ML13051A192

San Onofre, Unit 2, Enclosure 4, L5-04GA567, Rev. 6, Evaluation of Stability Ratio for Return to Service

ML13051A192
Person / Time
Site:	San Onofre
Issue date:	02/18/2013
From:	Mitsubishi Heavy Industries, Ltd
To:	Office of Nuclear Reactor Regulation
References
TAC ME9727 L5-04GA567, Rev 6, SO23-617-1-M1539, Rev 0
Download: ML13051A192 (150)

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{{#Wiki_filter:ENCLOSURE 4MHI Non-Proprietary DocumentL5-04GA567, Evaluation of Stability Ratio for Return toService(Non-Proprietary) I Non-proprietary Version() (1/149)San Onofre Nuclear Generating Station, Unit 2 & 3REPLACEMENT STEAM GENERATORSEvaluation of Stability Ratio for Return to ServiceSupplier Status StampVPL S023-617 M1539 Reo I QCN/ANo: R-DESIGN DOCUMENT ORDER NO. _ 8008734135REFERENCE DOCUMENT-INFORMIATION ONLY EIIVIRP 10M MANUALMFG MAY PROCEED: [YES []NO EN/ASTATUS -A status Is required for design documents and Is optional for referencedocuments. Drawings are reviewed and approved for arrangements and conformance tospecification only. Approval does not relieve the submilttr from the responsibility ofadequacy and suitability of design, materials, and/or equipment represented.E-1, APPROVED-]2. APPROVED EXCEPT AS NOTED -Make changes and resubmit013. NOT APPROVED .Correct and resubmit for review. NOT for field use.APPROVAL: (PRINT/ SIGN / ATE),RE: JFLS:Other.SCE DE(123) 6 REV. 3 07t11REFERENCE: 80123-XXIV-37.0.26Purchase Order No. 4500024051Specification No. S023-617-01R3HITUB8r1eer IUV' nlUnSTa., tIA.Page 1 of 149S023-617 M1539, REV. 0 I Non-proprietary VersionI11(2/149)AtRevision HistoryDocument No.L5-04GA567No. Revision Date Approved Checked Prepared0 Initial issue See cover sheetI -Revised in accordance withSCE comments ofRSG-SCE/MHI-12-5722.-Added the evaluation of out ofplane FEI.2 Revised in accordance with SCEcomments ofRSG-SCE/MHI-12-5729.3 -Revised the calculation methodof the virtual added mass oftube in Sec. 4.1(5).4 -Added Attachment-5 toevaluate the stability ratio of thetube which has tube-to-tubewear at 70% thermal power5 -Revised Attachment-5 toevaluate the effect of type Jstabilizer on stability ratio of thetube which has tube-to-tubewear at 70% thermal power-Added Attachment-6 toevaluate the uncertainty ofcalculated stability ratio6 -Revised in accordance withSCE comments ofRSG-SCE/M HI-12-5769-Revised stability ratios due tothe change of stabilizer type(Type J)-Revised out-of-plane FEIanalysis results in Sec.2 and 8 _MITSUBISHI HEAVY INDUSTRIES, LTD.Page 2 of 149S023-617 M1539, REV. 0 Non-proprietary Version I) (3/149)Document No. L5-04GA567(6)AtTable of Contents1. Purpose .................................................................................................................................... 42. Conclusion ............................................................................................................................... 52.1 Stability ratio of out of plane FEI ..................................................................................... 52.2 Stability ratio of in-plane FEI ............................................................................................ 63. Nom enclature ......................................................................................................................... 104. Assum ption ............................................................................................................................ 114.1 M odeling assum ption ..................................................................................................... 114.2 O pen item ............................................................................................................................ 125. Acceptance Criteria .......................................................................................................... 136. Design Input ........................................................................................................................... 146.1 G eom etry of tube bundle region ..................................................................................... 146.2 Thermal and hydraulic flow of steam generator secondary side .................................... 177. M ethodology ............................................................................................................................. 327.1 Fluid elastic vibration ...................................................................................................... 327.2 Calculation m odel .......................................................................................................... 498. Com putation Results ........................................................................................................ 608.1 O ut of plane FEI analysis results ................................................................................... 608.2 In-plane FEI analysis results .......................................................................................... 659. Reference .............................................................................................................................. 95Attachm ent-1 Com puter Input and O utput File List .............................................................. 96Attachment-2 Evaluation of Liquid Film Thickness of Tube at AVB Support Point ..................... 106Attachment-3 Evaluation of the Effective Distance of Liquid Film of Tube from the Contact Point forSqueeze Film Dam ping .............................................................................................................. 114Attachm ent-4 Confirm ation of Flow Regim e ............................................................................... 117Attachment-5 Case Study for Applying Split Stabilizers for TTW tube of Unit-2 at 70% ThermalPower ......................................................................................................................................... 118Attachm ent-6 Uncertainty of Calculated Stability Ratio .............................................................. 128Attachm ent-7 Selection of Evaluated Tubes ............................................................................... 145MITSUBISHI HEAVY INDUSTRIES, LTD.Page 3 of 149 S023-617 M1539, REV. 0 I Non-proprietary Version II) (4/149)Document No. L5-04GA567(6)At1. PurposeThe purpose of this document is to perform parametric calculations of stability ratios for the selected(limiting) tubes as a function of the number of consecutive inactive AVB support points and the reactor(thermal) power level. This calculation is performed in support of SONGS Units 2 return to service.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 4 of 149 S023-617 M1539, REV. 0 I Non-proprietary Version I) (5/149)Document No. L5-04GA567(6)At.2. ConclusionBy considering numbers of inactive support points as the parameter for the case study, the followingresults are obtained.2.1 Stability ratio of out of plane FEI2.1.1 Assuming all support points activeWith all AVB supports active, the stability ratios are less than 1.0 for all analyzed tubes, for the reactorpower levels up to, and including, 100% with no plugging.Table 2.1-1 Stabilitv Ratio with All Active Sunoort Points for 2A SGCase Thermal PowerRow Column 70 100 (No Plug)80 7080 80100 7010011 80(*)120 70120 8095(*) 85(*)125 85138 84Note(*): Plugged tube with Type J stabilizer2.1.2 Assuming 1 support points inactiveWith 1 AVB supports inactive, the stability ratios are less than 1.0 for all analyzed tubes, for the reactorpower levels up to, and including, 70%Table 2.1-2 Stability Ratio with I Inactive Su~oort Point for 2A SGCase Thermal PowerRow Column 70 100 (No Plug)80 7080 80100 701 00C) 80(*)120 70120 8095(1) 85(*)125 85138 84L YINote(*): Plugged tube with Type J stabilizerMITSUBISHI HEAVY INDUSTRIES, LTD.Page 5 of 149S023-617 M1539, REV. 0 I Non-proprietary Version II) (6/149)Document No. L5-04GA567(6)At2.2 Stability ratio of in-plane FEI2.2.1 Assuming 6 support points inactiveWith 6 consecutive AVB supports inactive, the stability ratios are less than 1.0 for all analyzed tubes,for the reactor power levels up to, and including, 90%.Table 2.2-1 Stability Ratio with 6 Consecutive Inactive Support Points for 2A SGCase Thermal PowerRow Column 50 60 70 80 90 100 100(No Plug)80 7080 80100 701 00M 80(.)120 70120 8095(') 85(*)125 85138 84Note(*): Plugged tube with Type J stabilizerMITSUBISHI HEAVY INDUSTRIES, LTD.Page 6 of 149S023-617 M1539, REV. 0 INon-proprietary Version j) (7/149)Document No. L5-04GA567(6)At2.2.2 Assuming 8 support points inactiveWith 8 consecutive AVB supports inactive, the stability ratios are less than 1.0 for all analyzed tubes,for the reactor power levels up to, and including, 80%.Table 2.2-2 Stability Ratio with 8 Consecutive Inactive Support Points for 2A SGCase Thermal Power100Row Column 50 60 70 80 90 100 (Pu80 7080 80100 701 O0) 80()120 70120 8095(*) 85(*)125 85138 84Note(*): Plugged tube with Type J stabilizerMITSUBISHI HEAVY INDUSTRIES, LTD.Page 7 of 149S023-617 M1539, REV. 0 INon-proprietary Version I) (8/149)Document No. L5-04GA567(6)At2.2.3 Assuming 10 support points inactiveWith 10 consecutive AVB supports inactive, the stability ratios are less than 1.0 for all analyzed tubes,for the reactor power levels up to, and including, 80% after plugging.Table 2.2-3 Stability Ratio with 10 Consecutive Inactive Support Points for 2A SGCase Thermal Power100Row Column 50 60 70 80 90 100 (Pu(No Plug)80 7080 80100 70I O0) 80(')120 70120 8095(") 85(*)125 85138 84Note(*): Plugged tube with Type J stabilizerMITSUBISHI HEAVY INDUSTRIES, LTD.Page 8 of 149S023-617 M1539, REV. 0 I Non-proprietary Version III ) (9/149)Document No. L5-04GA567(6)At2.2.4 Assuming 12 support points inactiveWith 12 consecutive AVB supports inactive, the stability ratios are less than 1.0 for all analyzed tubes,for the reactor power levels up to, and including, 60%.Table 2.2-4 Stability Ratio with 12 Consecutive Inactive Support Points for 2A SGCase Thermal PowerRow Column 50 60 70 80 90 100 100(No Plug)80 7080 80100 70100(*) 80(*)120 70120 8095() 85(')125 85138 84Note(*): Plugged tube with Type J stabilizer2.2.5 TTW tubes in Unit-2The stability ratios of TTW (tube-to-tube wear) tubes with type J stabilizer (split stabilizers) in Unit-2were evaluated and confirmed to be less than 1.0 as shown in Attachment-5.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 9 of 149 S023-617 M1539, REV. 0 I Non-proprietary Version I) (10/149)Document No. L5-04GA567(6)At3. NomenclatureSymbol Unit DefinitionE psi Modulus of elasticity of tubeFEI Fluid elastic instabilityG psi Shear modulus of tubeTav OF Primary side average temperatureTS OF Secondary side temperatureD, in Tube inside diameterDo in Tube outside diameterP in Tube pitchA Ibm/ft3 Density of water inside the tubeA_ Ibm/ft3 Density of tube materialPo Ibm/ft3 Average density of water outside the tubet in Tube thicknessm Ibm/ft Tube mass distribution per unit lengthmy Ibm/ft Virtual added mass per unit lengthh -Damping ratioh- Structural damping ratiohTp -Two phase damping ratioh- Viscous damping ratiohSF -Squeeze film damping ratioK -Critical factorMHI -Mitsubishi Heavy IndustriesM0 Ibm/ft Average tube mass per unit lengthU, ft/s Critical flow velocityf Hz Tube natural frequency6 -Logarithmic decrementU"n ft/s Nth mode effective flow velocityO(x)- Vibration modeTn(x) -Nth vibration modep, p(x) Ibm/ft3 Fluid density distribution of water outside the tube in tube axis directionU, U(x) ft/s Flow velocity distribution orthogonal to tube axis in tube axis directionx ft Coordinate component along tube axisL ft Tube lengthSCE Southern California EdisonSR, SR, (Nth mode) Stability ratioMITSUBISHI HEAVY INDUSTRIES, LTD.Page 10 of 149S023-617 M1539, REV. 0 I Non-proprietary Version I) (11/149)Document No. L5-04GA567(6)4. Assumption4.1 Modeling assumption(1) Nominal tube thickness and nominal tube length are used in the evaluation model because theeffect of the tolerances of these dimensions on the natural frequency is negligible.(2) Contact condition between tube and tube support plate is pin-supported. Fixed supportedcondition at tubesheet is added.(3) Contact condition between tube and active support points by the anti-vibration bar (AVB) ispin-supported.(4) Modulus of elasticity of tube is interpolated based on the tube average temperature of 2from table of ASME Boiler and Pressure Vessel Code, Sec II, Materials, 1998 Edition, 2000addenda (Ref.1).Where,Tav Primary side average temperature (OF)Ts :Secondary side saturation temperature (OF)(5) Tube has the virtual added mass due to the fluid-structure interaction (FSI) effect. The virtualadded mass in each region of the tube (the straight regions between TSPs and U-bend region)is calculated by using the following formula (Ref.24).rD~po f (De/Do)2+/-m = 4 [(D j D o)2-+ (Ibm /ft) ..................................................................... (1)D J Do = (I + ! P/ D , P/D * .............................................................................(2)Where,M, :Virtual added mass per unit length due to FSI effectp. Average water density outside the tube of each region obtained from ATHOSanalysisDo :Tube outside diameterP Tube pitch(6) Number of inactive AVB support points is a parameter for this case study. Consecutive 12,10(B01 to B10), 8 (B01 to B08) and 6 (B01 to B06) inactive support points biased to the hot sideare assumed for the evaluation of the stability ratio of in-plane FEI. All active support points and1 inactive support point are assumed for the evaluation of the stability ratio of out of plane FEI.The location of 1 inactive support is determined based on hydraulic pressure, void fraction andsupport span of each evaluated tube. The inactive support will be one of the 2 supports at thespan with the highest amplitude, whichever that has a higher hydraulic pressure. Themaximum stability ratio in each inactive support location is shown as the result of the stabilityratio with 1 inactive support.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 11 of 149 S023-617 M1539, REV. 0 I Non-proprietary Version II) (12/149)Document No. L5-04GA567(6)At(7) Type J stabilizers are assumed to be installed for all plugged tubes which have AVB wearindications. The additional structural damping ratio due to Type J stabilizer (split stabilizersinstalled to 60 degrees in the U-bend region at the both of hot and cold side) is assumed to be)which is based on the MHI test results of the medium amplitude (see Ref. 32 andAttachment-1 for details).4.2 Open itemThere is no open item remaining.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 12 of 149 S023-617 M1539, FREV. 0 INon-proprietary Version I] (13/149)Document No. L5-04GA567(6)At5. Acceptance CriteriaThe stability ratio against fluid elastic instability shall be less than 1.0. The analysis is performed inaccordance with the procedures given in ASME code section III Appendix N-1 330 (Ref.2).MITSUBISHI HEAVY INDUSTRIES, LTD.Page 13 of 149 S023-617 M1539, REV. 0 [Non-proprietary Version III] (14/149)Document No. L5-04GA567(6)At6. Design Input6.1 Geometry of tube bundle regionTube bundle consists of thermally treated Alloy 690 U-tubes which are supported in[ ]triangular pitcharrangement by the tube sheet, seven tube support plates, and six sets of anti-vibration bars (AVBs).Tube support plates (TSPs) have trifoil tube holes.All the contacting support structures above the tube sheet are made of 405 stainless steel (SA-240Type 405 Stainless steel).Nominal dimension of tube, TSPs and AVBs are listed in Table 6-1. The applicable design drawings tobe referred are listed in Table 6-2.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 14 of 149 S023-617 M1539, FREV. 0 11Non-proprietary Version I) (15/149)Document No. L5-04GA567(6)AkTable 6-1 Nominal dimensions of tubes, TSPs, and AVBsPart Item ValueMaterial Thermally treated SB-1 63 UNS N06690Outside diameter 0.75 inThickness 0.043 inTubesNumber of tubes 9727Tube pitch 1.0 inTube arrangement TriangularMaterial SA-240 Type 405ThicknessNumber of TSPsTSPsTube support span(between TSP centrals)Tube support span(from TS to No.1 TSP) IMaterial SA-479 Type 405TypeAVBsThicknessWidthStabilizer Unit weightMITSUBISHI HEAVY INDUSTRIES, LTD.Page 15 of 149S023-617 M1539, REV. 0 INon-proprietary Version I) (16/149)Document No. L5-04GA567(6)AtTable 6-2 A plicable design drawings (Ref.3 to 20)Drawing No. TitleL5-04FU001 COMPONENT AND OUTLINE DRAWING 1/3L5-04FU002 COMPONENT AND OUTLINE DRAWING 2/3L5-04FU003 COMPONENT AND OUTLINE DRAWING 3/3L5-04FU021 TUBE SHEET AND EXTENSION RING 1/3L5-04FU022 TUBE SHEET AND EXTENSION RING 2/3L5-04FU023 TUBE SHEET AND EXTENSION RING 3/3L5-04FU051 TUBE BUNDLE 1/3L5-04FU052 TUBE BUNDLE 2/3L5-04FU053 TUBE BUNDLE 3/3L5-04FU111 AVB ASSEMBLY 1/9L5-04FU112 AVB ASSEMBLY 2/9L5-04FU1 13 AVB ASSEMBLY 3/9L5-04FU1 14 AVB ASSEMBLY 4/9L5-04FU115 AVB ASSEMBLY 5/9L5-04FU116 AVB ASSEMBLY 6/9L5-04FU117 AVB ASSEMBLY 7/9L5-04FU118 AVB ASSEMBLY 8/9L5-04FU119 AVB ASSEMBLY 9/9MITSUBISHI HEAVY INDUSTRIES, LTD.Page 16 of 149S023-617 M1539, REV. 0 INon-proprietary Version] (17/149)Document No. L5-04GA567(6)At6.2 Thermal and hydraulic flow of steam generator secondary sideThe basic parameters for the thermal hydraulic analysis of unit-2 and 3 steam generators are shown inTable 6.2-1 to 6.2-4. As discussed in ATHOS analysis report (Ref. 22), the larger number of theplugged tubes of unit-2 (305 tubes for 2A) is used for the FEI evaluation. The flow characteristics of thetubes listed in Table 7.2-1 are obtained from ATHOS/SGAP analysis (See Ref.21 and 22 for detail) andused for the vibration analysis.The distributions of flow gap velocity normal to the in-plane direction of the tube, flow density and voidfraction are shown in Fig.6.2-3 to 6.2-11. Several of the flow gap velocity distributions indicate negativeflow velocities at lower thermal power on the cold leg side since the water flow is more likely to godownward on the cold leg side because the circulation ratio is higher and the water flow rate comparedwith steam flow rate at lower thermal power conditions is greater than higher thermal power condition.As shown in Section 7, the effective flow velocity Ue is calculated as function of the square of flowvelocity and mode shape in order to evaluate the actual tube vibration which is multi degrees offreedom system with beam type of vibration modes. Therefore, there is no adverse effect of negativeflow velocity.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 17 of 149 S023-617 M1539, REV. 0 cj~zCr:j~Table 6.2-1 Basic parameters for calculation for 2A SG evaluation after pluggingCase 50% 60% 70% 80% 90% 100% 100%withnopluggingPlugging 305 305 305 305 305 305 0869.5 1041.4 1213.3 1385.2 1557.1 1729(50%) (60%) (70%) (80%) (90%) (100%)RCS flow rate (gpm) *1 206,695 206,695 206,695 206,695 206,695 206,695 209,880Thot (Tsg-in) (°F)Tsg-out (°F)*2TcoId 2Saturation Steam Pressure (psia)Fouling Factor (ft2hr°F /Btu)Tfeedwater (OF)Circulation RatioSteam Mass Flow (lb/hr)Feed Water Mass Flow (lb/hr)*3Blowdown flow rate (gpm)z0'00)CDCD)Note *1: Obtained by interpolating the flow rate of 0% plugging and 8% plugging.*2: RCS flow temperature at SG outlet is assumed to be 0.3°F lower than that at RV inlet. The 0.3°F temperature increase between the SG outlet and RVinlet is caused by heat input from the reactor coolant pump.*3: Feedwater mass flow rate is the sum of the blowdown flow rate and the steam mass flow based on heat balance calculation.*4: Calculated by interpolating the data of other cases.*5: Assumed to be the same as Unit-3.*6: As discussed in ATHOS analysis report (Ref. 22), the larger number of unit-2 (305 tubes for 2A) is used for the evaluation. Fig.6.2-1 shows theaddress of the plugged tubes of 2A SG. Since ATHOS can only create a symmetrical half model of the tube bundle in reference to the center columnof the SG, the asymmetrical plugged tubes cannot be modeled. Therefore the plugged tubes are assumed to be overlapped as shown in Fig.6.2-2.0C)C)0c-I(A41Page 18 of 149S023-617 M1539, REV. 0 C-,Cd,C-,C-,Table 6.2-2 Basic parameters for calculation for 2B SG evaluation after pluggingCase 50% 60% 70% 80% 90% 100% 100 % with nopluggingPlugging*6 205 205 205 205 205 205 0869.5 1041.4 1213.3 1385.2 1557.1 1729(50%) (60%) (70%) (80%) (90%) (100%)RCS flow rate (gpm) 207,726 207,726 207,726 207,726 207,726 207,726 209,880Thot (Tsg-in) (°F)Tsg-out (OF)"*2TcoId (OF)*2Saturation Steam Pressure (psia) IFouling Factor (ft2hr°F /Btu)Tfeedwater (°F)Circulation RatioSteam Mass Flow (lb/hr)Feed Water Mass Flow (lb/hr)3Blowdown flow rate (gpm)z070CD0)Cn.0Note *1: Obtained by interpolating the flow rate of 0% plugging and 8% plugging.*2: RCS flow temperature at SG outlet is assumed to be 0.3°F lower than that at RV inlet. The 0.3°F temperature increase between the SG outlet andRV inlet is caused by heat input from the reactor coolant pump.*3: Feedwater mass flow rate is the sum of the blowdown flow rate and the steam mass flow based on heat balance calculation.*4: Calculated by interpolating the data of other cases.*5: Assumed to be the same as Unit-3.*6: As discussed in ATHOS analysis report (Ref. 22), the larger number of unit-2 (305 tubes for 2A) is used for the evaluation. Fig.6.2-1 shows theaddress of the plugged tubes of 2A SG.00zSC)Page 19 of 149S023-617 M1539, REV. 0 zFTable 6.2-3 Basic parameters for calculation for 3A SG evaluation after plugging100 % with noCase 50% 60% 70% 80% 90% 100%pluggingPlugging*4 387 387 387 387 387 387 0869.5 1041.4 1213.3 1385.2 1557.1 1729Thermal power (MWt) 1729(50%) (60%) (70%) (80%) (90%) (100%)RCS flow rate (gpm) -1 205,901 205,901 205,901 205,901 205,901 205,901 209,880-Thot (Tsg-in) (*F)Tsg-.out (F)"2TcoId (°F).2Saturation Steam Pressure (psia) IFouling Factor (ft2hr°F /Btu)Tfeedwater (OF)Circulation RatioSteam Mass Flow (lb/hr)Feed Water Mass Flow (lb/hr)3Blowdown flow rate (gpm) -zz0-7'0aCD(n)0'-3Note*1: Obtained by interpolating the flow rate of 0% plugging and 8% plugging.*2: RCS flow temperature at SG outlet is assumed to be 0.30F lower than that at RV inlet. The 0.30F temperature increase between the SG outlet and RVinlet is caused by heat input from the reactor coolant pump.*3: Feedwater mass flow rate is the sum of the blowdown flow rate and the steam mass flow based on heat balance calculation.*4: As discussed in ATHOS analysis report (Ref. 22), the larger number of unit-2 (305 tubes for 2A) is used for the evaluation. Fig.6.2-1 shows theaddress of the plugged tubes of 2A SG.C00Hoc~I(A 0Page 20 of 149S023-617 M1539, REV. 0 C,'~j)Table 6.2-4 Basic parameters for calculation for 3B SG evaluation after pluggingCase 50% 60% 70% 80% 90% 100% 100 % with nopluggingPlugging"4 420 420 420 420 420 420 0869.5 1041.4 1213.3 1385.2 1557.1 1729Thermal power (MWt) 1729Thermal power (M ____ (50%) (60%) (70%) (80%) (90%) (100%) 1729RCS flow rate (gpm) .' 205,545 205,545 205,545 205,545 205,545 205,545 209,880Thot (Tsg-in) (°F)Tsg.out (°F)'2TcoId (°F)*2Saturation Steam Pressure (psia)Fouling Factor (ft2hr°F /Btu)Tfeedwater (°F)Circulation RatioSteam Mass Flow (lb/hr)Feed Water Mass Flow (lb/hr)"3Blowdown flow rate (gpm)z00CDChD(n0L DNote*1: Obtained by interpolating the flow rate of 0% plugging and 8% plugging.*2: RCS flow temperature at SG outlet is assumed to be 0.3*F lower than that at RV inlet. The 0.3°F temperature increase between the SG outlet and RVinlet is caused by heat input from the reactor coolant pump.*3: Feedwater mass flow rate is the sum of the blowdown flow rate and the steam mass flow based on heat balance calculation.*4: As discussed in ATHOS analysis report (Ref. 22), the larger number of unit-2 (305 tubes for 2A) is used for the evaluation. Fig.6.2-1 shows theaddress of the plugged tubes of 2A SG.C.'>IPage 21 of 149S023-617 M1539, REV. 0 I Non-proprietary Version Ift ) (22/149)Document No. L5-04GA567(6)Tubes to be plugged of 2A SG3 -J, -j 4, -*...... ... ....s 4 4121 A 1!.L -L51 1 _ --------'- -3 .................- F.j -S -"- -...... ..-...--, -_- __ -- _ -. --.." t -" ---- ----- -----. .-.- -. .---.. ..... .....- ...... ....- ---.---41 --A --i- ------------ --- -------------- --17d 171 161 101 156 151 146 141 13 131 126 121 116 111 10L 101 9. 91 .. 1 1. 11 .. .1 ý. U 40 41 36 31 N 21 1. 1I .COLFig. 6.2-1 Plugging tubes of 2A SGI,-Fig.6.2-2 Tube plugging model of ATHOS for 2A SGMITSUBISHI HEAVY INDUSTRIES, LTD.S023-617 M1539, REV. 0Page 22 of 149 rCaaCaCCaCarz010CDCn.Y,>C000o-VFig.6.2-3 Flow Characteristics of Row 80 Column 70 (2A SG)Page 23 of 149S023-617 M1539, REV. 0 rz00CD(1)0C)>~Fig.6.2-4 Flow Characteristics of Row 80 Column 80 (2A SG)Page 24 of 149S023-617 M1539, REV. 0 C122C,,z00CD(1)0Y,>H-41Fig.6.2-5 Flow Characteristics of Row 100 Column 70 (2A SG)Page 25 of 149S023-617 M1539, REV. 0 rz_= o0Y,C>C ,)ri)CNFER0Fig.6.2-6 Flow Characteristics of Row 100 Column 80 (2A SG) -&Page 26 of 149S023-617 M1539, REV. 0 z0CA B10CICD---n.0°0CD> -F1Fig.6.2-7 Flow Characteristics of Row 120 Column 70 (2A SG) Page 27 of 149S023-617 M1539, REV. 0 z000Fig.6.2-8 Flow Characteristics of Row 120 Column 80 (2A SG)Page 28 of 149S023-617 M1539, REV. 0 r:j~zz0CDCD0Y,C)>K-IFig.6.2-9 Flow Characteristics of Row 95 Column 85 (2A SG)Page 29 of 149S023-617 M1539, REV. 0 K-zz -(D0,CDYlFig..2-0 Fow Caraterstis ofRow125Colun 8 (2 S0Page 30 of 149S023-617 M1539, REV. 0 z0,-CD0CD4nFig.6.2-11 Flow Characteristics of Row 138 Column 84 (2A SG) -Page 31 of 149S023-617 M1539, REV. 0 Non-proprietary Version I] (32/149)Document No. L5-04GA567(6)7. Methodology7.1 Fluid elastic vibrationThe term "fluid elastic vibrations" is generally used to refer to self-excited vibration of tube bundles dueto cross flow. In 1969, Connors disclosed the presence of this phenomenon for the first time (Ref.23).Fluid-elastic vibration occurs in tube bundles when the amount of energy absorbed by the tubes isgreater than the amount that the tubes can dissipate. The measure of the fluid-elastic vibrationthreshold for any given tube in the bundle (tube stability) is the ratio of the actual velocity of the fluidsurrounding the tube to the critical fluid flow velocity for this particular tube. The critical flow velocity Ucrequired to generate fluid-elastic vibration is obtained using Connor's formula (Ref.23).r 11/2U ' _ K [ m 2 .......................................................................... ......(3)Where,UV Critical flow velocityf Tube natural frequencyD, : Tube outside diameterK Critical factorM0 :Average tube mass per unit length5 Tube logarithmic decrement(= 2Trh)h Damping ratioPO Density of water outside the tubeThe critical flow velocity U, in eq. (3) is evaluated in case of tube vibration of single degree of freedomsystem with uniform cross flow along the tube axis. In actual tube, however, the vibration of the tubesupported by the tube support plate is multi degrees of freedom system with beam type of vibrationmodes. Therefore, considering the vibration mode and fluid distribution, the effective flow velocity Ue, isevaluated in the following formula.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 32 of 149 S023-617 M1539, REV. 0 Non-proprietary Version I] (33/149)Document No. L5-04GA567(6)Akp___ U(x) 2. 0 * (X) 1 dx0 PC)u .................................................................... (4 )f L MW 0 4(x) 2 dxWhere,Uen Nth mode effective flow velocity(Pn(X) Nth vibration modep(x) Fluid density distribution of water outside the tube in tube axis directionm(x) Tube mass distribution per unit length in tube axis directionU(x) Flow velocity distribution orthogonal to tube axis in tube axis directionx Coordinate component along tube axisPO Average density of water outside the tubem, : Average tube mass per unit lengthL : Tube lengthThe stability ratio is determined as follows in each vibration mode by calculating the ratio of eq. (3) andeq. (4).SR ......................................... ................................................. (5 )Ucnwhere,1/2f. D -- ...................... (6)This value is called the n-th mode stability ratio SRn, and if SR, > 1, fluid elastic vibration occurs.Generally, the maximum stability ratio in each mode is called the stability ratio of the tube, which issimply expressed as SR. The uncertainty of SR calculated by the methodology of this section isevaluated in Attachment-6.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 33 of 149 S023-617 M1539, REV. 0 Non-proprietary Version] (34/149)Document No. L5-04GA567(6)A&7.1.1 Damping ratio and Critical FactorAlthough the suggested value by ASME Sec. Ill Appendix N-1330 for damping ratio is 1.5% and thesuggested value for critical factor is 2.4, the values based on recent experimental data are used in thisevaluation as follows.7.1.1.1 Damping ratioFor U-bend tubes in two phase flow, there are four sources of damping: structural damping, two-phasedamping, viscous damping and squeeze film damping." s + ý T + "+ 's. ................................................................................... (7 )Where,:s :Structural damping ratioTwo-phase damping ratioViscous damping ratioýSF : Squeeze film damping ratioMITSUBISHI HEAVY INDUSTRIES, LTD.Page 34 of 149 S023-617 M1539, REN/.0 INon-proprietary Version) (35/149)Document No. L5-04GA567(6)At(1) Structural dampingThe structural damping ratio is estimated with the following experimental equation developed byPettigrew (Ref.25 and 27). In the case of plugged tubes with Type J stabilizers, the additional damping0.6% is addeds j= N -1 [ 5,L in gas ........................................................................ (8),s = (N N- 1 0.5( Lg m 7 ,in liquid ................................................................ (9)Where,4SNN-1L'Ira: Structural damping ratioNumber of free spans at U-bend regionAVB support points without assuming inactive AVB support pointsAVB widthCharacteristic tube length: average of the longest three free spans lengthsassuming active and/or inactive supports.This would give:1 inactive AVB support point (B02):Im = 1/3(tube length from TSP #7 hot to B04)6 inactive AVB support points (B01 to B06):Im = 1/3(tube length from TSP #6 hot to B07)8 inactive AVB support points (B01 to B08):Im = 1/3(tube length from TSP #6 hot to B09)10 inactive AVB support points AVBs (B01 to B10):Im = 1/3(tube length from TSP #6 hot to B131)12 inactive AVB support points AVBs (B01 to B12):Im = 1/3(tube length from TSP #6 hot to TSP cold).MITSUBISHI HEAVY INDUSTRIES, LTD.Page 35 of 149S023-617 M1539, REV. 0 Non-proprietary Version) (36/149)Document No. L5-04GA567(6)At(2) Two-phase dampingThe two-phase damping depends on the void fraction and fluid properties. Pettigrew's test result of thetwo phase damping shown in Figure 7.1-2 (Ref.26) is used for this evaluation.A semi-empirical expression was developed from the experimental data and the functional equation ofhomogeneous void fraction was obtained as shown in Figure 7.1.2.The effective homogeneous void fraction is calculated by using the ATHOS outputs and followingequation, considering vibration mode._ Jfg(x)¢2dx2l= SqZd ........................................................................................... (10)Where,Homogeneous void fraction@

• Vibration modex Tube axisThe two-phase damping along the tube length is calculated by using Pettigrew's data and the followingequationTp )f( ) 1 (D I) ........................................... ..(11)f([3)= P3/40 for 13 < 40%1 for 40% _<[3 _< 70% ............................................. (12)1 -(P3- 70) / 30 (for > 70%D , = ( 1+ 1 P /D ý o P ...................................................................................... (13)m 0 = nzm , + n p + n , ......................................................................................... (14 )= fD°p° f(DOe/OD)2 + I...........................................(154 l(D I/D o)2 -I(5Where,ýTP Two-phase dampingP3 Homogeneous void fractionD Tube outside diameterMITSUBISHI HEAVY INDUSTRIES, LTD.Page 36 of 149 S023-617 M1539, REV. 0 Non-proprietary Version Ifi) (37/149)Document No. L5-04GA567(6)jAkPpoPoPimvmtTube pitchDensity of secondary mixture flow (Calculated by ATHOS)Density of secondary liquid flowAverage tube mass per unit lengthVirtual added mass per unit lengthMass of primary coolant in tube per unit lengthMass of tube metal per unit length1- 7CM6Eca5(V4co 4t1='-.3_0I-- 2Eo0-'0AwUl 0'0090:0 123o 0 000A AAir-Water Stearn-Waler Freon, Nomal Trangle A Normal Triangle
• Frwn-22 (NTI)V Rotated Triangle T Rotated Triangle 0 Froon-22 (RT)0 Nortndr Square N Normal Square 0 Froon-l I (RT)0 RolaWed Squae_,00t20 40 60 80 100Void Fraction (%)(VTO)D = CT-A(pD2/m)-' {[1 + (DID,)']]/[I -(DID,)2]2}-'Fig 7.1-2 Effect of void fraction on two-phase dampingMITSUBISHI HEAVY INDUSTRIES, LTD.Page 37 of 149S023-617 M1539, REV. 0 INon-proprietary Version) (38/149)Document No. L5-04GA567(6)A(3) Viscous dampingSince the viscous effects are negligibly small in high void fraction (homogeneous void fraction is 40% orgreater) (Ref.27), it is not taken into account in this analysis.(4) Squeeze film dampingSqueeze film damping takes place at the supports and the following equation is based on the availableexperimental data. (Ref.26)YSF = ( N -{ f m o )(. L., ' ......................................................................... (16)Where,SFDNN-1fLImM0Squeeze film dampingSecondary flow liquid densityTube outside diameterNumber of free spans at U-bend regionAVB support points without assuming inactive AVB support pointsNatural frequencyAVB widthCharacteristic tube lengthAverage tube mass per unit lengthMITSUBISHI HEAVY INDUSTRIES, LTD.Page 38 of 149S023-617 M1539, REV. 0 Non-proprietary Version( ] (39/149)Document No. L5-04GA567(6)AiFor unplugqed tubesThe support damping (structural and squeeze film) depends on the void fraction. Since the structuraldamping is increased by a factor of I ) and the squeeze film damping ratio is zero at the "dry condition",the effect of void fraction is evaluated as follows.The effect of void fraction at each AVB support point of each tube is taken into consideration. Theeffective wetness of supports is estimated to determine the damping ratio used for the SR evaluation bythe following equations based on the assumptions listed below. (The basis of these assumptions isdescribed in Attachment-2)When the void fraction is smaller than[ )there is a continuous liquid film on the surface of tube.The support is considered "wet," structural damping corresponds to the liquid condition andsqueeze film damping is effective.When the void fraction is [ ]there is no liquid film on the surface of tube. The supportis considered "dry," structural damping corresponds to the gas condition and squeeze film dampingis not effective.When the void fraction is between ) ) there is a discontinuous liquid film on the surfaceof tube and the support is considered partially wet. The approach to calculate damping in this voidfraction range is described below.N-1s a ........ ......................................... ............... (17)a i ........................................................... (18 )N DS N -I -N s ..........................................N...... ....................................... (19)Where,N Number of free spans in U-bendN -1 Number of AVB support points in U-bendNWS Number of effectively wet AVB supportsNDS Number of effectively dry AVB supportsi :AVB support pointsa: Void fraction at AVB support pointsai Function of void fraction at AVB support pointsMITSUBISHI HEAVY INDUSTRIES, LTD.Page 39 of 149 S023-617 M1539, REV. 0 tNon-proprietary Version II (40/149)Document No. L5-04GA567(6)AtBy replacing the (N-i/N) term in equations 8 and 9 and combining, structural damping adjusted for voidfraction becomes:j................................. ....(20)Similarly replacing the (N-i/N) term in equation 16 with (Nws/N), squeeze film damping adjusted forvoid fraction becomes:Ni,'s (2 460) plD2 LýSF , Nf no .(.. ............................................................... (21)For pluaqed tubesThe plugged tubes are assumed to be in wet condition despite the void fraction. Equations 7 and 16 areused for structural and squeeze film damping, respectively.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 40 of 149 S023-617 M1539, REV. 0 INon-proprietary Version I] (41/149)Document No. L5-04GA567(6)At7.1.1.2 Critical FactorThe effect of void fraction, the effect of pitch to diameter ratio, the ratio between In-plane & Out-of-planeand the effect of flow direction are considered to estimate the Connor's constant as follows.(1) Effect of the void fractionBased on MHI experimental data (Ref.28), the critical factor K is evaluated using the equation shown inFigure 7.1-3 which indicates the relation between the superficial void fraction and the critical factor.This experiment was performed under two-phase flow condition using the straight tube bundle of thetriangular pitch as shown in Table 7.1-1 and Fig.7.1-4.The effective superficial void fraction along the tube length is calculated by considering vibration modeand using the following equation in the same manner as the two-phase damping. The obtained criticalfactor obtained is K1, when the value of P/D is 1.33.K, =() .................................................... (2 2 )Where,x-f/3(x)O252cy_= _' _ .......................................................... ..................... (2 3)Homogeneous void fractionVibration modeTube axisMITSUBISHI HEAVY INDUSTRIES, LTD.Page 41 of 149S023-617 M1539, REV. 0 INon-proprietary Version I) (42/149)Document No. L5-04GA567(6)Ak-/Fig.7.1-3 MHI Experimental Test Result (Relation between Critical Factor and Superficial VoidFraction)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 42 of 149S023-617 M1539, REV. 0 Non-proprietary VersionIIj (43/149)Document No. L5-04GA567(6)is&Table 7.1-1 MHI Test ConditionTube diameterTube pitchNumber of tubesFlow conditionPressureTemperaturei iSuoerficial void fractionFig.7.1-4 MHI Test EquipmentMITSUBISHI HEAVY INDUSTRIES, LTD.Page 43 of 149S023-617 M1539, REV. 0 Non-proprietary Version[ ) (44/149)Document No. L5-04GA567(6)A&(2) Effect of P/DThe greater the pitch is, the higher the critical velocity will be. Since the tube bundle has index and thenominal pitch depends on the number of tube Row, the effect of the tube pitch to diameter ratio (P/D) isadded to the value obtained in the previous section (K1). By taking into account of the index of the tube,the effective tube pitch (P.) is calculated as the average of the triangle sides which includes the tube tobe evaluated.P , -- P , + P + ...................................................................................... (24 )3Where, Evaluated tubes ,Pe Effective pitchP1,P2,P3 Pithes defined in Fig.7.1-5 P,Fig.7.1-5 Effective pitchThe effect of the tube pitch on the Connor's constant is calculated by using the following equationbased on Pettigrew's experimental data (Ref.29).Kp=4.76(P-D )/D +0.76 .................................................................................. (25)KpIK o = K P' D x K 1 ................................................................................ (26 )Where,KP "Equation 21K1 Critical Factor based on MHI experimental test results by taking into account of theeffect of void fraction (P/D=1.33)Kp.P/D : Critical Factor based on Pettigrew's experimental test results by taking into accountof the effect of P/DKp.P/D=.33 "Critical Factor based on Pettigrew's experimental test results when P/D is 1.33Ko Best estimated critical factor of out-of-plane FEIMITSUBISHI HEAVY INDUSTRIES, LTD.Page 44 of 149 S023-617 M1539, RE\/.0 Non-proprietary Version jt ] (45/149)Document No. L5-04GA567(6)A&-(3)Critical Factor of In-plane FEIIn accordance with the experiments by T. Nakamura (Ref.30), FEI is observed in the in-plane directionin a single-phase air flow when the tube pitch-to-tube ratio (P/D) is small. The Connor's constant ofIn-plane FEI is estimated in accordance with the following equation based on Nakamura's experimentaldata. The ratio between the Connor's constant of in-plane FEI and out-of-plane FEI depends on P/D asshown in Figure 7.1-6. In order to reinforce the basis of Connor's constant used for In-plane FEIevaluation, MHI performed air flow test by using the straight tube bundle of the triangular pitch asshown in Fig. 7.1-7. The ratio of Connor's constant between in-plane and out-of-plane FEI obtained byMHI test result is consistent with Nakamura's experimental data as shown in Fig. 7.1-6. Therefore, theConnor's constant of in-plane FEI for SONGS RSGs is calculated based on the effective tube pitchcalculated by taking into account of the index.K i = i xK .................................................................................................... (2 7)Where,K Ratio of critical factor of In-plane FEI and out-of-plane FEIKi *Best estimated critical factor of In-plane FEIKo Best estimated critical factor of out-of-plane FEIRatio KVc(In-flow)/Vc(Out-of-flow)Ratio ol Notecritical fl ýJ.cityK=Vc(ln-plane)fVc(0ut-4*plane)1.5 Air- 2.7 voletteetalWater (2006)1.37 Air 1.7 Khalvattl at al.(2010)1.2 Air 0.71 Naoa ur .... al.(2012)Fig.7.1-6 Experimental Test Result (Relation between Critical Factor In-plane FEI and P/D)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 45 of 149 S023-617 M1539, REV. 0 Non-proprietary Version II) (46/149)Document No. L5-04GA567(6)AtI-(a) Test equipmentrk-.(b) Test ResultsFig.7.1-7 MHI air flow testMITSUBISHI HEAVY INDUSTRIES, LTD.Page 46 of 149S023-617 M1539, REV. 0 Non-proprietary Version) ](47/149)Document No. L5-04GA567(6)A&(4) Effect of Flow DirectionThe effect of the flow direction on the critical velocity is also determined based on the test result(Ref.31). The greater the angle of the flow direction from the in-plane of tube, the greater the value ofthe critical velocity will be.The effect of the flow direction on the critical velocity (increase ratio" a(e)") is determined based on thetest result shown in Fig.7.1-8 (Ref.31). "a(8)" is defined by the upstream critical flow velocity; notin-plane flow velocitya (O ) _= U c(_ ) ...................................................................................... (28)Uc(Odeg)Where,0UcAngle of Flow directionCritical velocity0.410 .1 ..--6 °- , -0101 20 20PMALLflL NOOMATALANGLE FLOW DIRECTION dcjrc) "RII.Fig. 1O Ellectot Incident flOWdirection on critical VelocityFLCW0o degParallel (0 deg.)FLOW0000000600* 000.@Normal triangle (30 deg.)Fig.7.1-8 Effect of the flow direction (Ref.31)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 47 of 149S023-617 M1539, REV. 0 11Non-proprietary Version I) (48/149)Document No. L5-04GA567(6)Ak-Stability ratio is usually calculated by using in-plane flow velocity V. On the other hand, the functiona( e) is defined by the magnitude of normal flow velocity Vn to the tube. Therefore, Ki or K0 aremultiplied by the velocity ratio Vn/V and function a(O ) as shown in Fig.7.1-9, then K used for theanalysis is obtained.K = Kix Vn/Vxa(O) for in-plane FEI evaulation ................................................ (29)K = K. x Vn/Vxa('9) for out of plane FEI evaluation ........................................... (30)Vn/V = cos0 ..................................................................................................... (3 1)Where,aVnVK,K.Effect of Flow directionAverage in-plane velocityMagnitude of flow velocityBest estimated critical factor of In-plane FEIBest estimated critical factor of out of plane FEIBest estimated critical factor used for the evaluationRowMagnitude of FlowColumnFig.7.1-9 Effect of flow directionMITSUBISHI HEAVY INDUSTRIES, LTD.Page 48 of 149S023-617 M1539, REV. 0 I Non-proprietary Version It) (49/149)Document No. L5-04GA567(6)A7.2 Calculation modelStability analyses are carried out in the following manner.(1) Tube rowThe tubes shown in TableAttachment-7 for details).7.2-1 and Fig.7.2-1 are selected by SCE for the evaluation (see ATable 7.2-1 Evaluated TubesRow Column80 7080 80100 70100 80120 70120 8095 85125 85138 84* Plugged tubesO Representative tube for OA ---,-- -O'
• 0.--O .. - -. .--------i ,*
• Si .S S140135130125120115110105100 =959085807570---it-60 65 70 75 80 85COLFig.7.2-1 Evaluated TubesMITSUBISHI HEAVY INDUSTRIES, LTD.Page 49 of 149S023-617 M1539, REV. 0 INon-proprietary Version I] (50/149)Document No. L5-04GA567(6)At(2) Support conditions of AVB (Anti-Vibration Bar) and TSP (Tube Support Plate)AVB and TSP support points are modeled as pin-supported points. Analysis models includingnode number and coordinate of TSP elevation are shown in Fig. 7.2-1 to 7.2-9.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 50 of 149 S023-617 M1539, REV. 0 INon-proprietary Version I] (51/149)Document No. L5-04GA567(6)AtrFig. 7.2-1 Calculation model for Row 80 Column 70MITSUBISHI HEAVY INDUSTRIES, LTD.Page 51 of 149S023-617 M1539, REV. 0 Non-proprietary Version It) (52/149)Document No. L5-04GA567(6)AtFig. 7.2-2 Calculation model for Row 80 Column 80MITSUBISHI HEAVY INDUSTRIES, LTD.Page 52 of 149 SO2Z3-617 M1539, REV. 0 Non-proprietary Version() (53/149)Document No. L5-04GA567(6)AokFig. 7.2-3 Calculation model for Row 100 Column 70MITSUBISHI HEAVY INDUSTRIES, LTD.Page 53 of 149 S023-617 M1539, REV. 0 I Non-proprietary Version jt) (54/149)Document No. L5-04GA567(6)-AtFig. 7.2-4 Calculation model for Row 100 Column 80MITSUBISHI HEAVY INDUSTRIES, LTD.Page 54 of 149 S023-617 M1539, REV. 0 Non-proprietary VersionI] (55/149)Document No. L5-04GA567(6)AtI-2Fig. 7.2-5 Calculation model for Row 120 Column 70MITSUBISHI HEAVY INDUSTRIES, LTD.Page 55 of 149S023-617 M1539, REV. 0 Non-proprietary Version] (56/149)Document No. L5-04GA567(6)AtK-Fig. 7.2-6 Calculation model for Row 120 Column 80MITSUBISHI HEAVY INDUSTRIES, LTD.Page 56 of 149 S023-617 M1539, REV. 0 I Non-proprietary Version It] (57/149)Document No. L5-04GA567(6)At_-Fig. 7.2-7 Calculation model for Row 95 Column 85MITSUBISHI HEAVY INDUSTRIES, LTD.Page 57 of 149S023-617 M1539, REV. 0 INon-proprietary Version I] (58/149)Document No. L5-04GA567(6)AFig. 7.2-8 Calculation model for Row 125 Column 85MITSUBISHI HEAVY INDUSTRIES, LTD.Page 58 of 149S023-617 M1539, REV. 0 Non-proprietary Version I1 (59/149)Document No. L5-04GA567(6)AtI-Fig. 7.2-9 Calculation model for Row 138 Column 84MITSUBISHI HEAVY INDUSTRIES, LTD.Page 59 of 149 S023-617 M1539, REV. 0 Non-proprietary Version1 (60/149)Document No. L5-04GA567(6)A&8. Computation Results8.1 Out of plane FEI analysis resultsThe out of plane FEI analysis results for 2A SG are shown in Table.8.1.1-1 to 8.1.2-2 as follows.(1) Assuming all support points active:For 2A SGTable 8.1.1-1 All support points are active and the thermal power is 70%No oluggingTable 8.1.1-2 All support points are active and the thermal power is 100% with no plugging(2) Assuming 1 support point inactive:For 2A SGTable 8.1.2-1 1 support point is inactive and the thermal power is 70%No plugainaTable 8.1.2-2 1 support point is inactive and the thermal power is 100% with no pluggingMITSUBISHI HEAVY INDUSTRIES, LTD.Page 60 of 149 S023-617 M1539, RE\/.0 Table 8.1.1-1 Out of Plane FEI Analysis Results for 2A SG when the thermal power is 70% and all support points are active Tube Location Tube natural Damping Ratio Critical Average Average Maximum Critical Effectiveof inactive frequency h(%) coefficient fluid void void flow flow Stabilitysupport Mode density fraction fraction velocity velocity rati6point f(Hz) Structural Two SqueezeRow Col dal phase film Total K1 Ko Ke K Po(ibfft3) [-] [-] Uc(ft/sec) Ue(ft/sec)damping damping damping80 7080 80100 701 0(*) 80(')120 70120 8095(*) 85(')125 85138 84z0CDcnC,=0--nNote(*): Plugged tube with Type J stabilizerC,Page 61 of 149S023-617 M1539, REV. 0 ATable 8.1.1-2 Out of plane FEI Analysis Results for no plugging model when the thermal power is 100% and all support points are activeC,'C,'Locationof inactive Tube natural Damping Ratio Critical Average Average Maximum Critical Effectiveponsupport frequency h(%) coefficient fluid void void flow flow Stabilitypoint Mode density fraction fraction velocity velocity ratioStructural Two Squeeze 3RowSrcCaol phase film Total K1 Ko Ke K Po(lb/ft ) [-1 [-] Uc(ftlsec) Ue(ftlsec)damping damping damping80 7080 80100 70100 80120 70120 8095 85125 85138 84z00CDCD0n,=-"oI ~CD41~ '-0~\Page 62 of 149S023-617 M1539, REV. 0 Cc.4~CCI)CI)Table 8.1.2-1 Out of Plane FEI Analysis Results for 2A SG when the thermal power is 70% and 1 support point is inactiveLocationof inactive Damping Critical Average Average Maximum Critical EffectiveTube support Tube natural Ratio coefficient fluid void void flow flow Stabilitypoint Mode h(%) density fraction fraction velocity velocity ratiof(Hz) Structural Two Squeeze (Ib/ft) [-] Uc(ft/sec) Ue(ft/sec)Row Col phase film Total KI Ko Ke K POI I- damping damping damping80 70 B0380 80 B03100 70 B03100(*) 80(*) B03120 70 B03120 80 B0395(') 85(') B03125 85 B03138 84 B04Note(*): Plugged tube with Type J stabilizer0Y0C)>'-IPage 63 of 149S023-617 M1539, REV. 0 ATable 8.1.2-2 Out of plane FEI Analysis Results for no plugging model when the thermal power is 100% and 1 support point is inactiveLocationof inactive Damping Critical Average Average Maximum Critical EffectiveTube support Tube natural Ratio coefficient fluid void void flow flow Stabilitypoint Mode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) Structural Two SqueezeRow Col phase film Total K1 Ko Ke K po(Ift3) [-] [-] Uc(ft/sec) Ue(ftfsec)RowCol damping damping damping80 70 B0380 80 B03100 70 B02100 80 B02120 70 B02120 80 B0295 85 B03125 85 B02138 84 B02asz01002CDCO00KPage 64 of 149S023-617 M1539, REV. 0 Non-proprietary Version I[ 1(65/149)Document No. L5-04GA567(6)At8.2 In-plane FEI analysis resultsThe in-plane FEI analysis results are shown in Table 8.2.1-1 to 8.2.4-7 as follows.(1) Assuming 6 support points are inactive:For 2A SGTable 8.2.1-1 6 consecutive support points are inactive and the thermal power is 50%Table 8.2.1-2 6 consecutive support points are inactive and the thermal power is 60%Table 8.2.1-3 6 consecutive support points are inactive and the thermal power is 70%Table 8.2.1-4 6 consecutive support points are inactive and the thermal power is 80%Table 8.2.1-5 6 consecutive support points are inactive and the thermal power is 90%Table 8.2.1-6 6 consecutive support points are inactive and the thermal power is 100%No pluaainaTable 8.2.1-7 6 consecutive support points are inactive and the thermal power is 100% with noplugging(2) Assuming 8 support points are inactive:For 2A SGTable 8.2.2-1 8 consecutive support points are inactive and the thermal power is 50%Table 8.2.2-2 8 consecutive support points are inactive and the thermal power is 60%Table 8.2.2-3 8 consecutive support points are inactive and the thermal power is 70%Table 8.2.2-4 8 consecutive support points are inactive and the thermal power is 80%Table 8.2.2-5 8 consecutive support points are inactive and the thermal power is 90%Table 8.2.2-6 8 consecutive support points are inactive and the thermal power is 100%No pluggingTable 8.2.2-7 8 consecutive support points are inactive and the thermal power is 100% with nopluggingMITSUBISHI HEAVY INDUSTRIES, LTD.Page 65 of 149 S023-617 M1539, REV. 0 I Non-proprietary Version IIIJ (66/149)Document No. L5-04GA567(6)A&(3) Assuming 10 support points are inactive:For 2A SGTable 8.2.3-1 10 consecutive support points are inactive and the thermal power is 50%Table 8.2.3-2 10 consecutive support points are inactive and the thermal power is 60%Table 8.2.3-3 10 consecutive support points are inactive and the thermal power is 70%Table 8.2.3-4 10 consecutive support points are inactive and the thermal power is 80%Table 8.2.3-5 10 consecutive support points are inactive and the thermal power is 90%Table 8.2.3-6 10 consecutive support points are inactive and the thermal power is 100%No pluggingTable 8.2.3-7 10 consecutive support points are inactive and the thermal power is 100% with noplugging(4) Assuming All support points are inactive:For 2A SGTable 8.2.4-1 All consecutive support point:Table 8.2.4-2 All consecutive support point:Table 8.2.4-3 All consecutive support point:Table 8.2.4-4 All consecutive support point:Table 8.2.4-5 All consecutive support point:Table 8.2.4-6 All consecutive support point:No pluggingTable 8.2.4-7 All consecutive support poirpluggings are inactive and the thermal power is 50%s are inactive and the thermal power is 60%s are inactive and the thermal power is 70%s are inactive and the thermal power is 80%s are inactive and the thermal power is 90%s are inactive and the thermal power is 100%nts are inactive and the thermal power is 100% with noMITSUBISHI HEAVY INDUSTRIES, LTD.Page 66 of 149S023-617 M1539, REV. 0 C,'C,'Table 8.2.1-1 In-plane FEI Analysis Results for 2A SG when the thermal power is 50% and 6 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) Structural Two Squeezefilm po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)Row 0Col dampin phase Total Kf1 Ko K Ke Kdamping damping damping80 7080 80100 70100(*) 80(.)120 70120 8095(*) 85(*)125 85138 84z00'aCDC,0Note(*): Plugged tube with Type J stabilizerIAýY0>Page 67 of 149S023-617 M1539, REV. 0 Table 8.2.1-2 In-plane FEI Analysis Results for 2A SG when the thermal power is 60% and 6 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioRwof(Hz) Structural Squeeze film Tp(lb/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)Row Col f(Hz) Strrdamping phase Total K1 K0 Ki K,damping damping80 7080 80100 70100(*' 80(')120 70120 8095() 85(*)125 85138 8466z0,.-i0CDCDCn0tz0Note(*): Plugged tube with Type J stabilizer1j4a)40 Y>0Page 68 of 149S023-617 M1539, REV. 0 zTable 8.2.1-3 In-plane FEI Analysis Results for 2A SG when the thermal power is 70% and 6 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioTwo po(b/f3) [-] [-] Uc(ft/sec) Ue(ft/sec)Row Col f(Hz) Structural phase Squeeze film Total K1 Ko Ki Ke Kdamping damping80 7080 80100 701 00M 80M120 70120 8095(*) 85(1)125 85138 84Z0"{3-60CDW.(0604-INote(*): Plugged tube with Type J stabilizerýkPage 69 of 149S023-617 M1539, REV. 0 Table 8.2.1-4 In-plane FEI Analysis Results for 2A SG when the thermal power is 80% and 6 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioRow Col f(Hz) Structural Two Squeeze film po(lb/ft3) [-1 [-] Uc(ft/sec) Ue(ft/sec)Ro o ig phase apn Total K1 Ko Ki Ke Kdaming phase____ ____ damping_____damping damping80 7080 80100 701 00M 80(1)120 70120 8095(*) 85(*)125 85138 84z0'0CDW.0"33/Note(*): Plugged tube with Type J stabilizer[ýý ) 1 00.Page 70 of 149S023-617 M1539, REV. 0 M"MjTable 8.2.1-5 In-plane FEI Analysis Results for 2A SG when the thermal power is 90% and 6 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioTwo Squeeze3film p(Ib/ft3) [-] Uc(ft/sec) Ue(ft/sec)Row Col f(Hz) Structural phase Total KI Ko Ki Ke Kdamping damping damping80 7080 80100 70100(') 80(*)120 70120 8095(*) 85(*)125 85138 84Z07'0CD0)C-,6C0Note(*): Plugged tube with Type J stabilizerPage 71 of 149S023-617 M1539, REV. 0 Table 8.2.1-6 In-plane FEI Analysis Results for 2A SG when the thermal power is 100% and 6 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioRow Co f(Hz) Structural Two Squeeze film po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)Ro ~ apn phase dmig Total K1 KO Ki Ke Kdamping damping damping80 7080 80100 70100(*) 80(*)120 70120 8095(') 85(*)125 85138 84z0,0CD"(310CDC,5.Note(*): Plugged tube with Type J stabilizerký ) 1 0.Page 72 of 149S023-617 M1539, REV. 0 U)'W,Table 8.2.1-7 In-plane FEI Analysis Results for no plugging model when the thermal power is 100% and 6 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) Structural Two Squeeze film po(lb/ft3) H[ [-] Uc(ft/sec) Ue(ft/sec)Row Col phase Total K1 K0 Ki Kedamping damping damping80 7080 80100 70100 80120 70120 8095 85125 85138 84z00:3_D.n0CD0Page 73 of 149S023-617 M1539, REV. 0 rj2zcj~Table 8.2.2-1 In-plane FEI Analysis Results for 2A SG when the thermal power is 50% and 8 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioTwo p(bf3 --cf/e)U~tscRow 0ol f(Hz) Structural phase Squeeze film Total K Ko K Ke KUc(fsec) Ue(ftsec)damping dampin damping80 7080 80100 70100(') I 80()120 70120 8095(*) 85(*)125 85138 84I06 ý060VhNote(*): Plugged tube with Type J stabilizerkRýPage 74 of 149S023-617 M1539, REV. 0 Table 8.2.2-2 In-plane FEI Analysis Results for 2A SG when the thermal power is 60% and 8 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioRow Col f(Hz) Structura w Two Squeezefilm Total H I [-]dampin h p damping Total K1 Ko Ki Ke K P°(Ib/ft3) Uc(ft/sec) Ue(ftlsec)dmi 9 damping dmi80 7080 80100 701 00(*) 80(*)120 70120 8095(.) 85(*)125 85138 84I0-'CDl06>0hNote(*): Plugged tube with Type J stabilizerV~~1IPage 75 of 149S023-617 M1539, REV. 0 Table 8.2.2-3 In-plane FEI Analysis Results for 2A SG when the thermal power is 70% and 8 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) Structural Squeeze film po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)Row Col phase Total K1 Ko Ki KO Kdamping damping damping80 7080 80100 70100(*) 80(*)120 70120 8095(*) 85(*)125 85138 84I0'0CD00C)4ziNote(*): Plugged tube with Type J stabilizerýk~Page 76 of 149S023-617 M1539, REV. 0 rj~C,)C-,Table 8.2.2-4 In-plane FEl Analysis Results for 2A SG when the thermal power is 80% and 8 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) Structural Squeeze film po(lb/ft3) [-] [ Uc(ft/sec) Ue(ft/sec)Row Col damping phase Total K1 Ko Ki Ke Kdamping damping damping80 7080 80100 70100(*) 80(*)120 70120 8095(*) 85(*)125 85138 84z0,=660=30CDY,,3O03-L .-Note(*): Plugged tube with Type J stabilizerPage 77 of 149S023-617 M1539, REV. 0 C,'rj~zC')C"Table 8.2.2-5 In-plane FEI Analysis Results for 2A SG when the thermal power is 90% and 8 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioRow Col da n Pase lmpin Total Ki Ko K Ke Squeezefilm po(lb/ft3) [-] [-] Uc(ftlsec) Ue(ft/sec)_____ ___ _______ damping dapn80 7080 80100 701 00( ° 0(//120 70120 8095(*) 85(*)125 85138 84z0,=.60CD=3_j.OCD00CNote(*): Plugged tube with Type J stabilizer0>~0Page 78 of 149S023-617 M1539, REV. 0 C,'rj~Table 8.2.2-6 In-plane FEI Analysis Results for 2A SG when the thermal power is 100% and 8 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioTwo po(Ib/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)Row Col f(Hz) Structural phase Squeeze film Total K1 Ko Ki Ke Kdamping damping damping80 7080 80100 7010 0) 80(*)120 70120 8095(*) 85(*)125 85138 8466z00CD(n.0i0Note(*): Plugged tube with Type J stabilizerCD0Y.,Page 79 of 149S023-617 M1539, REV. 0 CI)Cl,Cl,Table 8.2.2-7 In-plane FEI Analysis Results for no plugging model when the thermal power is 100% and 8 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioTwo p(bf3) --cf/e)U~tscRow Col f(Hz) Structural phase Squeeze film T(lbft ) Uc(ftlsec) Ue(ftlsec)damping damping damping Total K1 Ko Ki K, K80 7080 80100 70100 80120 70120 8095 85125 85138 84z0'00)Cn0-i1 0 to '- Y> G8Page 80 of 149S023-617 M1539, REV. 0 Table 8.2.3-1 In-plane FEI Analysis Results for 2A SG when the thermal power is 50% and 10 consecutive support points are inactiveC,,Tube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioRow Col f(Hz) Structural Two Squeeze film po(lb/ft3) [-1 [-] Uc(ft/sec) Ue(ft/sec)damping phase damping Total K1 Ko Ki KO Kdamping80 7080 80100 70100(o) 80(*)120 70120 8095(*) 85(*)125 85138 84z00CDCD.0Note(*): Plugged tube with Type J stabilizerocPage 81 of 149S023-617 M1539, REV. 0 CI)CI)CI)Table 8.2.3-2 In-plane FEI Analysis Results for 2A SG when the thermal power is 60% and 10 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioCf(Hz) Structural Two Squeeze film po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ftlsec)Row Col f(z trcualp phase dmig Total K1 Ko Ki Ke Kd damping damping80 7080 80100 701 00M 80(*)120 70120 8095(*) 85(*)125 85138 84z0CD")CD.0ZI0Note(*): Plugged tube with Type J stabilizerV, NPage 82 of 149S023-617 M1539, REV. 0 C,,C,,Cj2Table 8.2.3-3 In-plane FEI Analysis Results for 2A SG when the thermal power is 70% and 10 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioRow Co f(Hz) Structural Two Squeezefilm po(Ib/ft) Uc(ft/sec) Ue(ft/sec)tur phase d ilm Total K1 Ko Ki Ke Kdamping damping damping80 7080 80100 70100(*) 80(*)120 70120 8095(*) 85(*)125 85138 84Z0CDCn.0n106Note(*): Plugged tube with Type J stabilizerýk ) 1111U0CDC)>J ~Page 83 of 149S023-617 M1539, REV. 0 Table 8.2.3-4 In-plane FEI Analysis Results for 2A SG when the thermal power is 80% and 10 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) Structural Two Squeeze film po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)Row Cola phase Total K1 Ko Ki Kedamping damping damping80 7080 80100 701 00M) 80C)120 70120 8095(*) 85(*)125 85138 846LZ0:2.0:3C0Note(*): Plugged tube with Type J stabilizer0Page 84 of 149S023-617 M1539, REV. 0 rj~C,,C,,C,,FTable 8.2.3-5 In-plane FEI Analysis Results for 2A SG when the thermal power is 90% and 10 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) Structural Squeeze film T po(Ib/ft3) [-] [-1 Uc(ft/sec) Ue(ft/sec)Row Ctrcdamping phase Total K1 Ko Ki Ke Kdmigdamping damping80 7080 80100 70100(') 80(')120 70120 8095(M 85(*)125 85138 84kz0CD(DC,.00 ENote(*): Plugged tube with Type J stabilizer0Page 85 of 149S023-617 M1539, REV. 0 Table 8.2.3-6 In-plane FEI Analysis Results for 2A SG when the thermal power is 100% and 10 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) Structural Squeeze film po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)Row Col dal phase damping Total K1 KO K Kedamping damping damping80 7080 80100 70100(*) 80(1)120 70120 8095(*) 85(*)125 85138 8466CD00Y,J0Z00DCDtn.0Note(*): Plugged tube with Type J stabilizerPage 86 of 149S023-617 M1539, REV. 0 r.j~rj,r.j~Table 8.2.3-7 In-plane FEI Analysis Results for no plugging model when the thermal power is 100% and 10 consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioRow Col f(Hz) Structural Two Squeeze film po(Ib/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)damping phase Total K1 K Ki K Kdamping damping80 7080 80100 70100 80120 70120 8095 85125 85138 84z0'00CDCn.0LOC)> -Page 87 of 149S023-617 M1539, REV. 0 X,X,Table 8.2.4-1 In-plane FEl Analysis Results for 2A SG when the thermal power is 50% and all consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) Structural Two Squeeze film po(Ib/ft) [-] [-] Uc(ft/sec) Ue(ft/sec)Row Col phaseToa K1 K i e Kdamping damping damping80 7080 80100 70100(*) 80(*)120 70120 8095(*) 85(*)125 85138 84z00CD0)Y,C)0>N(' 00*-\Note(*): Plugged tube with Type J stabilizer49Page 88 of 149S023-617 M1539, REV. 0 Table 8.2.4-2 In-plane FEI Analysis Results for 2A SG when the thermal power is 60% and all consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratioTwo p0Ibf3) [-] [-] Uc(ft/sec) Ue(ftsec)Row Col f(Hz) Structural phase Squeeze film Total K1 Ko Ki Ke Kdamping damping damping80 7080 80100 70100(*) 80(*'120 70120 8095() 85M'125 85138 846ýZ00CD0)0Note(*): Plugged tube with Type J stabilizerY0>-Page 89 of 149S023-617 M1539, REV. 0 Table 8.2.4-3 In-plane FEI Analysis Results for 2A SG when the thermal power is 70% and all consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) Structural Two Squeeze film po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)Row Col dal phase Total K1 Ko Ki Ke Kdamping damping damping80 7080 80100 70100(*) 80(')120 70120 8095(*) 85(*)125 85138 84z03 3CD(n.0Note(*): Plugged tube with Type J stabilizer'zCDJPage 90 of 149S023-617 M1539, REV. 0 Table 8.2.4-4 In-plane FEI Analysis Results for 2A SG when the thermal power is 80% and all consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) Structural ose Squeeze film po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)damping damping damping80 7080 80100 70100(*) 80(')120 70120 8095(*) 85(*)125 85138 84z00CD0)I Note(*): Plugged tube with Type J stabilizerC)>~( 'A!:7Page 91 of 149S023-617 M1539, REV. 0 Table 8.2.4-5 In-plane FEI Analysis Results for 2A SG when the thermal power is 90% and all consecutive support points are inactivez006CD(n.00Y0C~~->ANote(*): Plugged tube with Type J stabilizerPage 92 of 149S023-617 M1539, REV. 0 Table 8.2.4-6 In-plane FEI Analysis Results for 2A SG when the thermal power is 100% and all consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) structural Two po(Ib/f [-] [-] Uc(ft/sec) Ue(ft/sec)Ro o (z tutrlSqueeze film p(bf3Row Col damping phase damping Total K1 Ko Ki Ke Kdampinga80 7080 80100 701 00() 80(1)120 70120 8095(") 85(1)125 85138 84Z00'a0O,0©t-Note(*): Plugged tube with Type J stabilizer_Rý 0'CPage 93 of 149S023-617 M1539, REV. 0 Table 8.2.4 -7 In-plane FEI Analysis Results for no plugging model when the thermal power is 100% and all consecutive support points are inactiveTube Damping Critical Average Average Maximum Critical EffectiveTube natural Ratio coefficient fluid void void flow flow StabilityMode frequency h(%) density fraction fraction velocity velocity ratiof(Hz) Structural Two Squeezefilm po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)Row Col dal phase dampin Total K1 Ko Ki Ke Kdamping damping damping80 7080 80100 70100 80120 70120 8095 85125 85138 84z0'0CDCD.0i:3C)Page 94 of 149S023-617 M1539, REV. 0 Non-proprietary Version I[ 3 (95/149)Document No. L5-04GA567(6)At9. Reference1) ASME Boiler and Pressure Vessel Code, Sec II, Materials, 1998 Edition through 2000 addenda.2) ASME Boiler and Pressure Vessel Code, Sec III Appendix N-1330, 1998 Edition through 2000addenda.3) L5-04FU001 the latest revision, Component and Outline Drawing 1/34) L5-04FU002 the latest revision, Component and Outline Drawing 2/35) L5-04FU003 the latest revision, Component and Outline Drawing 3/36) L5-04FU021 the latest revision, Tube Sheet and Extension Ring 1/37) L5-04FU022 the latest revision, Tube Sheet and Extension Ring 2/38) L5-04FU023 the latest revision, Tube Sheet and Extension Ring 3/39) L5-04FU051 the latest revision, Tube Bundle 1/310) L5-04FU052 the latest revision, Tube Bundle 2/311) L5-04FU053 the latest revision, Tube Bundle 3/312) L5-04FU111 the latest revision, AVB assembly 1/913) L5-04FU112 the latest revision, AVB assembly 2/914) L5-04FU113 the latest revision, AVB assembly 3/915) L5-04FU114 the latest revision, AVB assembly 4/916) L5-04FU115 the latest revision, AVB assembly 5/917) L5-04FU1 16 the latest revision, AVB assembly 6/918) L5-04FU117 the latest revision, AVB assembly 7/919) L5-04FU1 18 the latest revision, AVB assembly 8/920) L5-04FU119 the latest revision, AVB assembly 9/921) Analysis of Thermal Hydraulics of Steam Generators/Steam Generator Analysis Package, Ver.3.1,1016564, EPRI.22) L5-04GA566 the latest revision, Case study of the input parameters and tube plugging impact oninternal SG thermal hydraulics parameters23) Connors, H.J., Fluid Elastic Vibration of Tube Arrays Excited by Cross Flow, ASME Annual Meeting,1970.24) Blevins, R. D., "Flow-induced Vibration", Krieger Publishing Company.25) M.J. Pettigrew.,et.al.,2011,Damping of Heat Exchanger Tubes in Liquids: Review and DesignGuidelines,Journal of Pressure Vessel Technology Vol.13326) M.J. Pettigrew.,et.al.,2003,"Vibration analysis of shell-and-tube heat exchangers" Journal of Fluidsand Structures 18 (2003) 469-48327) S. M. Fluit and M. J. Pettigrew, "Simplified method for predicting vibration and fretting-wear innuclear steam generator U-bend tube bundle", ASME PVP 2001 Vol.420-128) WJS16263, MHI Test Report of Fluid Elastic Vibration29) M.J. Pettigrew.,et.al.,2000, "The effects of tube bundle geometry on vibration in two-phasecross-flow",Flow Induced Vbration, Ziada&Staubi(eds) 2000 Balkema, RotterdamISBN905809129530) Flow-Induced VibrationMeskell & Bennett (eds) ISBN 978 9548583 6, "Study on In-flowFluid-elastic Instability of Circular Cylinder Arrays"], T.Nakamura, Y.Fujita, T.Oyakawa, Y.NI. July201231) H.C.Yeung, 1983, "The effect of Approach Flow Direction on the Flow-Induced Vibrations of aTriangular Tube Array", Transaction of ASME Vol.10532) L5-04GA587 the latest revision, Test result for damping ratio added by the stabilizer inserted forshort length (Row No. 106)Page 95 of 149S023-617 M1539, REV. 0 Non-proprietary Version I) (96/149)Document No. L5-04GA567(6)AkAttachment-1Computer Input and Output File ListPage 96 of 149S023-617 M1539, REV. 0 Non-proprietary Version(97/149)Document No. L5-04GA567(6)AtTable I-1 Input and Output file name of out of plane FEI evaluation for 2A SG when all support pointsare active AThermal Row Column Input 1) Output 1)Power(%)80 70 _80 80100 70100 8070 120 70120 8095 85125 85138 8480 7080 80100 70100 100 80120 70(No Plug) 120 8095 85125 85138 84 _____Table 1-2 Input and Output file name of out of plane FEI evaluation for 2A SG when 1 support points areinactiveThermal Row Column Input 1) Output 1)Power(%)80 7080 80100 70100 8070 120 70120 8095 85125 85138 8480 7080 80100 70100 100 80120 70(No Plug) 120 8095 85125 85138 84 ____Notes:1) All files are saved in the directory as below:Page 97 of 149S023-617 M1539, REV. 0 I Non-proprietary Version IJ (98/149)Document No. L5-04GA567(6)AtTable 1-3 Input and Output file name of in-plane FEI evaluation for 2A SG when 6 consecutive supportpoints are inactive (1/2)Thermal Row Column Input 1) Output 1)Power(%)80 70 ,80 80100 70100 8050 120 70120 8095 85125 85138 8480 7080 80100 70100 8060 120 70120 8095 85125 85138 8480 7080 80100 70100 8070 120 70120 8095 85125 85138 8480 7080 80100 70100 8080 120 70120 8095 85125 85138 8480 7080 80100 70100 8090 120 70120 8095 85125 85138 8480 7080 80100 70100 80100 120 70120 8095 85 1 1125 85138 84 .-Notes: 1) All files are saved in the directory as below: I APage 98 of 149S023-617 M1539, REV. 0 Non-proprietary Version[ 3(99/149)Document No. L5-04GA567(6)AtTable 1-3 Input and Output file name of in-plane FEI evaluation for 2A SG when 6 consecutive supportpoints are inactive (2/2)Thermal Row Column Input 1) OutputPower(%)80 7080 80100 70100 100 80120 70(No Plug) 120 8095 85125 85 11138 84 1Notes: 1) All files are saved in the directory as below:Page 99 of 149S023-617 M1539, REV. 0 Non-proprietary Version III) (100/149)Document No. L5-04GA567(6)AtTable 1-4 Input and Output file name of in-plane FEI evaluation for 2A SG when 8 consecutive supportpoints are inactive (1/2)ThermalPower(%) Row Column Input 1) Output 1)80 7080 80100 70100 8050 120 70120 8095 85125 85138 8480 7080 80100 70100 8060 120 70120 8095 85125 85138 8480 7080 80100 70100 8070 120 70120 8095 85125 85138 8480 7080 80100 70100 8080 120 70120 8095 85125 85138 8480 7080 80100 70100 8090 120 70120 8095 85125 85138 8480 7080 80100 70100 80100 120 70120 8095 85125 85138 84 1.Notes: 1) All files are saved in the directory as below:Page 100 of 149S023-617 M1539, REV. 0 Non-proprietary Version I3 (101/149)Document No. L5-04GA567(6)A&Table 1-4 Input and Output file name of in-plane FEI evaluation for 2A SG when 8 consecutive supportpoints are inactive (2/2) AThermalPower(%) Row Column Input ) Output 1)80 7080 80100 70100 100 80120 70(No Plug) 120 8095 85125 85138 84Notes: 1) All files are saved in the directory as below:I I IAPage 101 of 149S023-617 M1539, REV. 0 (Non-proprietary Version I) (102/149)Document No. L5-04GA567(6)AtTable I-5 Input and Output file name of in-plane FEI evaluation for 2A SG when 10 consecutive supportpoints are inactive (1/2) 14\ThermalPoer(%) Row Column Input 1) Output 1)Power(%)80 70 _80 80100 70100 8050 120 70120 8095 85125 85138 8480 7080 80100 70100 8060 120 70120 8095 85125 85138 8480 7080 80100 70100 8070 120 70120 8095 85125 85138 8480 7080 80 1100 70100 8080 120 70120 8095 85125 85138 84 180 7080 80100 70100 8090 120 70120 8095 85125 85138 8480 7080 80100 70100 80100 120 70120 8095 85125 85138 84 "-.Notes: 1) All files are saved in the directory as below:Page 102 of 149S023-617 M1539, REV. 0 Non-proprietary Version IIJ (103/149)Document No. L5-04GA567(6)At-Table I-5 Input and Output file name of in-plane FEt evaluation for 2A SG when 10 consecutive supportpoints are inactive (2/2) AThermal Row Column Input 1) OutputPower(%)80 70 r80 80100 70100 100 80120 70(No Plug) 120 8095 85125 85138 84Notes: 1) All files are saved in the directory as below:Page 103 of 149S023-617 M1539, REV. 0 I Non-proprietary Version I) (104/149)Document No. L5-04GA567(6)AtiTable 1-6 Input and Output file name of in-plane EIl evaluation for 2A SG when 12 consecutive supportpoints are inactive (1/2) Z6\Thermal Row Column Input Output 1)Power(%)80 7080 80100 70100 8050 120 70120 8095 85125 85138 8480 7080 80100 70100 8060 120 70120 8095 85125 85138 8480 7080 80100 70100 8070 120 70120 8095 85125 85138 8480 7080 80100 70100 8080 120 70120 8095 85125 85138 8480 7080 80100 70100 8090 120 70120 8095 85125 85138 8480 7080 80100 70100 80100 120 70120 8095 85125 85 1138 84 A tNotes: 1 ) All files are saved in the directory as below:MITSUBISHI HEAVY INDUSTRIES, LTD.Page 104 of 149S023-617 M1539, REV. 0 I Non-proprietary Version jI) (105/149)Document No. L5-04GA567(6)AtTable 1-6 Input and Output file name of in-plane FEI evaluation for 2A SG when 12 consecutive supportpoints are inactive (2/2)Thermal Row Column Input 1) OutputPower(%)80 7080 80100 70100 100 80120 70(No Plug) 120 8095 85125 85138 84Notes: 1) All files are saved in the directory as below:MITSUBISHI HEAVY INDUSTRIES, LTD.Page 105 of 149S023-617 M1539, REV. 0 INon-proprietary Version I) (106/149)Document No. L5-04GA567(6)A,&Attachment-2 Evaluation of Liquid Film Thickness of Tube at AVB Support Point1. SummaryIn order to estimate the effect of void fraction on the squeeze film damping, the relation between theliquid film thickness of tube at each AVB support point and void fraction is evaluated as shown inTable-1.Table-1 Relation between liquid film thickness of tube and void fractionVoid fraction Liquid Film Condition FigureNo Dry out Fig.l-1Discontinuous Dry & Wet Fig.1-2Continuous Wet Fig.1-3TubeAVB0DropletLiquid film(Thickness :6)SSS0e from thepoint (1*)0S0 *** 5 0eS S0Fig.1-1 No film (Dry out)Fig.1-2 Discontinuous (Dry & Wet)Fig. 1-3 Continuous (Wet)The boundary of void fraction is determined as follows and the flow regime is confirmed to beconsistent with the figures above as described in Attachment-4.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 106 of 149 S023-617 M1539, REV. 0 INon-proprietary Version I) (107/149)Document No. L5-04GA567(6)A,&2. Assumption of Liquid Film ThicknessFig.2 shows the relation between distance from the contact point (1*) and liquid film thickness (a),which is obtained by the following geometrical equation, where 0 and d are defined in Fig.3.-(1- cos0)~ =2S121*= dsin 02(1)(2)The thickness of the continuous liquid film is [ ) which is obtained in Fig.2assuming the effective distance from the contact point for squeeze film damping is)The basis of[ )of the effective distance is described in Attachment-3.The minimum thickness of discontinuous liquid film is assumed to be[ }whiclcomparable to the degree of surface roughness of tube.byIisLFig.2 Relation between distance from the contact point and liquid film thicknessMITSUBISHI HEAVY INDUSTRIES, LTD.Page 107 of 149S023-617 M1539, REV. 0 Non-proprietary Version IJ (108/149)Document No. L5-04GA567(6)AtTubeLiquid filmLiquidAVB61* IFig.3 Distance from the contact point and liquid film thicknessMITSUBISHI HEAVY INDUSTRIES, LTD.Page 108 of 149 SO23-617 M1539, REV. 0 Non-proprietary Version j[] (109/149)Document No. L5-04GA567(6)At3. Estimation of Void fractionFig.4 shows the relation between void fraction and liquid film thickness, which is obtained from thefollowing equations.Asub -(Af + Ad)= (3)AsubAf = [(d + 2,)2 -d2] (4)4Ad = -4,f (5)A,,,b =- -d (6)2 4Where,a Void fractionPt Tube pitchd Tube diameterAsub Flow area of sub channel (See Fig.5)Ad Sectional area of droplet (See Fig.5)Af Sectional area of liquid film, which is assumed to be a twice of the area of droplet (SeeFig.5) and the basis of this assumption is described as follows.The ratio between the flow rate of liquid film Gf and the flow rate of droplet GE can be assumed to be 0.2in accordance with the test results shown in Fig.6 (Ref.1).Fig.6 is the results of heating cylinder which indicates that the flow rate of liquid film, Gf, isapproximately 20% of the flow rate of droplet, GE, when the quality is 50%.(50% quality at SONGSRSG condition (steam pressure is 838 psia) corresponds to 91% of void fraction)..Gf 1 (7)GE 5On the other hand, the ratio between the flow velocity of droplet, Ue, and the flow velocity of liquid film,Uf, is approximately 10, which is obtained from Fig.7.Fig.7 is the air-water flow test results of cylinder at atmospheric condition where the flow velocity ofliquid film and the apparent gas velocity are measured in various conditions of the apparent liquidvelocity, ji, and the hydraulic equivalent diameter (Ref.2). Since ratio between the flow velocity of liquidfilm and droplet does not depend on the pressure (Ref.3), these data are applicable to SONGS RSGMITSUBISHI HEAVY INDUSTRIES, LTD.Page 109 of 149 S023-617 M1539, REV. 0 LNon-proprietary Version j) (110/149)Document No. L5-04GA567(6)Atevaluation.Assuming the velocity of the droplet, Ue, is identical to the apparent gas velocity, jg, the flow velocity ofdroplet, Ue, is approximately ten times the flow velocity of liquid film, Uf, at all conditions. The flowvelocity of the liquid film does not depend on the condition of the apparent liquid velocity or thehydraulic equivalent diameter.'l _= 10 (8)11f Uf*~lf *~lfFrom the equation of continuity (9), the ratio of sectional area between liquid film and droplet can bederived as follows. (Equation (10) is identical to Equation (5))Gf = PfQf _ -Af ,,fGE PsQE QE Ad 11EAf Qf "E -= =2Ad QE UfMITSUBISHI HEAVY INDUSTRIES, LTD.Page 110 of 149(9)(10)S023-617 M1539, REV. 0 INon-proprietary VersionJ (111/149)Document No. L5-04GA567(6)At-Fig.4 indicates;When void fraction is lower than 95%, there is a continuous liquid film on the tube since thethickness of liquid film is larger than( ]When void fraction is higher than 98%, there is no liquid film on the tube since the thickness ofliquid film is smaller than[ ]which is the assumed minimum thickness of thediscontinuous liquid film on the tube.Fig.4 Relation between void fraction and liquid film thickness4. References1) Akagawa,"Gas and liquid Two-phase Flow" p.1502) "Fluid characteristics of annular mist flow of gas and liquid" p.395-495, 49-4383) Nakazatomi, et.al, Experimental study of vertical upward gas-liquid two-phase annular flow (2ndreport, effects of system pressure on characteristics of waves)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 111 of 149 S023-617 M1539, RE\/.0 Non-proprietary Version I) (112/149)Document No. L5-04GA567(6)A~k6Droplet (Sectional area Ad)Liquid film (Sectional area Af)Fig. 5 Sectional area of droplet and liquid film1.0Gf is approximately 20 % of GEwhen the quality is 0.500)NE0zTest condition-Two-phase flow (steam/water) inheating cylinder (heat flix is 8.6x 104 W/ft2)film -At high pressure (427psia)o 0.60 QualityFig.6 Flow rate of liquid film and droplet (Ref.1)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 112 of 149S023-617 M1539, REV. 0 I Non-proprietary Version jII] (113/149)Document No. L5-04GA567(6)A&Shearer &Hall -Tayloret al.Uf is approximately 10 % of Jg in all cases,which does not depend on J, and thehydraulic equivalent diameterEEEr00°-LLTest condition-Water/air flow in a cylinder-At atmospheric pressure androom temperatureDefinition of symbolsJ~m 8 12 18 251260.04 *10~i oA v0.06 14) 1 A AV0.1
• 11 A Vot14 Al V8 10 15 20 30Hydraulic equivalent diameterFig.7 Flow rate of liquid film and droplet (Ref.2)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 113 of 149 S023-617 M1539, REV. 0 I Non-proprietary Version I] (114/149)Document No. L5-04GA567(6)Athfor Squeeze Film DampingThe effective distance of liquid film of tube from the contact point for squeeze film damping is evaluatedto be[ ] as calculated below.The calculation model of tube and AVB is shown in Fig.l. When the amplitude of gap velocity vibration innormal direction of AVB is v0, the velocity at x in horizontal direction is defined as equation (1) since theliquid volume pushed out by the tube is the same as the liquid volume which flows in the horizontaldirection.V(v) = v.5(x)(1)Tube{I'0 r~AVB~IFig.1 Calculation modelMITSUBISHI HEAVY INDUSTRIES, LTD.Page 114 of 149S023-617 M1539, REV. 0 I Non-proprietary Version I[ j (115/149)Document No. L5-04GA567(6)AOn the other hand, the force balance of the small volume in the gap flow area is presented as equation(2).v2 p v(x + dx)2 p(x + dx) v2dxv- + -_ + (2)2 p 2 p 25Where,p :Pressurep :Liquid densityA :Tube friction factor defined by equation (3).{48/Re if Re < 13000.26 Re24 if Re > 1300 (3)The equation (4) represents the pressure gradient, which is derived by differentiating the equation (3).dp p dv2 2 2(Re) (4)dx 2 dx 2 28(x)The pressure at x is shown as equation (5), which is obtained by integrating equation (4).p(x) -PV(x) jx(Pvx)2 +po (5)2 o 2 1(x)Since the shape of the gap flow area is divergent and the flow velocity at the exit of the gap flow area isnegligibly small, P0 can be determined by assuming that the hydraulic pressure is zero.The damping force Fd is presented in equation (6), which is derived by integrating pressure.F = 2HJ' p(x)dx (6)Where,H :AVB widthI" Effective distance of liquid film of tube from the contact pointTherefore, the damping coefficient Cd is,Cd = F/vo (7)Fig.2 shows the calculation results of the normalized damping coefficient which is a fraction to themaximum value obtained by using the equations above and the conditions listed in Tablel.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 115 of 149 S023-617 M1539, REV. 0 Non-proprietary Version[ ) (116/149)Document No. L5-04GA567(6)AtFig.2 indicates a trend that when the distance from the contact point is greater thanidamping coefficient will be saturated.ItheTable 1 ConditionsInitial gapTube diameterAVB widthAmplitude ofdisplacementFrequency of vibrationLiquid densityKinetic viscosityNote *: Values at BOL design condition (Th=598 deg.F)-11Distance from the contact point (mm)Fig.2 The damping coefficient and the distance from the contact pointMITSUBISHI HEAVY INDUSTRIES, LTD.Page 116 of 149 S023-617 M1539, REV. 0 Non-proprietary VersionII 3(117/149)Document No. L5-04GA567(6)A&Attachment-4 Confirmation of Flow Regime1. Flow regimeMHI has calculated the Grant flow regime map as shown in Figurel by using ATHOS computer codeoutputs of BOL design conditionI ] in accordance with Reference 1.12 tubes shown inFigure 1 are selected as representatives and each tube has 19 evaluation points in U-bend (10 degreespitch data such as 0, 10, 20 .180 degrees).The points at hot side (0, 10, 20 ...,90 degrees) are shown as filled markers and the points at cold side(100, 110, 120,...,180 degrees) are shown as non-filled markers in Figure 1. Most plots on the hot sideare in the spray flow regime, which is consistent with the methodology of the squeeze film evaluation.2. Reference[1] M. Pettigrew and C. Taylor, "Vibration Analysis of shell-and-tube heat exchangers: an overview-Part I: Flow, Damping, Fluidelastic Instability," Journal of Fluids and Structures 18 (2003) 469-483r)Note *: The points at 90 degrees are included in the hot side.Figure 1 Flow Regime of Representative Tubes at BOL Design ConditionMITSUBISHI HEAVY INDUSTRIES, LTD.Page 117 of 149S023-617 M1539, REV. 0 I Non-proprietary Version 1I ) (118/149)Document No. L5-04GA567(6)AAttachment-5 Case Study for Applying Split Stabilizers for TTW tube of Unit-2 at 70%Thermal Power1. PurposeThe purpose of this attachment is to confirm the effectiveness of applying the split stabilizers for TTW(tube-to-tube wear) tubes. In order to confirm the effectiveness of the split stabilizers, some casesshown in Table 2-1 are studied.2. ConclusionThe results of case study for applying type J stabilizer are shown in Table 2-1 and Figure 2-1. Type Jstabilizers are split stabilizers that extend approximately 60' into the U-bend, inserted on the hot andcold side of the tube. It has been confirmed that stability ratio of TTW tubes with type J stabilizer is lessthan 1.0.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 118 of 149 S023-617 M1539, RE\/. 0 Table 2-1 Natural Frequency and Stability Ratio6W,Tube Without Stabilizer With split Stabilizers(To 60 degrees in U-bend at both of hot and cold side)Small amplitudel I Medium amplitudel I Large amplitude I I Very large amplitudel IAdditional damping ratio Additional damping ratio Additional damping ratio Additional damping ratioSI I I INatural Stability Natural Stability Natural Stability Natural Stability Natural Stability RatioFrequency Ratio Frequency Ratio Frequency Ratio Frequency Ratio Frequency(Hz) (Hz) (Hz) (Hz) (Hz)R111C81R113C81Z0CD0/I'2!Y,(a) Relationship between stability ratio and additional damping (b) Relationship between stability ratio and tube amplitude (R1 13C81)Fig. 2-1 Effect of additional damping on the stability ratioPage 119 of 149S023-617 M1539, REV. 0 INon-proprietary Version] (120/149)Document No. L5-04GA567(6)At3. Assumption(1) Representative tubeRepresentative tubes (Row1 13 Col.81 and Row1 11 Col.81) are TTW tubes of Unit-2 (2 tubes).(2) AVB support pointsIn this evaluation, all AVB support points are assumed to be inactive for conservatism because thestability ratios of the tubes obtained from the evaluation will be the maximum possible values.(3)Plugging and StabilizerThe representative tubes are assumed to be plugged with or without split stabilizers.In the cases with split stabilizers, the stabilizers are assumed to be installed to 60 degrees in theU-bend region at the both of hot and cold side to maximize the structural damping. As shown in Table3-1, the additional damping ratio by the split stabilizers (Type J) is assumed to be the differencebetween the damping ratio of tube with and without split stabilizers based on the report of the dampingtest (Ref.32). Table 3-1 was derived for Row 106 but can be applied to all rows.AkTable 3-1 Additional dampina due to split stabilizersAmplitude Damping ratio (%)Without stabilizer With split stabilizers Additional dampingratioSmall I IMediumi ILarge I IVery large I _(4) Effect of primary water entering into the TTW tubesThe effect of primary water entering into the TTW tubes is not taken into account by assuming there inno leakage through the plugging.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 120 of 149 S023-617 M1539, REV. 0 Non-proprietary Version[ 1(121/149)Document No. L5-04GA567(6)At4. Acceptance criteriaThere are no criteria because of parametric case study.5. Design inputs5.1 GeometryThe tube bundle consists ofi diameter, thermally treated Alloy 690 U-tubes that are arranged in aI 1 equilateral triangular pitch and are supported by the tubesheet, seven tube support plates,and six sets of anti-vibration bars (AVBs). Tube support plates (TSPs) have broached trifoil tube holes.All the contacting support structures above the tubesheet are made of 405 stainless steel. The nominaldimension of tube, TSPs and AVBs are listed in Table 5-1.5.2 Thermal and Hydraulic flow of steam generator secondary sideThe ATHOS thermal hydraulic analysis program was used to determine the distributions of fluid gapvelocity in the normal direction to tube in-plane and fluid density. Table 5-2 and Fig 5-1, 5-2 show theflow characteristic that are applied to the tubes for the evaluation at 70% thermal power of Unit-2 withplugging.6. MethodologyThe analysis is performed in accordance with the same procedures provided in main report to evaluatethe best estimated stability ratio for in-plane FEI.7" ResultsThe analysis results are shown in Table 7-1 and 7-2.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 121 of 149 S023-617 M1539, REV. 0 INon-proprietary Version) (122/149)Document No. L5-04GA567(6)A&Table 5-1 Nominal dimensions of tubes, TSPs, and AVBsPart Item ValueMaterial Thermally treated SB-163 UNS N06690Outside diameter 0.75 inThickness 0.043 inTubesNumber of tubes 9727Tube pitch 1.0 inTube arrangement TriangularMaterial SA-240 Type 405ThicknessTSPs Number of TSPsTube support span(between TSP centers)Tube support span(from tubesheet to TSP-1)Material SA-479 Type 405TypeAVBsThicknessWidthStabilizer Unit weightAMITSUBISHI HEAVY INDUSTRIES, LTD.Page 122 of 149S023-617 M1539, REV. 0 INon-proprietary Version) (123/149)Document No. L5-04GA567(6)AtTable 5-2 Basic parameters for calculation for 2A SG evaluation after pluggingPlugging 305Thermal power (MWt) 1213.3 (70%)RCS flow rate (gpm) 206,695Thot (Tsg-in) (*F)Tsg..out (*F)TCOlId (F)Saturation Steam Pressure (psia)Fouling Factor (ft2hr°F /Btu)Tfeedwater ('F)Circulation RatioSteam Mass Flow (lb/hr)Feed Water Mass Flow (lb/hr)Blowdown flow rate (gpm)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 123 of 149S023-617 M1539, REV. 0 rCCl)z0'0CDCn)0Y,-IFig. 5-1 Flow Characteristics of Row1 11 Col81Page 124 of 149S023-617 M1539, REV. 0 7--NCl)z0CD0)0r,__S023-617 M1539, REV. 0Fig. 5-2 Flow Characteristic of Row 113 CoI.81Page 125 of 149 Thble 7-1 results for case study of solit stabilizers (Row 111 Column 81) /C,'Tube Damping Critical Average Average Maximum Critical EffectiveAdditional natural Ratio coefficient fluid void void flow flow StabilityStructural Mode frequencyh() density fraction fraction velocity velocity ratioTubeing cSqueezedmi Structural Two phase film Total Ki Ko Ki Ke Kf(Hz) damping damping damping po(Ib/ft3) [-] [-] Uc(ft/sec) Ue(ftlsec)Plugged withoutstabilizerPlugged with splitstabilizers whentube amplitude issmallPlugged with splitstabilizers whentube amplitude ismediumPlugged with splitstabilizers whentube amplitude islargePlugged with splitstabilizers whentube amplitude isvery large ___z0'0M..CD0)CD0.00 :>Page 126 of 149S023-617 M1539, REV. 0 M,Table 7-2 Analysis results for case study of stabilizer (Row 113 Column 81) A.Tube Damping Critical Average Average Maximum Critical EffectiveAdditional natural Ratio coefficient fluid void void flow flow StabilityTube condi sti n sructural Mo ef q enyh )Tube condition damping Mode frequency h(%) density fraction fraction velocity velocity ratioN%) Structural Two phase SqueezeHi film Total KS KK Ke K po(ib/ft3) [_] [-] Uc(ft/sec) Ue(ftlsec)f(Hz) damping damping dampingPlugged withoutstabilizerPlugged withstandardstabilizerPlugged with splitstabilizers whentube amplitude issmall _Plugged with splitstabilizers whentube amplitude ismediumPlugged with splitstabilizers whentube amplitude islargePlugged with splitstabilizers whentube amplitude isvery large _ _z000)CDCn.0 '> tPage 127 of 149S023-617 M1539, REV. 0 Non-proprietary Version) (128/149)Document No. L5-04GA567(6)AtAttachment-6 Uncertainty of Calculated Stability Ratio1. PurposeThe purpose of this attachment is to evaluate the uncertainty of stability ratio evaluation based on MHImethodology.2. SummaryThe uncertainty of the stability ratio (SR) evaluation based on MHI methodology is evaluated bysumming the uncertainties of critical parameters. As a result, the uncertainty of SR evaluation iscalculated to be in the range between -5 % and -57%. Therefore, the stability ratios are calculatedconservatively based on MHI methodology.Table 1 Difference between SR based on MHI evaluation method and best estimatedRelative stability Best estimated Uncertainty of MHI's SRratio based on evaluationMHI evaluation, Upper bound Lower boundR1H1MS Mean +/-20 SRmax SRminvalue deviation,o SR .Hr SRAHI3. Evaluation methodIn this evaluation, the standard deviation of SR evaluation multiplied by 2 is regarded as anuncertainty. Table 2 shows the parameters used in the SR calculation and includes whichparameters should be taken into account. The methodology of the uncertainty evaluation is shownas follows.3.1 Uncertainty of Each ParameterThe uncertainty of each parameter is estimated by the following equation. In this equation, it isassumed that the uncertainty of each parameter is equal to two times as large as standard deviationof relative error.i Xir f J ...................................................................(1)Where,MITSUBISHI HEAVY INDUSTRIES, LTD.Page 128 of 149 S023-617 M1539, REV. 0 Non-proprietary Version[ ](129/149)Document No. L5-04GA567(6)AXref :Reference value of each test dataX : test data0"N: Standard deviation of relative error of each test data: Number of dataAccording to error propagation law, the effect of the standard deviation of each parameter on that of SRis evaluated with the following equations (See Ref. 3) and 2O-SR is regarded as an uncertainty of SRevaluation.S p TH -Ay2-)T.......................................................... (2 )-(sr s + (7TpATP + CFSFýSF -OrT rP + C+/-ASF SF. ............................................... (3)ýST + TP + SF2K + a 7.2 .............................................................................................. (4 )Where,C-sR Standard deviation of SR uncertaintya7r,, Standard deviation of SR due to thermal hydraulic parameters evaluationUP Standard deviation of parameters used for SR evaluationTotal damping ratioýST Structural dampingýTp Two phase dampingýSF Squeeze film dampingIA: Standard deviation of 1"CYST Standard deviation of ýSTGr : Standard deviation of ýTpa's Standard deviation of ;SFa7K Standard deviation of K'KI :Standard deviation of KICa : Standard deviation of a(O)X- Standard deviation noted above ( usedparameter (dimensionless)for SR evaluationeviation of relative error of eachMITSUBISHI HEAVY INDUSTRIES, LTD.Page 129 of 149S023-617 M1539, REV. 0 Non-proprietary Version I[ )(130/149)Document No. L5-04GA567(6)At3.2 Difference between SR based on MHI method and that based on the best estimatedparametersIn MHI method, the Connor's constant and damping ratio are evaluated conservatively becauselower bounded data are used for some parameters. The difference between the stability ratio basedon MHI method and that based on the best estimated parameters is evaluated by the followingequation.S SR. RmR *,H, 7 7*-m K K ,'q m_ KBE [. ýBE .S
• n._. ................................... (5)A SRBE 1 HS* K V M AI l SR(KBE SSWhere,R,*HI : Relative stability ratio based on MHI evaluation methodSRAfH: Stability ratio based on MHI evaluation methodSRBE Mean stability ratio based on the best estimated parametersKMH : Connor's constant based on MHI evaluation methodKBE Mean Connor's constant based on the best estimated parametersMAMH: Damping ratio based on MHI evaluation methodýBE Mean damping ratio based on the best estimated parametersSR* Average of normalized SR based on three different TH codes (See Sec. 4.2)SR11Average of normalized SR based on MHI-ATHOS (See Sec. 4.2)When the relative ratio of Connor's constant and damping ratio are defined as shown in equation (6)and (7), equation (5) is converted to equation (9).R K K A H ........................................................................................................ (6 )KBER , .......................................................................................................... (7 )ýBESR .T H I .I. ... ........................................................................................... (8 )SR"R'M,="IT -R .................................................................... (9)RAIll -TR K R4ýMITSUBISHI HEAVY INDUSTRIES, LTD.Page 130 of 149 S023-617 M1539, REV. 0 Non-proprietary Version[ 3(131/149)Document No. L5-04GA567(6)AtBased on Table 2, the relative ratios of Connor's constant and damping ratio are converted toEquation (10) and (11).R K K 1 a( ) .... ..... ............. ............................................ (10)KBE KlBE a(O)BEý 1P ýTP-MHIf +ýSF 4SF-AIHf-ý ý1MHI -TP-BE 4SF-BE..............................()ýBEWhere,K1 Afi Connor's constant based on MHI evaluationKIBE Mean Connor's constant based on the experimental dataa(O)MHI" The effect of flow direction based on MHI evaluation methoda(O)BE Mean effect of flow direction based on the experimental dataýSF-MHI Squeeze film damping ratio based on MHI evaluation method4SFB-E Mean squeeze film damping ratio based on the experimental dataýTP-AIHI Two phase damping ratio based on MHI evaluation methodýTP-BE Mean two phase damping ratio based on the experimental data3.3 Uncertainty of SRBased on the standard deviation and the relative stability ratio, the uncertainty of stability ratio basedon the MHI method is obtained from the following equations.For the upper bound,SRmax I+ 2crsR .SRAfH........................................................................... (12)For the lower bound,SRmin 1 -2rsR.(13)SR A H RM(13MITSUBISHI HEAVY INDUSTRIES, LTD.Page 131 of 149 S023-617 M1539, REV. 0 Non-proprietary Version I[ ) (132/149)Document No. L5-04GA567(6),Ak-Table 2 Parameters used for SR calculationU, Effective flow YesvelocityUl Critical flow Yes The uncertainty of these parametersvelocity due to thermal-hydraulic parametersf Tube natural Yes analysis error is evaluated by thefrequency comparison of three independentAverage tube Yes analyses as shown in Section 4.2.massP0 Fluid density YesConnors'sThe uncertainty of KI is estimatedK1 constant based Yes based on MHI test data.on MHI testecoefficient to Lower limit of Pettigrew's test data isused for SR calculation. (Ref. 4)Kp consider the effect No It is not necessary to considerof tube pitch on K uncertainty of KpK The ratio of K The result of MHI air flow test was(See in the in-plane consistent with the public test dataSec.4.1 (1)) K FEI to that of the No (See Sec. 7.1.1.2 (3) of main report).out-of-plane Therefore the uncertainty of K is notFEI necessary to consider.Lower limit of Yeung's test data isTh cons eeffcint ts used for SR calculation. (Ref. 1)a(9) consider the effect Yes Teucranyo ()iof flow angle on K The uncertainty ofa(O) isestimated based on test data.Structural 4IST is relatively small compared to4'sT damping ratio No 'SFTwo-Phase Yes The uncertainty OfisF is estimated(e damping ratio based on Prof. Pettigrew's test data.(SeeVicuSec.4.1 (2)) ;'v Viscous No ;, is not used for SR calculationdamping ratio IImsF Squeezerfilm Yes The uncertainty of 4;s is estimateddamping ratio Ibased on Prof. Pettigrew's test data.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 132 of 149S023-617 M1539, REV. 0 Non-proprietary Version j[~ 1(133/149)Document No. L5-04GA567(6)At-4. Evaluation Result4.1Parameters Used for SR Evaluation(1) Connors' constantConnor's constant based on MHI testStandard Deviation of Connors' constant K is estimated based on MHI's steam water two phaseflow test data to investigate the fluid elastic vibration in the out of plane direction.Figure 1 shows Connors' constant data obtained by MHr's test (black points
• in Figure 1). HoweverConnors' constant data include the error due to estimating it without considering measuring error ofratio of volume flow rate, flow velocity and fluid density. Therefore it is necessary to consider theerror of both ratio of volume flow rate ,/ and Connors' constant K which are horizontal andvertical axis (these data are indicated as red points N in Figure 1). Equations for calculating theerror are as follows. Here the effect of error of damping ratio on Connors' constant K is neglected.Because damping ratio is determined with shape of the spectrum, therefore it is assumed thatestimation of damping ratio is not affected by measuring error.-Error of Connors' constant2e= ic + 6 .0) + ( 6 0 ...................................................................... (14)Where, Equation of Connors' constant : K = ) oD2EK Relative error of Connors' constant Kcuc Relative error of critical flow velocity6m0 Relative error of tube density considered added mass of outside water0,0 Relative error of fluid density E m.0)Error of ratio of volume flow rate-UU U2 2 _2(Ug +U)2 4U/(ugUg)2 +U2(EiU1)2 .(15)U 9 + U l f U 9 + U X1 U .Where, Equation of ratio of volume flow rate : 8 = UgUg + UIUg: flow velocity of vapor (gas)U,: flow velocity of water (liquid)Ep Relative error of ratio of volume flow rate6ug : Relative error of flow velocity of vapor (gas)cut Relative error of flow velocity of water (liquid)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 133 of 149 S023-617 M1539, REV. 0 I Non-proprietary Version I] (134/149)Document No. L5-04GA567(6)AtAccording to MHI's test data, measuring error ( ug, E'l, .0 and c.0 is as follows:E= IEuc =1 (max value of measuring error of flow velocity; max( 6ug', CCU))-.60 = EP0 =1 I(maximum value of measuring error of fluid density)Measuring error of each parameter is estimated based on proof reading result and inspection resultaccording to GUM (Guide to the expression of Uncertainty in Measurement, ASME).Table 3 Measuring error of each parametersteam watermeasuring error of pressure (%)fluid density at reference pressure;6MPa (kg/mA3)fluid density at the pressureconsidering error; 6.02MPa (kg/mA3)measuring error of fluid density (%)measuring error of flow rate (%) ILX 1X 2measuring error of cross section (%)3X 1 Relative error between fluid density ati landl Isteam Iwater IX-2 Proof reading result of flow rate measurementX-3 Measuring error of cross section is estimated by dimensional inspection result andmeasuring error of digital vernier calipers I IX-4 Measuring error of flow velocity is calculated by following equationin accordance with GUME26 ~2 C 2ELI = 2 x 3+ 3 + 33 3 3WhereEL measuring error of flow velocityEQ measuring error of flow rateCA measuring error of cross section6,p :measuring error of fluid densitysteam :MITSUBISHI HEAVY INDUSTRIES, LTD.Page 134 of 149 S023-617 M1539, 4. 0 Non-proprietary Version[ 3(135/149)Document No. L5-04GA567(6)AtwaterTherefore relative error of Connors' constant is estimated to be 6,K = fby using equation (14).Also E. is calculated with measuring error eug & E by using equation (15), the calculationresult is shown in Table 4. Both relative error of cK and e. are calculated according to errorpropagation law.Table 4 Calculation of relative error of 13P jg+jl'ýý(M/s) jg,*(mls) jlm, (mis) (%0.70.98_____0.93____ _X-1 Critical flow velocity obtained by MHI testCritical flow velocity of vapor and water calculated by test condition (linear interpolation)Then the uncertainty of KI is estimated from the measuring error of test data by calculating themaximum relative error of each data (red points E in Figure 1(a)) from fitting curve of original data.There are following 4 types of data when considering relative error of Connors' constant (+/-+K ) andratio of volume flow rate (v r. ), because each relative error has positive and negative value (+/-E).(1) Data with + cK and + v18(2) Data with + 'K and -- Ef(3) Data with -'K and + c#(4) Data with -cK and -e'lThere are data for uncertainty evaluation (red points E in Figure 1(a)) 4 times as much as test data(black points lue (+/-E). wing 4 types of data when KI is estimated by following equation as maximumrelative error from fitting curve.K ma ......... .............. (16)WhereKi each data for uncertainty evaluation; K1k approximate value at each 86 ( fitting curve)N Number of data for uncertainty evaluation ( 4 times as much as test data)Therefore, the standard deviation of K1 is assumed to be maximum relative error of all data (1)-MITSUBISHI HEAVY INDUSTRIES, LTD.Page 135 of 149 S023-617 M1539, RE'V. 0 Non-proprietary Version[ 3(136/149)Document No. L5-04GA567(6)At(4) at each ratio of volume flow rate ; 2-K =KI= I (UK =1 I)' Because measuring error ofKI and 61 are estimated as 2 times as large as standard deviation : 2a, it is assumed thatK1Since the mean data is used for the SR evaluation, the relative ratio of K1, KImH , isI IKIBEK -Figure 1 Experimental data of Connors's constant based on MHI test; KIMITSUBISHI HEAVY INDUSTRIES, LTD.Page 136 of 149S023-617 M1539, REV. 0 Non-proprietary Version I[ )(137/149)Document No. L5-04GA567(6)AtEffect of flow directionFigure 2 shows Yeung's test data of the coefficient to consider the effect of flow angle on K; a(0).Lower limit of the data is used for the stability ratio evaluation when the flow direction is smaller than20 degrees; the flow directions are smaller than 20 degrees in the center of the bundle (FEIsusceptible region) as shown in Figure 3.In accordance with Figure 2, the standard deviation below 20 degrees is obtained to bel landthe mean line is added, which isi larger than the lower limit used for the SR evaluation.a(o)AfH ii,Therefore, the relative ratio, a(O),E isl IConnor's constantTherefore, the standard deviation of Connor's constant, cKI, is I obtained by using Equation (4)and the relative Connor's constant, RK , isl jobtained by using Equation (10) as follows.ý, 2, + I"07 KI a I=RK = ______ a(9)Aff.KIBE a(O)BEMITSUBISHI HEAVY INDUSTRIES, LTD.Page 137 of 149 S023-617 M1539, RE\/.0 I Non-proprietary Version I) (138/149)Document No. L5-04GA567(6)AFigure 2 Experimental data of a(O)Figure 3 Region where the flow direction is greater than 20 degrees from the tube in-planedirection to out-of-plane directionMITSUBISHI HEAVY INDUSTRIES, LTD.Page 138 of 149 S023-617 M1539, RE'V. 0 INon-proprietary Version [)1(139/149)Document No. L5-04GA567(6)At(2) Damping RatioSqueeze film dampinqUncertainty of squeeze film damping ýSF is estimated based on Pettigrew's test data as shown inthe Figure 4 (See Ref. 2). According to this figure, the squeeze film damping ratio depends on thevibration frequency and the bounded line of 4-SF, with 90th percentile ( = 50 / f ) is used for the OAevaluation in accordance with Pettigrew's guideline.As shown in Figure 4, the bounded line based on 90th percentile ( = 50 / f) is used for MHI's SRevaluation. In order to obtain the standard deviation and the relative ratio, the lower bounded linewith 95th percentile (= 43.5 / f) and the average line ( = 100 / f )are added.Since the difference between 95th percentile and the average line is considered as 20SF, thestandard deviation is Iand the ratio between 90th percentile and theaverage line is the relative ratio of squeeze film damping, 7SF-Aff , which is]9SF-BEMITSUBISHI HEAVY INDUSTRIES, LTD.Page 139 of 149 S023-617 M1539, REV. 0 Non-proprietary Version II] (140/149)Document No. L5-04GA567(6)At/-Note) because there are 20 points below the Pettigrew's guideline with 90th percentile, the lowerbounded line with 95th percentile is determined such that there are 10 plot points belowthis lineFigure 4 Experimental data of squeeze film dampingMITSUBISHI HEAVY INDUSTRIES, LTD.Page 140 of 149 S023-617 M1539, RIEV. 0 Non-proprietary Version[ 3(141/149)Document No. L5-04GA567(6)AtTwo phase dampingqUncertainty of two phase damping is estimated based on Pettigrew's test data as shown inFigure 5 (See Ref. 5). In order to obtain the standard deviation and the relative ratio, the lowerbounded line of all the data, which is assumed to show 99. 7th percentile ( = -3aTp), is added. Sincethe difference between the gradient of the 99.7th percentile I and the gradient of theaverage linel I is considered as 3STp, the standard deviation is I Theratio between the gradient of guide line used for SR evaluation I and the gradient of theaverage line is the relative ratio of two phase damping, !which isTP-BEFigure 5 Experimental data of two phase dampingMITSUBISHI HEAVY INDUSTRIES, LTD.Page 141 of 149 S023-617 M1539, REV. 0 Non-proprietary Version) (142/149)Document No. L5-04GA567(6)AtTotal dampinq ratioAccording to equation (3), in order to estimate the standard deviation of total damping ratio 4,it isnecessary to consider absolute value of each damping ratio. According to damping ratio data usedin analysis shown in Table 5, it is found that ý4SF / =1 land Tp/IL=I ITherefore thestandard deviation of total damping ratio, c,, Iis estimated to bel Ias follows.a "- = S "F+ TpThe relative damping ratio is obtained to bel4'SF -H + 4"T ý'TP-MHIfR= SF-BE qTP-BE4-Iby using Equation (11) as follows.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 142 of 149S023-617 M1539, REV. 0 Non-proprietary Version I[ )(143/149)Document No. L5-04GA567(6)At4.2 SR due to Thermal-Hydraulic Parameters EvaluationIn order to evaluate the standard deviation of SR due to the thermal-hydraulic (TH) parametersevaluation, stability ratios for representative 8 tubes are calculated by using 3 independent THanalysis codes (MHI-ATHOS, CAFCA and WEC-ATHOS)Table 5 shows the results of SR calculation and the normalized values, which are the ratio betweenthe calculated SRs based on each TH analysis and the average of SRs based on 3 analysis codes.The standard deviation of normalized stability ratios obtained by the following equation isi landthe average relative stability ratio based on MHI ATHOS isi IA1 ............................N................................................. (17 )Where,-TTH Standard deviation of SR based on each TH codeSR* : Normalized SR (= each analysis result / average value of 3 analysis code result)SR* Average of normalized SRN :Number of dataTable 5 Comparison of Stability Ratio based on MHI-ATHOS, CAFCA and WEC-ATHOSMHI-ATHOS CAFCA WEC-ATHOS AverageRow Column SR Normalized Normalized SR Normalized SR NormalizedSR SR SR SR SR81 69 r81 89101 69101 89121 69121 89125 85105 69Average t,MITSUBISHI HEAVY INDUSTRIES, LTD.Page 143 of 149S023-617 M1539, REV. 0 I Non-proprietary Version I) ](144/149)Document No. L5-04GA567(6)4.3 Uncertainty of SRTable 6 shows the standard deviation and the relative ratio of each parameter. According to V6equation (2), the standard deviation of stability ratio is calculated to bel Ias follows.U'S, = + O"_ + O'7n2=The upper bounded and lower bounded of stability ratios are -5% and -57%, which are obtained byEquation (12) and (13).Table 6 Uncertainty of Stability RatioBest estimated Uncertainty of MHI's SR evaluationRelative Ratio Upper bound Lower boundParameters based on Mean ( Skax SRkinMHI methodSRMIII SRAfH,K1Connor'sconstant a(O)KDampingRatio TPThermal-HydraulicParametersStability Ratio5. References[1] "The Effect of Approach Flow Direction on the Flow-Induced Vibrations of a Triangular TubeArray" , H.C. Yeung et al, 1983, Transactions of the ASME Vol.105[2] "ransactions of the ASHEAT EXCHANGER TUBES: PART2: IN LIQUIDS" , M.J.Pettigrew et al.[3] "Advanced Estimation on Fluidelastic Instability U-bend Tube Bundle of Steam Generator (3rdReport, Advanced Estimated Method)St, 2002, T. Nakamura et al, Journal of The Japan Societyof Mechanical Engineers Vol 63 Issue 668[4] 3 Issue 668of tube bundle geometry on vibration in two-phase cross flowor, 2000, M. J.Pettigrew et al, Flow Induced Vibration, Ziada & Staubli (eds) © 2000 Balkema, Rotterdam, ISBN90 5809 129 5, 561-568[5] "Vibration analysis of shell-and-tube heat exchangers : an overview -Part1: flow, damping, fluidelastic instability ", 2003, M.J. Pettigrew et al, Journal of Fluids and Structures 18 469-483MITSUBISHI HEAVY INDUSTRIES, LTD.Page 144 of 149 S023-617 M1539, REV. 0 Non-proprietary Version I) 3(145/149)Document No. L5-04GA567(6)AtAttachment-7 Selection of Evaluated TubesAs shown in Table 1, 28 tubes are selected for thermal hydraulic analysis by ATHOS/SGAP (seeRef.21 for detail). Among these tubes, 8 tubes (#2,#3,#6,#7,#l0,#11,#14,#16) selected by SCE (Seethe emails shown in Appendix-I) and an additional tube (#28), which stability ratio of out-of-plane FEIwas the maximum when all AVB support points are active, are evaluated in the main report.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 145 of 149 S023-617 M1539, RE'V. 0 Non-proprrietary VersionI (146/149)Document No. L5-04GA567(6)AtTable 1 Evaluated Tubes (See Ref.22 for details)Tube # Row Column1 80 602"1 80 703"1 80 804 80 885 100 606*1 100 707*1 100 808 100 889 120 6010*1 120 7011"1 120 8012 120 8813 80 8414*1 95 8515 110 8416*1 125 8517 135 8518 40 3019 74 8020 95 6921 105 6922 111 6923 127 7324 138 8025 86 8026 95 7527 124 76282 138 84Notes:(*1) Representative tubes for evaluating stability ratio selected by SCE(*2) Selected as an additional representative tube because the stability ratio of out-of-plane isthe maximum when all AVB support points are activeMITSUBISHI HEAVY INDUSTRIES, LTD.Page 146 of 149S023-617 M1539, REV. 0 Non-proprietary Version II) (147/149)Document No. L5-04GA567(6)A&Appendix-1 E-mails from SCEMITSUBISHI HEAVY INDUSTRIES, LTD.Page 147 of 149S023-617 M1539, REV. 0 Non-proprietary Version I) 3(148/149)Document No. L5-04GA567(6)A&MITSUBISHI HEAVY INDUSTRIES, LTD.Page 148 of 149 S023-617 M1539, RE\/.0 Non-proprietary Version[ (149/149)Document No. L5-04GA567(6)Atr-IMITSUBISHI HEAVY INDUSTRIES, LTD.Page 149 of 149S023-617 M1539, REV. 0

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