONGS 94161168, Rev. 00 Appendix A3 Page A3 33 ofA3 50 Parallel Flow Evaluation - cont'd.

4 4

m, '

S:= $ = 0.095 (Range 0.00026 to 0.62) OK l

mt L

i e := - t =227.333 (Range 26.8 to 58.7)

I d 4

' I := 1-(d - d j#) (Tube moment ofinertia) 64 i

6 E := 29.210 psi (Tube modulus ofElasticity)

T i

• a ,y 2,g2 u :n I'

u = 0.205 3 E1 2

u = 0.042 (Range 0.0021 to 0.8) OK K n:=5 (Noise factor) lbf V

d := 3.46510'5 --

(dynamic viscosity) fi see

~I 2 v= v = 3.82 10 sec - ft (kinematic viscosity)

Ps Vd S R e := R , = 1.663 10 (Reynolds No. Range 2.6E4 to 7ES) OK v

CSE 97-158

A SONGS-94161168, Rev. 00 Appendix A3 Page A3-34 of A3-50 Parallel Flow Evalnadon - cont'd.

O:=2xf n O " 19 7*

sec

{mg_.L 4 ) **

a =4.282 a := h-( EI /I 1

a = 18.337 (Range 2.10 to 20.8) OK 2

l 510'd_Kn I u t.6,,1.8 R ,0.25 (d h S 6 max:=d- 4 (N-1345, Eq. 97)

( g / 1+u2 ( d ). 1 ,4.p max = 0.022 in 6

CSE 97-158

A SONGS 9416-1168, Rev. 00 1 Appendix A3 Page A3 35 ofA3 50 i

Tube Disolacements Due to Parallel Flow l Row 126. Two EC's ( 9 & 10) Inactive:

Reference:

ASME Code Section m Anoendix N. Article N-1345. Equation 97 V := 17.3 ft (Velocity of two-phase mixture between EC's 9 & 10) seC p , := 6.047 lbf (Density of two-phase mixture between EC's 9 & 10) a it d := 0.75 in (Tube OD) t := 0.048 in (Tube thickness) d h := 0.72 in (Tube Hydraulic diameter) m t := 0.0452 -

m lbf (Total tube Virtua Mass) 1 fn := 10.93 Hz (Tube first mode frequency w/two EC's missing)

L := 73.6 in (Span length, Dist. between EC#8 & BW)

F ent := 3.1 (Hydrodynamic added mass factor for surrounding fluid) 2 2 A o := d A o= 0.442 in d ; := d - 2 t m , := F ent'P s A o ma =0.00479 Ibf (Added Mass of Sec. Fluid) m m t = 0.0452 -

m Ibf (Total Virtual Mass)

CSE 97158

A-SONGS 9416-1168, Rev 00 Appendix A3 Page A3-36 ofA3-50 Parallel Flow Evalmtion - cont'd.

S:= = 0.106 (Range 0.00026 to 0.62) OK mt L

e := - t = 98.133 (Range 26.8 to 58.7) d 8

d 4 I :=641-(d - d g f (Tube moment ofinertia) 6 E := 29.210 . psi (Tube modulus ofElasticity) ma

,y 2,g2 u := -- 8 u = 0.123 3 E1 2

u = 0.015 (Range 0.0021 to 0.8) OK K n := 5 (Noise factoQ V

lbf d := 2.69810'5 --

(dynamic viscosity) <

A see

~

v := v = 4.46 10 sec 'ft 2 (kinematic viscosity)

Ps 8

R ,:= R , = 2.423 10 (Reynolds No Range 2.6E4 to 7ES) OK v

CSE 97158

A SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-37 of A3 50 i

1 l

This page left blank intentionally 3

P CSE 97158

A-SONGS 9416-1168, Rev. 00 Appendix A3 Page A3-38 of A3 50 Parallel Flow Evaln= don - cont'd.

O:=2xf n O = 68.7 *b sec Img 4)#

-.L a = 3.034 a := h-( EI /8 2

n = 9.203 ' (Range 2.10 to 20.8) OK 2

IS10'# Kn\ u ' t R ,0.25 /d h 6m := d- (N-1345, Eq. 97) -

( a / 1+u (d) 1+4.S 6

m,x = 0.01 in i

CSE 97158

A SONGS 9416-1168, Rev. 00 Appendix A3 Page A3-39 of A3 50 Tube Displacements Due to Parallel Flow Row 121, Two EC's ( 9 & 10) Inactive:

Reference:

AShiE Code Section III Anpendix N. Anicle N-1345. Equation 97 V := 17.3 A (Velocity of two-phase mixture between EC's 9 & 10) sec p , .= 6.047 lbf (Density of two-phase mixture between EC's 9 & 10) ft d := 0.75 in (Tube OD) t := 0.048 in (Tube thickness) d h := 0.72 in (Tube Hydraulic diameter) m t := 0.0452 -

lbf (Total tube Virtual hiass) m fn := 10.93 Hz (Tube first mode frequency w/two EC's missing)

L .= 69.3 in (Span length, Dist, between EC#8 & BW)

F ent := 3.1 (Hydrodynamic added mass factor for surrounding fluid) 2 A o := d A o= 0.442 in 2 d := d - 2 t m a := F ent'P s A o ma =0.00479 Ibf (Added hiass of Sec. Fluid) m mt =0.0452m Ibf (Total Virtual hiass)

CSE 97158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-40 of A3-50 Parallel Flow Evaluation - cout'd.

$:= = 0.106 (Range 0.00026 to 0.62) OK mt L

c := -- t = 92.4 (Range 26.8 to 58.7) d d d I :=641-(d - d g ) (Tube moment ofinertia) 6 E := 29.210 psi (Tube modulus ofElasticity)

Ima\

l ,y 2,g2 8

u := u = 0.ll6 3 EI 2

u = 0.013 (Range 0.0021 to 0.8) OK K n := 5 (Noise factor) lbf V (dynamic viscosity) d := 2.69810'5 --

ftsec 2

v := v = 4,46 10 sec ft (kinematic viscosity) 9s Vd 5 R e := R , = 2.423 10 (Reynolds No. Range 2.6E4 to 7ES) OK v

CSE 97158 e

A-SONGS 9416-1168, Rev. 00 Appendix A3 Page A3-41 of A3-50 Parallel Flow Evalnadon - cont'd.

O:=2xf n O = 68.7 b sec l

Im t 4

-_ .t a = 2.856 a:=h.1-) ( EI 2

a = 8.159 (Range 2.10 to 20.8) OK 2

t f 510'4 Kn) u .6,,1.8 R ,025 /d \

~

,0 max := d- ' h. S 4

(N-1345, Eq. 97) 2 1+4.p

( a / 1+u (d/

6, = 0.01 in CSE 97158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-42 of A3-50 Tube Displacements Due to Parallel Flow Row 110, EC 9 luactive:

Reference:

ASME Code Section III Anoendix N. Article N-1345. Equation 9*/

V := 16.4. ft (Velocity of two-phase mixture between EC 8 & bw) see p , := 5.89 Ibf (Density of two-phase mixture between EC 8 & bw) ft d := 0.75 in (Tube OD) t := 0.048 in (Tube thickness) d h := 0.72 in (Tube Hydraulic diameter) m t := 0.0452 m Ibf (Total tube Virtual Mass)

{

fn := 24.1 Hz (Tube first mode frequency w EC 9 missing)

L := 59.6 in (Span length, Dist. between EC#8 & BW)

F ent := 3.1 (Hydrodynamic added mass factor for surrounding fluid) 2 A o= .d A o= 0.442 in 2 d;'=d-2t m a := F ent'P s A o ma =0.00467 Ibf (Added Mass of Sec. Fluid) m mt =0.0452m Ibf (Total Virtual Mass)

CSE 97158

A SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-43 of.0-50 Parallel Flow Evaluation - cont'd.

p:= S = 0.103 (Range 0.00049 to 0.62) OK mt L

e := - e = 79.467 (Range 26.8 to $8.7) d 4 4 I:= 64 1-(d - d g ) (Tube moment ofinertia) 6 E := 29.210 psi (Tube modulus ofElasticity)

Img) l V 2,g2 .

u :=

8 u = 0.093 3 EI 2 -3 u = 8.69510 (Range 0.0021 to 0.8) OK Kn := 5 (Noise factor) lbf v d := 2.68710'5 --

(dynamic viscosity) ft sec

~I 2 v= v = 4.56 10 sec ft (kinematic viscosity)

Ps 5

R , := V d R , = 2.247 10 (Reynolds No. Range 2.6E4 to 7ES) OK v

CSE-97-158 l- ~

A-SONGS 9416-ll68, Rev. 00 1 Appendix A3 Page A3-44 ofA3-50 l i

l

Parallel Flow Evaluation - cont'd.

4 4 .

O := 2 x f n O = 151.4 rad -

sec 0

mt 4 \ .25

-L I -

a = 3.648 a := h- ( 8EI )

i 2

l. a = 13.306 (Range 2.10 to 20.8) OK r

2 l

[510'#K n Iu.6,,1.8R e o.25

/d h1 0'd 5 E (N-1345, Eq. 97) 6 ** = d - 4 2 (dj

( a 1+u i , 4.g

/

6 = 2,071 10~3 in

} max 4

t i

r i

P 6

4 4

CSE-97-158 v - , - - r.v,m--v - -- - ~~+--"v

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-45 of A3 50 Parallel Flow Evaluation - San Onofre 3 Row 83, EC 8 Inactive:

Reference:

ASME Code Section III Anoendix N. Article N-1345. Equation 97 (for displacement due to axial flow)

V := 13.08 ft (Velocity of two-phase mixture between EC's 7 & bw) sec p s := 6.737 lbf (Density of two-phase mixture between EC's 7 & bw) ft d := 0.75 in (Tube OD) ' t = 0.048 in (Tube thickness) d h := 0.72 in _ (Tube Hydraulic diameter) mt  := 0.0464 -

lbf (Total tube VirtualMass) m f .:=

n 18.75 Hz (Tube first mode frequency w EC 8 missing)

L := 66.8 in (Span length, Dist. between EC#7 & B%)

F ent := 3.1 (Hydrodynamic added mass factor for surrounding fluid) 2 A o := d A o= 0.442 in2 d ; := d - 2 t m ,:= F ent'P s' A o ma =0.00534 Ibf (Added Mass of Sec. Fluid) m m = 0.0464 g

m Ibf (Total Vinual Mass)

CSE-97-158

A-SONGS-9416-1168, Rev 00 Appendix A3 Page A3-46 of A3-50 Earallel Flow Evaluation - San Onofre 3 - cont'd.

$.= $ = 0.115 (Range 0.00049 to 0.62) OK

'" (

L c := - s = 89.067 (Range 26.8 to 58.7) d 4

1 := 1-(d - d ;4) (Tube moment ofinertia) 64 6

E := 29.210 psi (Tube modulus ofElasticity)

(m )

y,.L2 u :' - 8I u = 0.089 3 EI 2

u = 7.947 10he 0.0021 to 0.8) OK K n := 5 (Noise factor) lbf V (dynamic viscosity) d := 2.88810'5 --

A sec

~I 2 v := v = 4.29 10 sec A (kinematic viscosity)

Ps 5

R , := V d R , = 1.907 10 (Reynolds No. Range 2.6E4 to 7ES) OK v

CSE 97158

A-SONGS-9416-1168, Rev. 00 g Appendix A3 Page A3-47 ofA3-50

. Parallel Flow Evaluation - San Onofre 3 - cont'd.

, 0.=2xf n O = 117.8

• rad I rec fm t 4 a =3.63 a+=h(I EI /

a = 13.176 (Range 2.10 to 20.8) OK

- 2 l 510'#K I n u c ' R ,0.25 /d h S

6 max := d- d (N-1345, Eq. 97)

( a ) 1+u 2 (d/ 1+4.$

~3 6

max = 2.411 + 10 in i

l i

}

CSE-97 IS8 l

r -

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-48 of A3-50 Parallel Flow Evaluation - San Onofre 3 i

Row 49, Two EC's ( 6 & 7) Inactive:

Reference:

ASME Code Section III. Aopendix N. Article N-1345. Eauntion 97 V := 11.67 ft (Velocity of two-phase mixture between EC's 6 & 7) sec p s := 8.181 lbf (Density of tw> phase mixture between EC's 5 & 7) ft d := 0.75 in (Tube OD) t := 0.048 in (Tube thickness) d h := 0.72 in (Tube Hydraulic diameter) m t := 0.0475 m lbf (Total tubeVirtualMass) fn := 7.9 Hz (Tube first mode frequency w/two EC's missing)

L := 110.552 in (Span length, Dist. between EC#5 & BW)

F ent := 3.1 (Hydrodynamic added mass factor for surrounding fluid) 2 A o := d A o= 0.442 in 2 d := d - 2 t m a := F ent'P s A o ma =0 00648 .-

Ibf (Added Mass of Sec. Fluid) m m t = 0.0475 -

m Ibf (Total Virtual Mass)

CSE-97-158

A-SONGS-9416-1168, Rev. 00 Appendix A3 Page A3-49 ofA3 50 Parallel Flow Evaluation - San Onofre 3 - cont'd.

p:=

S = 0.137 (Range 0.00026 to 0.62) OK mt L

t := - t = 147,403 (Range 26.8 to 58.7) d -

4 I .= 1-(d - d ;4) (Tube moment ofinertia) 64 6

E := 29.210 psi (Tube modulus ofElasticity) 5 aI

,y 2,g2 u := -8 u = 0.145 3 EI 2

u = 0.021 '(P.ange 0.0021 to 0.8) OK K n=5 -(Noise factor) lbf V (dynamic viscosity) d := 3.0210'5 --

ft sec v := v =3.69107 seil .ft 2 (kinematic viscosity)

Ps 5

R , := V d R , = 1.976 10 (Reynolds No. Range 2.6E4 to 7E5) OK v

CSE-97-158 o

A-SONGS 9416-1168, Rev. 00

.,E Appendix A3 Page A3 50 of A3-50 <

i

.i 1

Parallel Flow Evaluation - San Onofre 3 - cont'd, D:=2xf n D = 49.6 b '

sec O.25 mt L4 8

a:=h.I,EI/ -

n = 3.922 a = 15.384 (Range 2.10 to 20.8) OK 2

I # t S 10T K n u .6,,1.8 R ,0.25 Idh p 6 max := d- (N-1345, Eq. 97) 7 ( a 4

) 1+u 2 (d) 1+4.p 6

max = 0.01 in 4

E - CSE 97158

A SONGS 9416-I168,Rev.01 Appendix A4 Page A4-1 of A4 34-ABB CENO I

APPENDIX A4 TUBE MODEL AND ANSYS MODE SHAPE PLOTS 4

i CSE-97-254

A SONGS 9416-1168,Rev.01 Appendix A4 Page A4-2 of A4-34 ABB CENO l

Appendix A4 Tube Model and ANSYS Mode Shape Plots i

i 2 97 g),Itu'ENT gI =1 SIk0

gux=i-

'6 b6 46 Row 147 with two uppermost eggerates inactive CSE-97-254

A SONGS-94161168, Rev. 01 Appendix A4 Page A4-3 of A4-34 ABB-CENO Appendix A4 Tube Model and ANSYS Mode Shape Plots 1

M 2 h97

• L & ENT 12.498

,=*

ry p .,

l i

l 46 Y

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A-SONGS 9416-Il68, Rev. 01 -

Appendix A4 Page A4-4 of A4 34 ABB-CENO Appendix A4 - Tube Model and ANSYS Mode Shape Plots 1

A 2197 6 14:1438 fC$ ' $dNT 4 ':

2 0.812 k rs -,

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l l

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A-SONGS 9416-1168, Rev. 01

- Appendix A4 Page A4-5 of A4-34 ABB-CENO Appendix A4 - Tube Model and ANSYS Mode Shape Plots

' I $??2%$e7 k@TP=1eIE8tu'aur l

i lhd.qse2 u"* " '

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A SONGS 9416-1168, Rev. 01

Appendix A4 Page A4-7 of A4-34 ABB-CENO '

Appendix A4 Tube Model and ANSYS Mode Shape Plots Tube Row 147 Critical Mode for Horizontal Span Cross Flow 1 ANSYS 5.3 MAY 241997 PIbk O.1 A' CEMENT i*

l y g=,=>56.127 l l 3""' .

!- DSCA=10.468 l M:1

!. S 114.555-

! Y =/h935

ZF =2.494 l

46 l

l 4

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A-SONGS-94161168, Rev. 01 Appendix A4 Page A4-9 of A4-34

. ABB-CENO Appendix A4 Tube Model and ANSYS Mode Shape Plots

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Appendix A4 Tube Model and ANSYS Mode Shape Plots l'

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'! 2

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f =1 l

l 1

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A-SONGS-9416-1168, Rsv. 01 Appendix A4 Page A4-11 of A4-34 ABB-CENO -

Appendix A4 Tube Model and _ANSYS Mode Shape Plots

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l

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A SONGS 9416-1168, Rev.01 Appendix A4 Page A4-12 of A4-34 ABB-CENO Appendix A4 Tube Model and ANSYS Mode Shape Plots-3 ANSYS 5.3 -

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l l

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A-SONGS-9416-1168, Rev. 01 -

Appendix A4 Page A4-13 of A4-34 ABB-CENO

' Appendix A4 Tube Model and ANSYS Mode Shape Plots 1 ANSYS 5.3 MAY 231997 13:0 :57 NO.2 LACEMENT 1

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- Appendix A4 Page A4-14 of A4-34__

,GB-CENO Appendix A4 ' Tube Model and ANSYS Mode Shape Plots 1 ANSYS 5.3 MAY 231997 bh NO.

OlSPLACEMENT '

S -1

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l l

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A-SONGS-S 4161168, Rev. 01

- Appendix A4 Ptge A4-15 of A4-34

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k A-SONGS 9416-1168, Rev,01-Appendix A4 Pcge A4-16 of A4-34 ABB-CENO Appendix A4 Tube Model and ANSYS Mode Shape Plots 1 ANSYS 5.3 MAY 231997 Lb O 6

DISPLAC$ MENT .

STgP.1 hEd=10.871 RSYS-0 ,

DMX=1-46- U

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_ _ _ . . ~ . . _ . - . . . . . _ _ .

A-SONGS-9416-1168, Rev. 01 Appendix A4 Page A4-17 of A4-34

. ABB-CENO 1

Appendix A4 Tube Model and ANSYS Mode Shape Plots 1 ANSYS 5.3 -

MAY 231997

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l l

l- l l

6 4&

b6~

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l; A-SONGS-9416-1168, Rev. 01 l _ Appendix A4 Page A4-18 of A4-34 ABB-CENO Appendix A4 Tube Model and ANSYS Mode Shape Plots -

1 ANSYS 5.3 MAY 231997 ONMENT l

SU

+

Y =O DMX -1 i U l

l l

l l

r l

'6 46 46 3

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A-SONGS-9416-1168, Rev. 01 Appendix A4 Page A4-19 of A4-34 ABB-CENO L-

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Appendix A4-- Tube Model and ANSYS Mode Shape Plots t

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g36 i

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i l

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A-SONGS 9416-1168, Rev,01 Appendix A4 Page A4-21 of A4-34 ABB CENO Appendix A4 Tube Model and ANSYS Mode Shape Plots -

1 JL 1s 7

4030 MkNT

2

> 1 d=59.602 ES S=0

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l l

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A-SONGS-9416-1168, Rev. 01 Appendix A4 Page A4-23 of A4-34

- ABB-CENO-

-- Appendix A4 Tube Model and ANSYS Mode Shape Plots 1 ANSYS S.3 -

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l l

l 46 46 Y

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l l

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-- Appendix A4 Page A4-26 of A4 ABB-CENO Appendix A4 Tube Model and ANSYS Mode Shape Plots 1 ANSYS 5.3 MAY 231997 L~ $ MENT P-1

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' A-SONGS-9416-1168, Rev. 01 .

Appendix A4 Page A4-33 of A4-34 ABB-CENO

- Appendix A4 T'ibe Model and ANSYS Mode Shape Plots 1 ANSYS 5.3 MAY 231997 14:30:38 bkPNhtdENT-STgP.1

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4

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o CSE-97-254

- A-SONGS-9416-1168, Rev. 01 4 Appendix A4 Page A4-34 of A4-34 T

ABB-CENO

. Appendix A4 Tube Model and ANSYS Mode Shape Plots l

1 1

i 1 ANSYS 5.3 MAY 231997

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4 CSE-97-254

A-SONGS 9416-1168, Rev. 01

~ Appendix AS Page AS-1 of A5-10 ABB-CENO -

t v

APPENDIX A5 ATHOS RESULTS

SUMMARY

FOR FIV INPUT CSE-97-254

A-SONGS 94161168, Rev. 01 Appendix A5 Page AS-2 of A5-10

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- A. SONGS 9416-1168, Rev. 01 Appendix A5 Page A5-4 of AS-10 ABB-CENO TABLE A51 IX Sector Resultant Gap Velocity (in/sec)

IZ -1 2 3 4 5 6 7 8 9 1 115.37 115.81 115.36 115.33 115.72 115.18 115.13 116.23 121.97 2 -110.50 110.95 110.44 110.41 110.88 110.28 110.27 111.24 117.22 3 6.94 6.93 7.05 7.10 7.14 7.12 7.01 8.68 9.51 4 4.13 4.55 5.12 5.84 -

6.61 7.35 7.84 7.13 11.%

5 3.01 4.27 6.05 7.78 9.00 10.03 10.97 11.19 14.42 6 4.24 5.63 6.69 7.20 7.30 7.29 6.24 4.74 4.37 7 6.36 -9.34 11.92 24.87 25.41 11.78 6.36 7.28 15.46 8 22.44 22.89 24.44 13.29 16.80 31.51 36.12 36.11 35.10 9 4.71 7.72 11.81 15.70 20.20 25.86 34.30 42.99 40.04 10 4.46 8.50 12.59 28.18 30.85 26.86 33.32 37.99 34.89 11 23.65 25.41 28.30 34.48 39.07 41.51 48.92 59.37 60.17 12 23.39 25.99 28.16 18.07 21.42 35.25 37.92 37.98 36.03 13 8.23 9.98 12.85 14.44 17.68 21.44 24.95 27.32 27.11 14 4.82 7.51 '10.11 32.69 - 33.87 17.75 20.47 21.92 20.78 15 28.67 30.14 32.15 33.87 35.79 38.05 40.80 46.00 47.27 16 29.68 31.56 33.53 35.52 38.16 39.95 41.66 40.47 55.52 17 12.79 14.40 16.33 18.16 20.83 24.28 25.59 32.98 -49.55 18 40.31 42.83 44.36 46.50 49.15 53.46 66.86 9.80 19 42.17 45.32 47.60 50.82 54.51 55.95 87.86 36.94 20 16.61 22.17 24.15 29.58 35.66 22.75 21 50.23 55.77 58.06 64.63 81.63 60.58 22 50.33 59.05 -63.37 - 67.60 71.06 53.11 23 23.48 44.04 46.81 45.41 33.81 24 55.85 53.52 86.08 79.60 100.48 25 77.78 78.56 -77.10 78.97 148.88 26 54.30 51.35 64.99 27 336.91 CSE-97-254

.~ _ . . __. -_ _ ._ - - . _ . - _ . . . _ . . _ _ . . _ .. _ _

A SONGS-9416-1168, Rev. 01 4

Appendix A5 Page AS-5 of A510 ABB-CENO TABLE AS-2 I IX Sector Secondary' Side Density (Ibm /ft')

IZ  ! 2 3- 4 5 6 7 8 9 48.865 48,865 48.865 1 48.865 48.865 48.865 48.865 48.865 48.865 4 2 48.865 48.865 48.865 48.865 48.865 48.865 48.865 48.865 48.865 3 46.956 46.956 46.956 46.956 46.956 46.956 46.956 46.956 46.956 4 46.956 46.956 46.956 46.956 46.956 46.956 46.956 46.956 46.956 5 46.956 46.956 46.956 46.956 46.956 46.956 46.956 46.956 46.956 6 42.176 37.070 34.771 43.285 36.918 46.956 46.956 46.956 46.956 7 19.217 19.979 19.903 19.965 19.858 19.413 18.638 21.694 33.1 j 8 15.537 15.608 15.385 15.412 15.415 15.274 15.069 16.258 20.357 9 13.157 12.952 12.632 12.592 12.645 12.543 12.418 12.96' 15.1 l 10 12.012 11.683 11.255 11.152 11.224 11.095 10.916 11.268 12.961 11 14.574 11.923 11.487 13.942 11.353 13.750 13.572 11.179 12.382 12 -10.538 10.208 9.820 9.696 9.691 9.535 9.326 9.442 10.689 13 9.286 8.996 8.649 8.537 8.528 8.381 8.185 8.283 9.531 14 8.657 8.332 7.958 7.833 7.833 7.682 7.477 7.570 8.773 15 10.034 8.510 8.141 9.214 7.980 9.045 8.885 7.704 8.595 16 8.274 7.953 7.606 7.477 7.446 7.303 7.094 7.080 8.016 17 7.806 7.503 7.169 7.040 7.009 6.857 6.644 6.679 7.526 ,

18 d.412 7.512 7.174 7.628 7.009 7.450 7.281 6.367 1

19 7.285 7.013 6.715 6.590 6.532 6.363 6.113 6.055 30 6.906 6.652 6.372 6.251 6.185 5.998 21 7.321 6.661 6.381 6.652 6.185 6.452 22 6.505 6.274 6.020 5.886 5.775 5.530 23 6.202 5.989 5.752 5.605 5.436 e

24 6.523 5.998 5.766 5.980 5.227 25 5.659 5.494 5.302 5.155 5.049 __

26 5.155 5.031 -4.928 27 5.191 CSE-97-254

A SONGS 9416-1168, Rev.01 Appendix A5 Page A5-6 of AS-10 ABB-CENO TABLE A5 3 SONGS 3 - CALCULATED VISCOSITIES - lY=14(LBM/FT-SEC) 12 IX=1 2 3 4 5 6 7 8 9 1 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 2 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 .I 3 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 4 6.346E-05 6.346F-05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E 05 6.346E-05 6.346E-05 5 6.346L 05 6.346E-05 6.346E-05 6.346E-05 6.346E-05 6.346E 05 6.346E-05 6.346E-05 6.346E-05 6 6.142E-05 6.047E-05 5.960E-05 5.960E-05 6.042E-05 6.129E-05 6.224E-05 6.346E-05 6.346E-05 7 5.001E-05 5.070E-05 5.063E-05 5.068E-05 5.060E-05 5.018E-05 4.944E-05 5.215E-05 5.891E-05 8 4.602E-05 4.61 IE-05 4.584E-05 4.586E-05 4.588E-35 4.569E-05 4.543E 05 4.687E-05 5.094E-05 .

? 4.280E-05 4.246E-05 4.201E-05 4.189E-05 4.201E-05 4.178E-05 4.167E-05 4.246E-05 4.545E-0_5_

i 10 4.092E-05 4.039E-05 3.968E-05 3.948E-05 3.958E-05 3.939E 05 3.909E-05 3.968E-05 4.246E-05 l 11 4.145E-05 4.081 E-05 4.009E-05 3.978E-05 3.978E-05 3.958E-05 3.919E-05 3.948E-05 4.156E-05 l 12 3.833E-05 3.769E-05 3.690E-05 3.664E-05 3.664E-05 3.630E-05 3.589E-05 3.614E-05 3.861E-05 13 3.581E-05 3.517E-05 3.433E-05 3.411 E-05 3.411E-05 3.374E-05 3.325E-05 3.346E-05 3.622E-05 14 3.441E-05 3.360E-05 3.269E-05 3.236E-05 3.236E-05 3.203E-05 3.146E-05 3.171E-05 3.463E-05 15 3.486E 05 3.403E-05 3.318E-05 3.283E-05 3.276E-05 3.243E-05 3.190E 05 3.203E-05 3.418E-05 16 3.346E-05 3.269E-05 3.177E-05 3.146E-05 3.139E-05 3.102E-05 3.043E-05 3.043E-05 3.283E-05 17 3.229E 05 3.152E-05 3.066E-05 3.031E-05 3.019E-05 2.979E-05 2.919E-05 2.919E-05 3.158E-05 18 3.236E-05 3.158E-05 3.066E-05 3.031E-05 3.019E-05 2.979E-05 2.919E-05 2.830E-05 3.054E-05 19 3.096E-05 3.019E-05 2.935E-05 2.903E-05 2.881E-05 2.835E-05 2.756E-05 2.732E-05 2.968E-05 20 2.991 E-05 2.919E-05 2.835E-05 2.800E-05 2.780E-05 2.722E-05 2.632E-05 2.649E-05 2.881E-05 21 2.996E-05 2.924E-05 2.840E-05 2.800E-05 2.780E-05 2.690E 05 2.559E-05 2.588E-05 2.820E-05 22 2.876E-05 2.805E-05 2.727E-05 2.685E-05 2.649E-05 2.572E-05 2.498E-05 2.551E-05 2.780E-05 73 2.785E-05 2.718E-05 2.640E-05 2.593E-05 2.538E-05 2.475E-05 2.463E-05 2.530E-05 2.756E-05

24 2.790E-05 2.722E-05 2.645E-05 2.576E-05 2.467E-05 2.425E-05 2.448E-05 2.514E-05 2.741E-05 25 2.610E-05 2.559E-05 2.490E-05. 2.440E-05 2.403E-05 2.403E-05 2.437E-05 2.502E-05 2.732E-05 26 2.440E-05 2.396E-05 2.360E-05 2.353E-05 2.360E-05 2.371E-05 2.403E-05 2.471h-05 2.708E-05 27 2.455E-05 2.407E-05 2.349E-05 2.346E-05 2.378E-05 2.385E-05 2.425E-05 2.490E-05 2.732E-05 CSE-97-254

A-SONGS 9416-1168. Rev. 01 App ndix AS Page A5-7 of A5-10 ABB-CENO TABLE AS-4.

50NGS UNIT 3 STEAM GENERATORS WITH EGGC.

EROSION - POST CHEM CLEANING ATHOS3 DATA AX1AL VELOCITIES (in/sec) l IZ/IX 1 2 3 4 5 6 7 8 9 1 25.54 25.56 25.44 25.42 25.58 25.4 25.2 24.11 20.56 2 59.06 58.94 58.94 58.9 58.98 58.86 58.5 56.38 48.27 3 40.55 40.83 40.55 40.51 40.87 40.35 39.88 38.14 33.46 4 27.25 27.84 -27.67 27.68 27.94 27.33 27.1 -25.78 -22.6 5 17.38 18.63 18.9 18.91 18.59 17.76 17.63 16.41 14.78 6 10.73 18.21 23.5 23.74 19.35 14.84 10.7 2.83 5.5 7 63.94 61.3 61.81 61.73 62.64 65 72.24 61.34 25.69 8 71.02 69.92 70.71 70.43 71.3 72.44 76.14 68.62 41.06 9 94.29 95.24 96.14 96.06 96.69 96.5 97.2 90.59 71.22 10 95 97.44 99.33 99.57 100.16 99.76 100.63 95.71 80.79 11 102.09 105.31 107.05 107.68 108.74 107.95 108.27 103.35 91.1 12 98.15 101.73 103.82 104.45 105.43 104.96 105.79 102.8 93.5 13 117.76 121.73 124.17 125.04 126.14 125.71 126.65 124.37 114.76 14 115.98 121.02 124.05 125.28 126.73 126.61 128.43 127.28 118.62 15 127.64 132.68 135.35 136.97 139.37 139.61 142.28 141.34 131.26 16 115.79 120.51 123.07 124.65 127.2 128.31 133.78 140.75 110.59 17 117.83 122.87 125.75 127.72 130.83 133.15 143.78 166.02 103.35 18 150.59 156.26 150.08 163.23 167.6 170 175.12 189.72 120.24

-19 137.87 143.03 146.57 150.12 156.73 168.07 180.71 184.09 154.53 20 141.I 146.61 150.55 154.92 164.45 197.72 199.05 204.76 212.99 21 177.99 184.76 190.2 195.83 199.92 226.69 219.8 256.26 267.05 22 161.65 167.87 174.45 187.16 201.77 217.24 253.54 304.21 311.34 23 162.72 168.62 176.81 207.56 229.29 221.93 295.75 341.14 344.53 24 200.79 203.35 200.47 224.53 232.24 257.87 327.05 369.33 370.35 25 203.42 204.45 200.55 209.13 246.97 294.41 357.48 399.61 398.82 26 238.11 231.69 199.17 215.31 280 334.92 403.94 453.54 450.79 27 193.5 191.61 162.72 192.28 259.61 308.31 370.75: 414.96 410.63 CSE-97-254 u

A-SONCS-9416-1168, Rev. 01

s. Appendix A5 Page A5-8 of A5-10 ABB-CENO .

TABLE A5-5 TUHE ROW 83, LINES:17 AND 159: IZ=23 (318 - 328.25 INCIIES AHOVE Tile TUHESIIEET)

DIS" FROM U-BEND Tprim AXIAL VOID Tprim Primary Primary Secondary Secondary GAP. VEL TUBE LANE POROSITY VEL. FRACT. Density Density Density Density

(!bfsec^2/ (Ibfsec^2/

(Inches) (Deg.K) (m/sec) (Deg. F) (ibm /ft^3) in^4) (ltun/ft^3) in^4) (in/sec)

O to 22.5 Deg, 0.8145 573 2.414' O.9298 571.73 45.233 6.78E-05 5.193 7.78E-06 198.11 45 Deg, 0.9198 572.7 4.180 0.9360 571.19 45.275 6.79E-05 4.915 7.37E-06 387.39 67.5 Deg, 0.8206 572.7 4.417 ~ 0.9463 571.19 45.275 6.79E-05 '4.452 6.67E-06 365.21 67.5 Deg to 90, 0.8843 572.4 3.235 0.9492 570.65 45.316 6.79E-05 4.322 6.48E-06 288.24

-21.5 0.8843 572.4 3.235 0.9492 570.65 45.316 6.79E-05 4.322 6.48E-06 288.25

-10.5 0.8393 571.8 2.561 0.9479 569.57 45.399 6.80E-05 4.380 6.57E-M 216.57 -

0.0 0.9008 571.5 2.610 0.9349 569.03 45.441 6.81E-05 4.964 7.44E-06 236?S 10.5 0.9008 570.8 2.224 0.9053 567.77 45.538 6.83E-05 6.294 9.43E-06 201.85 21.5 0.8393 570.8 1.965 0.9010 567.77 45.538 6.83E-05 6.487 9.72E-06 166.17 -

33.5 0.8843 571.5 2.464 0.9030 569.03 45.441 6.81E-05 6.397 9.59E-06 219.54 9_0 Deg to 67.5, 0.8843 571.5 2.464 0.903 56';.03 45.441 6.81 E-05 6.397- 9.59E-06 219.54 45 Deg, 0.8206 571.5 3.360- 0.8994 569.03 45.441 6.81 E-05 6.559 9.83E-06 277.81 22.5 Deg, 0.9198 572.0' 3.266 0.8911 569.93 45.372 6.80E-05 6.932 1.04E-05 302A8 22.5 to 0 Deg, 0.8145 571.8 1.900 0.8863 567.57 45.399 6.80E-05 7.147 1.07E-05 155.93 CSE-97-254

A-SONGS-9416-Il68. Rev. 01.

Appendix A5 Page A5-9 of A5-10 ABB-CENO TABLE A5-6 TUBE ROW 147. LINES:87 AND 89 IX = 1 lY = 14 (IlOT/ COLD LEG SIDE)

DISTIMOM U-BEND Tprim AXIAL VOID Tprim Primary Primary Secondary Secondary GAP. VEL TUBE LANE POROSITY VEL FRACT. Density Densi:y Density Density (Inches) (Deg.K) (m/sec) (Deg. F) (Ibm /ft^3) (Ibm /ft^3) in^4) (in/sec)

O to 22.5 Deg. 0.7353 569.8 2.209 0.9484 565.97 45.676 6.85E-05 4.358 6.53E-06 163.67 45 Deg. 0.9266 569.7 2.588 0.9551 565.79 45.690 6.85E-05 4.057 6.08E-06 241.62 67.5 Deg. 0.9336 569.7 3.046 0.9551 565.79 45.699 6.85E-05 4.057 6.08E-06 286.53 67.5-90.0 Deg. 0.8881 569.6 2.232 0.9584 565.61 45.704 6.85E-05 3.909 5.86E4)6 199.73 90 Deg to 59.4 0.8604 569.5 134I 0.9602 565.43 45.7I8 6.85E-05 3.828 5.74E-06 I16.25

-53.85 0.8621 5693 1.211 0.9610 565.07 45.745 6.86E-05 3.792 5.68E-06 105.19

-47.60 0.8608 569.2 1.153 0.9605 564.89 45.759 6.86E-05 3.814 5.72E-06 100.00

-41.36 0.8592 569.1 1.099 0.9579 564.71 45.773 6.86E-05 3.931 5.89E-06 95.15

-35.12 0.8577 569.0 1.002 0.9505 564.53 45.787 6.86E-05 4.264 639E-06 86.59

-28.99 0.8579 568.9 0.874 0.9376 56435 45.801 6.87E-05 4.843 7.26E-06 75.55

-22.75 0.8575 568.9 0.714 0.9188 56435 45.801 6.87E-05 5.687 8.52E4M 61.70

-15.94 0.8581 568.8 0.531 0.8961 564.17 45.815 6.87E-05 6.707 1.018-05 45.92

-8.03 0.8577 568.8 0.309 0.8768 564.17 45.815 6.87E-05 7.574 1.14E-05 26.67 0.00 0.8609 568.4 0.475 0.8448 563.45 45.870 6.88E-05 9.01I 135E-05 41.17 8.03 0.8601 568.4 0.488 0.8420 563.45 45.870 6.88E-05 9.137 1.37E-05 4233 15.94 0.8577 5683 0.440 0.8278 563.27 45.884 6.88E-05 9.775 1.47E-05 38.01 22.75 0.85RI 568.2 0.383 0.8318 563.09 45.898 6.88E-05 9.595 1.44E-05 33.12 28.99 0.8575 568.2 0.393 0.8400 563.09 45.898 6.88E-05 9.227 138E-05 33.94 35.12 0.8579 568.1 0.432 i 0.8499 562.91 45.912 6.88E-05 8.782 132E-05 37.36 41.36 0.8577 568.0 0.485 0.86N 562.73 45.925 6.83E-05 8310 1.25E-05 41.93 47.60 0.8592 567.9 0.545 0.8704 562.55 45.939 6.89E-05 7.861 1.18E.05 47.19 53.85 0.8608 567.8 0.607 0.8787 56237 45.953 6.89E-05 7.489 1.12E-05 52.64 ,

59.4 0.8621 567.7 0.680 0.8847 562.19 45.967 6.89E-05 7.219 1.08E-05 59.07 59.4* to 90 Deg. 0.8604 567.5 0.801 0.8878 561.83 45.995 6.89E-05 7.080 1.06E-05 69.40 90 to 67.5 Deg. 0.8881 567.4 1374 0.8890 561.65 46.009 6.90E-05 7.026 1.05E-05 122.95 67.5 Deg. 0.9336 5673 1.950 0.8877 561.47 46.022 6.90E-05 7.084 1.06E-05 183.45 45 Deg. 0.9266 567.3 1.659 0.8877 561.47 46.022 6.90E-05 7.084 1.06E-05 154.88 22.5 to O Deg. 0.7353 567.1 1.452 0.8807 561.I1 46.050 6.90E-05 7399 1.11E-05 107.57 CSE-97-254

A-SONGS 9416-1168. Rev.01 Appendix A5 Page A5-10 of A5-10 ABB-CENO '

TABLE A5-7 (Input for Revision I from Reference 11)

TUBE ROW II9, LINES:32 AND 138 IX = 5,IY = I4 (HOT! COLD I,EG SIDE)  ;

DIST fROM U.itEND .Tprini AXIAL VOID Tge m Primary hary Secondary Secondary GAP.VIL ,

1 UllE l.ANE POROSITY vfl IR ACT. IknsWy Density Iknuty IPnsmy (MsWN . (Msdy (Inches) (Ikt. K) (m/sec) (Ikg. I) (Hun /fta3) in*4) (!hm.Tia3) in^4) (in/sec)

O to 22.5 Ikg. 0.8509 571.8 0.0638 0.9366 569.57 45.399 6.80E05 4.883 7.33E06 5.47 45tkg. 0.9724 571.6 2.464 0.9406 569.21 45.427 6.81E-05 4.708 7.06E06 241.40 67.5 Ikg. 0.9215 571.5 3.433 0.9500 569.03 45.441 6.8 t E.05 4.286 6.42E-06 318.71  ;

90.0 lkg. 0.8627 571.3 3.475 0.9531 568.67 45.468 6.82E05 4.147 6.22606 302.04 90.0 lks to 43 0.8627 571.3 3.448 7 564.67 45.458 6.82E05 4.147 6.22606 303.19 40.5 0.7876 571.1 2.868 0.9557 568.3I 45.4 % 6.82E05 4.030 6 04E06 227.60 34.50 0.9034 570.9 2.531 0.9553 567.95 45.524 6.82E05 4.048 107E06 230.38 28.00 0.8223 570.4 2.194 0.9551 567.05 45.593 6.83E05 4.057 6.08E-06 181.78 23.00 0.9(W6 570.2 2.119 0.9508 566.69 45.621 6.84L US 4.250 0 37E06 200.62 17.5' 0.8207 569.7 1.914 0.9465 565.79 45.690 6.85E05 4.443 6.66606 158.27 8.50 0.8729 569.3 8.785 0.9368 565.07 45.745 6.86E.05 4.879 7.31E-06 156.99 0 0.9021 568.9 1.655 0.9162 564.35 45.801 6.87E05 5.804 4.70E06 150.43 8.50 0.9021 568.6 f.351 0.8838 563.81 45.842 6.87E-05 7.259 1.09E.05 122 80 17.50 0 8729 568.1 1.207 0.8729 562.91 45.912 6.88E05 7.749 1.16E.05 106.16 23 00 0.8207 567.5 1.224 0.8720 561 83 45.995 6.89E05 7.789 1.17E05 101.21 i 38.00 0.9096 569.1 1.403 0.88'9 564.71 45.773 6.86605 7.255 I.09E-05 128.58 34m 0.82I3 568.0 1.417 0.8867 562.73 45.925 6.88E 05 7.129 1.07605 117.40 40.50 0.903' 569.4 1.678 0.8937 565.25 45.732 6.85E.05 6.815 1.02E-05 152.74 43.00 0.7F74 ' 567.8 1.912 0.8911 56137 45.953 6.89E05 6.932 1.04 E05 151.73 43 to 90 lkg. 0.862. 568.9 2.394 0.8927 564.35 45.801 6.87E05 6.869 1.03E.05 108.10 r 67.5 Deg, 0.8627 568.9 2.384 0.8927 564.35 45.801 6.87:W5 6.860 1.03E05 207.22 45 Deg, 0.9215 569.9 2.397 0.8918 566.15 45.662 6.84E.05 6.900 1.03E.05 222.58 22.5 thg. 0.9724 570.6 1.773 0.8850 567.41 45.565 6.83E-05 7.206 i.08E.05 173.73 22.S ikg ro o 0.8509 570.4 0.039 0.8832 .567.05 45.593 6.83E05 7.286 1.09E-05 3.33 I

CSE-97-254  !

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A SONGS-34181168. Rev. 01 ABB-CENO Appendix A6 Pago A6-I of A6-Il APPENDIX A6 CALCULATIONS FOR REVISION 1 l

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CSE-97-254

A SONGS 94181168, Rev. 01 ABB-CENO . Appendix A6 Page A6 2 of A6 II J

Tube Virtual Mnec Calenistion

[ Tube Rows 110 - EC 9 & 7 inactive:

P t:=0.305 Tube Density (I-600)

D := 0.75 in Tube Dia.

pp := 42.642 Avg. Pri. Fluid Density

=0 m TuWehess

~

ft P := 1.0 in Triangular Phch p , := 7.46.Jbf Secondary Fluid Density ft' (vert. leg region, row 126, between ECs 9 A 8)

L 4

2 A t:= -

A n:=E D Ag: E-(D- 2 t)*

i 4 [D*- (D - 2 t)*) 4 4 A t=0.1059 in 2 Ao = 0.442*in* A g = 0.336*in*

Hydrodynamic Mass Coefficient (F):

Fent := 3.1 (factor for vertical leg region Ref. 3, Fig.14)

Virtual Mass Obf/in): Wy W v_ent : A t'P t + P p A + Fent'P s'Ao Ibr W (For Veritical) v_ent a0.0465 7 Virtual Density Obflin3 ): py py,ent := (for ANSYS input) t p y_ent =0.4392 %m CSE-97-254

A-SONGS-94181168, R:v. 01 ABB-CENO . ' . Appendix A6 Page AB 3 of A6 il Critical Flow Velocity for Tube Row 110 - Vertical Lee -hot side EC's 7 & 9 inactive Mode 2 Input Parametere I

D := 0.75 in (Tube Dia.)

K := 3.2 (Instability Constant, per Ref. 20, for triangular pitch CE bundles) f:= 17.91 Hz (Tube Natural Frequency, ANSYS result for row 110,1st out-of-pbne mode, max. disp. between ECs 6 & 8) m o := 0.0465- (Tube virtual mass per unit length) p := 7.4 (Avg. secondary fluid density, row 110, between ECs 7 & 9, hot side) ft

( := 0.0237 (Damping per Ref.10) 6 n:= 2 x-( (Log decrement) m6 o o Critical Flow Velocity :

V a := K f D-3 p D, Va = 72.58 A V eg:=48.2 A see see SR := SR = 0.664 <1.0 a ***e**********

CSE-97-254

A SONGS-9418-1168, Rev. 01 ABB-CENO ... Appondix A6 Page A6-+ of A6 II s

Critical Flow Veloci*r for Tube Row 110 - Elbow Recion hot side ,

EC's 8 & 9 inactive I

Input Parameters:

1

. D := 0.75 in (Tube Dia.)

K := 7.1 (Instability Constant, per Ref. 20, for CE bundles, rotated square pitch in horiz. span re l f := 59.6 Hz (Tube Natural Frequency, ANSYS result for row 110 out-of plane,

max. disp. at 90 deg. elbow region, Mode #7) m o

= 0.04565 (Tube virtual mass per unit length) m p :=4.147 (Secondary fluid density, row 110, Elbow region, hot side) ft Damping as a function of frequency (per Ref.10):

( := 0.0133 6n:=2 x-( (Log decrement) 4 mfo O Critical Flow Velocity - K'I'D' V cr ,

s p D*

V g =533.22 A V 4

See d:=282.6seeA i

SR:= SR = 0.53 < 1.0 Vg ***********

r CSE-97-254

A SONGS-94181968, Rev. 01 ABB-CENO Appendix A6 Page A6-S of A6-//

Effective Velocity Calculation for Circumferentini Sector 5 Tube Row 110 O/_grtical Spans from EC#4 to tube tangent point) with ecgerate #7 and #9 inactive xc: Spanwise coordinates (from ANSYS model) above tubesheet disp: Normalized Displacements perpendicular to span (z-dir) from ANSYS autput for Mode No. 2, frequency == 17.91 Hz.

Velo: Fluid Cross Flow Velocity (ATHOS results), xv: Velocity elevadons above tubesheet Node No. aP n := 0 61 ,' . n, := n + 1 g 136.25 136.25 1 .0 13935

~

13935 2 .01431 143.25 143.25 3 .02769 7.6 110.87 -1.09 146J5 14635 4 .03921

~

150.25 150.25 5 .04798 15335 augment (xc,n) = ~ 8 ~*

153.75 6 .05316 157.25 27.25 -6.78 -2.24 l

157.25 7 .05398 160J5 .0497 2735 -436 -4.97 l 160.75 8 164.25 .0E67 6 6 164.25 9 16735 .02329 44.85 -331 -837 167.75 10 171.25 .0 62.25 -331 -837 171.25 11 174.8;. .03103 6235 73 -11.74 174.85 12 178.45 178.45 13 .06569 182.05 8035 23.87 8.72 182 05 14 .09981 185.65 98.25 23.87 8.72 185.65 15 . 12929 189.25 9835 5.63 15.83 189.25 16 .15017 192.85 117.25 5.63 15.83 192,85 17 .15866 196.45 11735 432 19.74 196.45 18 .15118 200.05 136.25 432 1934 200.05 19 .12433 202.65 .07495 13635 -2235 21.27 203.65 20 207.25 .0

.53J5 -2235 21.27 207.25 21 211.05 153.85 2637 28.83 211.05 22 .10811 214.85 171.25 2637 28.83 214.85 23 .23782 218.65 17135 8.11 19.82 218.65 24 37918 222.45 189.25 8.11 19.82 222.45 25 .52263 226.25 18935 5.42 16.83 226.25 26 .65925 230.05 207.25 5.42 16.83 230.05 27 .78097 233.85 20735 -30.62 14.47 233.85 28 .88084 xy := velo :=

237.65 226.25 -30.62 14.47 237.65 29 .95319 241.45 22635 -30.62 18.52 241.45 30 .99378 xca 245.25 245.25 -30.62 18.52 245.25 31 disp : 1.0 24833 24535 3438 15.7 24833 32 .97913 251.4 251.4 33 .93532 254.48 255.6 1437 14.69 254.48 34 .86956

') S7.5 % oc r cc ac .7 R'44 5 CSE-97-254

~ .-- . . - - . _ . - - - _ . ~ . , -- - . . - ~ - - - . - . . . . - - . . . - -- -

1 A. SONGS 94181168, Rev. 01 j- ., .,

ABB-CENO Appendix A6 Page A6-6 of A6-l/

260.63 .67925 265.85 -4532: 19.02 260.63- 36

'263.7 .55976-276.0 -4532 19.02 l 263.7 37 266.78 276.1 50.86 - 19.61 l 266.78 - 38 .42827 269.85 286.25 50.86. 19.61 269.85 39 .28845 272.93 28635 19.83 29.64 272.93 40 .1443 296.5 19.83 29.64

. 276 276' 41 .0 i

279.08 296.6 -52.13 t' .81 l

. 279.08 42 .14031 '

282.15 306.75 -52.13 62.81-282.15 43 .27342 285.23 306.85 70.61 -8.02

285.23 44 - 39637 317.0 70.61 8.02 l 288.3 2883 45 .50641 29138 317.1 30.13 1532

} 29138 46 .60107 327.25 30.13 1532

} 294.45 294.45 47 .67822

. 297.53 32735 12.08 99.75 297.53 48 .73619 300.6 3373 _12.08 99.75 j 300.6 49 .77375 337.6 14.81 148,14 i 303.68 303.68' 50 . 79023 349.56 14.81 148,14 306.75 306.75 51 .7855

.66 0.0 0.0 309.91 309.91 52 .759 l_

61.63 0.0 0.0 313.07 313.07 53 .71165 l

361.73 0.0 0.0

l . 316.22 316.22 54 . 64511 370.59 0.0 0.0 31938 31938 55 .56164 ,

322.$4 322.54 56 .46396

{

325.7 325.7 57 - 35527 j

328.86 328.86 58 .23913 1

332.01 332.01 59 .11936 335.17 335.17 60 .0

,338.24 - , 338.24 61, .11245 ,

velo := (velo") +-(velo *)

CSE-97-254

A-SONGS 94181168, Rev. 01 ABB-CENO Appendix A6 Page A6 7 of A6-// ~

Normalized displacement ($) as a function of spanwise x-coordinate (cubic spline interpolation function)is shown below:

vs := cspline(xc, disp)

$(x) ::interp(vs.xc. disp,x)

Velocity (v) as a function of spanwise x-coordinate:

1

_v(x) := linterp(xv, velo,x)

. Integrallimits:

a := xe b := xe a = 136.25 b = 338.24 n

Assuming no spanwise variation in tube virtual mass or secondary fluid densi:y, the effective velocity equation reduces to the following:

"b v(x)2,44x)2dx Vd* "b V d = 48.2 in/sec-

$(x)2dx e a.

CSE-97-254

A SONGS-94181168, Rw. 01 ABB-CENO Appendix A6 Page A6-8 of A6-//

x := xe,.xe,+ 1 xc ,3 1 := 0,1 last(xc)

Cross Flow Gao Velocity Profile (in/sec) Mode 2 (17.91 Hz) Mode Shane 340 , 340..

(

320 320a -

300 300d' 280 I . ,,

l .

ggJL

~

240 240k

• ~

4 M xec 220 . ,, i 220 --

I gg . .

180 [ <-

% I-I 160 1602 i

(

140

- 140-0 50 100 150 a 4'.3 0 'l v( x) .O H z).0 CSE-97-254

A SONGS-94181168, Rev. 01 ABB-CENO Appendix A6 Page A6 9 of A6-//

, , Effective Velocitv Calculation for Tube Row 110 Elbow and Horizontal Snan Cross Flow Ton 2 Enocrates Inactive (8 and 9)

xc

Spanwise coordinates (from ANSYS model) disp: Normalized Displacements perpendicular to span (z-dir) from ANSYS output for Mode No.7, frequency = 59.6 Hz xv: Flow developed length horizontal coordinates trom bundle centerline to diagonal strip velo: Cross flow gap velocities,in/sec (ATHOS results) c :=x 20 dl := c 22.5 d=3.9U i 1: 0 18 n' := 60 + 1 n := reverse (n) 360 Velocity Normal Node No. Velo. Profile Coor. Tube Centerline 0 . 0

.0 78 0 '150.43' 4 .25738

4 77 8.5 g .618M 150.43 8 76 8.5 + .1 156.99 12 ,g9797 12 75 17.5 156.99 16 1.0 6 N 17.5 + .1 158.27

, 20 .8776 augment (xc.n) " 20 73 24 93

' 158'27

.69007 1

28 + .1 00.62

.49279 28 71 28 200.62 32 .29991 xes 28 + .1 181.78 35 disp ;: .12907 l 35 69 34.5 181.78 3g .0

' 68 W + ,1 230.38 41 .08326 l 41 67 40.5 230.38 44 .08798 1 4 66 w: 4 + .1 vel : .6 47 .04826 47 65 43 7.6 50.927 .0 50.927 64 43 + .1 303.19 54.854 .02619

. 63 47 303.19 58.781 .03026 62.708 4 + .1 302 M

.01905

62. M 61 4+d 302 N 65.788 '

.0 '

4

, 65.788 60, 47+ dl+.1 318.71

- 47 + 2 dl 318,71 node 60 is at diagonal strip (xc = 62.708 + 3.08= 65.788) 47 + 2 dl + .1 241.4 disp := reverse (disp) 47t 3 d! 241.4 47 + 3 d! + .1 100 47 + 4 dl 100 use 100 in/sec conser. for 100 65.788 last 31ocadons CSE-97 254

- - . .. . . - - . _. . .--- - ... . ~ - , _ . . , - . - - . _ -

A SONGS-94181168,' Rev. 01 ABB-CENO Appendix A6 Page AS-10of A6-//:

i l

Normalized displacement (4) as a function of spanwise x-coordinate (cubic spline interpolation

' function)is shown belov>:

I vs := cspline(xc. disp)

$(x) := interp(vs.xc. disp,x) 1 Velocity (v) as a function of spanwise x-coordinate:

v(x) := linterp(xv, velo,x) t Integrallimits:

1 a := xc b := xe a=0 b = 65.788 o

4 i Assuming no spanwise variation in tube virtual mass or secondary fluid density, the effective velocity equation reduces to the following:

' *b v(x)2,4[x)2dx

.a f

Vd 'b y d = 282.6 - in/sec j_ $(x),dx i 6 .a i

a k~

4 i

}

i

CSE-97-25 f

A-SONGS 9418 9168, Rev. 01 -

ABB-CENO Appendix A6 Page A6il of A61l l

4 Cross Flow Gan VejorJty Profile (in/sec) Mnde 7 (59.6 Hz) Mnde Shanc

• 10 70 -

l i [

65 65 -

i 60 t 60 -- i i

$5 g $$ = -

$0

$0 --

t 45 45--

/

b 40 . 40-- l R

35 e

, 35 --

i 4-30 .

30 N

25 25 --

/

i

~

l 20 go -

13 15 -

10 10-

. $=

I t

l l

0 100 200 3CJ 400 1 0 l 41).0 1

CSE 97 254 1

- ~ . . , _ _ _ _ . - . . - . . . . , . . . , _ _ . . . . _ _ _ , . . ~ , , , . _ , . . . . . . . . - , _ , . . _ , _ , _ - . , . . , , _ . , , _ , - . , . , . _ _ , , _ , , _ _ . . . , , , . _ _ , , , . _ , , , - , , _ , , , _ _ - _ . .

A SONGS 94161168 REV.01 Attachment Al Page Al 1 of Al 8 i

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ATTACHMENT Al I

l 4

1. Design Analysis In Process Approvals (1 page).

2. Verification Plan (I page).

]

4

3. Design Analysis Verification Checklist (4 pages).  ;

4. Reviewer's Comment Form (1 page). 1 l

(Copies in Q.A. Records Only) ii 1

4 4

4 1

k. :

CSE-97 254

,#.,, - .--,., -- - . , - - , --.,---_y,7 -- 4 , -.y.,. .-mr--p ,

A SONGS 94161168 REV.O',

Anachment A2 Page A2-1 of A2 ,

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Attachmen* u Mathcad Files & Excel Spreadsheets ,

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Hard copies of files were included in the appendices of this report.

1 1

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CSE-97 254 i

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- A SONGS 9416 ll68 REY.01 Attachment A3 Page A31 of A3 3 i

l Attachment A3 ANSYS Input and Output Files (Diskette in Q. A. Records Only)  ;

input and output files used in this calculation are listed on the following page. They are provided on the enclosed diskettes The files are in compressed form and are expanded into a directory by typing the executable file name. The files are in ASCII format and can be read with most word processor or text editor software, 4

CSE-97-254

_ . . _ - . - . . ._ _ _ _ _ . . . _ _ _ _~

e A SONCS 9416-ll68 REV.01 Attachmer . A3 Page A3-3 of A3 3 j Attachment A3 ANSYS Input and Output Files ANSYS Files for Cases with 2 Upper Eggerates Missing (Compressed File 'fivansys.exe")

fivinodel. inn May 22 Model Input renfiv. inn hhv 24 Generic Input rl08.out hby 24 Input / Output rl10.out hhv 23 Input / Output rlli.out hby 23 Input / Output rl20.out May 23 Input / Output r121.out May 23 Input / Output fl26.out hby 23 Input / Output rl27.out hby 23 Input / Output r138.out hby 23 Input / Output r139.out hhv 23 Input / Output f l44.out hby 23 Input / Output tl45.out hby 23 Input / Output fl47.out hby 23 Input / Output r70.out hby 23 input / Output r82.out hby 24 Input / Output r83.out hby 23 Input / Output r84.out hby 23 Input / Output r93.out hhv 23 Input / Output r94.out hby 23 Input / Output ANSYS Files for Other Vertical Cases (Compressed File "fivans2.exe")

fiv147_4.inp hby 22 Generic Input mod 147_4. inn hby 22 Modelinput fivfmod.iro hhv 20 Generic Input genfivf. inn hby 20 Model input fl10_9.out hby 30 Input / Output rl20_78.out hhv 23 Input / Output rl47_78.out hby 23 Input / Output rl47_89.out hby 23 Input / Output rl47_s3s.out hby 25 Input / Output rl47s.out hby 22 input / Output rl47s_4.out hby 22 Input / Output r22 full.out May 23 Input / Output r46 full.out hby 23 Input / Output r49 full.out hby 23 Input / Output r83_R.out hby 30 Input / Output r83s.out hby 22 Input / Output rl 10_79.out July 21 Input / Output l

CSE-97-254

e r A SONGS 94161168 REV.01 l

Attachment A3 Page A3 3 of A3 3 i 9

Attachment A3 ANSYS Input and Output Files (Cont'd)

ANSYS Files for Horiz. Span Cases (Compressed File *fivans3.exe') l fivmodel.ino May 23 Generic Input May Modellnput '

nenfiv.ino 23 tl47 exit.out May 24 Input / Output r83 exit.out May 24 Input / Output i rl10 exit.out July 21 input / Output l i

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5-

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4 CSE-97-254 4

- , , . - , - - ,,.~.,.,,..,-._s,~w,-, ,._,,,,_,-_.,-.,m,,, _, , .- ,,,m-...y,e. ..,n.-,,-.,.p.,. . . ,~..m..,,_r, . - . , _ , . . , ..mp,,,,y.,m.--, -,.m.,

1

SUMMARY

OF CONTENTS Calculation 2iPages Appendices .66 Pages  !

Attachments _ID Pages  !

Diskette Attached RNo __ __Yes l l

ATTACilh1ENT B TO A-SONGS-9416-1168, REV. 01 Evaluation of h!aximum Tube Stresses During a LOCA for l Southern California Edison SONGS Unit 3 Steam Generators with Degraded Eggerates CSE-97-211 Quhlity Class: X QC-1 (Safety Related)

PURPOSE: To present the evaluation of the SONGS SG degraded tubes for LOCA and SSE loading.

This Design Analysis is complete and verified. Management authorizes the use ofits results.

PREPARED BY: RE. Johnson ~ - - - DATE: 8/97/f7 hENTOR: PL Anderson DATE: 1 9,7 VERIFICATION STATUS: COMPLETE The Safety Related design information contained in this document has been verified to be correct by means of Design Review using the Checklist in QP 3,4 of QPM 101, Name LD. Kev Signature V

N #V" Date /

/

Independent Reviewer APPROVED BY: .IL}LSitka DATE: 8897 ABB CONIBUSTION ENGINEERING CHATTANOOGA, TENNESSEE

( This document is the property of ABB/ Combustion Engineering, Chattanoogs, Tennessee, and is to be used only for the purposes of the agreement with ABB/CE pursuant to which it is h mished.

A-SONGS 9416-1168, Rev. 01 Page B2 ofB24 j RECORD OF REVI" IONS PARAGRAPH (s) PREPARED INDEPENDENT APPROVED NUMBER D TE INVOLVED - DY REVIEWER BY 0 6/03/97 OriginalIssue J. Halliday R.E. Johnson D.P. Siska 01 8/27/97 1.0, 2.0, 4.0, 5.0, R.E. Johnson J.D. Key D.P. Siska 7.5,8.0, Appendices B2, B3, and B4

.a CSE-97-211

A SONGS-9416-ll68, Rev 01 Page B3 cfB24 TABLE OF CONTENTS P.ags I.0 OBJECTIVE OF THE DESIGN ANALYSIS......................................... 4 2.0 SIGNIFIC ANT RES ULTS . . . . . . . . . . . . . ... .. . . . . .. . . .. . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 4 3.0 ASSESSMENT OF SIGNIFICANT DESIGN CHANGES..................... 4 4.0 ANALYTICAL TECHNIQUES ....................................... ............. ......... 5 5.0 SELECTION OF DESIGN INPUTS ...................................................... 5 6.0 AS S UMPTI ON S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 7.0 DETAILED ANALYS I S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 6 7.1 Tube Lo ad i ng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 7.2 AN S Y S Tube Mod el s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

7. 3 S S E Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 7.4 LOC A Analysi s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

7. 5 Combined St resses . . . . . . . . . . . . . .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 7.6 LOCA Impact Loading Analysis....................................................... 22 8.0 RESULTS/CONCLU SIONS . . . . .. . .. .. . . .. . ...... . . .. .. . ..... . ... . .. . . . .. ... . . . .. ... . . .... . .. 23 9.0 RE FE RENC E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 Appendix B 1 Tube Loading. .. ..... .. . .. ..... ... .. .. . . . . . .. . .. .. .. .. . ... .. . .. .. . . . . . .. . ... .. .. ... . . . ...B l 1 Appendix B2 ANSYS Tube Models..... ....... ................................... .. .... .........B2 1 Appendix B3 ANSYS Time History Stress Plots............................................B3-1 Appendix B4 Sample Mode Shapes and Frequencies.......................................B4-1 Appendix B5 ANSYS Model and Stress Plots for LOCA Impact Loading.......BS-1 Attachment B1 Design Analysis In-Progress Approvah, Verification Plan, Design Analysis Verification Checklist, and Reviewer's Comment Form (included in Q.A. record copy only)

Attachment B2 ANSYS Computer Files (diskette in Q.A. records)

CSE-97-211

A SONGS 94161168, Rev. 01 Page B4 of B24 1.0 OBJECTIVE OFTHE DESIGN ANALYSIS This report presents the analyses of a series of single tube models of the SONGS SG outermost tubes with the top two eggerates ineffective, with the 2nd and 3rd eggerates from the top incFective, and with only the top eggerate ineffective using LOCA and SSE Seismic loadings. l These results are then combined with the results for other pertinent loadings to evaluate the tube's acceptability for AShE Code (Ref.1) faulted allowables.

2.0 SIGNIFICANT RESULTS Under the assumptions that eggerate number 10 is an effective support for the tubes in Family A and no tubes are plugged, the maximum stress intensities for 64% degraded tubes in each family with two adjacent upper eggerates ineffective as supports is listed in the table below. All tubes meet the AShE Code allowable as shown in this table.

E s 7Tube~ .

Vertical eMissing J Critical- fStress.- AShE Code; j~amilyl [ Rows) JEggeratest l Supports- Ekgeratek Ro'w Intensity; LAllowable*

^

= (ksi) '(ksi)

A 121 147 1-10 7 8&9 146 69.68 80.6 B 116-120 1-9 5 8&9 120 77.91 80.6 C 85-115 1-9 5 8&9 99 71.39 80.6 D 84 18 5 7&8 84 59.51 80.6 5 52-83 . 18 3 7&8 83 56.39 80.6 F 50-51 1-7 3 6&7 50 42.18 80.6 G 24-49 l-7 1 6&7 49 41.87 80.6

• Allowable = 1.44(.75.) per Reference 2.

If eggerate number 10 is assumed to be ineffective as a support for the tubes in Family A, tubes in rows 129 through 147 cannot meet the AShE Code allowable with 64% wall degradation and the upper two eggerates assumed to be ineffective. The maximum wall degradation for the tubes in row 147 must be reduced to 60% in order to meet the allowable of 80.6 ksi. In the other affected rows maximum degradations of 61 to 63% are acceptable.

For the case of 1000 tubes plugged,107% flow and Eggerate No. 9 ineffective, the maximum stress for the worst case tube row (tube row 120) is 72.87 ksi and the AShE Code faulted allowables are again met.

For further discussion of the results and conclusions see Section 8.0.

3.0 ASSESSMENT OF SIGNIFICANT DESIGN Cil ANGES There are no design changes considered in this report.

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AoSONGS 94160ll68, Rev. 01 Page B5 of B24 4.0 ANALYTICAL TECIINTOUFS The maximum bending stresses in the outermost tubes are calculated using ANSYS mocels of representative tube rows. The models duplicate the geometry, loading, boundary conditions, and material properties of the SONGS SG tubes. For LOCA loading and the cases with the top eggerate ineffective, a gap is modeled between the tube and the stiffening ring on the upper surface of the top eggerate. For LOCA loading, all of the models include the effect of the friction load introduced by the vertical strips along the horizontal run of the tube. For SSE seismic loading, the models include neither a gap nor the friction loading. The details of these models are presented in Section 7.2 and in Appendix B2.

The SSE seismic stress results are reviewed using the POST) postprocessor in ANSYS. The LOCA stress results are reviewed using both POSTI and POST 26 (time-Mstory postprocessor) in ANSYS. The maximum LOCA pressure stresses are combined with the axial stresses due to LOCA motion (taken from Reference 2), with the axial and radial stresses due to tube pressure loading (taken from Reference 2), and with the SSE seismic stresses. The critical results are presented in the tabular form in Section 7.5.

5.0 SELECTION OF DESIGN INPUTS The LOCA loads are taken from References 3 and 7, and are shown in Appendix B1 in graphical form and in tabular form. These LOCA loads are for 100% flow and no tubes plugged. Also considered is the increase in LOCA loads caused by the hypothetical case of 1000 tubes being plugged and 107% flow. This is accomplished by increasing the LOCA loads by 8.17% for 1000 tubes plugged and by 4.77% for 107% flow (these values are taken from Reference 7, Appendix C). The SSE seismic loads are also shown in Appendix B1 in graphical form and in tabular fonn.

These seismic loads are from Reference 4 and are the OBE seismic loads for the SCE SG feedwater nozzle (X response with 2% damping). The SSE seismic loads were calculated by assumig a conservative broadened spectrum as shown on page A3 and by multiplying the accelerations by a factor of 2.0. Th'e normal operating temperature of the tubes is conservatively taken to be 600* F.

The following material properties are used for the tube (Inconel 600 at 600* F):

E = 29200000 psi (Reference 1)

DENS = Tube Virtual Mass Density = .4173/386 slugs /in' (Reference 3, page 29)

Su = 80.0 (Reference 1)

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l A SONGS-9416-ll68, Rev. 01 Page B6 ofB34 l 6.0 ASSUMPTIONS i'

The assumptions included in this design analysis are:

1. The virtual mass is assumed to remain constant from tube to tube.

. 2. The entire friction load is assumed to act upon the tube at the top centerline node.

7.0 DESIGN ANALYSIS This section contains descriptions of the tube geometry, tube loading, SSE analysis, LOCA analysis, and the combined stresses.

7.1 Tube Loading The LOCA loads are taken from Reference 3, pages C.3 through C 6 (tabulated values are from

! Reference 7, page 25) and are shown in Appendix Bl. The LOCA loads for a specific tube are

found from these values by linear interpolation.

The seismic loads are developed from the OBE response spectrum given in Reference 4. This i

spectmm is for excitation parallel to the hot leg at the elevation of the feedwater nozzle It is broadened by *15% and adjusted from 2% to 3% damping in accordance with Reference 8. The damping adjustment is applied to the spectrurn as a factor of.912 for frequencies below 9 cps and

, 1.0 for frequencies above 33 cps; between 9 and 33 cps the factor is assumed to vary linearly with the log of frequency. The broadtned OBE spectra for 2 and 3% damping are shown in Appendix Bl. The SSE response spectrum is calculated as two times the OBE spectrum with 3% damping, The damping of 3% is consistent with Reference 9 which recommends damping of 3% or greater for the frequencies calculated for the tube geometries considered in this analysis.

4 CSE 97-211

A. SONGS.94161168, Rev. 01 l Page B7 of B24  !

7.0 DESIGN ANALYSIS (continued) 7.2 ANSYS Tube Models The geometry for the tubes is shown on the next two sheets and is based on Reference 6. The ANSYS (Reference 5) finite element models of the outermost tubes are organized by families of tube rows and by effective eggerates as shown below:

Number of Vertical Supports Top Eggerate No. 7 5 3 1 Tube Family A 19 121-147 Tube Family B Tube Family C 9 116 120 85-115 Tube Family D Tube Family E Tube Family F 8 84 52-83 50-51 Tube Family G 7 24-49 ,

Note: In this report, the case for the top two eggerates ineffective is referred to as Tube Families A through G and the case for the 2nd and 3rd eggerates from the top ineffective is referred to as Families Al through Gl.

ANSYS plots of these models are shown in Appendix B2. The models use element type PIPE 16 (clastic straight pipe) and element type PIPE 18 (elastic curved pipe, elbow) to represent the tube.

For the LOCA analysis, Element type COMBIN40 (combination spring / slider and damper gap element) is used to represent the gap between each tube and the ring at the uppermost ineffective I eggerate in models A through F (top two eggerates ineffective). Models Al through F1 do not need a gap representation. The friction force (eight pounds) on each tube caused by the the vertical strips along the horizontal run is accounted for in the LOCA analysis by logic in the ANSYS input for all models. This logic causes a zero applied load until the LOCA load exceeds eight pounds; thereafter, the LOCA load is reduced by eight pounds. The eight pound friction force is developed in Reference 2, page 12. The SSE seismic analysis models are exactly like the models used for the LOCA analysis but they do not include the gap or friction force capabilities.

The X-direction restraints 1.long the vertical runs of each tube model represent the effects of the six top eggerates. In this report, the X direction restraints are removed at the appropriate nodes to represent ineffective eggerates. The Y-direction restraints along the horizontal run represent 4 the restraint provided by the vertical strips at these locations.

i All ANSYS models used in this report include 3% damping. The LOCA models incorporate this damping with damping factors a and p as follows:

a = 1.2728 p = .0005306 4 These values are used because the tube first mode frequencies (m) are between 4.5X2n (radians per second) and 13.5X2x (see Appendix B4) and

i'

? = (a / 2m) + (pm /2) = .03 for all frequencies in this range.

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A SONGS 9416-1168, Rev. 01 ,

l Page B8 cf B24 i

I 7.0 DESIGN ANALYSIS (continued) i

7.2 ANSYS Tube Models (continued)

SONGS Steam Generator Tube Bundle Geometry E & E II lI II U l l' now e 141 r a0w e 144,145 i aow s im.t w I

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CSE-97 211

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A-SONGS-9416-1168, Rev. 01 Page B9 ofB24 4

7.0 DESIGN ANALYSIS (continued) l 7.2 ANSYS Tube Models (continued)

SONGS Steam Generator Tube Support Arrangement

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CSE-97-211 P

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i A-SONGS 941601168, Rev. 01 l Page B10 ofB24 l

7.0 DESIGN ANALYSIS (continued) i 7.3 SSE Analvia The stresses in the tube are calculated with the ANSYS finite element models using the response spectrum method of analysis. The first nine modes are considered in the stress caletdation of each  ;

tube. The modal stresses for the modes with significant response are calculated and summed by the square-root-of-the-sum-of squares (SRSS) method. The resulting maximum longitudinal i stress in each tube row analyzed is listed in the tables in Section 7.5. These stresses are the maximum membrane plus bending stresses on the outside surface of the tube at any point along its length and around its circumference. For the case of the top two eggerates ineffective on the hot leg side of the tube, they always occur at the top eggerate on the cold side. For the case with the top eggerate intact on the hot side, they may occur at either side of the top eggerate.  !

The resulting stresses are strongly dependent on the lowest natural frequency of each tube due to the shape of the response spectrum. With two adjacent eggerates assumed to be ineffective the lowest natural frequencies vary from 4 cps for the longest tubes in each family to 15 cps or more for the shortest tubes. From the response spectrum shown in Appendix B1 it can be seen that this range of frequencies extends from the valley at 5 cps to and beyond the peak centered at about

10 cps. Consequently, the calculated stresses can be expected to vary significantly with tube

] length within a family, i'

Appendix B4 provides mode shape plots for a number of tube rows to demonstrate the nature of the fiequency and mode shape dependence on tube length within each family. For each tube the first four mode shapes and the corresponding frequencies are shown. In the larger families (A, C, E & G) mode shapes e.nd frequencies are provided for two tubes - the longest tube (i.e., the highest row number in the family) and an intermediate length tube. In the three small families, which include only a few tube rows, only the longest tube is provided.

7.4 LOCA Analysis The LOCA loading described above is applied to the ANSYS model families A through F (top two eggerates ineffective) to calculate the maximum bending stresses in a number of representative tube rows. The ANSYS solution is performed as a transient dynamic analysis (sometimes called a time history analysis) using the full system matrices to calculate the transient 4

response and using the Preconditioned Conjugate Gradient (PCG) solver. The gaps between the i outer edge of each tube and the ring are calculated as follows: I Gap = A B where, A = 4 ( 76.25 2, x2) , where radius of ring inside surface is 76.25 in l B = Y + .375, where outside radius of tube is .375 in X = x-coordinate of tube row Y = y-coordinate of tube row The resulting calculated gaps are presented in the table on the next page.

] CSE-97-211 1

A SONGS-941601168, Rev. 01 Page B11 ofB24

, 7.0 DESIGN ANALYSIS (continued) 7.4 LOCA Analysis (continued)

Calculated Gaps ROW LINE X Y A B Gap 147 2 75.5 0.866 76.245 75.875 0.370 l

, 146 9 75 6.928 75.935 75.375 0.560  ;

l 145 14 74.5 11.258 75.414 74.875 0.539 J

144 17 74 13.856 74.980 74.375 0.605 143 20 73.5 16.454 74.454 73.875 0.579 142 23 73 19.052 73.831 73.375 0.456 141 24 72.5 19.918 73 603 72.875 0.728 140 27 72 22.516 72.850 72.375 0.475 139 28 71.5 23.382 72.576 71.875 0.701 138 29 71 24.248 72.292 71.375 0.917 137 32 70.5 26.846 71.368 73.875 0.493

136 33 70 27.712 71.036 70.375 0.661 135 34 69.5 28 "-78 70.692 69.875 0.817 134 35 69 29.444 70.336 69.375 0.961 133 38 68.5 32.042 69.191 68.875 0.316 132 39 68 32.908 68.783 68.375 0.408 131 40 67.5 33.774 68.362 67.875 0.487 .

130 41 67 34.640 67.927 67.375 0.552 129 42 66.5 35.506 67.479 66.875 0.604 3 128 43 66 36.372 67.016 66.375 0.641 4 127 44 65.5 37.238 66.539 65.875 0.664 126 45 65 38.104 66.047 65.375 0.672

125 46 64.5 38.970 65.539 64.875 0.664

124 47 64 39.836 65.017 64.375 0.642 123 48 63.5 40.702 64.478 63.875 0.603 122 49 63 41.568 63.923 63.375 0.548 121 50 62.5 42.434 63.352 62.875 0.477 120 51 62 43.300 62.763 62.375 0.388 119 52 61.5 44.166 62.156 61.875 0.281 5

116 53 60 45.032 61.532 60.375 1.157 115 54 59.5 45.898 60.889 59.875 1.014 114 55 59 46.764 60.226 59.375 0.851 i 113 56 58.5 47.630 59.544 58.875 0.669 112 57 58 48.496 58.840 58.375 0.465 l

CSE-97-211

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A-SONGS 9416-1168, Rev. 01 Page B12 of B24 7.0 DESIGN ANALYSIS (continued) 7.4 LOCA Analysis (continued)

^

Calculated Gaps i ROW LINE X Y A B Gap 109 58 56.5 49.362 58.116 56.875 1.241 108 59 56 50.228 57.369 56.375 0.994 107 60 55.5 51.094 56.599 55.875 0.724

, 106 61 55 51.960 55.805 55.375 0.430 105 60 54.5 51.094 56.599 54.875 1.724 104 61 54 51.960 55.805 54.375 1.430 103 62 53.5 52.826 54.986 53.875 1.111 102 63 53 53.692 54.141 53.375 0.766 101 64 52.5 54 558 53.268 52.875 0.393 100 63 52 53.692 54.141 52.375 1.766 99 64 51.5 54.558 53.268 51.875 1.393

98 65 51 55.424 52.366 51.375 0.991 97 66 50.5 56.290 51.434 50.875 0.559 96 65 50 55.424 52.366 50.375 1.991

95 66 49.5 56.290 51.434 49.875 1.559 94 67 49 57.156 50.470 49.375 1.095 93 68 48.5 58.022 49.472 48.875 0.597 92 67 48 57.156 50.470 48.375 2.095 I

91 68 47.5 58.022 49.472 47.875 1.597 90 69 47 58.888 48.438 47.375 1.063 89 70 46.5 59.754 47.366 46.875 0.491 88 69 46 58.888 48.438 46.375 2.063 87 70 45.5 59.754 47.366 45.875 1.491 86 71 45 60.620 46.252 45.375 0.877 85 70 44.5 59.754 47.366 44.875 2.491 84 71 44 60.620 46.252 44.375 1.877 83 72 43.5 61.486 45.095 43.875 1.220

, 82 73 43 62.352 43.890 43.375 0.515 81 72 42.5 61.486 45.095 42.875 2.220 80 73 42 62.352 40 J90 42.375 1.515 79 74 41.5 63.218 42.635 41.875 0.758 t

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A SONGS-9416-1168, Rev 01 Page B13 of BT.4 l l

7.0 DESIGN ANALYSIS (continued) 7.5 combined Stresses

The stresses calculated for SSE (Ssst)and the LOCA pressure wave (St.oc4 pa) are combined with the axial stress due to LOCA motion (Stoc4uono.4) and with the axial (Sx) cnd radial (Sa) stresses (Sa) due to pressure differential on the tube wall to calculate the resulting stress intensity in the tube wall. These additional stresses are taken from Reference 2. The axial stresses from SSE and i LOCA are combined by the SRSS method and summed with the axial stress due to pressure l differential. The stress intensity is then the difference in the ecmbined axial stresa and the radial i stress from pressure differential

v SI = [(Ssse)2 + (3,,cA,,)2 + (StoeA on,,)2 j . + 3x , g, l This is the maximum stress intensity listed in the following tables for a healthy tube.

For a tube with a degraded wall the stress intensity is increased to account for the decrease in the

, area and section modulus of the tube. The resulting stress intensity is given by the following equation:

SI = F6-[(Ssss)' + (S toc4 pa)2 + (Stoc4 Monos)2 )"' + F. Sx - Sa where F6 is the ratio of the section modulus of a healthy tube to that of a degraded tube and F. is the ratio of the tensile area of a healthy tube to that of a degraded tube. For a tube degraded on the outside surface:

4 p o)" - R g R o-xt

. F b ' (R o- x t)4 - Rg4 (R) o 2

F ..

(Ro)2 -R 1 (R o- x t)2 - R;2 where x is the amount of wall degradation expressed as a fraction and R o .= .375 t = .048 R g .= R o -t ,

With 64% (x= 64) wall degradation, F6 = 2.928 and F. = 2.905 4

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A SONGS 09416-116E, Rev. 01 Page B14 of B24 7.0 DESIGN ANALYSIS (continued) 7.5 Combined Stresses (continued)

The maximura bending stresses occur at the top eggerate located on the cold side of each tube (at node 25 fc,t tube model Family A). The critica' results are presented in the table below (the LOCA and SSE ctrecses with a **"are the ones run in ANSYS while the other LOCA and SSE stresses are conevatively chosen based on the ANSYS values). The column labeled 'k"is the pe cent degradation expressed as a decimal. For tubes which have x < .64, the x value shown is tha naxbru.y allowsNe degradation. For the tubes which have x = .64, the allowable degradation is at or gte4 Gtly the pertinent "line nurr.bers" are shown in the second column of the table.

Results for Top T vo Eggerates Ineffective. No ' lubes Plugted (stresses in ksi)

LOCA Stress Pressure Stress Stress intensity ROW LINE Press. Motion SSE Axial Radial Healthy Dord'd x

! l 147 2 21.61* 2.2 16.71* 2.3 -0.9 30.61 78.89 0.60 1 146 9 22.22* 2.2 15.6* 2.3 C.9 30.44 80.51 0.61 145  % 22.1* 2.2 14.54* 2.3 -0.9 29.75 78.64 0.61 144 17 22.12* 2.2 13.25* 2.3 -0.9 29.08 78.90 0.62 143 20 21.86* 2.2 12.95* 2.3 -0.9 28.70 80.00 0.63 142 23 21.42* 2.2 12.77* 2.3 -0.9 26.23 78.67 0.63 141 24 21.68* 2.2 13.17* 2.3 -0.9 26.66 79.88 0.63 140 27 21.14* 2.2 13.29* 2.3 -0.9 28.27 78.76 0.63 139 28 21.14* 2.2 13.4* 2.3 -0.9 28.33 78.93 0.63 138 29 20.92* 2.2 13.65* 2.3 -0.9 28.28 78.79 0.63 137 32 20.88* 2.2 14.13* 2.3 -0.9 28.51 79.44 0.63 136 33 20.55* 2.2 14.63* 2.3 -0.9 28.52 79,48 0.63 135 34 20.3* 2.2 15.16* 2.3 -0.9 28.63 79.80 0.63 134 35 20.14* 2.2 15.73* 2.3 -0.9 28.85 80.42 0.63 133 38 19.55* 2.2 16.32* 2.3 -0.9 28.76 80.17 0.63 132 39 19.5* 2.2 16.42* 2.3 -0.9 28.79 80.24 0.63 -

131 40 19.32' 2.2 17.63* 2,3 -0.9 29.45 79.92 0.62 130 41 19.02* 2.2 18.33* 2.3 -0.9 29.71 78.53 0.61 129 42 18.59* 2.2 17.66* 2.3 -0.9 28.94 78.50 0.62 128 43 18.24* 2.2 16.53* 2.3 4.9 27.91 79.95 0.64 127 44 17.94* 2.2 15.66* 2.3 -0.9 ?7.11 77.61 0.64 126 45 17.45* 2.2 14.79* 2.3 -0.9 26.18 74.87 0.64 125 46 16.73* 2.2 13.92* 2.3 -0.9 25.07 71.64 0.64 124 47 16.3* 2.2 13.03* 2.3 -0.9 24.18 69.03 0.64 123 48 15.75* 2.2 11.32* 2.3 -0.9 22.72 64.74 0.64 122 49 14.94* 2.2 9.69* 2.3 -0.9 21,14 60.12 0.64 121 50 14.15* 2.2 8.19* 2.3 -0.9 19.70 55.89 0.64 CSE-97-211

A. SONGS 94161168, Rev. 01 Page BIS cfB24 I 7.0 DESIGN ANALYSIS (continued) 7.5 Combined Stresses (continued)

Results for Top Two Eggerates Ineffective, No Tubes Plugged (stresses in ksi)

LOCA Stress Pressure Stress Stress intensity _

l ROW LINE Press. Motion SSE Axial Radis: Healthy Dord'd x i

! 120 51 15.55* 2.2 18.17* 2.3 -0.9 27.22 77.91 0.64 119 52 15.16* 2.2 17.03* 2.3 -0.9 26.11 74.66 0.64 118 15.41 2.2 15.89* 2.3 -0.9 25.44 72.72 0.64 117 15.41 2.2 14.83* 2.3 -0.9 24.70 70.54 0.64 j 116 53 14.96* 2.2 13.82* 2.3 -0.9 23.68 67.57 0.64 115 54 14.7* 2.2 15.58* 2.3 -0.9 24.73 70.64 0.64 114 14.7 2.2 14.57* 2.3 -0.9 24.01 68.53 0.64 113 56 14.43* 2.2 13.61* 2.3 -0.9 23.16 66.02 0.64 112 14.43 2.2 12.68* 2.3 -0.9 22.54 64.20 0.64 111 14.43 2.2 11.96* 2.3 -0.9 22.07 62.84 0.64 11C 14.43 2.2 12.04* 2.3 -0.9 22.12 62.99 0.64 109 14.43 2.2 12.31 2.3 -0.9 22.29 63.50 0.64 108 14.43 2.2 12.31 2.3 -0.9 22.29 63.50 0.64 107 14.43 2.2 12.31* 2.3 -0.9 22.29 63.50 0.64 106 14.43 2.2 12.79 2.3 -0.9 22.61 64.41 0.64 105 14.43 2.2 12.79* 2.3 -0.9 22.61 64.41 0.64 104 14.43 2.2 14.11 2.3 -0.9 23.50 67.03 0.64

, 103 14.43 2.2 14.11 2.3 -0.9 23.50 67.03 0.64 102 14.43 2.2 14.11* 2.3 -0.9 23.50 67.03 0.64 101 14.43 2.2 15.1 2.3 -0.9 24.20 69.08 0.64 j 100 14.43 2.2 15.1* 2.3 -0.9 24.20 69.08 0.64 99 14.43 2.2 16.18 2.3 -0.9 24.99 71.39 0.64 98 65 11.74* 2.2 16.18' 2.3 -0.9 23.31 66.47 0.64 97 66 11.57* 2.2 16,69* 2.3 -0.9 23.63 67.40 0.64 96 11.57 2.2 16.69 2.3 -0.9 23.63 67.40 0.64 95 11.57 2.2 15.07* 2.3 -0.9 22.33 63.59 0.64 94 11.57 2.2 15.07 2.3 -0.9 22.33 63.59 0.64 93 11.57 2.2 15.07 2.3 -0.9 22.33 63.59 0.64 92 11.57 2.2 12.43* 2.3 -0.9 20.32 57.72 0.64 91 11.57 2.2 12.43 2.3 -0.9 20.32 57.72 0.64 90 11.57 2.2 10.3* 2.3 -0.9 18.85 53.40 0.64 89 11.57 2.2 10.3 2.3 -0.9 18.85 53.40 0.64 88 11.57 2.2 10.3 2.3 -0.9 18.85 53.40 0.64 87 11.57 2.2 6.33* 2.3 -0.9 16.57 46.73 0.64 86 11.57 2.2 6.33 2.3 -0.9 16.57 46.73 0.64 85 11.57 2.2 4.41* 2.3 -0.9 15.78 44.41 0.64 CSE-97-211

AoSONGS 94161168, Rev. 01 Page B16 of B24 7.0 DESIGN ANALYSIS (continued) 7.5 Combined Stresas(contmued)

Results for Top Two Eggerates Ineffective, No Tubes Plugged (stresses in ksi)

LOCA Stress Pressure Stress Stress intensity

, ROW LINE Press. Motion SSE Axial Radial Healthy Dord'd x 84 11.57 2.2 13.26* 2.3 -0.9 20.94 59.51 0.64 i

83 72 7.54* 2.2 14.7* 2.3 -0.9 19.87 56.39 0.64 82 73 7.37* 2.2 13.76* 2.3 -0.9 18.96 53.74 0.64 81 7.37 2.2 13.76 2.3 -0.9 18.96 53.74 0.64 80 7.37 2.2 12* 2.3 -0.9 17.45 49.02 0.64 79 7.37 2.2 12 2.3 -0.9 17.45 49.32 0.64 78 7.37 2.2 12 2.3 -0.9 17.45 49.32 0.64 77 7.37 2.2 11.16* 2.3 -0.9 16.75 47.27 0.64 76 7.37 2.2 11.27 2.3 -0.9 16.84 47.54 0.64 75 7.37 2.2 11.27* 2.3 -0.9 16.84 47.54 0.64 74 7.37 2.2 12.42 2.3 -0.9 17.81 50.36 0.64 73 7.37 2.2 12.42 2.3 -0.9 17.81 50.36 0.64 1

72 7.37 2.2 12.42 2.3 -0.9 17.81 50.36 0.64 71 7.37 2.2 12.42 2.3 -0.9 17.81 50.36 0.64 70 7.37 2.2 12.42* 2.3 -0.9 17.81 50.36 0.64 69 7.37 2.2 14.14 2.3 -0.9 19.30 54.72 0.64

. 68 7.37 2.2 14.14 2.3 -0.9 19.30 54.72 0.64 67 7.37 2.2 14.14 2.3 -0.9 19.30 54.72 0.64 66 7.37 2.2 14.14 2.3 -0.9 19.30 54.72 0.64 65 7.37 2.2 14.14* 2.3 -0.9 19.30 54.72 0.64 64 7.37 2.2 14.14 2.3 -0.9 19.30 54.72 0.64 63 7.37 2.2 14.14 2.3 -0.9 19.30 54.72 0.64 62 7.37 2.2 14.14 2.3 -0.9 19.30 54.72 0.64 61 7.37 2.2 14.14 2.3 -0.9 19.30 54.72 0.64 60 7.37 2.2 11.36* 2.3 -0.9 16.92 47.75 0.64 59 7.37 2.2 11.36 2.3 -0.9 16.92 47.75 0.64 58 7.37 2.2 11.36 2.3 -0.9 16.92 47.75 0.64

57 7.37 2.2 11,36 2.3 -0.9 16.92 47.75 0.64 56 7.37 2.2 11.36 2.3 -0.9 16.92 47.75 0.64 i 55 7.37 2.2 6.52* 2.3 -0.9 13.28 37.11 0.64 54 7.37 2.2 6.52 2.3 -0.9 13.28 37.11 0.64 53 7.37 2.2 6.52 2.3 -0.9 13.28 37.11 0.64 52 7.37 2.2 6.52 2.3 -0.9 13.28 37.11 0.64 51 2.13* 2.2 5.3* 2.3 -0.9 9.32 25.51 0.64 50 2.13 2.2 11.41 2.3 -0.9 15.01 42.18 0.64 49 1.45* 2.2 11.41* 2.3 -0.9 14.91 41.87 0.64 CSE-97-211

. - . . - . . . _ _ = - _ _ - - . - - _ _ _ _ _ _ _ - _ _ - - _ - .- _ -- _ _.-.--

A. SONGS-94161168, Rev. 01 Page B17 cfB24 l

7.0 DESIGN ANALYSIS (continued) l 7.5 Combined Stresses (continued)

Results for Top Two Eggerates ineffective, No Tubes Plugled (stresses in ksi)

LOCA Stress Pressure Stress Stress Intensity ROW LINE Press. Motion SSE Axial Radial Healthy Dord'd x 48 1.45 2.2 11.41 2.3 -0.9 14.91 41.87 0.64 47 1.45 2.2 9.91* 2.3 -0.9 13.45 37.61 0.64 46 1.45 2.2 9.91 2.3 -0.9 13.45 37.61 0.64 45 1.45 2.2 9.53* 2.3 -0.9 13.09 36.53 0.64 44 1.45 2.2 9.66 2.3 -0.9 13.21 36.90 0.64 43 1.45 2.2 9.66 2.3 -0.9 13.21 36.90 0.64 42 1.45 2.2 9.66 2.3 -0.9 13.21 36.90 0.64 41 1.45 2.2 9.66 2.3 -0.9 13.21 36.90 0.64 40 1.45 2.2 9.66* 2.3 -0.9 13.21 36.90 0.64 4

e 4

~

CSE-97-211

A SONGS-9416-1168, Rev. 01 Page BIS of B24 7.0 DESIGN ANALYSIS (continued) 7.5 Combined Stressta(continuco, The LOCA and SSE seismic loading described above is also applied to the ANSYS model families Al through F1 (2nd and 3rd eggerates from the top ineffective) to calculate the maximum bending stresses in a number of representative tube rows. The maximum stresses again occur at the top eggerate located on the cold side of each tube. The results are presented in the table below:

Results for the 2nd and 3rd From the Top Eggerates Ineffective, No Tubes Plugged ( ksi)

LOCA Stress Pressure Stress Stress Intensity ROW LINE Press. Motion SSE Axial Radial Healthy Dgrd'd x 147 2 19.24* 2.2 8.22* 2.3 -0.9 24.24 63.19 0.64 146 9 19.24 2.2 8.64 2.3 -0.9 24.41 69.68 0.64 145 14 19.24 2.2 8.64 2.3 -0.9 24.41 69.68 0.64 144 17 18.62* 2.2 8.64* 2.3 -0.9 23.84 68.03 0.64 143 20 18.62 2.2 8.93 2.3 -0.9 23.97 68.39 0.64 142 23 18.62 2.2 8.93 2.3 -0.9 23.97 68.39 0.64 141 24 17.96* 2.2 8.93* 2.3 -0.9 23.38 66.67 0.64 140 27 17.96 2.2 8.93 2.3 -0.9 23.38 66.67 0.64 139 28 17.96 2.2 8.93 2.3 -0.9 23.38 66.67, 0.64 138 29 17.23* 2.2 8.75* 2.3 -0.9 22.65 64.53 0.64 137 32 17.23 2.2 8.75 2.3 -0.9 22.65 64.53 0.64 136 33 17.23 2.2 8.75 2.3 -0.9 22.65 64.53 0.64 135 34 16.35* 2.2 8* 2.3 -0.9 21.53 61.27 0.64 134 35 16.35 2.2 8 2.3 -0.9 21.53 61.27 0.64 133 38 16.35 2.2 8 2.3 -0.9 21.53 61.27 0.64 132 39 15.2* 2.2 7.54* 2.3 -0.9 20.31 57.68 0.64 131 40 15.2 2.2 7.54 2.3 -0.9 20.31 57.68 0.64 130 41 15.2 2.2 7.54 2.3 -0.9 20.31 57.68 0.64 129 42 13.64* 2.2 6.8* 2.3 -0.9 18.60 52.67 0.64 128 43 13.64 2.2 6.8 2.3 -0.9 18.60 52.67 0.64 127 44 13.64 2.2 6.8 2.3 -0.9 18.60 52.67 0.64 126 45 12.04* 2.2 5.27* 2.3 -0.9 16.53 46.60 0.64 125 46 12.04 2.2 5.27 2.3 -0.9 16.53 46,60 0.64 124 47 12.04 2.2 5.27 2.3 -0.9 16.53 46.60 0.64 123 48 10.3* 2.2 2.76* 2.3 -0.9 14.09 39.46 0.64 122 49 10.3 2.2 2.76 2.3 -0.9 14.09 39.46 0.64 121 50 10.3 2.2 2.76 2.3 -0.9 14.09 39.46 0.64 CSE-97-211

A-SONGS 9416 ll68, Rev. 01 Page B19 of B24 ,

7.0 DESIGN _ ANALYSIS (continued) 7.5 Combined Stresses (continued)

Results for the 2nd and 3rd From the Top Eggerates Ineffective, No Tubes Plugged (ksi)

LOCA .egess Pressure Stress Str_ess Intensity 1 ROW LINE Press. Motion SSE Axial Radial Healthy Dard'd x 120 51 13.7* 2.2 8.38* 2.3 -0.9 19.41 55.05 0.64 119 13.7 2.2 8.71 2.3 -0.9 19.58 55.55 0.64 118 13.7 2.2 8.71 2.3 -0.9 19.58 55.55 0.64 117 13.17* 2.2 8.71* 2.3 -0.9 19.14 54.26 0.64 116 13.17 2.2 8.71 2.3 -0.9 19.14 54.26 0.64 115 54 12.94* 2.2 8.39* 2.3 -0.9 18.78 53.20 0.64 114 12.94 2.2 8.79 2.3 -0.9 19.00 53.84 0.64 113 12.94 2.2 8.79 2.3 -0.9 19.00 53.84 0.64 112 57 12.39* 2.2 8.79* 2.3 -0.9 18.55 52.53 0.64 I

111 12.39 2.2 9.22 2.3 -0.9 18.80 53.26 0.64 110 12.39 2.2 9.22 2.3 -0.9 18.80 53.26 0.64 109 58 11.88* 2.2 9.22* 2.3 -0.9 18.40 52.09 0.64 108 11.88 2.2 9.68 2.3 -0.9 18.68 52.92 0.64 107 11.88 2.2 9.68 2.3 -0.9 18.68 52.92 0.64 l 106 61 11.31* 2.2 9.68* 2.3 -0.9 18.25 51.65 0.64 105 11.31 2.2 9.68 2.3 -0.9 18.25 51.65 0.64

) 104 11.31 2.2 9.68 2.3 -0.9 18.25 51.65 0.64

! 103 62 10.65* 2.2 9.65* 2.3 -0.9 17.74 50.16 0.64 102 10.65 2.2 9.65 2.3 -0.9 17.74 50.16 0.64 1

101 64 10.22* 2.2 9.24* 2.5 -0.9 17.15 48.44 0.64 100 10.22 2.2 9.24 2.3 -0.9 17.15 48.44 0.64 99 10.22 2.2 9.24 2.3 -0.9 17,15 48.44 0.64 98 10.22 2.2 9.24 2.3 -0.9 17.15 48.44 0.64

, 97 66 9.1

• 2.2 6.88* 2.3 -0.9 14.82 41.60 0.64 96 9.1 2.2 6.88 2.3 -0.9 14.82 41.60 0.64 95 9.1 2.2 6.88 2.3 -0.9 14.82 41.60 0.64 94 67 7.92* 2.2 4.91* 2.3 -0.9 12.77 35.62 0.64 93 7.92 2.2 4.91 2.3 -0.9 12.77 35.62 0.64 92 7.92 2.2 4.91 2.3 -0.9 12.77 35.62 0.64 91 7.92 2.2 4.91 2.3 -0.9 g 12.77 35.62 0.64 90 7.92 2.2 4.91 2.3 -0.s 12.77 35.62 0.64 89 7.92 2.2 4.91 2.3 -0.9 12.77 35.62 0.64 88 7.92 2.2 4.91 2.3 -0.9 12.77 35.62 0.64 87 7.92 2.2 4.91 2.3 -0.9 12.77 35.62 0.64 86 7.92 2.2 4.91 2.3 -0.9 12.77 35.62 0.64 85 7.92 2.2 4.91 2.3 -0.9 12.77 35.62 0.64 CSE-97-211 f

-.__ - =__-..- - - . __-. -__- - - . - - . - - - -

A SONGS-9416-1168, Rev. 01 Page B20 of B24 7.0 DESIGN ANALYSIS (continued) l 7.5 Combined Stresses (continued)

Results for the 2nd and 3rd From the Top E ggerates Ineffective, No Tubes Plugged (ksi)

LOCA Stress Pressure Stress Stress Intensity ROW LINE Press. Motion SSE Axial Radial Healthy Dord'd x 84 71 6.93* 2.2 9.64* 2.3 -0.9 15.27 42.94 0.64 83 72 6.82* 2.2 9.13* 2.3 -0.9 14.81 41.57 0.64 82 73 6.66* 2.2 9.28* 2.3 -0.9 14.83 41.64 0.64 l 81 6.66 2.2 9.75 2.3 -0.9 15.21 42.75 0.64 80 6.66 2.2 9.75 2.3 -0.9 15.21 42.75 0.64 79 74 6.15* 2.2 9.75* 2.3 -0.9 14.94 41.95 0.64 78 6.15 2.2 10.23 2.3 -0.9 15.34 43.12 0.64 77 6.15 2.2 10.23 2.3 -0.9 15.34 43.12 0.64 76 5.63* 2.2 10.23* 2.3 -0.9 15.08 42.38 0.64 75 5.63 2.2 10.42 2.3 -0.9 15.25 42.86 0.64 74 5.63 2.2 10.42 2.3 -0.9 15.25 42.86 0.64 73 5.13* 2.2 10.42* 2.3 -0.9 15.02 42.20 0.64 72 5.13 2.2 10.42 2.3 -0.9 15.02 42.20 0.64 71 5.13 2.2 10.42 2.3 -0.9 15.02 42.20 0.64 70 4.59* 2.2 9.71* 2.3 -0.9 14.16 39.68 0.64 69 4.59 2.2 9.71 2.3 -0.9 14.16 39.68 0.64 68 4.59 2.2 9.71 2.3 -0.9 14.16 39.68 0.64 67 4.59 2.2 9.71 2.3 -0.9 14.16 39.68 0.64 66 4.59 2.2 9.71 2.3 -0.9 14.16 39.68 0.64 65 4.59 2.2 5.97* 2.3 -0.9 11.05 30.55 0.64 64 4.59 2.2 5.97 2.3 -0.9 11.05 30.55 0.64 63 4.59 2.2 5.97 2.3 -0.9 11.05 30.55 0.64 62 4.59 2.2 5.97 2.3 -0.9 11.05 30.55 0.64 61 4.59 2.2 5.97 2.3 -0.9 11.05 30.55 0.64 60 4.59 2.2 4.56* 2.3 -0.9 10.03 27.59 0.64 59 4.59 2.2 5.07 2.3 -0.9 10.38 28.62 0.64 t 58 4.59 2.2 5.07 2.3 -0.9 10.38 28.62 0.64 57 4.59 2.2 5.07 2.3 -0.9 10.38 28.62 0.64 56 4.59 2.2 5.07 2.3 -0.9 10.38 28.62 0.64 56 4.59 2.2 5.07 2.3 -0.9 10.38 28.61 0.64 l 54 4.59 2.2 5.07 2.3 -0.9 10.38 28.62 0.64 53 4.59 2.2 5.07 2.3 -0.9 10.38 28.62 0.64 52 4.59 2.2 5.07 2.3 -0.9 10.38 28.62 0.64 S1 1.59* 2.2 5.07* 2.3 -0.9 8.95 24.42 0.64 50 1.59 2.2 5.07 2.3 -0.9 8.95 24.42 0.64 49 1.33* 2.2 10.16* 2.3 -0.9 13.68 38.27 0.64 48 1.33 2.2 10.4 2.3 -0.9 13.91 38.95 0.64 CSE-97-211

A-SONGS 9416-1168, Rev. 01 -

Page B21 sfB24 7.4 DESIGN ANALYSIS (continued) .

7.5 Cambined Stresans (continued)1 Resuhs for the 2nd and 3rd From the Top E tacrates Ineffective, No Tubes Plunged (ksi)

LOCA Stress Pressure Stress Stress intensity ROW LINE Press. Motion SSE Axial Radial Healthy Dord'd x

-47 1.33 2.2 10.4* 2.3 0.9 13.91 38.95 0.64 46 1.33 2.2 10.51 2.3 -0.9 14.02 39.27 0.64 48 1.33 2.2 10.51* 2.3 -0.9 14.02 -39.27 0.64 44 1.33 2.2 10.51 2.3 -0.9 14.02 39.27 0.64

'43 1.33 2.2 10.36* 2.3 -0.9 13.87 38.84 0.64 42 1.33 2.2 10.36 2.3 -0.9 13.87 38.84 0.64 41 1.33 2.2 10.36 2.3 -0.9 13.87 38.84 0.64 40 1.33 2.2 9.42* 2.3 -0.9 12.96 36.17 0.64 The case of 1000 tubes plugged and 107% flow is considered below by a calculation of the combined LOCA and SSE stresses in the most highly stressed tube. The critical tube for this case -

is Tube 120 with the top eggerate (Eggerate No. 9) ineffective. Tube 120 is the first tube to <

• iniss"eggerate No.10. From Reference 7, appendix C, the increase in the LOCA loading for 1000 tubes plugged is 8.17% and for 107% flow is 4.77%. For tube 120 with 64% degradation and assuming 1000 tubes are plugged and 107% flow, the stress evaluation is shown below :

Suxwn = (1+.0817+ 0477) X 16.06 = 18.14 ksi F6 = 2.928 Sux:Awonow = 2.2 ksi Sx = 2.3 ksi Ssas = 12.78 ksi Sa = -0.9 ksi F. = 2.905 SI = F6-((Ssss)' + (Swc4 pa)* + (Swc4 wonow)* ] + F. Sx - Sa SI = 72.87 ksi < l.44 X .7 X Su = 80.6 ksi The:4 ore, the hypothetical case of 1000 tubes plugged and 107% flow meets the ASME Code-faulted allowable for combined LOCA and SSE stresses in the tubes.

= ,

CSE-97-211

A SONGS 9416-ll68, Rev. 01

! Page B22 of B24 7.0 DESIGN ANALYSIS (continued) 7.6 LOCA Impact Loadine Analvsis For tube rows 120 and below (first tubes to 'iniss"Eggerate No.10), impact with the ring does I occur for some tubes during the LOCA event ifit is assumed that the top two eggerates for these tubes are ineffective. The ANSYS models icere used to calcula*e these impact forces and the maximum was found to be 33.6 lbs and occurs at tube row 119. The stresses in the tube due to i this 33.6 lbs impact force are calculated using a 3-dimensional ANSYS model. The model and its  !

loading are described below (see Appendix B5 for plots of the model):

4 1 Element type used SOLID 45 ( eight noded " brick" element)

Tube Inner Diameter .654" Tube outer Diameter .750" Tube Wall Thickness ,048"

, Model Length 1.0" Extent ofModelin Hoop Direction 180 degrees

Model Loading Nodal Fx loading (radial direction), equivalent to a uniform load of 16.33097 lbs4n along a .51436" line which represents a 33.6 lbs impact force along a 1.028" line.

I; j The impact model and the stresses that result from the impact loading are shown in Appendix B5.

4 The maximum stresses on the inside surface of the tube due to the 33.6 lbs. impact loading s!ong a 1.028"line are shown below. The inside surface of the tube is chosen because it has positive stresses which add to the positive stresses for pressure loading.

SX (bearing stress) = 0 psi from page B5-4 SY (hoop stress) = 6479 psi from pags B5-5 S' (axial stress) = 1712 psi from page B5-6 The SY and SZ stresses are now multiplie:1 by F. = ?. 905 to account for 64% wall degradation and combined with the pressure stresses for a tube with 64% wall degradation from Reference 2,

Table 4.3.l(SX due to pressure on the inside surface is conservatively assumed to be -1500 psi)

, SX = 0 - 1500 = -1500 psi l SY = F. (6479) + 12760 = 31581 psi SZ = F. (1712) + 6670 = 11643 psi MAX SI = 31581-(-1500) = 33081 psi < l.44 X .7 Su = 80,600 psi 1

Therefore, the 64% degraded tube with the highest impact loading due to LOCA meets the ASME Code faulted allowables.

CSE-97-211

A-SONGS 9416-1168, Rev. 01 j Page B33 ofB24 i

8.0 RESULTS/ CONCLUSIONS r

} .With the assumption that eggerate number 10 is intact and provides efective support, the results l presented in Section 7.5 show that all tubes meet the ASME Code Appendix F allowable with two adjacent eggerates ineffective, 64% tube wall' degradation and no tubes plugged. For the

tubes in rows 121 through 147 which pass through eggerate number 10, the most critical stress ,

intensity of 69.68 ksi is c&ulsted in tube row 146 with eggerates 8 and 9 assumed to be missing i or ineffective. For tubes wisch do not pass through eggerate number 10, the Itighest calculated 4-stress intensity is 77.91 and occurs in tube row 120 for the case of the top two eggerates ( Nos. 8 -

4 and 9 for this tube) inerTective. For the case of 1000 tubes plugged and 107% flow, the

! ar.t.ximum stress for Eggerate No. 9 missing is 72.87 ksi (in Tube 120) and the Code faulted

i. allowables are again met. The ASME Code Appendix F faulted condition allowable for primary

membrane plus primary bending stress intensity of 1.44(.7S.) = 80.6 ksi (per Reference 2) is met in allinstances.

}

l If eggerate number 10 is assumed to be ineffective and no tubes are plugged, the tubes in rows i 129 through 147 have unacceptable stress intensities with 64% wall degradation and with

! egger.ites 9 and 10 ineffective. In tih case the maximum wall degradation must be reduced to i meet the allowable of 80,6 ksi. For tubes in row 147, the maximum allowable wall degradation is t

60%. In the other affected rows, maximum degradations of 61 to 63%, as shown in Section 7.5, are required to meet the ASME Code allowable. 1 L

l t-

}

L i

i i

[ CSE-97-211 i

A SONGS-9416-1168, Rev. 01 Page B24 ofB24 9.0 REEEEENCES 1.0 ASME Boiler and Prersure Vessel Code,Section III for Nuclear Vessels,1971 Edition, and addenda through Summer 1971.

i-

, 2.0 ABB/CE Report No. CENC- 1645, " San Onofre Steam Generator Revised LOCA Tube l Analysis", July,1984.

3.0 ABB/CE Report No. CENC-1327," San Onofre Steam Generator Pipe Break Accident Analysis", May 26,1978.

4.0 ABB/CE Report No. S-PEC-070, Rev.2, " Reanalysis of SONGS with RCS Model

Coupled with Building Model", J.T. Hsu,1976.

, 5.0 Computer Code, ANSYS, Revision 5.3, ANSYS, Inc., June,1996.

6.0 ABB/CE dnwings:

SE-71270-48 Rev.01," Upper Tube Support Layout - SONGS Steam Generator" E-234-722 Rev.01, " Tube Details - San Onofre III Steam Generator E-234-723 Rev.01, " Tube Details - San Onofre III Stcam Generator E-234-724 Rev. 01, " Baffle and Tube Support Assembly - San Onofre III Steam I Generator" 7.0 ABB/CE Report No. CENC-1850, Rev.1, " Evaluation of Corrosion for Eggerate Tube Supports San Onofre Steam Generators", March,1989.

8.0 NRC Regulatory Guide 1.60," Design Response Spe4tra for Seismic Design ofNuclear Power Plants," December 1973.

9.0 ASME Boiler and Pressure Vessel Code, Code Cases , Nuclear Components, Code Case 411-1," Alternative Damping Values fur Response Spectra Analysis of Class 1,2 and 3

Piping,"Section III, Division 1.

l l

4 CSE-97-211 -

. _ ~ . - .- . - - .-_. - - .. .. . - -._. - - ._ - ..- .-.. - . _ . - - .

k l A-SONGS-94161168, Rev. 01 l Appendix B1 Page B1-1 of B1-4 i-APPENDIX B1 l Tube Loading L

a 9

i e

1 h

d CSE-97-211

Appendix B1 Page B1-2 cfBI-4 i i l

, APPENDIX B1 This appendix contains the LOCA and SSE loading m ' formation presented in both tabular and graphical form. The LOCA loading is taken from Reference 3 (tabulated values are from Reference 7, pnge 25) and the SSE loading is taken from Reference 4.

1 LOCA LOADING J

1 Tube 147 j Tube 114 Tube 82 Tube 49

. 50 -

, Tube 147 40 -

Tubell4 l

i o 30 -

Tube 82 t .

Tube 49 CO -

j o

" 20 -

i O .

! O /

4 10 -

i 0 -

l . t . l . t . f . l . I a 0.00 0.02 0.04 0.06 0.08 0.10 0.12 i

i Time (sec) i CSE-97-211 t

Appendix B1 Page B1-3 cfBI-4 APPENDIX B1 LOCA LOADING Load (Ibs) Load (Ibs) - Load Sbs) Loads (Ibs)

. Time (sec) Row 147 Row 114 Row 82 Row 49 0.002 2 2 1 1 0.004 2 2 1 1 a

0.006 2.5 2.5 1.5 1 0.008 2.75 3 2 1 0.01 3 3.5 3 5 0.012 5 5 5 8 4 0.014 10 10 7.5 11 l 0.016 20 27 18 12 0.018 30 32.5 23.5 13 O.02 44 36 24.5 11

0.022 48.5 36 23 10.5 0.024 47 27.5 20 10.5 O.026 43 30.5 18 10 O.028 40 28 17 8 0.03 38 27 16 7 0.032 36 25 15.5 6

0.034 34.5 24 15 5 0.036 33 22 14 3.5 0.038 31.5 21 12.5 3 j 0.04 30 19.5 11 2.5 0.045 25.5 10 5 5

0.05 14.5 2 0 5.5

- 0.055 6 1 5 4 4 0.06 5 10 9 2 0.065 5 11 5 -0.5 0.07 17 7.5 4 1

! 0.075 14.5 7 3.5 1 0.08 13 5 0.5 1 i

0.085 14 2 -0.5 2.5 0.09 14.5 1 2.5 5 0.095 11 5 5 4.5 l 0.1 9 7 5 4.5

. 0.105 9 5 2.5 2.5

! 0.11 11 3.5 3 1.5 0.115 11 3.5 3.5 2 0.12 13 7 5 1 CSE-97-211

A-SONGS-9416-1168, Rey, 01 Appendix B1 Page B1-4 cfB1-4 2-

! APPENDIX B1

OBE Response Spectrum for SONGS Tubes I--4 4' \

q f/ \

1 1

3 4 d

fr -

I A'

M m }

[

jr 4

1 ,

. j N l

I l

i

!'

• b.1 1 10 100 4

Frequency (eps) -

2% Damping

3% Damping i

OBE' Spectrum Acceleration (g's) -

l . Frequency Damping Frequency Damping

'~

(eps) .02 .03 (cps) .02 .03 0.46 1.26 1.15 12 4.00 3.73 1.5 10.20 9.30 16 2.80 2.66 4

2 10.20 9.30 19 2.80 2.70

2.9 2.20 2.01 20 1.60 1.55

3.8 2.20 2.01 30 1.36 1.35 4

5- 1.60 1.46 50 1.26 1.26 j 6 2.00 1.82 100 1.26 1.26 8.7 -4.00 3.65 I- ' Note: SSE =2 OBE i'

CSE-97-211 1

A SONGS-94161168, Rev. 01 Appendix B2 Page B2-1 ofB2-16 4

+

1-1 i

1 I,

i

(

i i#

1-1.

i

APPENDIX B2

ANSYS Tube Models-i i

k i

i

,k i

4 4

i I

i-2 4

i

! CSE-97-211 i

1

A-SONGS-9416-1168, Rev 01 Appendix B2 Page B2-2 cfB2-16 APPENDIX B2 ANSYS Tube Models Too Two Reocratae Inaweetive i r> m m an an o as as #UDIE7 i4 6 5 5 5 ^ ^ ^ ^

N ,p y,i 24 12 p25 11 26 10 p27 B 28 5 k3 DI so 5 p31 p5 52 4 DD S3 M 2 Y

Family A: R -Top 2 ECs ineffectrve CSE-97-211

A-SONGS 9416-1168, Rev. 01 Appendix B2 Page B2-3 cfB2-16 APPENDIX B2

- ANSYS Tube Models Iop Two Eggerates Ineffectlyg 1

mm m an na av ans EElb7 a a a a a a 3,4 (4 a gag 25 13 U 26 12 p27 11 28 10 p3 D 30 B p31 pl 32 s p33 p5 34 4 .

DE b3 36 2 Farr.1y B: Row 120- 2 ECs inenectwo CSE-97-211

A-SONGS 9416-1168, Rev. 01 Appendix B2 Page B2-4 cfB2-16 i

APPENDIX B2 ANSYS Tube Models Too Two Foocrntaa ineffective I 91 on de da d7 da 7 15 h 14 0 5 23 13 U 24 I2 p25 11 N 10 pH B M B 53 DI 30 5 p31 pS 32 4 DN D3 34 2 Y

l Family C: Row 115 N

2 ECs ineffectwo k CSE-97-211

A-SONGS-9416-1168, Rev. 01 Appendix B2 Page B2-5 cf B2-16 APPENDIX B2 ,

ANSYS Tube Models Too Two Roemeae Inarective I m an am 47 aus b

(& & & & &T g4 9 7 23 13 U 24 12 p25 11 26 10 pH B 28 B P3 WI 30 . 5 p31 p5 32 4 DN D3 34 2 FamBy D: Row 84-Top 2 Ed ineffectu h CSE-97-211

A-SONGS-9416-1168, Rev. 01 Appendix B2 Page B2-6 cfB2-16 i

APPENDIX B2 ANSYS Tube Models Too Two Romerates ineffective 6 ^ ^ ^ T,i g}ggje 21 13 U 22 12 p23 11 24 10 p2 B 26 5

>U SI as s p29 p5 30 4 p31 p3 32 2 FamBy E: Row 83. Top 2 EC CSE-97-211

A-SONGS-9416-1168, Rev. 01 Appendix B2 Page B2-7 cfB2-16 APPENDIX B2 +

ANSYS Tube Models Top Two Eggerates Ineffective 1

1 15 dd 13 b 12 il a

ta p17 11 U 18 10 p19 B 20 B p21 p2 l

22 S

>23 >0 24 4 p25 p3 26 2 h

FamBy F: Row 51 -Top 2 ECs V k

CSE-97-211

A-SONGS-9416-1168, Rev, 01 Appendix B2 Page B2-8 ofB2-16 APPENDIX B2 ANSYS Tube Models Ton Two Ennerates Ineffective i

17 an is EENb 6 ^ T.

19 i

13 gg is U

20 12 p21 11 22 to p23 B 24 5 S3 SI

~

m B 1

pN p5 28 4 6

30 2 Famey G: Row 49. Top 2 ECs 4

\

CSE-97-211

A-SONGS-9416-1168, Rev. 01 Appendix B2 Page B2-9 cfB2-16 APPENDIX B2 ANSYS Tube Models Too Reacrate Intact and Next Two Feocrates Ineffective i

e m m an am n na as $4 EE*stis7 a a a a a a a T 13 6 g2 24 12 p25 pli 26 to p27 B 26 B p29 7 30 S p31 p5 32 4

>U >3 54 2 FamByA1:

Lx 47 Top EC Intact & Ned 2 ECs ineffective CSE-97-211 i

A-SONGS-9416-1168, Rev. 01 Appendix B2 Page B2-10 cfB2-16 APPENDIX B2 ANSYS Tube Models 2

Too Ennerate Intact and Next Two Ennerates Ineffective I 9e9 31 m an an 47 aa5 kO O O O O O OD g4 y 4 l N 13 N 12 p27 pt1

[ N 10

>= a

, 30 5 p31 7 32 S j

SN >5 34 4 s

p35 p3 X 2

>?

Famih B1: Row 120 ' Top EC Intact & Next 2 ECs ineffectne k CSE-97-211

A-SONGS-9416-1163, Rev. 01 Appendix B2 Page BT,-lI cfB216 APPENDIX B2 ANSYS Tube Models Top Foucrate Intac+ and Next Two Eggerates Ineffective I 91 m an da 47 da 7 is h 14 6 23 13 U 24 12 p25 pit 26 10 pH B Zu 5 pN 7 30 5 p31 p5

. M 4 kN D3 M 2 Y

l

>Y U Famfy C1:i<aw 115 'fbp EC Intact & Next 2 ECs ineffectwo &

CSE-97-211

A-SONGS-9416-1168, Rev. 01 Appendix B2 Page B2-12 cfB2-16 APPENDIX B2 ANSYS Tube Models Too Enecrate Intact and Next Two Eggerates Ineffective I mm an an a7 aus k7 14 8 23 13 U 24 12 p25 pli 26 10 p27 D 28 B pN

• 7 30 $

p31 p5 32 4 PM P3 34 2 Femuy D1: Row 84 -Top EC L

& Ned 2 ECs ineffectwo CSE-97-211

A-SONGS-9416-l l68, Rev, 01 Appendix B2 Page B213 cf B2-16 APPENDIX B2 ANSYS Tube Models Too Ennerate Intact and Next Two Ennerates Ineffective 4

1 to da a7 da 15 7 h 14 10

, 21 13 y 22 12 p23 pli 24 10 i 63 B N B 90 7 N $

DN 95 30 4 b31 P 32 2 Famih E1: Rw 83 -Top EC & Next 2 ECs ineffective CSE-97-211

A SONGS-9416-1168, Rev. 01 Appendix B2 Pag) 32-14 ofB2-16 APPENDLY 32 ANSYS Tube Models Top Eggcrate Intact and Next Two Engerates ineffective

' I is sa k7 is

[6 12 g12 pi7 p:1 u 18 to p19 B 20 B p21 7 22 S j

PU >5 24 4 p2 p3 -

26 2 Y

Nf FamBy F1: Row 51 Top EC Intact & Next 2 ECs D'

a L

CSE-97-211

A-SONGS-9416-1168, Rev. 01

' Appendix B2 Page 32-15 cfB2-16 APPENDIX B2 ANSYS Tube Models Top Enacrate Intact and Next Two Eggerates Ineffective i

17 as 15 b k 14 14 19 13 u-20 12 p21 pit 22 to p23 B 3

24 B

>0 I 26 5 4

p27 p5

- 4 28 2 p3 p3 N 2 h I

, Nf Femty G1: Row 49-Top EC Intact t 2 ECs inecoccot _

e CSE-97-211

. . . .. . -~ - . . - - ~ . - - . . . - . . . . . . .

A-SONGS-9416-1168, Rev. 01 Appendix B2 Page B2- ofB2-16 APPENDIX B2 ANSYS Tube MWels Too Ennerate Ineffective 1

999 21 90 ~1n in 17 1a5 7 A A %. A A 11

{A & 3'"

25 13 U I

1)'

26 12 kST=

11 Fe0d[AE 28 10 53 >0 30 B p31 p7 32 S PU >5

. 34 4.

DE S3 ,

36 2 p37 -

1 Row 120- Topics ' Mb CSE-97-211

A-SONGS-9416-1168, Rev. 01 Appendix B3 Page B3-1 of B3 i i

i i

i i-1 i

4 i

4 i

i 1

i i APPENDIX B3 d

i

! ANSYS Time-History Stress Plots 4

i i

4 a

s i

4 4

CSE-97-211

A-SONGS-9416-1168, Rev. 01 Appendix B3 Page B3-2 cfB316 APPENDIX B3 This appendix contains the ANSYS time-history plots of the maximum bending stress due to LOCA loading in the critical tube for each family of tubes as desenhd in Section 7.2. The peak stress values are tabulated in Section 7.4.

1 ANSYS 5.3 0 1 40 Bending Stress at Node 25 ggo.1 8

c . i o.e ti g3 ,1,73 22so' XF =.5 i:1 z

Z-BUFFER 2 coo" s no' 35co' 4290' 1o00' "0 '

Stress Soo" 2So' o

felone.t) o  ! .25 .5 l 15 a 1.25

.ies .sn .62s .sn i . ir:

TIME

, SONGS Tube 147 LOCA Loading (top two E.C.'s ineffective)

CSE-97-211

A-SONGS-9416-1168, Rev, 01 Appendix B3 Page B3-3 ofB3-16 APPENDIX B3 -

9 ANSYS 5.3 Be n d i n g St r e s s a t No d e 27 f 3g

.2 c.io .n 5

isoo-ZF =

.oo- Z-BUFFER i.e.-

1200' 3000'

> aoo-soo-Strees do0' 2aa- .

0 -

,,,, , , , , , l . io..- n 0 .25 .5 .75 l 1.25

.125 .375 .625 .875 4.825 TIME SONGS Tube 120 LOCA Loadng (top two E.C.'s ineffective) t i CSE-97-211

A-SONGS-9416-1168, Rev. 01  ;

Appendix B3 Page B3-4 cfB3-16 APPENDIX B3 1

1 i

1 MA 21 k7 12- 47 Pbg: "

Be ndi n g Str e s s at Node 25 YT26' l -

t. ios e n f1 x,ST.75 s.oo- 17 Z-8U ")FER 140a*

{

12co' D 3000' i- Y Stress 6oo-4.o' 200' J

j .. te10ss t) o I .n I .. l .n I i I i .a J .125 .375 .625 .871 1.125

TIME SONGS Tube 115 LOCA Loading (top two E.C.'s ineffective) '

1 a

p CSE ' . .:11

A-SONGS-9416-1168, Rev. 01 l

Appendix B3 Page B3-5 cfB3-16 APPENDIX B3 1 ANSYS 5.3 I

MAY 211997

' 1 42 NO. 5 Bendi n g Str e s s a t No d e 25 T2s N'

e, ..

ZF =

mo ' Z-BU FER 70 o'

.ooo-Sooo'

"' stress 2o00' icoo-o -

i . io...n

.iooo '

a I '. n I '. 9 I 6 1 i I '.n i

. in .m .us .m i.,n TIME SONGS Yube 84 LOCA Loadne (top two E.C.'s ineffectwe)

CSE-97-211

- . - -. .~ - - - _ - . . . . -. . _ - . . . . .

A-SONGS-9416-1168, Rev. 01 i- Appendix B3 Page B3-6 cf B3-16 APPENDIX B3 i

ANSYS 5.3 a MAY 211997 Be ndi n g Stress at Node 23

.3 i ._. 9, v

ZF =

Z-8UFFER sooo-1 70o0' 5

eooo"

) S000' i Y 400o' Stress 3000' 200o' 3000' 4

. ,g g ( e los 9*ll o .2S .5 75 l 1.25

. 25 .ns .+2S .stS i.i:S TIME SONGS Tube 83 LOCA Loading (top two E.C.'s ineffem) 4-s i

CSE-97-211

A SONGS 94161168, Rev. 01 l Appendix B3 Page B3-7 cfB3-16 i f APPENDIX B3 i .

! i

' ler 4

Bending Stress et Node 17 6

e.

i

! eooo' ER isoo<

i 1:00'

? ew m T

> .w a

j 4o0'

.o'

• l900' ,

s . io.. n o I

.n I ,.

I '. t. I i I 'i . e.

.in .m . .a .an i. ire  ;

TIME

. SONGS Tee 51 LOCA Loading (top two E.C.4 ineffacew) r

?

CSE-97-211

..~ ,,, . . . . . . _ _ _ . , . . . . - _ _ . . _ . - -- .

. . _ . _ . . _ . _ . . _ _ . _ - ~ _ . . . _ . _ _ _ . _ _ _ _ . , _ . _ .

A SONGS 9416-1168, Rev. 01 Appendix B3 Page B3-8 CfB3-16 4

APPENDIX B3 i i

.i g

Bendi n g Str e s s at Node 21 ,

,g 8

ieoo-i

)

seco. ER enaa-1900' D n ow -

s saa-saa.

400'

,,, swees 0

, , , , , , , s . i o. . . n 0 ! ,%

.2 i .9 I .?S  ! I 4 29

.179 .375 .629 .879 1.179 TIME SONGS Tute de LOCA Loadng (top two E.C.'s ineffecta)

CSE-97-211

A-SONGS-9416-1168, Rev. 01 Appendix B3 Page B3-9 cfD316 APPENDDC B3

' '[' " Bending Stress at Node 25 (7s

a. ,

me - UNEER I790' I900' 3 .

s 4000' 190' 900'

1. 90' Stress

- e

.pgg is6088*l8 o I .= I .. l .n I i I i .n

.It9 .3?S .629 .871 4.I19 TIME SONG 8 Tube 147 LOCA (2nd & 3rd E.C.'s from top ineffective)

CSE-97-211

A-SONGS-94161168 Rev 01 Appendix B3 Page B3-10 cfD3-16 APPENDIX B3 1

21 7 Bendi n g Str e s s at Node 27 'fo.I 6 c.iesei s

ll/ .

isoo. 2,4U ER 1400' l

It00' 3

600*

400' 200' Stroes

,, tel0es.1)

. I .n I .. l .n I i I i.n

.an .m .sn .sn s.an TIME SONGS Tube 120 LOCA Loading (2nd & 3rd E.C.'s from top ineffectve)

CSE-97-211

AsSONGS-9416-1168, Rev. 01 Appendix B3 Page B311 ofB316 APPENDIX B3

' s s.

Bending Stress at Node 25 g%'b' 7 l

c.io.. :

75 ssoo- .

i oo- ER atoo-1000-D =-

> 600-4oo-m-

0 200- Stress

,, , <. io... o o I

.n I ,.

. l

.n I i i .n

.an ,m .sn .m s.an TIME 60NGS Tube 115 LOCA Loading (2nd & 3rd E.C.'s from top ineffectrve)

CSE-97-211

A. SONGS 94161168, Rev,01 Appendix B3 Page D312 ofB316 APPENDIX B3

' Y21N7 8

B.o di n . su... os u 4. 2s roe

• 75

.t.o. .

noo ' ER ano -

sooo-375o*

am-0 -

-I no '

-""' stress

.mo

, , ,i. ion.n 0 .a .5 .ts ! l  ! 3.n

.in .m .an ,ets i.in TIME SONGS Tube 84 LOCA Loading (2nd & 3rd E.C.'s from top ineffective)

CSE-97-211

A-SONGS 9416.ll68, Rev. 01 Appendix B3 Page B3-13 ofB316 APPENDIX B3 1

i h7 Bending Stress at Node 23 .9 75 fooo- .

.ooo- ER sooo -

dooo' D sooo-

1. tooo*

toco'

.iooo-2000*

Stress

,3 , , , , , , s . io.. in o .

.29 ! .5 .?S  ! l 1.25

.129 .379 .625 .475 4.125 TIME SONGS Tube 83 LOCA Loading (2nd & 3rd E.C.'s from top ineffecove)

CSE-97-211

A-SONGS 9416 ll68, Rev. 01 Appendix B3 Page B314 cfB3-16 APPENDIX B3 7

Bending Stress at Node 17 3 FF noo . h. T.= 75 5 ** l

• • • ' 4Uf FER toco-16.o' IPoa' s o.

strees 4o0-o 40'

. o-i . io.. o o I

.a I '., I '. n I \ l- ',n

.in .m . .a .m i.in TIME SONGS Tube 51 LOCA Loading (2nd & 3rd E.C.'s from top ineffectMr)

CSE-97-211

A SONOS 94161168, Rev. 01 Appendix B3 Page B315 ofB316 APPENDIX B3 1

21 S7 Bendi n g Str e s s at Node 21

.1

,. S{* 75 a no ' Z-SUFFER Iooo' 790' D soo' s no-0 33o'

..oo-790' .

.ioo, , , , , b 8'" il 0  ! .25 ! .9  ! ,. 7%  ! l  ! I,25

.125 .379 .629 .875 1.125 TIME SONGS Tube 49 LOCA Loadne (2nd & 3rd E.C.'s from top Ineffeebwe)

CSE-97-211

A-SONGS 94161168, Rev. 01 1 Appendix B3 Page B316 cfB316 i APPENDIX B3 i

ANS'rs -1,3 1- , it 11 < 397

• I Sir

,,,,,,,, Bendin g Str e e e at Node 27 1 8*' .. f 5 i+oo' ..- UFFER sm- .

I 1200' D im-a Strees 1 i

400' m-0 -

t

.. , , , ,i.io...is o I .n- I .9 I , ,9

. I i I ..n

.189 .379 .679 .379 4.179 TIME ,

Row 120. Top EC Ineffaceve I

t L

s t

i I

I h

k

+

v CSE.97-211

i A SONGS 94161168, Rev. 01 Appendix B4 Page B41 ofB4 24 APPENDIX B4 Sample A,fode Shapes and Frequencies CSE 97-211

A SONGS 94161168, Rev. 01 Appendix B4 Page B4-2 cfB4 24 APPENDIX B4 Sample Mode Shepa and Frequencies Ton Two Roacrates inesective I .18 784

/ CEMENT 1.381 MX=1 .186 g.P%p CEMENT

= .111 L.X LX MX =11.813 3 4 P, CEMENT

( 5h$Y MX =10.906

){

f ( )

>(

Row 40 Mode 2 ;

x

.Tw 2 ECs insneceive

( LL CSE-97-211

A SONGS-9416-ll68, Rev. 01 Appendix B4 Page B4 3 cfB4-24

< APPENDIX B4 Sample Mode Shapes and Frequencies Top Two Eggcrates Ineffective l

1 r ,, 2 h$pg7 f

QMNT Y0 lNXes.119 I fl ,PgCEMENT 527 y

n4X *11.676 4

i O PYi L 1L Mt:

3 4 } g CEMENT i

q) Mgic.=

,' lNX *13.971 s ) (

n .u a SEc. - L(

CSE-97-211

A-SONGS 9416-1168, Rev. 01 Appendix B4 Page B4-4 cfB4-24 APPENDIX B4

. Sample Mode Shapes and Frequencies i

Too Two Roem*= Ineff'ective 0

I m-hk?pY1"#

$N.!8*

DMX 10.006 p

]SPQCEMENT

L_2 L.; b5.h2h" 3 4 fl . PLACEMENT i .206 DMX .16A06 (i )

) (

l Y Y Row 51 Mode S 2 ECs inenecove _ _ _

CSE-97-211

.- . - _ . . - . . . = - - -_ - . .-_. _ . _. .-- ..

A-SONGS-9416-1168, Rev. 01 l Appendix B4 Page B4-5 cfB4-24 APPENDIX B4 Sample Mode Shapes and Frequencies Ton Two Foocrates Ineffective i

i I

17 2

h((Q7 i NT x _

%u

/ m- 1 3.714 m .,zm gSPp CEMENT T

r__x L*x llEjb,z BMx.

a , 4 r , 33PtAcEMENT 7

1. ff

• m.%.

4 1

(

. _ . , _ _ L Ec. -_. > Lx CSE-97-211

A SONGS-9416-1168, Rev. 01 Appendix B4 Page B4-6 cfB4-24

~

APPENDIX B4 J

Sample Mode Shapes and Frequencies j

Too Two Moocrate: Ineffective

$ r am 2 'y I r ,

=

\ 1 ..,

k h.306

)  %.% E i

i w==

j QQm2 NX .12.342 gP% p CEMENT Y Y g 83 2

L_x i L_x i Bu.$'74 3 ., 4 ~-

%P% p CEMENT 4 7

,I k1E' 2

' t a &m

/ $ l .

s ) (

i Y

Row 83 Mode Shapes CCs ineffaceve CSE-97-211

A-SONGS 9416-1168, Rev 01 Appendix B4 Pag) B4-7 cfB4-24 APPENDIX B4 Sample Mode Shapes and Frequencies Top Two Eggerates ineffective i ,, 2 r E21kk7

}

r{ y $

1 lbi t .%

b.es2k!q%,

[ l

}$P,% CEMENT k

- .,a PgCEMENT Y Y "3

=

. , , 4 - , w ,- MENT E

[i7

, ). t s ( L

) ) ( ,

Y

(! Y ,

Row 84 Mode Shapes I!Cs inoflective CSE-97-211

A SONGS-9416-1168, Rev. 01 Appendix B4 Page B4-8 of B4-24 APPENDIX B4 Sample Mode Shapes and Frequencies Top Two Eggerates Ineffective 1 ,, 2 r r 3 fj"***!aie7

\ i.,'"'

ud.Le .624

/ w,c-g g CEMENT gyeen l DMX .12.e26 3 , 4 ]PgCEMENT p

7 y ,

[.

• llNX .T,3.293

) (

Y i

) y Row 100 h M d 2 ECs ineffectu '

i CSE-97-211 J

A SONCS 94161168, Rev,01 Appendix B4 Page B4-9 cf B4-24 APPENDIX B4 Sample Mode Shapes and Frequencies Top Two Eggcrates Ineffective i ,, 2 f q ANSY g

\ "&4NT 1

xa-

54X e6.994 f

g.PgCEMENT R Y 13.004 DMX

[fIpYgCEMENT Y Y jI 83 b X . p 3 m- _, 4 --

, ffPY,p CEMENT I 40.003 six.fs. s f

I f

Row 115

(

dode C , . id 2 ECs inoflecthe '

?

CSE-97-211 i

l A-SONGS-9416-1168, Rev 01 '

Appendix B4 Page B410 cfB4-24 APPENDLX B4 Sample Mode Shapes and Frequencies i

Ton Two Ennerates inetective 1 r ,, 2 r 1 hW kk7 y eg,b1ENT ib*

44X =6.762

]l p, CEMENT 1.216 e13.061 gCEMENT f l .916 -

L- X 75 3 r , 4 ., $PQgCEMENT p

I 40.578

44X =15.345 i

I (

)

Row 120

[

M C , . Th 2 ECs inesecthe 7

U f

4 5

f CSE-97-211 1

-.,.,-.y,e.~~ -

--n --

m-. . , , - - , , e ---., ,. ., , ,

A-SONGS-9416-1168, Rev. 01 Appendix B4 Page B4-11 cfB4-24 APPENDIX B4 Sample Mode Shapes and Frequencies InaJwo E== crates Ineffective i ,, 2 AN YS r r 3

)P 1 k .88 N k748

[p 1 1 5.178 i  ::NK .13.936

, g PLACEMENT Y

k k.212

Ex Ex 41.13,,.

3 4 P CEMENT r 7 r , P DMX=te.145 Y Y Row 136 Mode C+ Td 2 ECs hoffective CSE-97 211

A-SONGS-9416-1168, Rev. 01 Appendix B4 Page B4-12 cf B4-24  !

APPENDIX B4 Sample Mode Shapes and Frequencies Ton Two Roomtm Inefective i r ,, 2 r , ANSYS 5.g MEm fn DMX=6.514 SPyCEMENT p

'Q!,s,'o L. -

• MfpYgCEMENT Y Y } g b L.x Lzsr 4 c ,

pSag, CEMENT df.ma22 OMx.T52' Y

( Y A

)

Row 147 Mode Stape 2 ECs ineffectNo CSE-97-211 1

A-SONGS-9416-1168, Rev. 01 ,

Appendix B4 Page B4-13 CfB4-24 1 APPENDIX B4 j Sample IVode Shapes and Frequencies Top Eggerate Ineffective gnlENT L \ s E.10.100 M

) p1 i

0 21 " "

lMX m8.837

, gliPgCeMENT E Y Lx u jQ,,

, 4 n=eg,ceMcNT hh"5

f'

< )

) (i

( )

1 Y

1 )(Y

^

Row 40 Mode Sh pas kC Intact & Ned 2 I!Cs inenective CSE-97-211

A-SONGS 9416-1168, Rev 01 Appendix B4 Page B4-14 cfB4 24 APPENDIX B4 Sample Mode Shapes and Frequencies Too hocrate Ineffective l

I 2 ANSYS S 3 r ', 1997 4

k1 htMENT 1

9.027 g PLACEMErdT  ;

_ .,1, pQCEMENT

( L( . .

3 4 CEMENT r , fSPYg p

I 42.568 6.w I

I Y Y 3

L l Row de Mode Shapes kkC Ireact & Ned 2 ECs ineffsAve

. CSE-97-211 i

.-- -- _ .,. - ,w. - , - . . . , - ,_ -p _ - y y - y  !, ., - -- .-

4 / 50NGS-94161168, Rev. 01 Appendix B4 Page B4-15 cfB4-24 APPENDIX B4 Sample Mode Shapes and Frequencies

^

Top Eggerate Ineffective j g ANSYS

! w/=1 Nr

! l

\ t fb"0

M .13 456 l I! CEMENT F .709 10.34 Pp CEMENT 7 7 Li.b,,. ,'

o o M 1 3 4 y ,  !?%PMgCEMENT T -1 0 4 o

esY.#

M 16.41 #

/

, s

)

._ ,, M. = t. ., E. _ . M Ec. . M_ L i

4 CSE-97-211

.g -. _ _ . , _ . _ . . , _ . _ _ . _ . , , , . _ . _ . _ , . _ , . _ . _ . . ,

A-SONuJ.94161168, Rev. 01 Appendix B4 Page B416 cfB4 24 APPENDIX B4 Sample Mode Shapes and Frequencies Top EggcrateIneffective i

1 2 ANSYS5.g l ( } [ ]  ?$'

\

j

\ \ (Nh?

DMK .11 A01 CEMENT R' so es.3 Pt,ACEMENT p

i Y Y B "3 e 86 3 ,r , 4 r , g PgCEMENT

[:o* '5' lNX .16.243

)

) (

. , _ i .a_2 ,. _ >L CSE-97-211 I

i A-SONGS 9416-1168, Rev. 01 Appendix B4 Page B417efB4 24 APPENDIX B4  ;

Sample Mode Shapes and Frequencies Igtfagcrate Ineffective 1 r , 2 r , g5Ysjgp ENNT f .962

=8.152 ftP f hpQCEMENT N* **'

DMX =12.941 EMENT y =3

(

L.- X kg.537=12.218 3 r 4 - -

!)fpYgCEMENT DMx =12.882

/

( )

Y Y l L ShepesNEC intact & Ned 2 ECs ineffectwo l Raur 83 Met l CSE-97-211

A SONGS-9416-il68, Rev,01 Appendix B4 Page B4-18 ofB4-24 APPP.NDIX B4 Sample Mode Shapes and Em des i

Top Eggerate Ineffective i 4

1 r , 2 ,

ANSYS6

{ r htMENT I

\ '

ik" Pp CEMENT j ]bfb""

M *12.790 CEMENT

]

g,*p.835 g g L- X l-- X DMX =12.477 3 r 4 r ,

ft P, CEMENT

( )

) (

( )

1

, Row 84 h Shapes kECIntact - & Ned ECsineneceve

) 2L(

I i

4 1

1 4

CSE-97-211

+ M e e *- - - . - , - - - , . . ~ --.wm-.-. y % - .e-y -e.e.,g. y

. - . . . . . - _ . . . . . .. - - ..~.-- -. - - . - . - . . . - - . .- - . . . - ..

A SONGS-94161168, Rev 01

Appendix B4 Page B4-19 cfB4-24 APPENDIX B4 L Sample Mode Shapes and Frequencies Top Eggende Ineffective i

1 2 ANSYS5.g'

( } 7 7 DT YPY,1 p .

4SIk

i M =9.743

. ng Pt.ACEMENT p

l l i!?=

M =9.92 l- j?g pQCEMENT Y  :

h 3

'I p716

k__x M =nau 3 4 f r , r ,

khP CEMENT i hpi$'"

DMX =13.296 4

1 L

5 Row 100 Hode 1ECIntact & Ned:n !ECs L CSE-97-211

A-SONGS-9416-Il68, Rev, 01 Appendix B4 Page B4-20 ofB4-24 APPENDIX B4 Sample Mode Shapes and Frequencie-Too Foocrate Ineffective 1 < --

, 2 r ,.

NSY .g k

?'hl Jeu'ENr l

\ YNi.L'"*

ISPLACEMENT R

DMX s13.419 S P, CEMENT Y Y ",3 9,37

$N =12.148 4

3 y 4 -- -

h$PpCEMENT i i k 48.631

[ b =13.42 t f f

(~

)

> l Row 115 M 0; (x.iu, EC lntact & Ned:t ECs ineffe.%e L}

CSE-97-211

A-SONGS-9416-1168, Rev. 01 Appendix B4 Pag)B4-21 cfB4 24 APPENDIX B4 Sample Mode Shapes and Frequencies Top Eagcrate ineffective 1 r , 2 r- , ANSYS 5.g M ur l

\ e r' SPp CEMENT f kli$s" DMX =13.497 gP pCEMENT Y Y Lx Lx ({hlf.'gi.ai D .

3 r -- 4 hSPLACEMENT

\ th;2

. (

l

{

,- - = 1aEe- - Ec. _ LA CSE-97-211 J

A-SONGS-9416-1168, Rev. 01 Appendix B4 Page B4-22 cfB4-24 APPENDIX B4 Sample Mode Shapes and Frequencies Too Foocrate ineffective 1 - - -

2 ANSY

-3 ,

bkNO. 1 gP CEMENT hN1$N.971

=6 711 glSPp CEMENT 3.840

$ =13,222 ggSP p CEMENT Y Y fg f,3 L_x l_x "uSt&us o

3 4 r , r ,

kf P 1 E

g1,618 DMX =16.147 Y

) ( Y Raw 136 Mode 0;%.ik EC intat & Ned :'ECs ectin CSE-97-211

A-SONGS-9416-1168, Rev. 01 Appendix B4 Page B4-23 cfB4-24 APPENDIX B4 Sample Mode Shapes and Frequencies Top Eggerate Ineffective I e- 3 2 r , hk21b kLbkNO syk bMX =6.802 ISP, CEMENT

= R 2.928 DMX =14.177 SP CEMENT p

l Y Y pg g"32.631 i

b b BESTi.57.

=

, 3 --

4 ,

CEMENr 7 3

=4 4

g1.53 DMX =15.481

) (

. _ ,. , _ . 1E. ._E_ _ L CSE-97-211

A-SONGS-9416-1168, Rev. 01 Appendix B4 Page B4-24 ofB4-24 APPENDIX B4 Sample Mode Shapes and Frequencies Too Ennerate Ineffective -

1 r , 2 r , ph7 RMENT

=1

=0 DMX =7.132 ISP CEMENT hp5?F" DMX =15.177 DISP CEMENT

!kfpf!sS474 T

LX L' jMX =15.523 3 4 glSPLACEMENT p

= 1.

) ,

t (

i Y

> Y Row 120 hiode Shapes Eggerate ineffectoe CSE-97-211

A-SONGS-9416>1168, Rev. 01 1 Appendix B5 Page B5-2 of B5-6 i

APPENDIX B5 This appendix contains plots of the ANSYS model and the stress results for the largest LOCA impact loading. The results are for a healthy tube 119 with a 33.6 lbs calculated impact force applied along a 1.028"line.

CSE-97-211

__- ~ ~

_ _ ' ~ K-SUN US~9M 1168, Rev. 01 j Appendix B5 Page BS-3 of B5-6 1

l 1 APPENDIX B5

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CSE-97-211

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! MAY 30 1997

' 13:50:21 '

"-, PLOT No. 2

NCDAL SOLUTION

[ 'N$- STEP =1 j SUB =1

! < TIME =1 i SX 4

(AVG) l  :

RSYS=0 l

DMX s.136E-03

+ SMN s-3144 SMNB=-4515

l. SMX =1240 i + SMXB=2191 l .

F x -3144

(-- . -2656

. g -2169

. = :l "91 i

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CSE-97-211 l

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APPENDIX B5 l- i I

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i:6 MAY 30 1997 l

i kl 4 '~.i 13:50:54 rt0T No. 3 i

"l' NODAL SOLUTION i

'M STEP =1 I

'gg . SUB al

• si TIME =1 ,

. SY. (AVG) 7.< -iN RSYSs0

! . h <;4 DMX a.136E-03

' . , . SMN =-7977 N #i I' ^:I i- SMNBs-9598 1

'i 3 SMX e6479

'}id p-} . SMXBa7629

{ .

i , ! -7977

+$ '

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j A-SONGS-9416-1168, Rev. 01 l Appendix B5 Page B5-6 of B5-6 i

l f APPENDIX B5 ,

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i t

ANSYS 5.3

. MAY 30 1997 13:53:41

. PLOT NO. 6 NODAL ECLUTION STEP =1

! SUB =1

(. TIME =1 l 57. (AVG) l .

RSYS=0

' DMX s.136E-03 i SMN =-5474

l.  ;. SMNB=-7095 l SMX =1712

SMXB=2812

! F

-5474

-4675

." -3877

-3079 g -2280 l 374 l 'l ~115.03 913.434

&> 1712 k.

t. 'a K .;.

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I CSE-97-211 .

i l

A-SONGS-9416-1168, Rev. 01 Attachment B1 Page B1-1 ofB1-8 ATTACHMENT B1

1. Design Analysis In-Process Approvals (1 page).

2. Verification Plan (1 page).

3. Design Analysis Verification Checklist (4 pages).

4. Reviewer's Comment Form (1 page).

(Copies included in Q.A. Record Copy only)

CSE-97-211

A-SONGS-9416-1168, Rev. 01 Attachment B2 Page B2-1.of B2-2 ATTACHMENT B2 ANSYS COMPUTER FILES The following output files are provided on a floppy disk with the QA record copy only: l ANSYS Output Files for LOCA Stress Calculations Filename Date Time Filename Date Time locall2.out 22-May 17:03 loca51.out 21-May 11:36 local 13.out 22-May 15:59 loca82.out 19-May 13:33 locall5.out 21-May 11:28 loca83.out 21-May 11:35 loca116.out 22-May 15:54 loca84.out 21-May 11:09 local 19.out 22-May 15:53 loca97.out 19-May 8:50 local 20.out 21-May 11:27 loca98.out 19-May 8:49 local 21.out 19-May 8:20 locabl01.out 19-May 18:19 local 22.out 19-May 11:14 locabl03.out 19-May 18:18 local 23.out 19-May 11:13 locabl06.out 19-May 18:11 local 24.out 19-May 8:19 locabl09.out 19-May 18:10 local 25.out 19-May 10:57 locabil2.out 19-May 17:33 local 26.out 19-May 10:56 locabil5.out 21-May 11:42 local 27.out 19-May 8:11 locabil7.out 19-May 17:18 local 28.out 19-May 10:43 locabl20.out 21-May 11:40 local 29.out 19-May 10:42 locabl23.out 19-May 17:10

. local 30.out 19-May 8:09 locabl26.out 19-May 16:36 local 31.out 19-May 10:28 locabl29.out 19-May 16:35 local 32.out 19-May 8:00 locab132.out 19-May 16 29 loca133.out 19-May 10:28 locabl35.out 19-May 16:28 local 34.out 19-May 10:16 locabl38.out 19-May 16:00 local 35.out 19-May 7:50 locabl41.out 19-May 15:59

local 36.out 19-May 10:12 locabl44.out 19-May 15:51 local 37.out 19-May 10:22 locabl47.out 21-May 9:01 I local 38.out 19-May 7:39 locab49.out 21-May 11:57 I local 39.out 19-May 10:05 locab51.out 21-May 11:56 l local 40.out 19-May 9:58 locab70.out 19-May 18:49 local 41.out 19-May 7:29 locab73.out 19-May 18:49 ,

local 42.out 19-May 9:57 locab76.out 19-May 18:47 l local 43.out 19-May 9:20 locab79.out 19-May 18:36 local 44.out 16-May 16:58 locab82.out May 18:35 local 45.out 19-May 9:13 locab83.out 21-May 11:50 local 46.out 19-May 9:05 locab84.out 21-May 11:49 loca147.out 21-May 8:56 locab94.out 19-May 18:29 loca49.out 21-May 13:23 locab97.out 19-May 18:28 _

local 20t.out 10-Jun 08:57 l

• locaxxx.out = output file for tube row xxx without top 2 eggerates.

locabxxx.out = output file for tube row xxx without 2nd and 3rd eggerates from top.

locaxxxt.out = output file for tube row xxx without top eggerate. l CSE-97-211

i l

A-SONGS-9416-1168, Rev. 01 l Attachment B2 Page B2-2 of B2-2 i ANSYS Ouput Files for SSE Stress Calculations Filename Date Time Filename Date Time Filename Date Time sse040.out 18-May 20:06 ssell6.out 18-May 18:31 sse040a.out 20-May 8:56 sse045.out 18-May 20:06 ssel17.out 18-May 18:30 sse043a.out 20-May 8:58 sse047.out 18-May 20:10 ssell8.out 18-May 18:30 sse045a.out 20-May 8:53 sse049.out 18-May 19:32 ssel19.out 18-May 18:29 sse047a.out 20-May 8:55 sse051.out 18-May 19:31 ssel20.out 18-May 17:50 sse049a.out 20-May 8:51 sse055.out 18-May 20:00 ssel21.out 18-May 17:13 sse051a.out 20-May 8:49 sse060.out 18-May 20.00 ssel22.out 18-May 17:12 sse060a.out 20-May 8:46 sse065.out 18-May 19:59 ssel23.out 18-May 17:1I sse065a.out 20-May 8:43 sse070.out 18-May 19:58 ssel24.out 18-May 17:10 sse070a.out 19-May 16:24 sse075.out 18-May 19:01 ssel25.out 18-May 17:09 sse073a.out 19-May 16:22 sse077.out 18-May 19:46 ssel26.out 18-May 17:08 sse076a.out 19-May 16:20 sse080.out 18-May 19:01 ssel27.out 18-May 17:07 sse079a.out 19 May 16:13 sse082.out 18-May 19:55 ssel28.out 18-May 17:06 sse082a.out 19-May 16:11 sse083.out 18-May 18:57 ssel29.out 18-May 17:05 sse083a.out 19-May 15:29 sse084.out 18-May 18:49 ssel30.out 18-May 17:04 sse084a.out 19-May 15:25 sse085.out 18-May 17:57 ssel31.out 18-May 17:03 sse094a.out 19-Miy 16:09 sse087.out 18-May 19:45 ssel32.out 18-May 17:01 sse097a.out 19-May 16:08 sse090.out 18-May 18:08 ssel33.out 18-May 17:00 sse101a.out 19-May 16:04 sse092.out 18-May 19:44 ssel34.out 18-May 16:56 sse103a.out 19-May 16:02 sse095.out 18-May 18:07 ssel35.out 18-May 16:56 sse106a.out 19-May 16:00 sse097.out 18-May 18:45 ssel36.out 18-May 16:55 sse109a.out 19-May 15:58 sse098.out 18-May 19:53 ssel37.out 18-May 16:54 ssell2a.out 19-May 15:09 sse100.out 18-May 17:53 ssel38.out 18-May 16:53 ssellSa.out 19-May 14:42 sse102.out 18-May 19:42 ssel39.out 18-May 16:52 ssel17a.out 19-May 14:40 sse105.out 18-May 17:52 ssel40.out 18-May 16:51 ssel20a.out 19-May 14:38 sse107.out 18-May 19:42 ssel41.out 18-May 16:50 ssel23a.out 19-May 14:36 ssel10.out 18-May 17:51 ssel42.out 18 May 16:49 ssel26a.out 19-May 14:34 sseill.out 18-May 18:40 ssel43.out 18-May 16:48 ssel29a.out 19-May 14:33 ssell2.out 18-May 18:39 ssel44.out 18-May 16:47 ssel32a.out 19-May 14:31 ssell3.out 18-May 18:38 ssel45.out 18-May 16:45 ssel35a.out 19-May 14:29 ssell4.out 18-May 18:37 ssel46.out 18-May 16:44 ssel38a.out 19-May 14:27 ssell5.out 18-May 17:50 ssel47.out 18-May 16:42 ssel41a.out 19-May 14:19 ssel20b.out 10-Jun 08:56 ssel47a.out 19-May 14:14 ssel44a.out 19-May 14:17 l Note: ssem.out = output file for tube row no. m with top 2 eggerates missing.

ssema.out = output file for tube row no. m with 2nd and 3rd eggerate from top missing.

ssemb.out = output file for tube row no. m with top eggerate missing. l The ANSYS runs were made on a HP9000/800 computer using the HP-UX 10.20 Operating System. Version 5.3 of ANSYS was used. The validity of the ANSYS 5.3 code has been demonstrated in ABB report A-ABBBP-9416-1141, Rev. 00 (Reference 9.7).

CSE-97-211

A-SONGS-9416-1168, Rev. 01 Page C1 cf C38

SUMMARY

OF CONTENTS

Calculation H Pages Appendices H Pages Anwh-* 2Pages No. of Diskettes A 4

ATTACHMENT C TO

. A-SONGS-9416-1168, REV. 01 l

1 EVALUATION OF LOCA ON THE TUBE BUNDLE FOR i SOUTHERN CALIFORNIA EDISON SONGS UNIT 3 STEAM GENERATORS WITH DEGRADED EGGCRATES CSE-97-255 I Quality Class: X QC-1 (Safety-Related) i

! PURPOSE: 1. To illustrate that with a certain percentage of the lattice bars and connections to the eggerate rings missing, there is a redistribution of the loads such that the

! remainder of the eggerate structure is not overstressed.

2. To illustrate that the eggerate remains intact under LOCA+SSE loads for the geometry conditions reflected by the examination results.

4 This Design Analysis is complete and verified.- Management authorizes the use ofits results.

PREPARED BY: M. Buol //. DATE: 8/2.7 b7

', MENTOR: P. L. Anderson ,

DATE: #F ,

7 i

VERIFICATION STATUS: COMPLETE

{ 'Ihe Safety-Related design infonnation contamed in this document has been verified to bc

correct by means of Design Review using the Chectlist in QP-3.4 of QPM 101.

Name R. E. Johnson Signature

~

Date h/ -

i Independent Reviewer #

APPROVED BY: D. P. Siska DATE: O2M7

+ ABB COMBUSTION ENGINEERING CHATTANOOGA, TENNESSEE i * '

1 _ . . .

CIh}s document is the ptoperty of ABB/ Combustion Engineering l Chattanooga, Tennessee, and is to be used 5

~

Is ly for the purposes of the agreement with ABB/CE pursuant to which it is fumishedi w .

I CSE-97-255 J

d

A-SONGS-9416-1168' Rev. 01 Paga C2 of C38 l

)

RECORD OF REVISIONS t ^ ' "

41

s te t

t. p .

1 v i<

.g

.i A s ,.. s 4p

.;e.

-. r .- - s:  : PARAGRAPH (s); :' PREPARED -INDEPENDENT MAPPROVED KEIO e DATE;!<

q -

VINVOLVED '

QBy , [ REVIEWER ~ , -l:t;?-BY) c - 4 O 6/2/97 OriginalIssue ,M. Basol J. T. Wrenn D. P. Siska 4

t

I 8/27/97 Parag. 7.0 - Case M. Basol R. E. Johnson D. P. Siska

2A (pages C26,C27)- Added

more detail.

4 .

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CSE-97-255

A-SONGS-9416-1168, Rev. 01 Page C3 ef C38 TABLE OF CONTENTS f ERSA 4 - 1.0 OBJECTIVE OF THE DESIGN ANALYSIS ......................................... 4 2.0 ASSR'SMENT OF SIGNIFICANT DESIGN CHANGES ..................... 5 3.0 ANALYTICAL TECHNIQUES .......................... ............................. .... 5 4.0 SELECTION OF DESIGN INPUTS ...................................................... 7 5.0 AS S UMP TI ON S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 6.0 DETAILED ANALYSIS . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . 9 7.0 RESULTS/ CONCLUSIONS ..... .. . ... ... ... . ... .... .. .... ........ .. ... .... . . .. ......... . 24 8.0 REFERENC E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..................................37 Attachment Cl Design Analysis In-Process Approvals, Verification Plan, Design Analysis Verification Checklist, & Reviewer's Comment Form (Copies in Q.A. Records Only)

Attachment C2 ANSYS Input & Output Files (Copies in Q.A. Records Only)

Appendix C1 Detailed Results Tables For Degraded Eggerate Number 91oad Cases 2A and 2B CSE-97-255

--. - . - . . - _ . - - - - . ~ - - - - - - - - . -

. A-SONGS-9416-1168' Rev. 01 j Page.C4 cf C38

- 1.0 Q33CQyg&fIggg4EijiMALygg This design analysis presents the results of the evaluation of Loss of Coolant Accident (LOCA) and seismic SSE loads on the tube bundle for Wharn California Edison SONGS

! ' steam generators with degraded eggerates. The objective of this a:Wysis is twofold:1 (a) to illustrate that with a certain percentage of the lattice bars and ' connections to the eggerate

! rings micsing, there is a redistribution of the loads such that the remainder of the eggcrate

! structure is not overstressed, (b) To illustrate that the eggerate remains intact under  :

LOCA+SSE loads for the hot-side degraded strip geometry conditions reflected by the

examination results, and that the integrity of the steam generator tubes is not jeopardized.

} The eggerate tube suppon assemblies are mainly designed to prevent harmful tube vibrations. However, during a LOCA event, the upper eggerate supports provide-l horizontal support for the tubes and thus receive substantial loading from the tube

[ reactions. In this analysis, the two uppermost panial eggerate supposta desipetM as

. Numbers 9 and 10, are investigated for LOCA and seismic loading. The two uppermost L eggerate supports are chosen for analysis because the LOCA loads are maximum on the

l. tubes with the longest horizontal spans.which are located at the top of the tube bundle.

i LOCA loads decrease as the horizontal span lengths decrease. Additionally, further .

investigation into the stresses and strains in the peripheral strips of Number 9 eggerate

support is performed in order to evaluate the impact of the observed strip degradation in l this eggerate at the hot-side. Eggerate 9 was selected as the critical case for the degraded

. eggerate evaluation. This eggerate was the most critical eggerate evaluated for LOCA plus j SSE in CENC-1850-1 (Reference 8.2) and the present analysis confirms eggerate 9 to be

[ more critical than eggerate 10 for the same degradation. Since praliminary inspection results indicate less degradation in eggerate 10, this eggerate is judged to be less severe

i. . than eggerate 9.

, In eggerate 8, the LOCA loads decrease because the shorter span of the additional tubes l that are supported by this eggerate have less load and the tubes which also pass through

! eggerates 9 and 10 have even less load. The net load on eggerate 8 is estimated to be 50%

l of the load on eggerate 9. The analysis of eggerate 9 assumes that virtually 'all peripheral

i. strips are degraded to 10% of the nominal thickness. It is estimated that at least 50% of this

~ number of strips are at least 10% of nominal thickness on the periphery of eggerate 8 and

! the condition of this eggerate is less severe than eggerate 9. Because of the diminishing l_ LOCA loads at the lower elevation eggerates, the conclusion for egerate 8 also applies to

eggerates 7 and below, i .

~

The results of this design analysis are intended to justify the continued operation of i SONGS Unit 3 steam generators with degraded eggerate strips.

1 I.

CSE-97-255 1

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- A-SONGS-9416-1168' Rev. 01 Page C5 of C38 - I l -2.0 ASSESSMENT OF SIGNIFICANT DESIGN CHANGES j ABB-CENO in Chattanooga, Tennessee, has not been informed of any significant s. sign- ~

l telated changes in the structural components ofinterest.

3- .

[ 3.0 M6 i .

The design analysis is performed utilizing the ANSYS (Reference 8.1) finite element analysis

! software. The two uppermost eggerates, that is, Eggerate Numbers 9 and 10 are modeled l_ for aralysis. The models are detailed full scale models including all of the 1 inch and 2 inch i~

strips, support rings, and the scallop bars that make up the eggerate suppo t e====hua= iiw support conditions for the eggerate support assemblies at the outer edge at the baffle is l duplicated by applying the appropriate support conditions representing the baffle stiffness

! and the support configuration. Only 90 degree segments of the eggerate support assemblies i _ are modeled, taking advantage of the symmetry conditions. The eggeri.te models are loaded by the reduced tube reactions to cold leg LOCA loads taken from the tube bundle analysis

that was performed earlier (Reference 8.2). Additional consideration is given to the effect of  ;

seismic SSE loads. The details of the procedure for loading the eggerate models, and the

. - loads are dixussed in Section 6.0.

, The worst time points from the LOCA analysis are analyzed for each eggerate to obtain the

stress distributions in the eggerate support assemblies utilizing linear elastic theory. The

! initial stress runs are made considering~no degraded or missing strips in the eggerate support F usemblies.

, In the firs'. case, in order to pave that there would be a significant load redistribution in a

! supoort structure such as the eggerates, the eggerate models are somewhat arbitrarily modified to simuk te the missing and/or degraded strip conditions at the outer periphery of the eggerates. The results indicated local areas of highly stressed strips. However, the eggerate support assemblies are highly redundant structures capable of a high degree ofload i redistribution. - Therefore, as the structure is loaded and deflects with plastic deformation j beginning, the loads in the 1.ighly strersed region would be expected to experience some degree of redistribution. This load redistribution is investigated by making the highly _

, stressed elements, or strips in the model inactive, and observing the changes in the stress

distribution. This procedure is an estimate of the true loading in the structure. An analysis j to provide a more accurate picture of the final load and stress distribu.lon in the eggerate structures would be an inelastic time history loading of the structures. However, this type of

analysis for th: whole eggerate support assembly is beyond the scope of this design analysis.

A locc u. zed elastic-plastic analysis was performed for the degraded strips at the periphery of the suoport essembly, which is discussed below.

l-s=

4 i

CSE-97-255 4

i

L .01 l- A-SONGS-9416-1168 Page Cd c RfC38 i.

_ 3.0 ANALYTICAL TECHNIOUES (Continued)

In the second case, the eggerate geometry and the loads for the more critical egge sta support assembly (i.e., Number 9 eggerate) is modi 6ed to re6ect the strip degradation around the periphery of the eggerate structure based on the actual results of the visual i

examination. The degraded strips are represented by elements which have only membrane

, load carrying capability with clastic-plastic material properties. Both tensile and

compressive loads are evaluated. The resulting strip stresses and strains are compared to the

! strip material allowables in order to show that the structure can withst-nd the LOCA plus SSE loads, even in the degraded condition, and that the displacement of the eggerate at the

! outer tube locations do not jeopardize any tube integrity.

The results of this analysis are processed utilizing ANSYS General Postprocessor (POST 1).

The computer runs were made on HP9000/800 machine using HP-UX 10.20 Opvating System. Version 5.3 of ANSYS was used.

i i

f CSE-97-255

A-SONGS-94161168 Rev. 01 Page C1 cf C38 4.0 SELECl10XOF_DESIGNlNEUTS The primny input for this design analysis was obtained from the earlier evaluation of corrosion for eggerate tube supports for San Onofre steam generaters (Reference 8.2).

This input consisted of cold leg LOCA tube reaction loads on Number 9 and 10 eggerate

- suppo.1 :rerr$ lies. The hot leg LOCA loads were derived utilizing the information given in the SO Onofre steam generator pipe break analysis report (Reference 8.10). The eggerate support essembly geometry information were derived from the various drawings listed as reference in Section 8.0. The degraded eggerate information was taken from Reference 8.19.

4 4

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A-SONGS-9416-1168, Rev. 01 <

Page C8 cf C38 5.0 ASSUMPTIONS The assumptions included in this design anaiysis are:

1. Conservatively, the LOCA+SSE loads are applied to the eggerate support assemblies as static loads, without taking credit for the differing dynamic responses of the tubes and the eggerate support assemblies.

{

2. Conservatively, for Number 9 eggerate analysis, the degraded strip thickness for all strips that are identified to have 10 to 50% thickness remaining, are modeled as having only 10% thickness remaining. Similarly, all strips that are identified to have greater than 50% thickness remaining are modeled as having 50% thickness remaining.

! 3. For the load case (Case 2A) representing the hot leg LOCA which results in a net tension load on the degraded side (hot-sidt;) of the eggerate, the slots in the 2 inch strips can i>e simulated by assuming 2 inch strips to be 1 inch strips.

L i 4. The material behavior for the strips is represented by a tri-linear stress-strain curve.

j

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4 o

CSE-97-255 1

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f A-SONGS-9416-1168, Rev. 01

- Page C9 cf C38 r

6.0 DETAILED ANALYSIS t - This section contains a description of the geometry, analytical model used in the design analysis loadings applied on the two uppermost eggerate suppon assemblies, and calculated

real constants and other appropriate inputs used in the ANSYS models.

i

[ 6.1 Geometry j _1 4

The geometries of the eggerate support assemblies number 9 and 10 are given in Figures 6.1 and 6.2, respectively. These geometries are based on information given in References 8.3

and 8.4.

i 6.2 Analvtical Model p

i The design analysis is performed utilizing the ANSYS-(Reference 8.1) finite element

analysis software. For both eggerate support assemblies, the 1 inch and 2 inch strips, as t

well as tae 0.75 inch square support rings at the periphery of the eggerates and the scallop bars are au modeled as 2-D Ela:: tic Beams utilizing ANSYS BEAM 3 elements. The Snite -

element models are full scale detailed models of the eggerate support assemblies.

j' Appropriate real constants representing the. varying cross-sectional properties of these ,

components were input to the eggerate models. The eggerate support assemblies are -

l symmetrica! Therefore, only half of the -each eggerate assembly is modeled with

! symmetrical boundary conditions applied. Figures 6.3 and 6.4 provide the finite element l models for eggerate support assemblies 9 and 10, respectively. The intersections of the 2-i inch and 2 inch strips, and the intersections of the 2 inch and 1 inch strips are modeled as l rigid connections. The 1 inch strips do not physically intersect each other, and are modeled j in that fashion. The nodes at the outer suppon locations are coupled to form rigid regions.

! The master node at each support location is connected to fixed nodes through ANSYS Spring-Damper elements-(COMBIN14),- which have longitudinal and torsional spring

. capabilities. Appropriate spring constants representing the stiffness of the surrounding baffle and the attachment geometry were used as an input to these spring-damper elements.

I When evaluating the case representing the actual results of the visual examination (i.e.,

degraded strips at the periphery of the Number 9 eggerate support assembly), modifications are made to this finite element model. The strips at the periphery of the eggerate support i as.embly which are attached to the support rings are all modeled as LINK 12-D Spar

elements which have elastic-plastic analysis capability and only membrane load carrying

capability. A;.propriate cross-sectional properties representing the degraded strips (i.e.,

[ 10% of the thickness remaining, and 50% of the thickness remaining), and trilinear elastic -

l plastic material properties and buckling constants for these elements are input to-the

modified model. Nodal constraints to the eggerate suppon assembly models are illustrated in Figures 6.5 and 6.6. The ANSYS input data for both eggerate models is given in Attachment C2 to this design analysis.

l CSE-97-255 t

A-SONGS-9416-1168' Rev. 01 Page C10 ef C38  ;

6,0 DETAILED ANALYSIS (continved) 6.3 Real Constants a) 2 inch Strip:

, e Area = 2 in. x .090 in. = 0.I80 sq. in.

Moment ofInertia = 2 in. x (.090 in.)* /12 = 0.0001215 in'

• Height = .090 in.

b) 1 inch Strip:

. Area = 1 in. x 090 in. = 0.090 sq. in.

Moment ofInertia = 1 in. x (.090 in.)3 /12 = 0.0000608 in' i o Height = .090 in.

c) Support Ring:

• Area = 2 x (0.75 in. x 0.75 in.) = 1.125 sq. in.

Moment ofInertia = 2 x [0.75 in. x (0.75 in.)' /12] = 0.05273 in'

+ Height a 0.75 in.

d) Scallop Bar:

• Area = 2 x (0.75 in. x .1175 in.) = 0.17625 sq. in.

Moment ofInertia = 2 x [0.75 in. x ( 1175 in.)' /12) = 0.00020028 in'

• Height = .1175 in.

e) Baffle Stiffness (Spring) Rates:

. Longitudinal (Radial) Spring Rate = 680,000 lbs/in. This spring rate was conservatively calculated using the Reference 8.5 expressions for a spherical shell loaded at it's apex and having a mid-surfac.s radius of 78.125 in.

• Torsional (Circumferential Moment) Spring Rate = 2,500 in-lbs/ degree or 143,239.5 in-lbs/ radian. This spring' rate was calculated using the procedures of Reference 8.6 for a cylindrical shell.

CSE-97-255

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A-SONGS-9416-1168, Rev. 01

Page Cll of C38 i

, 6.0 DETAILED ANALYSIS (continued!

6,4 Material Properties

_J

, The material propenies used are at 532' F, which corresponds to the saturation l j temperature. The following values are used in the elastic Snite element analysis and 1 in the stress evaluations:

)

'1' 4

i e For all eggerate suppon assembly components:

1 E = Young's Modulus ofElasticity = 26.8 E6 psi.

j -y = Poisson's Ratio = 0.3 I In the elastic-plastic analysis, where the strips attached to the support rings at the

[ - periphery of the Number 9 eggerate support assembly are modeled as LINK 1 j- elements, a tri-linear stress-strain curve using ANSYS kinematic hardening material l behavior option is used. The constants used in the evaluation are:

[ C1 - Yield Stress = 31,400 psi. (see below)

C2 - Second Break Point = 43,200 psi.

j C3 - Tensile Strength = 55,000 psi. (see below) 1-The corresponding strain values are:

i '

! el = 0.001172 in/in '

c2 = 0.01 in/in

e3 = 0.20 in/in i In addition, when evaluating the Number 9 eggerate support assembly for reversed (compressive) LOCA+SSE loads, the material properties for the strip elements at the periphery of the model are modified to account for buckling loads. In order to

accomplish that, four different buckling load limits as a function of the strip element i

length, using elastic-perfectly plastic material properties, is utilized. The buckling -

load limits are calculated using the following formula for plates under compression:

! Per = 4x2 EI/L2 (g,y2 ) (Ref. 8.18) .

and Ucr = Per/A where, L=Lera'h, A= Cross-sectional Area

! The buckling stresses used are:

2 l *- Uct = 7,848 psi. for L h 1 in.

CSE-97-255 f_

i 1

i

A-SONGS-9416-1168, Rev. 01 Page C12 Cf C38 l 6.0 DETAILED ANALYSIS (conti.D.MED e Uct = 15,6% psi for 0.71 in. 8 L < 1 in.

• Ucr = 23,544 psi. for 0.58 in. 8 L < 0.71 in. l

• Uct = 31,392 pd. for 0.50 in. 3 L < 0.58 in.

. l The tri 'Jnear stress-strain curve with a yield point at 31,400 psi is used for elements having a length less than 0.5 inches.

e Mechanical Properties The ASTM carbon steel components used in a typical eggerste support assembly are specified by Reference 8.7 and are as follows :

COMPONENT MATERIAL i 2" Strip A-570, Gr. D 1" Strip A-569 3/4" x 3/4" Bar A-108, Gr.1018 Scalloped Bar A-108, Gr.1018 A-570. Gr. D The properties of A-570, Gr.D, strip material are found in Reference 8.8 as Grade

40, which is the revised grade for this material.

Su = 55 ksi Sy = 40 ksi Sy* = 31.4 ksi @ 532*F (see next page)

A-569 Reference 8.8 does not specify the properties for this material; therefore, they are assumed to be the same as A-570,Gr. D.

A-108. Gr.1018 The properties ofinterest are found in Reference 8.9.

Su = 69 ksi CSE-97-255

i A-SONGS-9416-1168, Rev. 01 1~ Page Cl3 of.C38 6.0 DETAILED ANALYSIS (continued) '

h Sy = 40 kai

[

1 Sy* = 31.4 ksi @ 532' F -

• Using the degradation trend methodology of the ASME Code for carbon steels,

the yield strength is decreased by 21.3 percent to account for an elevated temperature of 532' F.

c 6.5 - Loadings

Case 1:

4 I The eggerate support models described in Section 6.2 are loaded by hydraulic tube

j. loads. _ These loads, which are taken from _ Reference 8.2, are developed during a j cold leg Loss of Cooling Accident (LOCA). The LOCA condition can be postulated p to be initiated by seismic loading. Therefore, one has to evaluate the stresses in the L

eggerate structures considering the LOCA and seismic SSE loads concurrently.

l Reference 8.2 indicated that the increase in the stresses in the eggerate strips due to -

the SSE contribution to be about 4.7%. The LOCA load conditions assumed for

_ this analysis are 120% flow and 1000 tubes plugged. Reference 8.2 also states that

[ these load conditions result in 7.5% higher loads than the 107% design flow-of interest. -Due to the conservatism in the LOCA loads conditions esenmad for this i analysis, seismic SSE loads are not separately addressed r

$ Since there are partial eggerate supports on either side of the tube bundle, the horizontal LOCA~ loads are reacted such that each support takes half of the tube

[ load. Therefore, the half tube bundle model is loaded by one half the LOCA loads, i The tube reaction loads on the Numbers 9 andT10 eggerate supports are from-Reference 8.2. Only the loads for the worst time' points for each eggerate support assembly are used in this analysis. These time points correspond to .075 seconds for v

the Number 9 eggerate support, and .051 seconds for the Number 10 eggerate

- support. These cold leg LOCA loads are presented in Tables 6.1 and 6.2.

The eggerate models are loaded using the same load reduction method given in

]- Reference 8.2 whereby the loads are input at the strip intersections. The eggerate 4- models 'r.: loaded in zones with each zone representing the number of tube rows included in the appropriate tube bundle model row per Reference 8.2. Figures 6.5 I and 6.6 depict the finite element models with the boundary conditions and the loadings, along with the deformed shapes.

l' l CSE-97-255

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' A-SONGS-9416-1168, Rgv. 01

[ Page Cl4 cr C38 l 6.0 DETAILED ANALYSIS (continued) l CSEtli The degraded Number 9 eggerate support assembly (hot-side) is evaluated for two variations for this load case. The first case (Case 2A) is for LOCA+SSE loads due to

- the hot leg pipe break accident which results primarily in horizontal tensile loads on the eggerete support assembly's outer periphery, and the other case (Case 2B) is for LOCA+SSE loads due to the cold leg pipe break accident which results primarily in

{ horizontal compressive loads on the eggerate support assembly's outer periphery.

c 2

Case 2A:

4 l" The LOCA+SSE loads acting on the degraded (hot-side) Number 9 eggerate

support assembly are derived from the cold leg LOCA loads given in Table 6.1 in 4

order to better account for the distribution ofloads between the hot-side and cold-i side eggerate support assemblies as a result of a hot leg LOCA condition. A review

' ofReference 8.10 indicates that the stress results, hence the LOCA loads for hot leg LOCA condition resulted in stresses 55% of the stresses for the cold leg LOCA.

j- Therefore, the loads given in Table 6.1 are reduced to 55%_ of their values when

evaluating the effect of hot leg LOCA on the degraded (hot-side) Number 9

eggerate support assembly. The method ofloading the finite element model is the i same as described for Case 1 above.

L Case 2B:

1

[ The forces reacted by the eggerates are based on the calculation in Reference 8.2

[ for a cold leg LOCA. That calculation assumed that the corresponding eggerates i on the hot and cold sides provide parallel load prhs of equal Wfba, each of j which reacts half of the applied load. This assump6n is valid when the eggerates -

are undegraded or have slight degradation which is insufficient to affect their stitinesses significantly. However, the amount of degradation on the hot side eggerates considered la this report is sufficient to cause a significant decrease in the stiffness of the degraded eggerate and to result in a reduction in the forces which are reacted by that eggerate.

The reduction in the applied forces can be estimated by comparing the stiffhess of a degraded eggerate to an undegraded eggerate. These ~ stiffnesses can be calculated from the finite element models described in Section 6.2. Since the degraded eggerate behaves in an inelastic manner, its stiffness is dependent on the magnitude of the applied load. Consequently, it is necessary to assume a magnitude ofload on the degraded and undegraded eggerates and then confirm by calculation of the resulting stiffnesses that the assumed magnitude is conservative.

f CSE-97-255 l

" " Sis'M'< *M i

l I

6.0 DETAILED ANALYSIS (continmed)

t Table 6.3 shows a comparison of the stifthesses with 85% of the calculated reaction forces from Reference 5.2 applied in compression to the degraded

, eagerate. The table lists the calculated displacements at nodes along the

• l centerlines of a undegraded eggerate (UYi) and of a degraded oggerate (UY:). ,

l The corresponding stiffnesses (ki and km) are calculated as the inverm of the

! displacements. Then the relative reduction in the force (AF/F) on the degraded eagerate is calculated based on the relative stifthesses of the two parallel load paths.

l Table 6.3 shows that for all nodes the calculated decrease in stiffhess of the  !

i degraded eggerate is sufficient to result in a reduction in excess of 15% in the '

i reaction force. Consequently, the forces reacted on the degraded hot side oggerate i can be conservatively taken as 85% of the values calculated in Reference 8.2 or i

listed in Table 6.1. The method ofloading the finite element model is the same as described for Case 1 above, i

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CSE.97 255 I

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I A-SONGS-9416-1168 Rev.01 Page Clf of C38 6.0 p_ETAILED ANALYSIS (contimmed) 3 l

'l 1

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IM 80.

1 e w so 10 p to 16e sie i ' :o 1e

' 147 - 147

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- sm h l 3 > lcu lt20  :=

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i Figure 6.2 - No. It Eggerate Geeneetry i

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A-SONGS-9416-1168, Rev. 01 Page C20 of OS 6.0 DETAILED ANALYSIS (coatissed) 1 ANSY353 m

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i, 3.,3 we .o 4 SONGS EGGCRATE NO. 9 MODEL- BAFFLE STFFNESS MODELED Figure 6.5 - No. 9 Eggerate FEM Model Boundary Conditions and Leedings CSE-97-255

A-SONGS-94 IgRyg 6.0 DETAILED ANALYSIS feestiewed)

Ansvasa r

b ll lllJ!!!f!lllllWlIlites

'll,.ll"l[,,ll"ll,.ll"ll,,]l"llmll"ll,,y"ll,,ll"ll.ll"ll,f"ll,,ll" ll m l["l[;,;;',,I somos toocam no.to escoet Figere 6.6 - No. le Eggerate FEM Moski S:::' :, Ceeditions and Leadings CSE-97-255

- - - _ . . - = - . . . _ _ .._.. - .. -_- ... _ .-. - _..-._..

i A-SONGS-9416-1168,4 01  !

Page C22 or C38 l I

6.0 DETAILED ANALYSIS (continued) 2 t

, l Table 6.1 - Number 9 Erecrate Loads (Cold Ler LOCA)

, I Time Tube Bundle Model Row Loads fibs)  !

(Sec) 19 20 21 22 1 23 24 25 26 27 28 29 3e 31 i .075 -7.9 -5.8 -13.7 -22.3 -26.3 -26.8 -28.1 10.1 9.5 16.4 21.9 24.2 24.7 I

I i

i Table 6.2 - Number 10 Eercrate Leeds (Cold Lee LOCA) '

j Time Tube Bundle Model Row Loads (Ibs)

! (Sec) 26 27 28 29 30 31

.051 -31.0 -38.5 -36.9 -32.2 -28.1 -24.5 i

i I

l CSE-97-255 t

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A-SONGS 9416 ll68, Rev. 01 Page C23 cf C38 ,

6.0 DETAILED ANALYSIS (continued)

Table 6.3 - Effect of Eggerate Degradation on Stiffness and Applied Forces

~ '

Node y UYi UY: ki k2 (in.) (in.) (in.) (1/in.) (Ifin.)

1 44.0 0.12922 0.17976 7.74 5.56 2.176 0.164 2 45.0 0.12698 0.17757 7.88 5.63 2.244 -0.166 3 46.0 0.12363 0.17355 8.09 5.76 2.327 -0.168 4 47.0 0.11956 0.16843 8.36 5.94 2.427 -0.170 5 48.0 0.11422 0.16164 8.76 6.19 2.568 -0.172 6 49.0 0.10817 0.15397 9.24 6.49 2.750 -0.175 7 50.0 0.10098 0.14533 9.90 6.88 3.022 -0.I80 8 51.0 0.09311 0.13654 10.74 7.32 3.417 0.I89 9 52.0 0.08438 0.12881 11.85 7.76 4.087 -0.208 10 53.0 0.07510 0.12149 13.32 8.23 5.085 -0.236 11 54.0 0.06542 0.11472 15.29 8.72 6.570 -0.274 12 55.0 0.05553 0.10773 18.01 9.28 8.725 -0.320 13 56.0 0.04635 0.10005 21.58 10.00 11.582 -0.367 14 57.0 0.03777 0.09158 26.47 10.92 15.555 0.416 15 $8.0 0.03132 0.08208 31.93 12.18 19.750 -0.448 i 16 59.0 0.02585 0.07164 38.69 13.96 24.731 -0.470 17 60.0 0.02194 0.06042 45.59 16.55 29.037 -0.467 18 61.0 0.01854 0.04990 53.95 20.04 33.904 -0.458 19 62.0 0.01634 0.04474 61.21 22.35 38.854 -0.465 l

20 63.0 0.01472 0.04214 67.94 23.73 44.208 -0.482 i

21 64.0 0.01384 0.04009 72.28 24.94 47.333 -0.487 22 65.0 0.01288 0.03745 77.63 26.70 50.925 -0.488 i 23 66.0 0.01190 0.03425 84.05 29.20 54.857 -0.484

24 67.0 0.01092 0.03104 91.57 'l2.22 59.348 -0.479

] . 25 68.0 0.00974 0.02749 102.71 36.37 66.333 -0.477

! 26 69.0 0.00856 0.02398 116.83 41.70 75.127 -0.474 i 27 70.0 0.00730 0.02080 137.06 48.07 88.996 -0.481 28 71.0 0.00623 0.01777 160.52 56.28 104.232 -0.481 29 72.0 0.00524 0.01593 190.89 62.79 128.100 -0.505 30 73.0 0.00445 0.01471 224.93 68.00 156.927 -0.536 31 74.0 0.00399 0.01334 250.92 74.96 175.965 -0.540 32 75.0 0.00414 0.01209 241.42 82.71 158.711 -0.490 33 76.0 0.00450 0.01281 222.10 78.07 144.029 -0.480 where, y = distance from centerline of steam generator.

W = calculated displacement for 85% of LOCA load from Ref. 8.2.

k = relative stiffness = 1/UY.

Ak = ki - k =

2 reduction in stiffness due to degradation.

AF/F = -Ak/(k +ki 2) = change in reaction force due to decreased stiffness.

Subscripts: 1 - undegraded eggerate; 2 - degraded eggerate in compression.

CSE-97-255

A-SONGS 9416-1168, Rev 01 Page C24 of C38 7.9 RESULTS/ CONCLUSIONS j 1he results of the eggLrate support stress analysis are stress distributions in the  !

eggemse strips for the elastic analysis, and stress and strains values in the  :

eggerate strips for the elastic-plastic analysis. ANSYS General Postprocessor (POST 1) was used to examine the remits of the various stress runs that wers ,

made for the Number 9 and 10 eggerate support assemblies. t i

7.1 Number 9 Enacrate Support  !

in this design analysis, only the LOCA loads corresponding to the time point of .075 seconds is chosen for this eggerate based on the results of the earlier evaluation (Reference 8.2). As indicated in the previous sections, Number 9  ;

eggerate is evaluated for two cases, each with a different objective. -l Case 1:

The purpose of this evaluation is to show that the eggerate support structures i are highly redundant structures capable of a high degree- of load '

redistribution, even when a certain number of the strips around the periphery-- ,

- of the eggerate support stmeture are arbitrarily removed, or assumed - '

completely degraded. In order to prove this point, first, an all intact eggerate '

model stresses were obtained using conservative loading described in Section 6.5. Figure 7.1 gives the stress contour plot for the worst location for this load and geometry condition. Then, the Number 9 eggerate support assembly finite element model was modified to reflect a geornetry where every other  !

(i.e., 50%) of the 1 inch strips around the periphery are removed from service. As discussed earlier, in general, the eggerate supports are capable of load redistribution from highly stressed areas to less highly stressed areas.

The yield strength of the strip material used is 25 ksi at 532* F (Note: 1his i value, instead of the 31.4 ksi value given in Section 6.4 was used in this ,

evaluation for agreement with Reference 8.2, and . for conservatism). j Applying a shape factor of 1.5 gives a stress of 38 kai for a fully plastic strip.

The table below gives the number of strips in the first modified model stres run that meet or exceed 38 ksi., as well as the number of strips that exceed the Leai D membrane plus bending stress allowable of 1.05 Su = 1.05 x 55.0 = $7.75 ksi.

Stries Range - No. of 1 inch Strips No. of 2 inch Strips

-(ks0

>57.75 6 0 38.0 to 57.75 35 8 i CSE 97-255 9

-- .,-si,-===,,rs3.rr. -.----.mw e. .- - e - --w --.>---r--r-ww.er-,;we. . -*---.e v.m .,----,-ev. g.- - -e--w-.r- -- m,-n.m,-s- ----a-a

4 i

A-SONGS 9416-ll68' Rev. 01 l- Page C25 of C38 l

7,9 -

RESULTS/ CONCLUSIONS (Continued) s

! To demonstrate the load redistribution in the oggerate support, all 1 inch

[ strips with a stress above 38.0 kai are assumed to be inactive. The 2 inch i strips are retained to preserve the continuity of the finite element model and the loads. The results of this second modified stress run are given in the j table below.-

1 1

Stress Range No. of 1 indi Stdps No. of 2 indi Strips

! M i > 57.75 0 0 38.0 to 57.75 0 8 l

The above table shows the redistribution of the stresses which have occurred all below the 38.0 ksi range. It should be noted that the fully plastic strips have been removed from the model while in reality, these strips still carry a load compatible with their yield strength. Considering the small number of strips that are in the plastic range, an inelastic analysis of the fbli eagerate support structure would most probably show a favorable redistribution of loads.

Call 21 In this case, the eggerate geometry for the more critical eggerate support assembly (i.e., Number 9 eggerate)-is modified to reflect the strip degradation around the periphery of the eggerate stmeture based on the actual results of the visual examination. The resulting strip stresses are compared to the appropriate material allowables, in order to show that the structure can withstand the LOCA plus SSE loads, even in the degraded condition, and that the integrity of the steam generator tubes is not jeopardized. In order to reflect the results of the visual examination, all strips that connect to the support rings at the outer periphery of the eggerate structure - except for eleven (11) 2 inch strips and three (3) 1 inch strips which are only degraded to 50% of their original thickness - are degraded to 10% of their original thicknen. Since the main concern is with these degraded strips either pulling apart or buckling at the support rings, the elements representing these strips are changed to LINK 1 elements which have only membrane load carrying capability. Additionally, these elements are given elastic-plastic analysis capability via tri-linear stress-strain material properties and bi-linear (clastic-perfectly plastic) buckling pror; ties, in order to better represent the real stre.=s and load distribution expected in the CSE-97 255

9 A-SONGS-9416-1168 Rev. 01 Page C28 of C38

.- l 7.0 RESULTS/ CONCLUSIONS (Continued) .

structure. As described in Section 6.5. two vadations to this case me- ^

evaluated; one case (Case 2A) is for LOCA+SSE loads due to the hot leg

! pipe break accident which results primadly in horizontal tensile loads on the  !

l eggerate support assembly's outer periphery, and the other case (Case 2B) is  !

for LOCA+SSE loads due to the cold leg pipe break accident which results primarily in horizontal compressive loads on the oggerate support assembly's  !

outer periphery. For Case 2A, where most of the degraded strips are under tension, all 2 inch strips are changed to 1 inch strips in order to simulate the

slots in the 2 inch strips.

l Case 2A* .

The resulting strip stresses are compared to the tensile strength of the strip l

material at temperature. Additionally, the total strain (elastic p:us plastic)in the strips at the periphery of the eggerate support assembly are e leal =+ed to make sure that the resulting strains in these elements are acceptable. The

results of the stress and strain evaluations are provided below, i .

. At the Perinhery of the Ennerate

As a result of this loading condition, highest stresses and strains were i observed in the degraded strips (1 inch strips, and the 2 inch strips that are

! simulated as 1 inch stdps) around the periphery of the eggerate support

! assembly. The following table provides a summary of the membrane stresses i and the total strains (clastic plus plastic) for the ten worst stressed degraded i i

strips.

l ELEMENT No. MEMBRANE TOTAL STRAIN i

STRESS (KSI) (%)

2898 44.5 3.1 1640 44,0 2,3

. 1655 43.4 1.3 1641 43.3 1.1 3

2881 41.9 0.9 1622 41.1 0.8 2882. 38.5 0.6 2899 37.8 0.6 2880 37.0 0.5

) 1599 31.1 0.1 I ;

Maximum Strip Membrane Stress = 44.5 ksi. -< Su = 55.0 ksi. (@ 1" strip with 10% thickness remaining) l CSE-97-255

_ _ __ _ .- . _ _ _ _ _ . _ ~ _ _ _ . _ _.__ ._ _ _. . ._.. _ _ _ _ _ _ -_

i A-SONGS-9416-1168 Rev. 01

Page C21 of C38 i

i 7.0 RESULTS/ CONCLUSIONS (Continued) i

, Maximum Total Strain = 3.1 % -< Ultimate Strain = 20 % (@ 1" strip with

! 10% thickness remaining)

Appendix Cl provides detailed listing of stresses and strains for all degreded 4

strips for this case. Given the magnitude of stress and the low strain value presented above for the highest stressed degraded strips, the degraded strips

, are expected to remain intact, and the stmetural integrity of the eggerate 3 support assembly is not compromised during a hot leg LOCA+ SSE

condition.

Egr the Remainder of the Emmerate:

i Stress Range No. of I ladi Stdps No. of 2 inch Stdps ,

l (ksi) ~

(Simulated as 1 Indi Strips)

> 55.0 0 - _

0 _

Maximum Strip Stress = 30.3 ksi. -< Su = 55.0 ksi. (@ 1" strip)

Maximum Ring Stress = 37.0 ksi < l.05 Su = 1.05 x 69.0 = 72.5 ksi.

Further stress runs were made for this case, by assuming that the few strips

, at the periphery of the eggerate support assembly that have appreciable

compressive stress, are inactive. The results showed that due to the location of these elements, displacements at the end nodes of these elements are self-

! limiting, hence buckling in these strips is not of any concern. For this case, i the effect of the removal of these strips on the stresses in the remaining

{ strips at the periphery of the structure is negligible.

4 -

Case 2B:

For this case where most of the loading on the degraded strips at the periphery of the eggerate support structure is compressive, the resulting strip stresses are compared to the tensile strength of the strip material at temperature, and the total strain (clastic plus plastic) in the strips at the periphery of the eggerate support assembly are calculated to make sure that 4

the resulting strains in these elements are acceptable. Additionally, the horizontal displacements at the periphery of the assembly are calculated and compared to the minimum clearances available between the peripheral tubes and the support ring, to ensure that the structural integrity of these tubes is i not compromised. The results of these evaluations are provided below.

i Appendix Cl provides detailed listing of stresses and strains for this case.

4

+

CSE 97 255

, - - , n -.- - -.,,a-v,, ,c-., , , ,e, ,c---. , - , - . ,- - .,.-..a,., r,--,w..-, r,

A-SONGS-9416-1168, Rev. 01 Page C28 of C38 7.0 RESULTS/ CONCLUSIONS (Continued)

Maximum Compressive Strip Stress = -51.1 ksi. < Su = 55.0 ksi.

(@l" strip with 10% thickness remaining)

Maximum Total (Compressive) Strain = 13.8% < Ult. Strain = 20 %

(@ 1" strip with 10% thickness remaining)

Maximum Compressive Strip Stress @ 1" strip with 50% thickness Remaining = -26.2 ksi. < Su = 55.0 ksi.

Maximum Horizontal Displacement of Eggerate @ Outer Strips :

UY = 0.088 in. < Min. Tube / Ring Clearance = 0.132 in. (*)

l l

(*) This comparison is very conservative due to the fact that the location of the maximum horizontal displacement is different than the location of the minimum tube / ring clearance. For a better comparison, the fo!!owing table is presented for the five locations with minimum tube / ring clearance.

Row # Line # UY Minimum (Inch) Gap (Inch) 147 8 0.011 0.132 146 13 0.015 0.160 143 22 0.020 0.163 134 37 0.058 0.174 119 52 0.072 0.196 The above results indicate that, under compressive LOCA+SSE loads due to

. cold leg break accident, the eggerate stmeture with its degraded strips at the outer periphery, remains stable, and the stmetural integrity of the tubes is not compromised.

7.2 Number 10 Eggerate Support In this design analysis, only the LOCA loads corresponding to the time point of .051 seconds is chosen for this eggerate based on the results of the earlier evaluation (Refert e A.2). Number 10 eggerate is evaluated only for tie first case since the results of the visual examination showed this eggerate to be in a very healthy condition.

CSE-97-255

A-SONOS-9416-1168, Rev. 01 i Page C29 of C38 a

7.0 RESULTS/ CONCLUSIONS (Continued)

Case 1:

De purpose of this evaluation is to show that the eggerase support structures are highly redundant structures capable of a high degree of load '

redistribution, even when a certain number of the strips around the periphery of the eggerate support structure are arbitrarily removed, or assumed completely degraded. In order to prove this point, first an all intact egacrate  !

model statsses were obtained using conservative loads described in Section 6.5. Figure 7.2 gives the stress contour plot for the worst location for this load and geometry condition. %en, the Number 10 eggerate support s cably finite element model was modified to reflect a geometry where .

eye.v other (i.e.,50%) of the 1 inch strips around the periphery are removed from service. As discussed earlier, in general, the eggerate supports are capable of load redistribution from highly stressed areas to less highly stressed areas. De yield strength of the strip material is 25 ksi at 532' F (Note: Wh value, instead of the 31.4 ksi value given in Section 6.4 was used in this evaluation for agreement with Reference 8.2, and for conservadsm).

Applying a shape factor of 1.5 gives a stress of 38 ksi for a fully plasde strip.

De table below gives the number of strips in the first modified model stress run that meet or exceed 38 ksi., as well as the number of strips that exceed the Level D membrar , plus bending stress allowable of 1.05 Su = 1.05 x ,

55.0 = 57.75 ksi.

Stries Range No. of 1 inch Stdps No. of 2 indi Strips (ks0

> 57.75 5 4 38.0 to 57.75 27 23 To demonstrate the load redistribution in the eggerate support, all 1 inch strips with a stress above 38.0 ksi are assumed to be inactive. The 2 inch strips are retained to preserve the continuity of the finite element model and the loads. The results of this second modified stress run are given in the -

table below.

Striss Range No. of 1 inch Strips No. of 2 inch Stdps (ks0 '

> 57.75 0 2 38.0 to 57.75 l 0 19 CSE-97-255

A-SONGS 9416-1168, Rev. 01 1 Page C30 of C38 7.0 RESULTS/ CONCLUSIONS (Continued)

The above table shows the redistribution of the stresses which have occuned mostly below the 38.0 kai range it should be noted that the fbily plastic strips have been removed from the model while in reality, these strips still cany a load compatible with their yield strength. Considering the small number of strips that are in the plastic range, an inelastic analysb of the .

eggcrate _ support structure would most probably show a favorable )

redistribution ofloads. i 7.3 Strio to Rine Bar Welds The one inch strips are attached to 3/4" x 3/4" ring bars about the circumference of an eggerate by two 1/16" fillet welds. The objective of this calculation is to evaluate the maximum shear stress imposed on these welds. Conservatively, the applied force ( F = V ) is developed as the product of the maximum stressed strip having the least degraded area, i.e.,

F = V = A o . This force is applied to the throat area of the fillet welds to determine the shear stress. The stress intensity is then calculated and compared to the faulted condition stress allowable for the A-569 strip material.

ts' t l

v-r -

9 e

Maximum Axial Stress = o = 26.151 ksi. Compression for Eggcrate Number 9 for 1" strip with 50% thickness remaining (see Sect.7.2, Case 2B)

Area of 50% Degraded Strip = A = .5( .09 )1 = .045 in' V = F = A(e) = 1.177 kip Dimension of 1/16" Fillet Weld Throat = .0625 Sin 45' 2

Area ofTwo Fillet Welds = A. = 2( .75 ( .0625 Sin 45' ) ] = .06629 in Weld Shear Stress = t = V/A. = 17.755 ksi Stress Intensity = SI = 2t = 35.51 ksi < 0.7SU = 38.5 ksi CSE-97-255

A SONGS 94161168, Rev. 01 1 Page C31 cf C38 7.0 RESULTS/ CONCLUSIONS (Continued) i 7.4 Reacrate No.10 Suonort Welds ,

Using the analytical procedures of Rei.rence 8.14, this evaluation addresses the stresses induced in the number 10 oggerate/ baffle support 3/8" fillet welds. Number 10 eagerate is chosen for evaluation due to the higher eggcrate/ baffle support weld stresses than the Numbe 9 oggerate.

The cold leg LOCA reaction loads for eggerate number 10 from Reference 8.2 are shown in the table below. 'Ihis load is resolved into tangential forces ( Hi ), which are muhiplied by the eagerate/ baffle radial offset to determine the support moment. The stress intensity ( SI ) is then ,

calculated and compared to the faulted condition primary membrane plus l primary bending allowable for the weakest interface material, SA-515, Gr. l 70.

Eggerate No.10 Lead ( W ),Ibs :

Tube Total Load / Total Load Model No. Tubes, Tube 26 240 34.3 8232 27 215 38.5 8277.5 28 188 41.2 7745.6 29 151 42.5 6417.5 30 90 43.2 3888 31 37 44 1628

-Wa=

36188.6

• This Load is increased by 15% to account for the stiffness difference between degrahd and undegraded eggerates.

i.i:s-Y

, we

-ains an a.

t 4 ,

s.

h = sg* \ Crane ,'

7 \

t.isw ( \ A h-w v4- v y v N ' - - n m.

sONI.ons CSE-97-255

A0 SONGS-Ig, g 7.0 RESULTS/ CONCLUSIONS (Continued)

Evaluation of Eggerate / Bame Attachment Welds l

W = 36.189 kips H i= Cos(i( l.1SW ) / INiCos'44 = .944( 1.1SW ) = 39.29 kips; Where l INi = 2 '

M = LH = 44.2 in kips ; Where L = off' set = 1.125" For two 3/8" welds each 6"long :

Dimension of weld throat = .375 Sin 45'

.375 Sin 45') = 3.181 in' A

I == 2( 6p/12 ) = ( .375 Sin 45')6 ; Where h = 6" 2[ bh 2

c = 3" Z = I/c = 3.181 in' -

Weld Shear Stress = t = Hi/A = 12.351 ksi Weld Bending Stress = o = M/Z = 13.895 ksi Streu Intensity = SI = [ o' + 4t' ] = 28.342 ksl < 1.5( 0.7SUa ) =

56.3 ksi

• Mat'l = SA-515,Gr. 70; SU = 53.6 ksi 7.5 ymtical Grid Evaluation The tubes in the upper bundle are supported by a vertical grid consisting of 2 in. venical strips and horizontal bars. The venical strips are notched and welded to the base of crescent plates, which are bolted to base of three horizontal beams. The beams span the baffle diameter and are welded to it's inside surface. This assembly forms the basic structure of the " Vertical Support Grid ". The conservative objective of this evaluation is to show that a single vertical support beam assembly can sustain the total load from the highly loaded tubes passing through eggerates 9 and 10. This is accomplished by imposing the total load (89.039 kips ) on the outer most beam and comparing the induced stresses to the faulted condition stress allowables. The shear stress induced on the minimum section of the 114 attached 2 in. vertical strips is calculated, a stress intensity determined and compared to the 0.7SU faulted allowable of the strip material ( A 570, Gr. D ). Next, the shear stress imposed on the threaded shank of the 16-3/4 in. bolts connecting the crescent plate to the base of the beam is evaluated to the bolt faulted shear stress allowable.

CSE-97-255 i

A SONGS 9416-1168 Rev. 01 Page C33 cf C38 7.0 RESULTS/ CONCLUSIONS (Continued)

Vertical Grid Total Load,lbs :

ube Model No. Total Tubes Load / Tube Total Load 19 350 15.7 5495 20 ,,336 18.8 6316.8 21 326 21.6 7041.6 22 313 23.7 7418.1 23 298 26.3 7837.4 24 281 28.6 8036.6 25 313 34.2 10704.6 26 240 34.3 8232 27 215 38.5 8277.5 28 188 41.2 7745.6 29 151 42.5 6417.5 30 90 43.2 3888 31 37 44 1628 Total 89038.7

( s l

l

• *"T

,4 L

V a.ws l

l l l n.-

I j t l t  :

-[-c--

w f

\ '\ , I 1

?

c -! i i -

%  % i - 1 A y =m> r -

r law. w"Tm

, _ = ____ =_

" M- . Land j m . ,, & v _ r e _ ., -i 1 CSE-97 255

___ __ J

A-SONGS-9416-1168, Rev. 01 Page C34 of C38 7.0 RESULTS/ CONCLUSIONS (Continued)

Shear Evaluation of Vertleal Support Strips :

Number of Strips = 144 Strip Material = A 570, Gr.D Strip Thickness = t = .09 "

Efrective Minimum Width = w = .5(32 28/32 ) = .5625" Total Area = A = 144( tw) = 7.29 in Fores = F = 89.039 kips Shear Stress = t =F/A = 12.214 N Stress Intensity = SI = 2t = 24.43 ksi < 0.75U = 38.5 ksi Bolt Shear Stress Faulted Allowable :

Note : The faulted allowable shear stress for bolts is the sneller of 0.42SU or 0.6SY. However, the yield stress values at elevated temperatures for the SA-325 bolting material is not found in the Coda Using the Code method of establishing the SM allowable for Class I bolting as SY/3 and knowing the allowable stress ( S = 20.2 ksi @ 532' F ) for the bolts in question, the allowable faulted shear stress is calculated as follows:

SU = 105 ksi .

S = 20.2 = SY/3-SY = 3S = 3( 20.2 ) 60.6 ksi @ 532' F Faulted Allowable Shear Stress = 0.6SY = 36.3 ksi < 0.42SU = 44.1 ksi Shear Stress Evaluation of Bolts :

Note : The force ( 89.039 kips ) is transmitted to the tube bundle support beam by 16-3/4" bolts in single shear.

Bolt Size = 3/4" Material = SA-325 ; S = 20.2 ksi @ 532' F Threads = 3/4" - 10UNC ; Minor Diameter of External Threads = D =

.6255" 2

Total Shear Area of Bolts = A = 16 ( ( n/4 )D ) = 4.916 in' Shear Stress = t = F/A = 18.112 ksi < 0,6SY = 36.3 ksi CSE-97-255

)

A-SONGS-9416-1168.Rev 01 PappC35 of 633 (Continued) 1 sr l

SONGS EGGCRATE M. 3 m.g Figure 7.1 -Stress Centeur.% forIntact No.9 Eggrate CSE-97-255

A-SONGS-94 Igg 7.0 RESULTS/ CONCLUSIONS (Continued)

&7

&shunon i

bT ,

m . e 8

8 8

ca I

w s.

SONGS EGO g hTE_NO.10MODEL Figert 7.2 - Sims Centeur Plot for Istact No. le Eggerate CSE-97-255

A SONGS-9416-1168 Rev. 01 l

Page C31 cf C38

8.8 REFERENCES

8.1 - ANSYS Computer Program, Revision 5.3, ANSYS, Inc.,1996.

8.2 ABB-CE Report CENC-1850-1, Evaluation of Corrosion for Eggerate Tube Supports San Onofre Steam Generators, March,1989.

8.3 ABB-CE Drawing No. E 234-717, Rev.' 0, " Partial Eggemte Tube Support Assembly".

8.4 ABB-CE Drawing No. E 234-719, Rev. O, " Partial Eggerate Tube Support Assembly".

8.5 " Local Stresses in Spherical Shells from Radial or Moment Loadings", by P.

P, Bijlaard, Welding Research Supplement.

8.6 " Stresses from Radial Loads and External Moments in Cylindrical Pressure Vessels", by P. P. Bijlaard, Welding Research Supplement.

8.7 ABB-CE Drawing No. E-234-118, Rev. O, "Panial Eggcrate Tube Support Details". l 8.8 Annual Book of ASTM Standards,1993 Edition - Volume 01.03; American Society for Testing and Materials.

8.9 Ryerson Data Book - Specifications, Tolerances, Properties, Weights, Safe Loads, Machining, and Fabrication Data, Joseph T. Ryerson & Son, Inc.).

8.10. . ABB-CE Report CENC-1327, San Onofre Steam Generator, Pipe Break Analysis, May,1978.

8.11 ABB-CE DWG.: E-234-727, Rev.1, " Tube to Tubesheet Assembly -

Sectional Views" 8.12 ABB-CE DWG: E-234-712, Rev.1, " Tube Support Details "

8.13 ABB-CE DWG: E 234-725, Rev. O," Baffle and Tube Support Assembly

- Section Views" 8.14 ABB-CE Report No. CENC-1298, " Analytical Report for Southern -

California Edition San Onofre Unit No. 3 Steam Generator", September 1977.-

CSE-97-255

A-SONGS 9416-1168' Rev 01 Page C38 of C38

8.0 REFERENCES

(Continued) 8.15 ABB<E DWG.: E 234-747, Rev.0, " Tube Suppon Details" 8.16 ABB-CE DWG,: E-234-749, Rev. O, " Tube Support Details" 8.17 ABB-CE DWG.: E-234-726, Rev.1, " Tube to Tubesheet Assembly"

, 8.18 " Mechanics ofMaterials", Higdon, et al., Third Edition, John Wd' ey & Sons, Inc.,1976.

l 8.19 Fax dated May 23,1997, from Mike Wade to Don Siska and Paul Anderson, l " SG 88 Degraded Eggerate Data Maps for Eggerate # 9".

1 CSE-97-255

1 l

A SONGS-94 ? 6-1168, Rev. 01 Page Cl-1 ofCl-8 ABB - CENO PROPRIETARY ATTACHMENT C1

1. Design Analysis In Process Approvr.ls (1 page).

2. VerlGcation Plan (1 page).

3. Design Analysis Verincation Checklist (4 pages).

4. Reviewer's Comment Form (1 page).

(Copies in Q.A. Records Only)

CSE-97-255

A-SONGS-9416-1168, Rev. 01 Page C21 ofC2-1 ATTACHMENT C2 A. ANSYS Input Fdes:

1. Eggerate Number 9

• Case 1:

, e ect09m.in (Intact Eggerate Model)

• ect09m-1.in (Eggerate w/50% of 1" Strips Deleted)

• Case 2A:

• ect9pl8.in (Degrtded Strips w/ Hot Leg LOCA+SSE)

• Case 2B:

.

• ect9pl7.in (Degraded Strips w/ Cold Leg LOCA+SSE)

2. Eggerate Number 10

• Case 1:

• ect10.in (Intact Eggerate Model)

• ect10-1.in (Eggerate w/50% of 1" Strips Deleted)

B. ANSYS Output Ms:

1. Eggerate Number 9

• Cait1:

• ect09m.out (Job. I.D. = 2cj90w2)

• ect09m-1.out (Job. I.D. = 2cjf53xq)

.I

• Case 2A:

• ect9pl8 out (Job. I.D. = 2cjez7s6)

• Case 2B:

• ect9pl7.out (Job. I.D. = 2cjkrvk6)

2. Eggerate Number 10

• Case 1:

• ect10.out (Job. I.D. = 2cj6fx3w)

• ect10-1.out (Job. I.D. = 2cjfe284)

Two diskettes containing zipped files for the above list ' ' .YS Input & Output files are sent to QA files only.

CSE-97-255

l 1

A-SONGS-94161168, Rev. 01 Palw Cl-1 ofCl-11 ,

l APPENDIX C1 DETAILED RESULTS TABLES FOR DEGRADED EGGCRATE NUMBER 9 LOAD CASES 2A AND 2B CSE-97-255

A-SONGS-9416-1168, Rev. 01 Page C1-2 ofCl-11

1. Eggerate No. 9 - Case 2A Derraded Strio Membrane Strism EL12d SAEL 2898 44534.

1640 44001.

1655 43394.

1641 43252.

2881 41866.

1622 41082.

2882 38455.

( 2899 37834.

2880 36957, 1599 31087.

l 2900 29599.

l 2466 28666.

827 -28461.

2917 -23917.

2914 23894.

1668 23622, 2901 23106.

1657 22885, 1621 22654. .

1658 21932.

2902 21288.

1661 21242, 1663 21025.

1660 20967.

1659 20945.

1575 20928.

2904 20781.

1662 20750.

2903 20743.

2905 20558.

2879 19902.

2915 19785.

2906 19703.

2025 -18328.

2911 17851, 2907 17730.

2474 -17651, 2433 -17607.

1669 17491.

1654 17482.

2916 17404.

CSE-97-255

_ _ _ _ \

A-SONGS-94161168, Rev. 01 Page Cl-3 ofCl-11 EL12d SAEL t: 416 17355.

1956 17230, 773 -17046.

1598 16979, 1639 14871.

2353 14518.

liiS6 - 14458.

2475 14451, 1574 13710.

1619 13566.

2918 13284.

2897 13061.

2913 12723, 2910 12595.

1638 12355, 2827 12226.

378 -11598.

2895 10928.

270 10707.

2877 10560.

1665 10056.

2908 10029.

2765 9558.2 1425 8958.7 2854 8860.4 643 -851ts.6 1547 8498.1 -

1548 8283.1 2058 -8017.2 2797 7118.2 1664 5729.9 1620 5598.9 1653 5152.1 2079 4814.5 2912 4550.3 1652 4260,1 1361 -3390.9 2894 2850.8 440 2728.7 1519 2676.1 436 -1346.4 453 -1072.6 2081 -707.'en 2909 641.45 MINIMUM VALUES ELEM 2466 VALUE -28666.

MAXIMUM VALUES ELEM 2898 VALUE 44534.

CSE-97-255 1

A-SONGS-9416-1168, Rev. 01 Page Cl-4 ofCl-11

1. Eggerate No. 9 - Case 2A (Continued) l f

Derraded Strio Elastic and Plastic Strains 1 ELEM ELSTRAIN BJIRADi 2898 0.16617E 02 0.296625 01 1640 0.16418E-02 0.21099E 01 1655 0.16192E 02 0.11351E 01 1641 0.16139E-02 0.90690E-02 2881 0.15622E 02 0.74328E 02 1622 0.15329E-02 0.687$4E-02 2882 0.14349E 02 0.50077E-02 2899 0.14117E 02 0.45668E 02 2880 0.13790E-02 0.39435E 02 1599 0.ll600E 02 0.00000E+00 2900 0.11044E-02 0.00000E+00 2466 0.106%E-02 0.00000E+00 827 0.10620E 02 0.00000E+00 2917 0.89244E-03 0.00000E+00 2914 0.89157E-03 0.00000E+00 1668 0.8814IE-03 0.00000E+00 2901 0.86216E 03 0.00000E+00 1657 0.85393E-03 0.00000E+00 1621 0.84531E-03 0.00000E+00 1658 0.81835E 03 0.00000E+00 5

2902 0.79434E 03 0.00000E+00 1661 0.79262E-03 0.00000E+00 1663 0.78450E 03 0.00000E+00 1660 0.78234E 03 0.00000E+00 1659 0.78152E-03 0.00000E+00 1575 0.78090E 03 0.00000E+00 2904 0.77542E-03 0.00000E+00 1662 0.77426E 03 0.00000E+00 2903 0.77398E-03 0.00000E+00 2905 0.76708E 03 0.00000E+00 2879 0.74260E-03 0.0X00E+00 2915 0.73825E-03 0.00000E+00 2906 0.73518E 03 0,00000E+00 2025 -0.68386E-03 0.00000E+00 2911 0.66609E 03 0.00000E+00 2907 0.66156E 03 0.00000E+00 2474 0.65861E 03 0.00000E+00 2433 -0.656%E-03 0.00000cer00 1669 0.65263E-03 0.00000E+00 1654 0.65232E 03 0.00000E+00 2916 0.64939E 03 0.00000E+00 CSE-97-255

A-SONGS-94161163, Rev. 01 Page Cl-5 of Cl-11 i

ELEM ELSTRAIN PLSTRAIN 4

416 0.64758E 03 0.00000E400 1956 0.64293E 03 0.00000E+00 773 0.63605E 03 0.00000E+00 1598 0.63356E 03 0.00000E+00 1639 0.55488E 03 0.00000E+00 2353 0.54171E 03 0.00000E+00 1656 0.53948E-03 0.00000E+00 2475 0.53922E 03 0.00000E+00 1574 0.51158E 03 0.00000E+00 1619 0.50620E 03 0.00000E+00 2918 0.49567E 03 0.00000E400 2897 0.48737E 03 0.00000E+00 2913 0.47475E 03 0.00000E+00 2910 0.46996E-03 0.00000E+00 1638 0.46101E 03 0.00000E+00

, 2827 0.45621E 03 0.00000E+00 378 -0.43277E 03 0.00000E+00

, 2895 0.40775E-03 0.00000E+00 3'

270 0.39952E-03 0.00000E+00 2877 0.39404E 03 0.00000E+00 1665 0.37522E 03 0.00000E+00 2908 0.37422E 03 0.00000E+00 2765 0.35665E 03 0.00000E+00 1425 0.33428E-03 0.00000E+00 2854 0.33061E 03 0.00000E+00 643 0.31778E-03 0.00000E+00 1547 0.31709E 03 0.00000E+00 1548 0.30907E 03 0.00000E+00 2058 -0.29915E 03 0.00000E+00 2797 0.26561E 03 0.00000E+00 1664 0.21380E 03 0.00000E+00 1620 0.20891E OS 0.00000E+00 1653 0.19224E-03 0.00000E+00 2079 0.17964E 03 0.00000E+00 2912 0.16979E 03 0.00000E+00 1652 0.158%E-03 0.00000E+00 1361 0.12652E-03 0.00000E+00 2894 0.10637E 03 0.00000E+00 449 0.10182E 03 0.00000E+00 1519 0.99854E 04 0.00000E+00 436 -0.50240E 04 0.00000E+00 453 -0.40023E-04 0.00000E+00 2081 0.26409E-04 0.00000E+00 2909 0.23935E-04 0.00000E+00 MINIMUM VALUES ELEM 2466 1599 VALUE 0.10696E-02 0.00000E+00 MAXIMUM VALUES ELEM 2898 2898 VALUE 0.16617E-02 0.29662E-01 CSE-97-255

1 A-SONGS-9416-1168, Rev. 01 Page Cl-6 ofCl-ll

2. Eggerate No. 9 - Case 2B Deeraded Strio Membrane Stresses >

ELEM M

2898 51134, 1655 -47286, 1621 -38519, 2899 31392.

2917 -30595.

2914 -30511.

. 2915 -29504.

1668 -28074.

2913 -26151, 1669 -25581.

2916 -25183.

1665 -23672.

1656 -23544.

2907 -23544.

2879 -23564, 1663 23544.

1640 -23544, 2475 -22 % 5.

4 2911 19451, 2880 -156 % .

2353 156 % .

416 156 % .

1622 -156 % .

2908 -15696.

2433 156 % .

378 15696.

1641 -156 % .

827 15696.

2025 15696.

1599 156 % .

I 2900 -156 %.

t 2466 15696.

1657 -156 % .

1658 -156 % .

2901 -15696.

2905 -156 %.

1661 -156 %.

1662 -15696.

1575 -156 %.

2906 -15696.

1598 -156 %.

CSE-97-255

A SONGS-94161168, Rev. 01 l' Page Cl-7 ofCl-11 ELEM SAXL l 773- 15696. i

, 1956 15696.

2918 15143, 2897 -14386.

2058 13576.

1361 13273.

2910 -12534.

1619 -12402.

1574 -12243.

1664 11146, 1654 -10826.

2912 -10737.

2909 10256.

1548 9338.1 1547 -9286.6 1660 -7848.0 i- 2903 -7848.0 2765 -7848.0 2079 -7848.0 643 7848.0 2854 -7848.0 449 -7848.0 2474 7848.0 2797 -7848.0-1425 -7848.0 2827 -7848.0 2882 -7848.0 2881 -7848.0

^

1659 -7848.0 2902 -7848.0 2904 -7848.0 4 2877 -7615.0 1638 -7239.8 I 2895 -6398.1 453 -5773.8 1620 -5228.1 4

1639 -4048.9 1652 3973.9 1519 -3956.4 2081 3537.3 2894 -2715.3 1653 -2479.8 270 -1935.1 436 -395.16 MINIMUM VALUES ELEM 2898 VALUE -51134.

MAXIMUM VALUES ELEM 2353 VALUE-- 156%.

CSE-97-255

A-SONGe,-9416-1168, Rev. 01 -

Page Cl-8 ofCl-11

2. Eggerate No. 9 - Case 2B (Continued)

Derraded Strio Elastic and Plastic Strains ELEM ELSTRAIN PLSTRAIN 2898 0.19080E 02 0.13570 1655 -0.17644E-02 0.73871E 01 1621 0.14373E 02 0.50539E 02 2899 0.I1713E 02 0.53445E-01 2917 0.11416E 02 0.00000E+00 2914 -0.11385E 02 0.00000E+00 2915 0.11009E 02 0.00000E+00 1668 -0.10475E-02 0.00000E+00 2913 0.97578E-03 0.00000E+00 1669 -0.95452E 03 0.00000E+00 2916 0.93%7E-03 0.00000E+00 1665 -0.88329E-03 0.00"03E+00 16% -0.87851E 03-0.33958E-01 2907 0.87851E 03-0.51966E 02 2879 0.87851E-03-0.99887E 03 1661 -0.87851E 03-0.11581E 01 1640 -0.8785IE-03 0.73112E-01 2475 -0.8%92E 03 0.00000E+00 2911 0.72579E 03 0.00000E+00 2880 -0.58567E-03-0.16578E-01 2353 0.58%7E 03 0.43736E 02 .

416 0.58567E 03 0.ll454E-02 1622 -0.58567E 03-0.27396E 01 2908 0.58567E-03-0.59071E 03 2433 0.58567E 03 0.40631E-02 378 0.58%7E 03 0.10445E-02 1641 0.58567E 03-0.40410E 01 -

827 0.58567ti 03 0.46348E-02 2025 0.58567E-03 0.20486E 02 1599 0.58567E 03-0.25507E 02 2900 0.58567E-03 0.35064E-01 2466 0.58567E-03 0.44686F-02 1657 -0.58M7E-03 0.28346E-01 1658 -0.58567E 03 0.33049E-01 2901 -0.58M7E-03-0.30934E 01 2905 -0.58%7E-03-0.20924E-01 1661 -0.58567E-03-0.25749E-01 1662 -0.58M7E-03 0.15621E 01 1575 4.58%7E-03 0.73888E-03 2906 -0.58567E-03-0.14555E 01 1598 0.58567E-03-0.51687E-03 CSE-97-255

. - - - =_. - .-

A-SONGS-9416-1168, Rev. 01 Page Cl-9 ofCl-11 ELEM ELSTRAIN PLSTRAIN 773 0.58567E 03 0.42980E 02 1956 0.58567E43 0.21904E 03 2918 -0.5650$E-03 0.00000E+00 7

- 2897 0.53677E-03 0.00000E+00 2058 0.50658E-03 0.00000E+00 i

1361 0.49525E 03 0.00000E+00 2910 0.46768E-03 0.00000E+00 1619 -0.46277E-03 0.00000E+00

, 1574 -0.45684E-03 0.00000E+00 1664 -0.41591E 03 0.00000E+00 1654 -0.40397E 03 0.00000E400 2912 0.40065E-03 0.00000E+00 2909 -0.38268E-03 0.00000E+00 1548 -0.34844E 03 0.00000E400 1547 -0.34651E-03 0.00000E+00 1660 -0.29284E-03 0.33041E 01 2903 -0.29284E-03-0.34657E-01 2765 0.29284E-03 0.15876E 02 2079 0.29284E 03-0.10177E 02 643 0.29284E-03 0.39976E-02 2854 -0.29284E-03 0.21721E-03 449 0.292**c 03-0.88457E-03 2474 0.29284E 03 0.17581E 02 4

2797 0.29284E-03-0.12026E 03 1425 0.29284E 03-0.18485E 02 2827 0.29284E 03 0.87746E-03 2882 0.29284E-03-0.21355E-01 2881 0.29284E-03 0.28468E 01 i 1659 -0.29284E-03-0.35358E-01 4 2902 0.29284E-03 0.34778E-01 2904 -0.29284E-03 0.30079E-01 2877 -0.28414E-03 0.00000E+00 1638 -0.27014E-03 0.00000E+00 2895 -0.23873E-03-0.I1862E-04 453 -0.21544E-03 0.00000E+00 1620 -0.19508E-03 0.00000E+00 1639 -0.15108E-03 0.00000E+00 1652 0.14828E 03 0.00000E+00 1519 0.14763E 03 0.00000E+00 2081 0.13199E-03 0.00000E+00 2894 0.10132E-03 0.00000E+00 1653 0.9253IE-04 0.00000E+00 270 -0.72207E-04 0.00000E+00 436 -0.14745E-04 0.00000E+00 MINIMUM VALUES ELEM 2898 2898

' VALUE 0.19080E 02 0.13570 MAXIMUM VALUES ELEM 2353 827 VALUE 0.58567E-03 0.46348E-02 CSE-97-255

)

l

A-SONGS-94161168, Rev. 01 Page Cl-10 ofCl-11

2. Eggerate No. 9 - Case 2B (Continued)

Nodal Disolacements at Peripheral Strios NODE 13. lH_ BQIZ 32 0.00000E+00 0.12091E 010.54455E 03 33 0.00000E+00 0.12809E-010.14288E-02 65 -0.16248E 03 0.12264E 010.31295E 03 98 0.32%1E 03 0.12994E 010.10490E 02 99 0.40775E-03 0.10286E-010.15133E-02 131 0.90009E 03 0.11569E 010.78165E 03 164 0.12226E-02 0.12181E-010.44938E 03 197 0.17126E-02 0.ll261E-010.81592E-03 230 0.1971lE-02 0.11787E-010.12989E-02 263 0.21741E-02 0.11056E 010.43808E-03 296 0.25198E-02 0.11718E-010.35897E-03 329 0.27458E 02 0.lll39E-010.35660E-03 362 0.3530$E 02 0.12606E-010.27237E-02 394 0.44163E 02 0.14249E-010.48094E 04 428 0.42174E 02 0.14449E-010.13172E-02 460 0.52467E-02 0.16244E 010.17086E-02 494 0.49183E-02 0.16744E-010.ll199E 02 526 0.58995E-02 0.18313E-010.11524E-02 559 0.69068E-02 0.19937E 010.20509E-02 592 0,66641E-02 0.19055E-010.13939E-02 625 0.75357E-02 0.20451E-010.11787E-02 657 0.83026E-02 0.21664E 010.63305E-03 690 0.79423E-02 0.20941E-01-0.22713E-02 691 0.71531E-02 0.I8273E 010.I8370E 02 723 0.83147E-02 0.20150E-010.25443E-03 756 0.75564E-02 0.IS747E-010.27168E-02 788 0.64017E-02 0.16658E-01-0.13312E 02 822 0.60975E-02 0.15877E-010.4665IE 02 854 0.12380E-010.26558E-010.11736E 01 887 0.17136E 010.34604E 010.48513E 02 919 0.20552E-010.40282E-010.59992E 02 952 0.23245E-010.44706E-010.17519E-02 953 0.24922E-010.44444E-01-0.16525E-02 985 0.24147E 010.42983E-01-0.16525E-02 1018 0.26312E-010.46576E-010.73356E 02 1050 028913E-010.50925E 010.93144E 04 1083 0.30602E-010.53639E-010.44990E-02 1115 0.31798E-010.55498E-01-0.13807E-02 1116 0.30%8E-010.51302E-010.21073E-02 1148 0.33197E-010.57739E-010.49414E 02 1149 0.32506E-010.53938E-010.18944E-02 1181 0.34117E 010.56662E-010.19400E-02 1214 0.35178E-010.58459E-010.323%E-02 1246 0.39806E-010.66357E-010.88338E-02 1279 0.43546E-010.72722E-010.34923E-02 1311 0.46195E 010.77137E-010.46059E-02 1344 0.48499E-010.80945E 010.22460E-02 CSE-97-255

A-SONGS-9416-1168, Rev. 01 Page Cl-11 ofCl-11 NODE IIK. IlY. RQ12 1376 0.50395E 010.84015E-010.30768E-02 1409 0.51845E 010.86310E 010.87150E 03 -

1441 0.52664E 010.87495E 010.96925E-03 1474 0.53102E-010.88023E 010.47903E 03 1506 0.52928E 010.87486E-010.10837E-02 539 0.52312E-010.86191E-010.17809E-02 1571 0.51403E-010.84388E 010.22694E 02 1604 0.50246E-010.82156E-010.25795E 02 1636 0.48683E-010.79214E-010.37140E-02 1669 0.46788E 010.75705E-010.34142E-02 1701 0.44765E-010.71994E-01-0.47435E-02 i 1733 0.40027E 010.67336E 01-0.30681E-02 1734 0.42408E-010.676%E-010.32459E-02 1765 0.38619E-010.64735E 010.26812E-02 1766 0.41409E 010.65714E-010.17827E-02 1798 0.36738E-010.61312E-010.45746E-02 1830 0.34742E-010.57690E 01-0.31405E-02 1863 0.32293E-010.53266E 01-0.60955E-02 1894 0.25715E 010.45889E 010.46323E-02 l 1895 0.2%81E-010.48557E-010.37970E 02 1927 0.23380E 010.41688E 010.39059E-02 192. 1.269'0E-010.43604E-01 0.40811E-02 19.~ .4E-010.37572E-01-0.44262E-02 l

1991 v .as/8E-010.33789E-010.37449E-02 2023 0.53822E-010.28186E-010.28825E-02

,. 2024 0.16668E-010.29667E 010.43888E 02 4 2056 0.11639E 010.242%E-01-0.52451E-02 2087 0.66806E-02 0.I8990E-01-0.31158E 02 2088 0.94648E-02 0.20420E-010.28494E-02 2120 0.50966E-02 0.16132E 010.28498E-02 2121 0.76306E-02 0.1713IE 01-0.28%1E-02 2152 0.34239E-02 0.13127E-01-0.32497E-02 2184 0.30ll3E-03 0.10388E-01-0.19314E 02 2185 0.19576E-02 0.1048IE-01-0.23198E-02 2216 -0.5834IE 03 0.87547E-02 0.1705IE-02 2248 -0.31703E-02 0.68098E-02-0.16559E-02 2249 -0.15148E 02 0.70288E 02-0.17882E-02 2279 0.53171E 02 0.42133E-02-0.82578E-03 2280 -0.42554E 02 0.49146E-02-0.19246E 02 2312 -0.58506E 02 0.32308E-02-0.12635E 02 2313 0.50421E-02 0.35428E-02-0.10370E-02 2344 -0.48601E 02 0.26762E-02-0.13684E-02 MAXIMUM ABSOLUTE VALUES NODE 1474 1474 854 VALUE 0.53102E-010.88023E-010.11736E-01 CSE-97-255

A-SONGS-9416-1168, Rev 01 Page D-1 of D-39

SUMMARY

OF CONTENTS Calculation 3.2 Pages Appendices 11 Pages Attachments .Q0.Pages

THERMAL-HYDRAULIC ANALYSIS OF THE SOUTHERN CALIFORNIA EDISON SAN ONOFRE NUCLEAR GENERATING STATION UNIT 3 STEAM GENERATORS WITH DEGRADED EGGCRATES A-SONGS-9416-1168, REV. 01 (ATTACHMENT D)

Quality Class

X QC-1 (Safety-Related)

PURPOSE: To evaluate steam generator performance with clean tubes and degraded eggerates.

This Design Analysis is complete and verified. Management authorizes the use ofits results.

PREPARED BY: N. U. Karim / 4A DATE: @- 2&- 97 VERIFICATION STATUS: COMPLETE The Safety-Related design information contained in this document has been verified to be correct by means of Design Revi"w using Chwklist in QF-3 A of QPM-101.

Name J. G Thakkar Signa .7d44/ DateN- 2f-47 Independent Reviewers #

APPROVED BY: D P. Siska DATE P-AP-97 ABB COMBUSTION ENGINEERING CHATTANOOGA, TENNESSEE

' Ibis document is the property of ABB/ Combustion Engineering, Chattanooga, Tennessee, and is to be used only for the purposes of the agreement with ABB/CE pursuant to which it is furnished.

CSE-97-253

. - . . . - _ - - _ _ . . . _ . _ _ . _ _ . - - . - - . - . - ~ _ . . . . - .

1 A-SONGS-9416 ll68, Rev. 01 l

. Page D-2 of D-39 l l l

RECORD OF REVISIONS  !

4 4

NUMBER ~ DATEISSUED PARAGRAPH (s): PREPARED - INDEPENDENT APPROVED

-INVOLVED BY REVIEWERS -- 'BY-l 0 6/04/97 OriginalIssue J.G. Thakkar J.C Lowry D.P. Siska N.U. Kanm J.R. Schwall l Included additional data N.U. Kanm J.G. Thakkar D.P. Siska l

l 1 8/28/97 for tube Row 110 (Table 6-13) . Table 6-13 ,-

p,pej)gg h I

became 6-14. 1 j 8- 2fd2

?-27 47 f4.f'I7 1

i t

J 4

I l

,, 1 CSE-97-253

A-SONGS-9416-1168, Rev. 01 Page D-3 Cf D.39 TABLE OF CONTENTS SECTION East 1.0 OBJECTIVE OF THE DESIGN ANALYSIS ........................................................ 4 1.1 Background Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Reason for the Design Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Applicability and Intended Use of the Analysis Results.................................... 5 2.0 ASSESSMENT OF SIGNIFICANT CHANGES IN PERFORMANCE ........................ 6 3.0 ANALYTICAL TECHNIQUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1 ATHOS3 and ATH OSGPP3 Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 7 3.2 ATH OS 3 M odel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 M ethodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.0 S ELECTION OF DESIG N INPUTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 5.0 ASS U MIrrlONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 6.0 RESULTS..................................................................................................17 6.1 Steam Generator with Degraded Eggerates .................................................. 17 6.2 Fluid Dynamic Data for Flow Induced Vibmtion Analysis................................ 18 6.3 Steam Generator Performance with Tube and Eggerate Fouling .........................19 7.0 CONCLU SION S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8.0 REFEREN C ES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9.0 APPENDIX A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A l A. QPM-101 Approvals, Checklists and Results of Review.................................. ..Al Design Analysis In-process Approvals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A2 Continge ncies and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A3 Verification Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A4 Design Analyses Verification Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A5 Reviewer's Comment Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A9 AP P ENDIX B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l. . . . . .-B1 B. Computer input / output files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B2 l CSE-97-253

A-SONGS-9416 ll68, Rev. 01 Page D-4 of D-39 1.0 OIUECTIVE OF THE DESIGN ANALYSIS 1.1 Ra@rotmd Information

. De San Onofre Nuclear Generating Station (SONGS) Unit 3 steam generators have experienced tube surface and eggerate (EC) tube support fouling during a recent operating period. De secondary side visual and Eddy Current inspections indicate degradation of the eggerate strips. The degradation is limited to EC04 through EC10 in the outermost and innermost regions of the tube bundle (Reference 1). The eggerate degradation is believed to be due to a flow accelerated corrosion phenomena. Further investigations of the phenomena at SONGS Unit 3 and other plants is currently in progress (Reference 2),

ne San Onofre Nuclear Generating Station (SONGS) Units 2 and 3 steam generators have also experienced a loss of pressure at full power over several cycles of operaticn. For i

instance, between Cycle 4 (1989) and Cycle 8 (1995), the Unit 3 Steam Generator 1 average pressure decreased from 918.8 to 847.0 psia (Reference 3). The fouling of steam generator tubes occurring over a number of years of plant operation can cause a substantial decrease in steam generator pressure as evxlenced by the operatmg history of this unit from Cycles 4 through 8.

Fouling of tube surfaces and tube supports also increases resistance to the secondary flow. In the Virginia Power Surry Unit 2 steam generators, accumulated corrosion deposits in the upper level of the quatrefoil tube-to-tube support intersections resulted in excessive pressure drops and fluctuations across these areas (Reference 4). Such a high level of accumulations not only causes steam pressure decrease but also tube degradation and operational difficulties such as water level oscillations.

1.2 Reason for the Desien Analysis The thermal-hydraulic analyses presented in this report address the SONGS Unit 3 full power steam generator operation for Cycle 8, steam generator performance with various combinations of assumed tube surface and eggerate fouling, and the expected Cycle 9 steam generator performance with clean tubes and degraded eggerates. The primary objecuves are:

. To evaluate the Cycle 9 fluid dynamic conditions experienced by the outer periphery tubes where the eggerate degradation is observed. The ATHOS3 calculated secondary side fluid velocities, densities and dynamic viscosities as well as the primary fluid densities are used as an input for the flow induced vibration analysis of the tube bundle with degraded q eggerates (Attachment A). )

• To support additional limited evaluations performed by Southern California Edison (SCE) ,

with the Cycle 8 operating conditions and three different tube bundle fouling assumptions to better understand the eggerate degradation phenomena. Also, an analytical assessment of eggerate erosion phenomena is in progress using the ABB-CENO proprietary model q (Reference 2).

CSE-97-253

A-SONGS-9416-Il68, Rev. 01 Page D-5 of D-39 4

1.3 Anolicshility and Intendad Use of the Analysis Recults lhe ATHOS3 code is utilized to simulate the Cycle 9 steam generator thermal-hydraulic cimracieristics with a chemically cleaned tube bundle. The steam generator cruing conditions for Cycle 9 are asenmed to be the same as Cycle 4, when the plant was operating with the average steam pressure of 918.8 psia and the downward trend in the steam pressure was not evident. Also, for the post-chemically cleaned steam generator, average eggerate strip erosion of 20% (decreased strip thickness from 0.09 inches to 0.072 inches) is assumed for tMs analysis.

The ATHOS3 calenimaA thermal-hydraulic parameters for the Cycle 9 operating conditions are provided as input for the flow induced vibration analysis of the tube bundle with degraded eggerates.

4 4

9 l

CSE-97-253 i

A-SONGS-9416-1168, Rev. 01 Page D-6 of D 39 2.0 ASSESSMENT OF SIGNIFICANT CHANGES IN PERFORMANCE The observed eggerate erosion at the inner and outer most periphery of the tube bundle does not significantly affect the over all thermal-hydraulic characteristics of the steam generators.

Also, as a result of the chemical cleaning, the Unit 3 steam generators are expected to recover steam pressure and operate closer to the original design pressure of 900 psia than was experienced during Cycle 8 when the tube surface fouling caused an approximately 70 psi reduction in steam pressure. The erosion of the eggerate strips, however, may affect the local flow conditions and thus the flow induced loading on the tubes. The details of the Cow induced vibration analysis are provided in Attachment A.

I i

I CSE-97-253

A SONGS-9416-Il68, Rev. 01 Page D 7 cf D-3.6 i

. 3.0 ANALYTICAL TECHNIQUE

'the thermal-hydraulic analysis of the SONGS Unit 3 Steam Generator 1 is performed using the ATHOS and ATHOSGPP Version 3 Mod 01 computer codes (Reference 5).

3.1 ATHOS3 and ATHOSGPP3 Codes 4

ATHOS3 (Analysis of the Ibermal-Hydraulics Of Steam Generators) is a three-dimensional,

tw@, steady state and transient computer code for thermal-hydraulic analysis of recirculating U-tube steam generators. It was created by upgrading an earlier code, ATHOS

(Reference 6) which had been developed for the Electric Power Research Institute (EPRI) by e CHAM of North America. A' more detailed desmytion of the aM+-Al and physical models, finite <lifiererce equations, the mde structure and solution procedure is presented in Reference 6. ATHOS3 (Reference 7) has been developed for EPRI by the CFD Research

{ Corporation. 'Ihe most recent improvements irggan.=4 into ATHOSGPP3 (the AT!!OS3 Geometry Pre-Processor program) include the geometry representative of anti-vibration bars in the U-bend region of the steam generators, the refinement of the geometry representative of tubes, te rods and other structures to improve the accuracy of the velocity field calculation, and the optional extension of the grid to include the downemer and spiuivis to improve the codes capability to simulate steam generator operation at low power. 'Ihe ATHOS3 and ATHOSGPP3 computer codes have been verifed and validated in accordance with the applicable ABB CENO quality assurance procedures as described in Reference 8.

3.2 ATHOS3 Model

'Ihe ATHOS model of the SONGS Unit 3 Steam Generator 1 includes speciEcations for the geometric details, transport conclations, and operating conditions. Details of geometric specifications are input to the ATHOS3 Geometry Pre-Processor (ATHOSGPP3) code. The

==ry geometric data include the followmg:

1. Finite-difference grid.

2. Shell and shroud dimensions.

3. Tube bundle details.

4. Tube dimensions and number of tubes in each row.

5. Locations of the plugged, sleeved, and temoved tubes in each tube row.

6. Locations and characteristics of tube supports.

7. In:ation and characteristics of steam separators.

The ATHOSGPP program processes these data and generates the geometric parameters ,,

utiliud by the ATHOS code. The finite-difference grid selected for the SONGS Uni 3 steam generator ATHOS model is 18 x 15 x 32 in the circumferential (0), radial (R) and axial (Z) directions, respectively.

CSE-97-253

..-____._.__m.

A-SONGS 9416 il68 Rev. 01 L . . _ . . . .

Page D 8 of D-39

A secondary fluid flow diagram of the SONGS Unit 3 steam genemsor is depicted in Figure 3-

. 1. De steam generator schematic with dimensions used in the ATHOS3 model is shown in l . Figure 3-2. De finite difference grid is illustrated in Figure 3-3. The SONGS Unit 3 Seam-

!T Gecerssor 1 is modeled with 322 plugged tubes. The plugged tube tacminns are obtained ,

L from Reference 9. De ADIOS 3 model includes 161 plugged tubes per one-half steam  !

l generator, which are identified in Figure 3 4. . De ATHOS3 code treats these blocked tubes L as offering flow resistance without capability to tramport the primary fluid or to transfer heat.

i Due to thermal-hydraulic symmetry, the ATHOS3 code models one-half of the steam i

generator,90 degrees of the hot and cold skies each. The ATHOS3 model of the SONGS Unit 3 steam generator consists of 8640 nodes or cells and is considered adequate for investigating the Cycle 8 as well as v~I Cycle 9 performance.

3.3 Methodology t The ATHOS3 code has the capability for computing the steady state and time dependent

! behavior of thermal-hydraulic behavior of Pressurized Water Reactor (PWR) steam .

generators.

l

! Cycle 9 with Clean Tub: Bundle and Degraded Eggerates i

i ne ATHCS3 code is utilized to calculate the steady state primary and secondary side thermal- '

! hydraulic pa ameters for clean tubes and degraded eggerate mnditions. As a result of erosion

{ and chemicd cleaning h is assumed that the eggerate strip thickness has been uniformly

reduced by 20 percent from 90 mils to 72 mils. As a result, the approach area (the secondary l side flow area in the tube bundle) to the device area (the flow area through the eggerates) ratio increases from 0.6 to 0.68.- His requires the following ch== in the ATHOS3 model: .

j

!

• De area density of eggerate mesh, ADENME, input in the ATHOSGPP3 code changes by approximately 20 percem.

i * . The eggerase pressure loss factor which includes the losses due to flow area reduction,

area expansion, and friction decreases. De ATHOS3 input value of CLEGC clanges by 4 sixteen percent.

1 Cycle 8 with Tube Bundle and Eggerate Fouling '

[

~

Hree cases are considered to provide input for a SCE root cause evaluation to assess the causes of eggerate erosion. De analyses consist of simulation of the Cycle 8 steam generator operatmg conditiom with the followmg assumed tube surface and eggerate strip fouling.

l l Case 1: Uniform tube surface fouling of 12 mils and the eggerate strip surface fouling

? of 5 mils at EC01 and EC05 through EC10.

i ..

i - For this case the tube outer diameter, DIATUB, in the ATHOSGPP3 input data increases from 0.75 to 0.774 inches and the ADENME for EC01 and ECOS through EC10 changes l by approxirately five percent. De increase in the tube diameter decreases the flow area j available to die secondary side fluid from approximately 49.0 percent to 45.4 percent of the 4

- A. SONGS 9416 Il68 Rev. 01

]. Page D 9 of D-39

! tomi area in the vertical section of the tube bundle, in the U-bend _ region the area reduction is i

! from 70.6 to 68.7 percent of the total area. )

j "Ihe CLEGC in the ATHOS3 input data changes for all eggerates. 'Ihe uniform increase in tube diameer also increases the secondary side heat transfer anta in the tube bundle. Also, the i differences in the thermal conductivity between the fouling material, mostly iron oxide, and the tube amerial, inconel 600, causes a reduction in the composite thermal conductivity from 10.84 for inconel 600 to 5.94 Btu /br-ft *F for the tube with 12 mils of' corrosion. - The

! ATHOS3 analysis'with the composite thermal conductivity of 5.94 Bru/hr-ft 'F did not match the measured primary side temperatures. Hence,' the ATHOS3 results indicate that either the l thermal Maivity of 2 Bru/hr-ft *F for the fouling surface or the uniform 12 mils thickness i for tube fouling assumed for the analysis are mconsistent with the measured primary temperatures and steam pressure. The ATHOS3 analysis for this and the other two subsequent ,

l cases are analyzed with the Inconel 600 conductivity and the fouling resistance value to match

! the measured plant data for the primary fluid hot and cold leg temperatures as well as the

steam pressure.

Case 2

Uniform tube surface fouling of 12 mils and the eggerate strip surface fouling i of 24 mils or 12 mils on each side for all ten eggerates.

For this case the tube ouer diameter, DIATUB, in the ATHOSGPP3 input data increases

from 0.75 to 0.774 inches and the ADENME for EC01 through EC10 changes by

! approximately 25 percent. The decreases in the secondary side flow areas in the vertical and U-bend regions of the tube bundle are the same as Case 1.

I The CLEGC in the ATHOS3 input data changes from the asAig=1 eggerates. The uniform

) increase in tube diameter also increases the mehy side heat transfer area in the tube j bundle.

! Case 3: Uniform tube surface fouling of 20 mils and the eggerate strip surface fouling of 40 mils or 20 mils on each side for all ten eggerates.

l

! For this case the tube outer diameter, DIATUB, in the ATHOSGPP3 input data increases

from 0.75_ to 0.79 inches and the ADENME for EC01 through EC10 changes by

approximately forty percent. The seccialmy side flow areas in the verucal and U-bend regions F . of the tube bundle are 43.1 and 67.0 percent of the total areas, respectively.

5

! The CLEGC in the ATHOS3 input data increases by approximately 100 percent from the as-l designed eggerate . The uniform increase in tube diameter also increases the secondary side 4

heat transfer area in the tube bundle.

m 9

I i

CSE 97-253 I

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CSE-97-253

A SONGS-9416-Il68, Rev. 01 -

Page D 12 of D 39

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VERTICAL NODAUZATION Figure 3-3 ATHOS Model of the SONGS Steam Gererator CSE-97-253

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A-SONGS-9416-1168 Rev. 01 Page D-13 of D-39 SCE-SAN ON0fR[ (NTS 2 AND 3 SIfMI CENERATOR ATH0S 3 WODEL e FilECEITIUBE - SC88 (NOMBER 1993) v E e g .2, ee . .. ........_...............y .

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Figure 3-4 ATIIOS Model of the SONGS Unit 3 Steam Generator Tube Bundle - IIorizontal Nodalization CSE-97-253 i

_. _, - - _ . -. . . . - _ _ _ .- - ~ _ - _. . .

l A SONGS-9416-Il68, Rev. 01 Page D-14 of D-39 4.0 SEIECTION OF DESIGN 1h7UTS

. In performing the thermal-hydraulic analysis, the SONGS Unit 3 steam generator geometry is pertinent in defining the ATHOS model as part of the design input. This information is obtained from the following drawings in Reference 14:

E-234-690-01, April 1976, " General Arrangement and Assembly - Elevation" E-234-694-01, May 1973, " Tube Sheet Drilling Patterns" E-234-721-00, January 1974, "Eggerate Tube Support Assembly"

) E-234-717-00, January 1974, " Partial Eggerate Tube Support Assembly" E-234-719-00, January 1974, " Partial Eggerate Tube Support Assembly" E-235-161-00, December 1973, " Partial Eggerate Tube Support Assembly" E-2464)02-05, February 1973, " Steam Separators

• E-246-026-01, December 1973, " Separator Support Casting" The Unit 3 Steam Generator 1 operating conditions are also rwy for the design input and they are utilized in the ATHOS3 simulations. The expected operating conditions for Cycle 9

, and Cycle 8 steam generator operating conditions with the assumed tube bundle and eggerate conusion levels are describui in Table 4-1. The steam generator operating conditions in Table 4-1 are obtained from References 3 and 10. The pressure loss factors and the friction factors are obtained from the formulas and curves provided in Reference 11. The thermodynamic and physical properties of the primary and secondary fluids are obtained from Reference 12.

The physical properties of the Inconel 600 are obtained from Reference 13.

l e

o a

i CSE-97-253

A SONGS-9416-1168, Rev,01 Page D-15 of D-39 l Table 4-1 SONGS Unit 3 STEAM GENERATOR FULL POWER OPERATING CONDITIONS (Rderences 3 and 10)

Plas Parameters Design Cycle 4 Cyde8 Cycle 9 Sanranon Pressure, psia 900 918.8 846.% 918.8

-(4/5-7/10/89) (10/11/95) June '97 - Feb. '99 (ExpectaD Smam Flow Rate,Itun'br 7.565 x 10' 7.339 x 10' 7.297 x 10' 7.339 x 10' Feedwater T< .. - - e, *F 445 422 422 422 Pnmary Pressure, psia 2250 2250 2250 2250 Prunary Flow Rate, Itun'br 74 x 10' 78.2 x 10' 78.2 x 10' 78.2 x 10' Prunary Hotleg T%cume, F 611 605.60 605.79 605.60 Prunary ColdlegTPenn, F 553 553.18 552.20 553.18 1

9%

CSE-97-253

- - . . - -- _. - . - ~. -

A-SONGS-9416-1168, Rev. 01 Page D-16 of D-39 l 5.0 ASSUMPTIONS The following assumptions are utilized in pufunning the thermal-hydraulic analysis for the SONGS Unit 3 Steam Cenerator 1.

1. The ATHOS3 model includes 161 plugged tubes per one-half steam generator. The plugging locations are based on Reference 9.

2. The steam generator operating conditions are those listed in Table 4-1 (References 3 and 10).

' 3. The primary flow rate, at 100 percent power, is assumed to remain constant at the value in Table 4-1 (78.198 x 10' Ibm /hr per steam generator) for Cycles 4 through 9.

! 4. 'Ihe carry-over and carry-under values used for the ATHOS analyses are for nominal design

conditions.

5. 'Ihe normal water level of 36.552 feet above the tubesheet is assumed for all cases.

6. 'Ihe two-phase flow on the secondary side is homogeneous, which is one of the options of

, ATHOS3. The homogeneous two-phase flow model is adequate to investigate the effects of eggerate erosion and tube outer surfa:e and eggerate strip fouling.

7. Tube fouling on the primary side is assumed to be negligible.

8. As a result of the chemical cleaning, the Unit 3 steam generators are expected to recover approximately 70 psi of steam pressure and operate at the similar conditions as Cycle 4, prior to the observed pressure reduction phenomena.

9. For the post-chemically cleaned Cycle 9 operation, the tubes are assumed to be free of tube outside surface fouling and the eggerate strips are assumed to have a 20 percent decreased thickness, from 90 mils to 72 mils.

s

}

. CSE-97-253

_ . - . _ _ _ _ _ . _ . _ _ _ _ _ . _ _ _ _ _ _ ~ _ _ . _ . . _ _ _ . . . _ ___ _ _ _ _ _ _ _ _ . _ _ _ _

l l

l A-SONGS-9416 tl68, Rev. '01 -

Page D-17 of D-39 l 6.0 RESUL'IS l The following ATHOS3 results have been obtained for Cycle 9 with degraded eggerates, and Cycle 8 with three diflerent amnwl lev;;1s of corrosion at the full power operating conditions.

'Ihe Cycle 9 operating conditions are assumed to be the same as the pre-steam pressure reduction operation during Cycle 4. The operating conditions are presented in Table 4-1.

! 6.1 Stamm Generator Performance with Deerwlad up=

A summary of Unit 3 Steam Generator 1 ;..rformance data is presented in Table 6-1. For F Cycle 4, the plant data listed represents averages for the early part of the cycle before a downward trend in steam generator pressure is evident. A combination of the lowest steam

[

generator pressure and highest power level is the basis for selectmg plant data for Cycle 8 (Reference 10). For Cycle 9, the tube bundle is assumed to be clean and it is ex=wl that

the op.ing conditions will be similar to Cycle 4.

] 'Ihe same ATHOS3 geometry model with 161 plugged tubes per one-half steam generator is used for all analyses. Some of the cW ing plant data needed for ATHOS3 input are not available at each analysis point. 'Ibese data are listed as " common input' and ' input data' in j Table 6-1 and are the same for each cycle. Besides the values for carry-under and carry-over, the input data consist of the primary fluid pressure, the primary flow rate, the feed water

! temperature, and the dowrmmer water level.

In Table 61, the ATHOS3 results for cycles 4 and 8 are obtained from Reference 10. For

- Cycle 9 the over-all thermal-bydraulic performance is similar to Cycle 4. The circulation ratio

increases slightly, from 3.09 to 3.13, due to the assumed eacrate erosion. The primary

! temperatures for Cycle 9 are approximately 3 'F higher, because the iriitial positive effects of fouling such as additional nucleation sites and mereased turbulence are not included in the

. Cycle 9 performance analysis.

'Ihe secondary side v+ city vectors at the tubesheet and the tube support elevations are

, depicted in Figure 6-1. The dominant flow direction is axial, except at the downcomer entrance region. The velocities are higher on the hot leg side and they increase as a function

[ of the elevauon. The highest velocities are in the tube lane region and above eggerate EC10.

• At this elevauon, the frictional effects are minimum because of the fewer number of tubes.

, On the cold side, the velocities are low because of lower heat flux and higher secondary side j fluid densities. Figure 6-2 illustrates the velocity vectors at IY=15, in the annular gap

between the tube bundle and the shroud (wrapper). The velocity magninwie is very small at

eggerate locations EC03, ECOS, and EC(T/ through EC10 because the flow deflectors obstruct i the upward direction flow. Figure 6-3 shows the color plot of the axial velocity surface. 'Ihe

{ numerical values of the axial velocities at IY=15 are also provided in Table 6-14. The axial l

} - velocities are less than 10 ft/sec in-the vertical tube region. In the U-bend region, the i

1-i CSE-97 253

- . _ . _ _ . _ _ _ . _ - . _ _ _ _ . _ _ _ _ , .~ ... _. _ __

i A-SONGS-9416-1168, Rev. 01 Page D-18 of D-39 l 4

velocities are higher in vicinity of the tube lane as there is less frictional resistance to the flow j W~ the number of tubes as a function of elevation decreases.

6.2 Fluid Dvnnmic Data for Flow Indivwi Vibrntinn Analysis t

j De primary objective of this analysis is to provide the primary and Mry fluid parameters needed for the flow induced vibration (FIV) evaluations of the tubes lamwi in the i degraded eggerate regiom. The tubes in the outer periphery of the hot side bundle are

identified as the most susceptible tubes. De ATHOS3 calculated secerniery side fluid density, dynamic viscosity and velocity components, as well as the primary side fluid demity at IY=14, as a function of elevation, are provided in Tables 6-2 through 6-13. De secondary l

fluid densities are calculated as function of void fraccon, tiu dynamic viscosities are a function of quality and the sub-cooled prunary fluid densities are a furvii;c of temperature.

The ATHOS3 muitawd radial and circumferential velocity cuupoitents are used to abi1=*

the gap velocities in the swdve direcuons. These two components are perpendWilar to the 4

tubes in the vertical tube sections. De gap velocities are obtained as follows:

i l

Vaxp = V Amos (POR Amos / PORoxp) i

VGAP

Gap velocity component for FIV input j V Amos: ATHOS3 calculated velocity component PORAmos: ATHOGPP3 calculated porosity for the node

! PORAmos ~ 0.77 in the Radial direction j PORAmos - 0.54 in the Circumferential direcuon PORoxp: Tube gap porosity, (P-D)/P=0.25, minimum flow area between the tubes j P: Tube pitch, P=1.0 Inches for the SONGS tube bundle i D: Tube outside diameter, D=0.75 Inches for the SONGS tube bundle his meth:xi is conservative because the velocity is increased by a ratio of the porosity as i shown above. De equation conserves mass; however, the increase in pressure drop associated with an increase in velocity by a factor of three is not accounted for, which may i reduce the gap velocity as the momentum is conserved in all three directions.

4 4

i i

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1 I

e C:ui-97 253 m . w-7

. A-SONGS-9416-1168, Rev,01 Page D-19 of D-39 l 1

6.3 Staam Generator Pefwounce with Tube and hocrate Fouline Three cases are considered to assess the causes of eggerate erosion. The analyses consist of l simulation of the Cycle 8 steam gene 13 tor operatmg conditions with the assumed tube surface and eggerate strip fouling:

Case 1:

Uniform tube surface fouling of 12 mils and the eggcrate strip surface fouling of 5 mils at i EC01 and ECOS through EC10.

a Case 2:

j Uniform tube surface fouling of 12 mils and the eggerate strip surface fouling of 24 mils or 12 mils on each side for all ten eggerates.

Case 3:

Uniform tube surface fouling of 20 mils and the cws.ie strip surface fouling of 40 mils or 20 mils on each side for all ten eggerates.

1 I

i CSE-97-~253

- - _ _ - - - - - . - _ . - _ - . . . ~ - -

A SONGS-9416 l!68. Rev. 01 Page D 20 of D-39 l TABLE 61 SAN ONOFRE UNI'IS 3 STEAM GENERA'IDRS EGGCRATE DEGRADATION STUDY THERMAI HYDRAULIC (ATHOS3, Mod 1) ANALYSIS RESUL'IS COMMON INPUT- No. of Tubes: 9,350 No. of Tubes P!ugged: 322 (ATHOS3 Model)

Carry Under: 0.75% Carry Over: 0.25% .

PLANT DATA CCLE4 CYCLE 8 CYCLE 9 (Reference 3)

Apet 5. July le. '99 Oct.11,1995 June 97-Feb.19

- (Reference 10) - (Reference 10) (Espemed)

1. Stearn Pressure, psia 918.8 846.96 918.8

2. Feed Water Flow, K1b / Hr 7339.15 7297.37 7339.15

1. Primary Hot Leg Temperature. T 605.60 605.79 605.60

. Primary Cold 14g Tamperature T $$3.18 552.20 553.18 INPUT DATA

5. RCS Pressure, psia 2250 2250 2250

6. Pranary Flow Rate, Ibid / Hr 78,198 x 10' 78.198 x 10' 78.198 x 10'

7. Feed Water Temperature, T 422 422 422

8. Downcomer Water Level, laches abo /e TS 438.625 438.625 438.625 OYERALL PERFORMANCE (ATHOS3)

1. Calculated Heat Transfer Rate, MW / SG 1709 1704 1709

2. Circulation Ratio: Over All 3.09 3.15 3.13

3. Circulation Ratio: Hc Side 2.55 2,64 2.65

4. Circulation Ratio: Cold Side 3.78 3.79 3.72

5. Prumry Hot les Temperature, T 605.57 605.80 608.86

5. Primary Cold Leg Temperature. *F $50.09 550.48 553.38

6. Fouling Factor M' K / W 1.25 x 10'8 2.1467 x 10'8 0.0

- 7. Conductivity of Fouling Material. Btu / Hr-Ft 2.0 2.0 N/A

• P ,,

8. Calculattd Fouling nickness, Mils - 2.93 0.0 t

CSE 97 253

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A-SONGS-9416-il68, REV. 01 Page D-22 of D-39 HOT SIDE COLD SIDE. _ g SEP. DECK-

• SONGS Ur4T 3 STEAM GENERATORS - CYCLE 9

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CSE-97-253

A-SONGS-9516-1168. REV. 01 Page D-23 cf D-39 HOT SIDE COLD SIDE

"' I FIGURE 6-3 SEP. DECK SONGS 'J4T 3 STEAM GENERATORS-CYRE 9 AWLMOOTES AT XY=15 BETWEEN THE TUBE BUNCLE AND THE SHROUD FARAPPE70 BW1 W2 EC1C EC09 ECOS ECO ECOE ECOS 45.3 EC04 6 d 35.9 26.4 ECO3 ECO2 7.5 EC01

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TUBESHEET CSE-97-253

A SONGS 9416 il68. Rev. 01 Page D-24 of D 39 ]

TABLE 6 2 SONGS UNIT 3 STEAM GENERATOR DATA FOR MODAL ANALYSIS TUBE ROW 9, LINES 1 AND 175 Elevation Primary Secondary Secondary Gap Ydocity Gap Velocity Noen. Velocity Huld Huld Muld Radial Cirrunderential Atlal Density Density Dynamic Viscosity 8 8 (inches) (Ibf sec /lai (Ibf sec /ini (Ibm /ft sec) (in/sec) (in/sec) (in/sec) 0.0 7.5 6.36E-05 7.32E 05 6.35E-05 121.95 1.96 20.56 15.00 DC 6.38E 05 7.32E 05 6.35E-05 . 117.20 1.93 48.27 28.25 EC1 6.40E 05 7.04E 05 6.35E-05 7.36 -6.03 33.46 45.75 6.43E 05 7.04E 05 6.35E-05 -4.66 1i.02 22.59 I 63.25 EC2 6.45E-05 7.04E-05 6.35E-05 2.67 14.17 14.78 l

81.25 6.48E 05 7.04E-05 6.35E-05 4.38 17.94 5.50 99.25 EC3 6.51E-05 4.96E 05 5.89E-05 -4.06 14.92 25.69 118.25 6.53E-05 3.05E-05 5.10E-05 21.05 28.09 41.06 137.25 EC4 6.56E-05 2.26E 05 4.5sE-05 4.13 39.83 71.22 154.75 6.58E-05 1.94E 05 4.25E 05 4.35 34.62 80.79 172.25 ECS 6.60E 05 1.86E-05 4.16E-05 22.36 55.86 91.10 190.25 6.62E 05 1.60E 05 3.87E-05 22.73 27.95 93.50

[2'.'3.25 EC6 6.64E 05 1.43E-05 3.63E 05 4.02 26.81 114.76 227,25 6.66E 05 1.32E-05 3.47E-05 3.71 20.45 118.62 246.25 EC7 6.68E45 1.29E-05 3.43E-05 30.89 35.78 131.26 253.344 6.69E-05 1.20E-05 3.29E45 51.76 20.08 110.59 CSE-97 253

-- . - . - - - . - . . . _= -

J A SONGS-9416-ll68, Rev. 01 Page D 25 of D-39 l i

J TABLE 6-3 l

SONGS UNIT 3 STEAM GENERATOR LATA FOR MODAL ANALYSIS TUBE ROW 38, LINES 4 AND 172 Elevation Primary Secondary f+:: ig Gap Yelocky Gap Vdocity Nom. Velectly Mund Mund Muld Radial Circuanferential Asial Density Derrity Dynamic Vlecesity (inclus) (Ibf-sec'/lai (Ibf eec'/ini (Ibm /ft sec) (kn/se:) (la/sec) (in/sec) 0.07.5 6.36E-05 7.32E-05 6.35E-05 115.05 16.53 24.11 15.00 DC 6.38E-05 7.32E-05 6.35E-05 110.48 12.99 56.38 28.25 EC1 6.40E 05 7.04E-05 6.35E-05 -7.05 5.07 38.14 45.75 6.43E-05 7.04E 05 6.35E-05 -4.40 5.61 25.78 63.25 EC2 6.46E 05 7.04E-05 6.35E-05 2.90 10.81 16.41 81.25 6.49E-05 7.04E-05 6.35E 05 4.74 14.69 2.83 99.25 EC3 6.51E-05 3.25E45 5.22E-05 7.01 1.95 (t.34 118.25 6.54E 05 2.44E-05 4.69E-05 25.12 25.94 68.62 137.25 EC4 6.57E 05 1.94E-05 4.25E-05 6.16 42.55 90.59 154.75 6.59E 05 1.69E-05 3.97E-05 5.89 37.53 95.71 172.25 EC5 6.61E-05 1.68E 05 3.%E-05 20.59 55.69 103.35 190.25 6.63E-05 1.42E-05 3.62E-05 24.72 28.83 102.79 208.25 EC6 6.65E-05 1.24E-05 3.35E-05 5.93 26.67 124.37 227.25 6.67E-05 1.13E-Os 3.17E 05 4.91 21.36 127.28 246.25 EC7 6.69E 05 1.15E-05 3.21E-05 30.78 34,18 141.34 256.50 6.71E-05 1.%E 05 3.05E 05 40,47 0.21 140.75 266.75 6.72E-05 1.00E-05 2.93E-05 19.43 26.65 166.02 275.219 EC8 6.72E-05 9.54E-06 2.83E 05 8.88 -4.15 189.72 CSE 97 253

A-SONGS-9416 il68. Rev. 01 Page D-26 of D-39 l TABLE 6-4 SONGS UNIT 3 STEAM GENERATOR DATA FOR MODAL ANALYSIS TUBE ROW 49, LINES 7 AND 169 Elevation Primary Secondary Secondary Gap Velocity Gap Velocity Nom. Yelocity -

Muld Mund Mund Radial C1munferential Axlal Density Density Dynamic Viscosity (Inches) (Ibf sec'/lai (Ibf sec'/ini (Ibm /ft sec) (in/sec) (in/sec) (in/sec) 0.07.5 6.37E-05 7.32E-05 6.35E-05 115.05 4.33 25.21 15.00 DC 6.38E-05 7.32E-05 6.35E-05 110.23 3.14 58.50 28.25 EC1 6.40E-05 7.04E-05 6.35E-05 7.01 0.19 39.88 45.75 6.44E-05 7.04E 05 6.35E-05 -4.68 -6.29 27.10 63.25 EC2 6.46E-05 7.04E-05 6.35E-05 -3.46 10.41 17.63 81.25 6.49E 05 7.04E-05 6.22E-05 -6.24 -14.98 10.70 99.25 EC3 6.52E-05 2.76E-05 4.95E-05 1.84 6.09 72.24 118.25 6.55E-05 2.22E-05 4.55E-05 26.34 24.71 76.14 137.25 EC4 6.57E-05 1.82E 05 4.17E-05 7.30 33.52 97.21 154.75 6.60E-05 1.59E 05 - 3.91E-05 6.62 32.65 100.63 172.25 EC5 6.62E-05 1.99E-05 3.92E-05 20.57 44.38 108.27 190.25 6.64E-05 1.35E-05 3.59E-05 27.10 26.52 105.79 208.25 EC6 6.66E-05 1.18E 05 3.33E-05 8.36 23.51 126.65 227.25 6.68E-05 1.07E-05 3.15E-05 6.17 19.52 128.46 246.25 EC7 6.70E-05 1.29E-05 3.2E-05 -30.42 27.19 142.28 256.50 6.71E-05 1.01E-05 3.05E-05 38.15 16.74 133.78 266.75 6.72E-05 9.47E 06 2.92E-05 16.87 19.25 143.78 277.00 EC8 6.73E-05 1.04E-05 2.92E-05 -40.76 53.00 175.12 284.84 6.74E-05 8.67E 06 2.76E 05 65.49 -58.57 180.71 CSE 97 253

A-SONGS-9416 il68. Rev. 01 Page D-27 of D 39 l TABLE 6-5 SONGS UNIT 3 STEAM GENERATOR DATA FOR MODAL ANALYSIS TUBE ROW 83, LINES 17 AND 159 Elevation Primary Secondary Secondary Gap Velocity Gap Velocity Nom. Velocity Muid Muid Muld Radial Cimanferential Axial Density Density Dynamic Viscosity (loches) (Ibf sec'/In') (Ibf eec'/in') (Ibm /ft sec) (in/sec) (in/sec) (in/sec) 0.0 7.5 6.37E 05 7.32E 05 6.35E-05 -115.18 0.26 25.39 15.00 DC 6.38E-05 7.32E 05 6.35E-05 110.28 0.03 58.86 28.25 EC1 6.41E-05 7.04E 05 6.35E-05 -6.89 -1.79 40.35

~

45.75 6.44E-05 7.04E-05 6.35E-05 -4.56 -5.76 27.33 63.25 EC2 6,47E-05 7.04E-05 6.35E 05 -3.53 9.39 17.76 81.25 6.50E-05 7.04E-05 6.13E 05 7.29 -13.24 14.84 99.25 EC3 6.52E 05 2.88E-05 5.02E 05 9.67 6.72 64.99 118.25 6.55E-05 2.25E 05 4.57E 05 24.78 19.45 72.44 137.25 EC4 6.58E-05 1.84E 05 4.19E 05 6.40 25.05 96.49 154.75 6.60E-05 1.62E-05 3.94E 05 5.33 26.32 99.76 172.25 EC5 6.63E-05 2.02E-05 3.96E-05 -21.59 35.45 107.95 190.25 6.65E-05 1.38E-05 3.64E-05 26.62 23.10 104.96 208.25 EC6 6.67E-05 1.21E-05 3.38E-05 8.14 19.84 125.71 227.25 6.69E-05 1.10E-05 3.20E-05 5.43 16.90 126.61 246.25 EC7 6.71E-05 1.31E 05 3.25E 05 30.86 22.27 139.61 256.50 6.72E-05 1.05E-05 3.10E 05 35.68 17.% 128.31 266.75 6.73E-05 9.79E-06 2.98E-05 15.87 18.37 133.15 I'[7.00 EC8 6.74E-05 1.07E-05 2.98E45 -44.69 29.34 169.99 287.25 6.76E-05 9.04E-06 2.84E-05 55.63 5.99 168.07 297.50 6.76E 05 8.49E-06 2.73E-05 22.25 4.74 197.72 +

307.75 EC9 6.77E-05 9.18E-06 2,69E-05 -17.68 57.94 226.69 314.60 6.78E-05 7.78E-06 2.57E-05 41.% 32.56 217.24 CSE 97 253 1

A SONGS-9416-il68 Rev.01 Page D-28 of D-39 l TABLE 6-6  !

i SONGS UNIT 3 STEAM GENERATOR DATA FOR MODAL ANALYSIS U-BEND REGION - TUBE ROW 83 LINES 17 AND 159 Dbtance From Primary Secondary Secondary Gap I Tubelane Muld Huld Huld Velocity Densky Densky Dynamic Viscosity (laches) (Ibf-sec'/ini (Ibf sec'/inD (thm/ft-sec) (in/sec) 1 0 to 22.5 Deg, 6.78E 05 7.78E-06 2.476E-05 198.1I l 45 Dec. 6.79E-05 7.37E46 2.476E-05 387.39 l

67.5 Deg, 6.79E-05 6.67E-06 2.312E-05 365.21 67.5 to 90 Deg, 6.79E 05 - 6.48E-06 2.264E-05 288.24 21.5 6.79E 05 6.48E-06 2.264E-05 288.25

-10.5 6.80E-05 6.57E-06 2.492E-05 216.57 0.0 6.81E-05 7.44E-06 2.286E-05 236.88 TUBE LANE 10.5 6.835-05 9.43E-06 2.909E 05 201.85 21.5 6.83E-05 9.72E-06 2.965E-05 166.17 33.5 6.81E-05 9.59E-06 2.939E-05 219.54 90 to 67.5 Deg, 6.81E-05 9.59E-06 2.985E-05 219.54 45 Deg, 6.81E-05 9.83E-06 2.939E-05 277.81 22.5 Deg, 6.80E-05 1.04E-05 2.985E-05 302.68 22.5 to 0 Deg, 6.80E-05 1.07E-05 3.087E-05 155.93 CSE 97 253

A-SONGS-9416 il68, Rev. 01 1%ge D-29 of D-39 l TABLE 6-7 l

l SONGS UNIT 3 STEAM GENERATOR l DATA FOR MODAL ANALYSIS TUBE ROW 101, LINES 25 AND 151 Elevation Primary Secondary Secondary Gap Velocity Gap Velocity Nom. Yelocity l Muld Muld Muld Radial Circumfesintial Axial r

Density Density Dynamic Viscosity 8 8 (laches) (Ibf sec /in') (ibf sec /in') (Ibm /ft sec) (in/sec) (in/sec) (in/sec) 0.07.5 6.35E-05 7.32E-05 6.35E-05 115.71 1.13 25.58 15.00 DC 6.35E-05 7.32E-05 6.35E 05 110.87 1.09 58.98 28.25 EC1 6.36E-05 7.04E 05 6.35E-05 -6.78 2.24 40.87 45.75 6.36E-05 7.04E-05 6.35E-05 -4.36 -4.97 27.94 63.25 EC2 6.36E-05 7.04E 05 6.35E 05 3.31 -8.37 18.59 81.25 6.37E-05 6.77E-05 6.04E 05 7.30 11.74 19.35 99.25 EC3 6.37E 05 2.94E-05 5.06E-05 23.87 8.72 62.64 118.25 6.37E45 2.27E-05 4.59E-05 5.63 15.83 71.29 137.25 EC4 6.37E-05 1.85E-05 4.20E-05 4.32 19.74  %.69 154.75 6.38E-05 1.64E-05 3.97E-05 22.35 21.27 100.16 172.25 EC5 6.38E45 2.04E 05 3.99E-05 26.37 28.83 108.74 190.25 6.38E-05 1.41E-05 3.67E-05 8.I1 19.82 105.43 208.25 EC6 6.38E-05 1.23E-05 3.41E 05 5.42 16.83 126.14 227.25 6.39E 05 1.13E 05 3.24E 05 30.62 14.47 126.73 246.25 EC7 6.39E-05 1.33E-05 3.28E-05 -30.62 18.52 139.37 256.50 6.39E-05 1.07E 05 3.14E 05 34.78 15.70 127.21

'266.75 6.39E-05 1.00E-05 3.028-05 14.77 14.69 130.83 277.00 EC8 6.39E 05 1.09E-05 3.02E-05 45.32 19.02 167.59 287.25 6.39E-05 9.30E-06 2.89E-05 $0.86 19.61 156.73 297.50 6.39E-05 8.77E-06 2,78E-05 19.83 29,64 164.45 307.75 EC9 6.39E-05 9.37E-06 2.78E-05 52.13 62.81 199.92 318.00 6.39E-05 8.15E-06 2.65E-05 70.61 -8.02 201.77 328.25 6.39E-05 7.64E-06 2.54E-05 30.13 15.32 229.29 330.344 EC10 6.39E-05 7.33E-06 2.47E-03 12.08 99.75 232.24 CSE 97-253

~

i A SONGS-9416-il68. Rev. 01 Page D-30 of D 39 l TABLE 64 SONGS UNIT 3 STEAM GENERATOR DATA FOR MODAL ANALYSIS TUBE ROW 121, LINES 39 AND 137 I

Einstion Primary Secondary Secondary Gap Yeiocity Gap Velocity Nous. Velocity Huld Huld Muld Radial Cittwnferential Axial Density Density Dynamic Viscosity (inches) (Ils-sec'/in') (Ibf sec'/in') (Ibevft sec) (in/sec) (in/sec) (in/sec) 0.0 7.5 6.35E-05 7.32E-05 6.35E 05 -115.33 0.00 25.42 15.00 DC 6.35E-05 7.32E-05 6.35E 05 -110.41 -0.08 58.89 28.25 EC1 6.36E-05 7.04E-05 6.35E-05 -6.92 -1.59 40.51 45.75 6.36E-05 7.04E-05 6.35E-05 -4.39 -3.85 27.68 63.25 EC2 6.36E-05 7.04E-05 6.35E-05 -3.32 7.04 18.91 81.25 6.37E-05 6.48E 05 5.%E-05 -7.20 -9.74 23.74 99.25 EC3 6.37E-05 2.%E-05 5.07E-05 23.64 7.72 61.73 118.25 6.37E-05 2.27E-05 4.59E-05 5.20 12.23 70.43 137.25 EC4 6.37E-05 1.85E-05 4.19E45 3.66 15.26  %.06 154.75 6.38E-05 1.63E-05 3.95E-05 -22.75 16.63 99.57 172.25 EC5 6.38E 05 2.05E-05 3.98E-05 25.95 22.71 107.68 190.25 6.38E-05 1.41E-05 3.67E-05 8.05 16.17 104.45 208.25 EC6 6.38E 05 - 1.23E-05 3.42E-05 5.07 13.52 17:,.M 227.25 6.39E-05 1.13E 05 3.24E-05 -30.49 11.80 125.28 246.25 EC7 6.39E-05 1.34E 05 3.28E-05 -30.49 14.74 ' 136.97 256.50 6.39E-05 1.07E-05 3.15E-05 33.14 12.77 124.65 266.75 6.39E-05 1.01E-05 3.03E 05 14.06 11.49 127.72 277.00 EC8 6.395-05 1.10E-05 3.03E-05 44.31 14.11 163.23 287.25 6.39E-05 9.39E-06 2.91E-05 47.57 17.88 150.12 297.50 6.39E45 8.87E 06 2.80E-05 18.78 22.86  !$4.92 307.75 EC9 6.39E-05 9.48E-06 2.80E-05 -53.76 35.87 195.83 318.00 6.39E-05 8.32E-06 2.69E 05 61.41 28.24 187.16 328.25 6.39E-05 7.90E-06 2.60E-05 27.02 36.49 207.56 ,

338.50 EC10 6.40E-05 8.46E-06 2.58E-05 -19.35 77.22 224.53 347.84 6.40E-05 7.22E-06 2.45E-05 52.33 59.15 209.13 CSE 97-253

1 l A-SONGS-9416-ll68, Rev. 01 F i

Page D-31 of D-39 l TABLE 6-9 l

SONGS UNIT 3 STEAM GENERATOR DATA FOR MODAL ANALYSIS TUBE ROW 134, LINES 52 AND 124 Elevation Primary Secondary " :: tg Gap Velodty Gap Velocity Noen. Velodty Muid Muld Huld Radial Circumferential Axial Densley Density Dynande Viscosity 8

(laches) (Ibf sec /in') (Ibf sec'/in') (Ibm /h-sec) (in/sec) (in/sec) (in/sec) 0.0 - 7.5 6.37E 05 7.32E-05 6.35E-05 115.36 -0.35 25.44 15.00 DC 6.38E 05 7.32E-05 6.35E-05 -110.44 0.37 58.94 28.25 EC1 6.41E-05 7.04E-05 6.35E-05 -6.94 1.24 40.55 45.75 6.44E-05 7.04E-05 6.35E-05 -4.35 2.69 27.67 63.25 EC2 6.47E-05 7.04E-05 6.35E-05 3.25 5.10 18.90 81.25 6.51E-05 6.44E 05 5 %E-05 6.69 -6.24 23.50 99.25 EC3 6.54E-05 2.95E-05 5 %E-05 11.44 3.35 61.81 118.25 6.56E-05 2.27E-05 4.58E-05 23.11 7.94 70.71 137.25 EC4 6.59E-05 1.85E-05 4.20E-05 4.53 10.91 96.14 154.75 6.62E-05 1.64E-05 3.97E-05 3.06 12.22 99.33 172.25 EC5 6.645-05 2.07E-05 4.01E-05 -23.01 16.48 107.05 190.25 6.66E-05 1.43E-05 3.69E-05 25.33 12.31 103.82 208.25 EC6 6.69E-05 1.25E-05 3.43E-05 7.98 10.07 124.17 227.25 6.71E-05 1.15E-05 3.27E 05 4.74 8.92 124.05 246.25 EC7 6.73E-05 1.36E-05 3.32E-05 30.43 10.37 135.35 256.50 6,74E-05 1.09E-05 3.18E-05 32.16 9.48 123.07 266.75 6.75E-05 1.03E-05 3.07E-05 13.91 8.55 125.75 277.00 EC8 6.76E-05 1.12E-05 3.07E-05 43.28 9.77 160.08 287.25 6.77E-05 9.58E 06 2.94E-05 45.70 13,32 146.57 297.50 6.78E-05 9.06E-06 2.83E-05 17.86 16.25 150.55 307.75 EC9 6.79E-05 9.69E-06 2.84E 05 -52.99 23.72 190,19 318.00 6.80E-05 8.52E-06 2.73E-05 56 10 29.48 174.45 328,25 6.81E-05 8.12E-06 2.64E-05 24.01 70.10 176.61 f38.50 EC10 6.82E-05 8.67E-06 2.64E-05 -49.% 77.22 200.47 ,s 350.56 6.83E-05 7.44E-06 2.49E-05 77.06 2,48 200.55 362,625 6.84E-05 6.88E-06 2.36E-05 57.12 31.00 199.17 CSE-97-233 m

A SONGS-9416-1168. Rev. 01 Page D-32 of D-39 l TABLE 610  ;

I l

SONGS UNIT 3 STEAM GENERATOR i DATA FOR MODAL ANALYSIS TUBE ROW 144, LINES 70 AND 106 Elevation Prknary Secondary Secondary Gap Velocky Gap Velocky Nom. Velocky Muld Muld Mdd Radial Circumferential Axial Densky Densky Dynaanic Viscosky 8

(loches) (ltisec /ini (Ibf sec'/ini (Ibm /ft sec) (in/sec) (in/sec) (in/sec) l 0.07.5 6.37E-05 7.32E 05 6.35E-05 115.81 0.91 25.56 15.00 DC 6.38E-05 7.32E-05 6.35E45 -110.95 -0.79 58.94 28.25 ECl 6.41E-05 7.04E 05 6.35E-05 -6.80 -0.99 40.83 45.75 6.43E-05 7.04E-05 6.35E-05 -4.24 -1.66 27.84 63.25 EC2 6.47E-05 7.04E-05 6.35E-05 2.% 3.11 18.63 81.25 6.51E-05 5.56E-05 6.05E-05 5.63 -2.91 18.21 99.25 EC3 6.54E-05 2.99E-05 5.07E-05 9.27 -1.15 61.29 118.25 6.57E-05 2.34E-05 4.61E-05 22.54 4.04 69.92 137.25 EC4 6.59E-05 1.94E-05 4.25E-05 3.74 6.80 95.24 154.75 6.62E-05 1.75E-05 4.04E-05 3.15 8.28 97.44 172.25 EC5 6.64E-05 1.79E-05 4.08E-05 -23.13 10.58 105.31 190.25 6.67E-05 1.53E-05 3.77E-05 24.49 8.77 101.73 208.25 EC6 6.69E-05 1.35E 05 3.52E-05 7.54 6.58 121.73 227.25 6.71E-05 1.25E-05 3.36E-05 4.21 6.26 121.02 246.25 EC7 6.73E-05 1.28E-05 3.40E-05 -29.55 5.97 132.68 256.50 6.74E-05 1.19E-05 3.27E-05 31.44 6.38 120.51 266.75 6.75E-05 1.12E45 3.15E 05 13.36 5.73 122.87 277.00 EC8 6.76E-05 1.13E-05 3.16E-05 -41.96 5.42 156.26 287.25 6.77E-05 1.0$E-06 3.02E 05 44.08 8.66 143.03 297.50 6.78E-05 9.97E-06 2.92E-05 16.65 10,62 146.61 307.75 EC9 6.78E-05 9.98E-06 2.92E45 -51.74 14.73 184.76 318.00 6.80E-05 9.40E-06 2.80E-05 52.91 20.95 167.87 328.25 6.81E-05 8.98E-06 2.72E-05 22.10 26.40 168.62 ,.

338.50 EC10 6.82E 05 8,99E-06 2.72E-05 -52,72 38.33 203.35 350.56 6.83E-05 8.24E-06 2.56E-05 77.99 9.27 204.45 362.625 6.84E-05 7.54E-06 2.40E-05 51.41 -10.26 231.69 370.594 6.84E-05 7.54E-06 2.41E 05 369.02 -45.85 191.61 CSE-97-253

l l

A-SONGS 9416.ll68. Rev. 01 Page D 33 of D-39 l TAB 116-11 SONGS UNIT 3 STEAM GENERATOR DATA FOR MODAL ANALYSIS TUBE ROW 147, LINES 87 AND 89 Elevanon 1 % nary Secondary Secondary Gap Velocity Gap Velocky Nosa. Velocky Huid Muid Muld Radial Circundenadal Axial Dansky Densky Dynande Viscosity 8

(inclus) (lld sec'/In$ (Itd eec /ini (Iben/ft sec) (in/sec)- (in/sec) (in/sec) 0.0 - 7.5 6.37E 05 7.32E-05 6.35E 05 115.36 0.45 25.54 15.00 DC 6.38E-05 7.32E-05 6.35E-05 -110.50 0.34 59.06 28.25 EC1 6.41E 05 7.04E-05 6.35E-05 -6.94 -0.09 40.55 45.75 6.44E 05 7.04E-05 6.35E-05 4.10 0.53 27.25 63.25 EC2 6.48E 05 7.04E-05 6.35E-05 -2.71 1.29 17.38 81.25 6.51E-05 6.32E-05 6.14E-05 4.19 -0.66 10.73 99.25 EC3 6.54E-05 2.85E-05 5.00E-05 5.9) 2.37 63.94 118.25 6.57E-05 2.29E-05 4.60E 05 22.41 1.08 71.02 137.25 EC4 6.60E-05 1.93E-05 4.28E 05 3.17 3.48 94.29 154.75 6.62E-05 1.76E 05 4.09E-05 1.46 4.22 94.99 172.25 EC5 6.64E-05 2.15E-05 4.15E-05 23.00 5.50 102.09 190.25 6.67E 05 1.54E-05 3.83E-05 22.91 4.74 98.15 208.25 EC6 6.69E-05 1.35E-05 3.58E-05 7.58 3.22 117.76 227,25 6.71E45 1.25E45 3.44E-05 3.51 3.31 115.98 246.25 EC7 6.73E-05 1.46E-05 3.49E 05 -28.54 2.67 127.64 256.50 6.74E45 1.19E-05 3.35E45 29.50 3.28 115.79 266.75 6.76E-05 1.12E-05 3.23E-05 12.48 2.80 117.83 277.00 EC8 6.77E-05 1.21E 05 3.24E-05 -40.26 2.19 150.59

287,25 6.78E-05 1,04E-06 3.10E-05 41.97 4.16 137 87 297.50 6.79E-05 9.86E-06 2.90E-05 15.79 5.15 141.10 307.75 EC9 6.80E-05 1.05E-05 3.00E-05 -49.74 7.00 177.99 318.00 6.80E-05 9.26E-06 2.88E-05 49.29 10.18 161.65 328.25 6.82E45 8.80E-06 2.78E-05 20.04 12.22 162.72 ,.

338.50 EC10 6.82E-05 9.29E-06 2.79E-05 -53.35 16.50 200.79 350.56 6.83E-05 7.98E-06 2.61E-05 77.67 4.19 203.42 362.625 6.84E-05 7.22E-06 2.44E 05 53.93 -6.34 238.11 370.594 6.85E-05 7.27E-06 2.46E-05 336.90 31.27 193.50 CSE 97 253 1

A-SONGS-9416-Il68. Rev. 01 Page D 34 of D-39 l l

TABLE 6-12 l l

SONGS UNIT 3 STEAM GENERATOR I DATA FOR MODAL ANALYSIS TUBE ROW 147 - U-BEND REGION LINES 87 AND 89 Distance From Primary Muid --: 7 Muid Secondary Huid Gap Veeocity Tubeiane Density DanCy Dynamk Viscosity 8

Onches) Obf sec /in') (Ibf secin') Obm/R-sec) (in/sec)

O to 22.5 Deg. 6.85E-05 6.53E-06 2.278E-05 163.67 45 Deg. 6.85E-05 6.08E 06 2.164E-05 241.62 67.5 Deg. 6.85E-05 6.08E-06 2.164E-05 286.53 67.5 90.0 Deg. 6.85E-05 5.86E-06 2.106E-05 199.73 90 Deg to 59.98" 6.85E-05 5.74E-06 2.074E-05 116,25

-53.85 6.86E 05 5.68E-06 2.061E 05 105.19

-47.60 6.86E-05 5.72E-06 2.070E 05 100.00

-41.36 6.86E-05 5.89E-06 2.116E-05 95.15 35.12 6.86E 05 6.39E-06 2.243E-05 86.59

-28.99 6.87E-05 7.26E-06 2.451E-05 75.55 22.75 6.87E45 8.52E-06 2.728E-05 61.70

, 15.94 6.87E 05 1.01E 05 3.027E-05 45.92

-8.03 6.87E-05 1.14E-05 3.253E-05 26.67 0.00 6.88E-05 1.35E 05 3.586E-05 41.17 TUBE LANE

~

8.03 6.88E-05 1.37E 05 3.613E-05 42.33 15.94 6.88E-05 1,47E-05 3.743E 05 38.01 22.75 6.88E-05 1.44E-05 3.707E-05 33.12 28.99 6.88E-05 1.38E-05 3.632E-05 33.94 35.12 6.88E-05 1.32E-05 3.536E-05 37.36

^

41.36 6.88E-05 1.25E-05 3.430E-05 41.93 47.60 6.89E-05 1.18E-05 3.324E-05 47,19 53.85 6.89E-05 1.12E-05 3.232E-05 52.64 59.4 6.89E-05 1.08E-05 3.163E-05 59.07 7 '

' " to 90 Deg. 6.89E-05 1.06E-05 3.126E 05 69.40

9. 37.5 Deg. 6.90E-05 1.05E-05 3.113E-05 122.95 ,s "6I.5 Deg. 6.90E-05 1.06E-05 3.128E-05 183.45 45 Deg. 6.90E-05 1.06E-05 3.12SE-05 154.88 22.5 to O Deg. 6.90E-05 ' l.I1E-05 6.346E-05 107.57 CSE-97 253

1 A-SONGS-9416-1168. Rey,01 Page D-35 of D-39 l TABIR 6-13 l SONGS UNIT 3 STEAM GENERATOR DATA FOR MODAL ANALYSIS TUBE ROW 110 - U-BEND REGION LINES 32 AND 130 Distance From Prheary Huld Secondary Huid Secondary Huid Gap Velocity Tid =h== Density Density Dynnade Ylecesity d

(Laches) (Ibf sec'/in') (ibf.eec'/In ) (Iban/ft sec) (in/sec)

O to 22.5 Deg. 6.8E-05 7.33E-06 2.467E 05 5.469877 45 Deg, 6.81E 05 7.%E-06 2.405E 05 241.3953 67.5 Deg, 6.81E 05 6.42E46 2.251E 05 318.7109 67.5 to 90.0 Deg, 6.82E 05 6.22E-06 2.199E-05 302.0425 90.0 Deg to 43*, 6.82E 05 6.22E 06 2.199E-05 303.1899 40.5 6.82E45 6.04E-06 2.154E-05 227.5953 34 6.82E-05 6.07E-06 2.160E 05 230.3831 28 6.83E-05 6.08E-06 2.I64E-05 181.7797 23 6.84E-05 6.37E-06 2.238E-05 200.6202 17.5 6.85E-05 6.66E-06 2.309E-05 158.2722 8.5 6.86E-05 7.31E-06 2.464E-05 156.9933 0 6.87E-05 8.7E-06 2,764E-05 150.4288 TUBE LANE 8,5 6.87E 05 1.09E 05 3.174E 05 122.7972 17.5 6.88E 05 1.16E-05 3.297E-05 106.1574 23 6.89E-05 1.17E 05 3.306E-05 101.2149 28 6.86E-05 1.09E-05 3.173E 05 128.5839 34 6.88E-05 1.07E-05 3.141E-05 117.4028 40.5 6.85E 05 1.02E 05 3.055E-05 152.7392 43" to 90 Deg . 6.89E-05 1.04E-05 3.088E-05 151.7302 90,0 to 67.5 Deg, 6.87E-05 1.03E-05 3.068E 05 208.0953 67.5 Deg, 6.87E-05 1.03E-05 3.068E-05 207.2174 45 Deg, 6.84E-05 1.03E-05 3.078E 05 222.5758 22.5 Deg, 6.83E-05 1.08E-05 3.159E-05 173.7325 22.5 to 0 Deg 6.83E-05 1.09E 05 3.181E-05 3.326509 e,

CSE-97 253

I A SONGS-9416-1168. Rev. 01 Page D-36 of D-39 l TAHLE 6-14 l SONGS UNIT 3 STEAM GENERATOR AXIAL VELOCITIES (FEET /SEC.) AT IY=15 BETWEEN TUDE BUNDLE AND TIIE SIIROUD OVRAPPER)

Elevation Row Row Row Row Row Row Row Row Row IZ No.9 No.38 No.49 No.83 No.101 No.121 No.134 No.144 No.147 (inclus) IX = 9 IX =8 IX = 7 IX = 6 IX= 5 IX = 4 IX=3 IX = 2 IX = 1 1 0.07.5 0.817 0.994 1.052 1.064 1.000 1.067 1.068 1.061 1.069 2 15.00 DC 2.219 2.684 2.815 2.840 2.819 2.846 2.846 2.819 2.846 3 28.25 EC1 1.229 1.501 1.633 1.682 1.691 1.706 1.706 1.694 1.701 4 45.75 0.602 0.689 0.795 0.839 0.854 0.878 0.876 0.848 0.838 5 63.25 EC2 0.323 0.272 0.336 0.390 0.462 0.546 0.573 0.524 0.411 6 81.25 0.374 0.642 -0.992 1.351 -1,371 -1.126 1.109 -1.066 -0.881 7 99.25 EC3 0.294 0.194 0.798 0.817 0.807 0.811 0.806 0.777 0.763 8 118.25 4.550 6.092 6.355 6.106 6.014 5.%1 5.981 5.899 6.066

) 9 137.25 EC4 5.403 6.506 6.857 6.772 6.726 6.706 6.696 6.588 6.630 10 154.75 6.342 7.034 7.270 7.165 7.113 7.073 7.008 6.808 6.762 11 172.25 ECS 1.222 1.344 1.396 1.399 1.401 1.402 1.393 1.365 1.352 12 190.25 6.716 7.146 7.211 7.093 7.080 7.014 6.919 6.663 6.319 13 208.25 EC6 7.890 8.507 8.671 8.622 8.599 8.573 8.478 8.225 7 %3 14 227.25 9.176 9.747 9.842 9.724 9.669 9.616 9.465 9.111 8.740 15 246.25 EC7 1.814 1.958 1.977 1.952 1.936 1.924 1.896 1.839 1.783 16 256.50 7.474 8.530 7.198 6.522 6.339 6.148 6.024 5.823 5.512 17 266.75 12.067 13.238 9.531 8.412 8.143 7.913 7.733 7.461 7.083 18 277.00 EC8 16.2M 17.588 3.108 2.074 2.033 1.995 1.952 1.888 1.825 19 287.25 20.088 21.201 13.297 10.443 8.655 7.972 7.671 7.415 7.077 20 297.50 23.7M 24.74) 19.675 15.023 10.955 10.079 9.688 9.340 8.930 21 307.75 EC9 27.060 28.258 24.875 14.498 2.466 2.425 2.352 2.268 2.196 22 318.00 29.878 31.168 28.363 18.894 13.313 10.820 9.160 8.540 8.120 23 328.25 31.968 33.399 30.925 23.159 18.983 14.878 11.345 10.567 10.141 24 338.50 EC10 33.595 35.039 32.706 26.214 22.864 12.752 2.459 2.467 2.452 25 350.56 35.564 37.007 34.514 28.618 25.495 17.585 14.265 14.527 14.527 .-

26 362.625 44.061 45.308 41.601 34.711 30.213 23.231 21.739 22.936 23.402 27 370.594 36.253 37.532 34.481 28.851 25.105 19.422 17.939 18.376 17.959 U-Bend Region Open Tube Pitch and Fewer Tubes CSE-97-253

I A SONGS-941&l168, Rev 01 Page !>37 of D 39 l

7.0 CONCLUSION

S 4

, 'Ihe following corriusions are drawn from the thermal hydraulic analyses with ATilOS3:

1. 'Ihe assumed eggerate erosion only affects the local fluki velocities.

2. 'Ihe assumed erosion of the eggerate str4s irca the circulation ratio. For all practical purposes the thermal-hydraulic performance is es.mtially the same as Cycle 4 or the original design.

es CSE 97 2$3

1 A SONGS M16 il68. Rev. 01 Pay D-38 ofD 39 l

8.0 REFERENCES

l

1. Evaluadon of the San Onofre Unit 3 Steam Generator Eggerate Support Condition - Cycle 9.

Southern California Edison, San Onofre. June 05,1997,

2. ABB Combustion Engineering Report, A MY 94161171, Rev.00, " Thermal Hydraulle and Eggerate Erosion Analysis of Maine Yankee Steam Generators", September 1997 (To Be  ;

Published).

3. Facsimile Transmission from Mike Wade (SCE) to Don Siska (ABB), l

a. SG Pressure Loss at SONGS, November 21,1995. l

b. Operating Plant Data, January 19,1996.

4. " Chemical Cleaning of Surry's Steam Generators", Nuclear News, December 1995.

5. ABB Combustion Engineering Report, CSE 95-470W, Code Nane - AMOSGPP3 and

) ATHOS3, Version 3, Mod 01, November 1995.

6. Singhal, A. K., et al., ATHOS A Caputer Prognunfor 7hermal Hydrauuc Analysis of Steam Generators. Volume 1: Mahanadcol and Pitysical Models and Mehods of Soludon: Volwne 2:

Progranmer's Manual; Volume 3; User's Manual, EPRI Repon EPRI NP 2698-CCM, October 1982.

7. Singhal, A. K., et al., ATHOS3 Model: A Corrputer Progranfor Thermal-Hydraulic Analysis of Steam Generators. Volume 1: Mahanatical and Physical Models and Mehods of Soludon (Revision 1); Volume 2: Programmer's Manual (Revision 1); Volume 3; User's Manual (Redsion 1), EPRI Report EPRI-NP-4604-CCML, September 1990.

8. - ABB Combustion- Engineering Nuclear Operations, Quality Procedures Manual QPM-101, Revision 0, December 01,1995.

9. Facsimile Transmissian from- Ron _ I.ow (Rockridge Technologies) to AL Matheny (SCE),

" Cumulative Report -11/93, Southem California Edison, San Onofre, Unit 3", May 25,1995. -

. 10. ABB Combustion Engineering Report, A SONGS-9419-1109, Rev. 00, "7hermal Hydraulic Analysis to Support he inwstigation of Pressure Reduction in he SONGS Units 2 and 3 Steam '_'

Generators", April 13, 1996.

l1. Crane Technical Pnper No. 410,

• Flow of Fluids brough Valves, Fittings, and Pipe",1981.

CSE 97 253

A-SONGS-9416-ll68. Rev. 01 -

Page D 39 of D 39 l

12. ASME Steam Tables - %ermodynamic and Transport Properties of Steam, The American Society of Mechanical Engineers, New York,1993.

13. "Inconel Alloy 600", Huntington Alloys, Inc., Fifth Edition,1978.

$ [

l '. _ J

14. ABB Combustion Engineering Drawings: , k A. E-234-69M)l, April 1976, " General Arrangement and Assembly - Elevation" B. E 234-694-01, May 1973, " Tube Sheet Drilling Patterns" C. E 234-72100, January 1974, "Eggerate Tube Support Assembly" Y,M D. E-234-717 00, January 1974, " Partial Eggerate hbe Support Assembly" E. E 234-719-00, January 1974, " Partial Eggerate Tube Support Assembly" F. E-235-161-00, December 1973, " Partial Eggerate Tube Support Assembly" G. E-246-002-05, February 1973, " Steam Separators" H. E 246-02641, December 1973, " Separator Support Casting" l

9 CSE 97 233 i w _ _ _ _