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{{#Wiki_filter:ENCLOSURE 4 MHI Non-Proprietary Document L5-04GA567, Evaluation of Stability Ratio for Return to Service (Non-Proprietary)
{{#Wiki_filter:ENCLOSURE 4 MHI Non-Proprietary Document L5-04GA567, Evaluation of Stability Ratio for Return to Service (Non-Proprietary)
I Non-proprietary Version () (1/149)San Onofre Nuclear Generating Station, Unit 2 & 3 REPLACEMENT STEAM GENERATORS Evaluation of Stability Ratio for Return to Service Supplier Status Stamp VPL S023-617-1-M1539 Reo I QCN/A No: R-DESIGN DOCUMENT ORDER NO. _ 8008734135 REFERENCE DOCUMENT-INFORMIATION ONLY EIIVIRP 10M MANUAL MFG MAY PROCEED: [YES []NO EN/A STATUS -A status Is required for design documents and Is optional for reference documents.
 
Drawings are reviewed and approved for arrangements and conformance to specification only. Approval does not relieve the submilttr from the responsibility of adequacy and suitability of design, materials, and/or equipment represented.
I Non-proprietary Version
E-1, APPROVED-]2. APPROVED EXCEPT AS NOTED -Make changes and resubmit 013. NOT APPROVED .Correct and resubmit for review. NOT for field use.APPROVAL: (PRINT/ SIGN / ATE), RE: J FLS: Other.SCE DE(123) 6 REV. 3 07t11  
(                                                 ) (1/149)
San Onofre Nuclear Generating Station, Unit 2 & 3 REPLACEMENT STEAM GENERATORS Evaluation of Stability Ratio for Return to Service Supplier Status Stamp VPL No:        S023-617-1-M1539                                   Reo
* I QCN/A R-DESIGN DOCUMENT                 ORDER NO.             _
REFERENCE DOCUMENT-INFORMIATION ONLY EIIVIRP 10M MANUAL 8008734135 MFG MAY PROCEED: [YES []NO EN/A STATUS - A status Is required for design documents and Is optional for reference documents. Drawings are reviewed and approved for arrangements and conformance to specification only. Approval does not relieve the submilttr from the responsibility of adequacy and suitability of design, materials, and/or equipment represented.
E-1, APPROVED
                    -]2. APPROVED EXCEPT AS NOTED - Make changes and resubmit 013. NOT APPROVED . Correct and resubmit for review. NOT for field use.
APPROVAL: (PRINT/ SIGN / ATE),
RE:                                                                           J FLS:
Other.
SCE DE(123) 6 REV. 3 07t11                            


==REFERENCE:==
==REFERENCE:==
80123-XXIV-37.0.26 Purchase Order No.          4500024051 Specification No.          S023-617-01R3 HITUB8r1eer      IUV'    nlUnSTa.,      tIA.
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At Revision History Document No.L5-04GA567 No.              Revision                    Date        Approved      Checked          Prepared 0              Initial issue                                See cover sheet I  -Revised in accordance with SCE comments of RSG-SCE/MHI-12-5722.
    -Added the evaluation of out of plane FEI.
2  Revised in accordance with SCE comments of RSG-SCE/MHI-12-5729.
3  -Revised the calculation method of the virtual added mass of tube in Sec. 4.1(5).
4  - Added Attachment-5 to evaluate the stability ratio of the tube which has tube-to-tube wear at 70% thermal power 5  - Revised Attachment-5 to evaluate the effect of type J stabilizer on stability ratio of the tube which has tube-to-tube wear at 70% thermal power
    - Added Attachment-6 to evaluate the uncertainty of calculated stability ratio 6  -Revised in accordance with SCE comments of RSG-SCE/M HI-12-5769
    -Revised stability ratios due to the change of stabilizer type (Type J)
    -Revised out-of-plane FEI analysis results in Sec.2 and 8                  _
MITSUBISHI HEAVY INDUSTRIES, LTD.
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Document No. L5-04GA567(6)
At Table of Contents
: 1. Purpose ....................................................................................................................................          4
: 2. Conclusion ...............................................................................................................................          5 2.1 Stability ratio of out of plane FEI .....................................................................................                          5 2.2 Stability ratio of in-plane FEI ............................................................................................                      6
: 3. Nom enclature .........................................................................................................................            10
: 4. Assum ption ............................................................................................................................            11 4.1 Modeling assum ption .....................................................................................................                        11 4.2 O pen item ............................................................................................................................          12
: 5. Acceptance Criteria ..........................................................................................................                      13
: 6. Design Input ...........................................................................................................................          14 6.1 G eom etry of tube bundle region .....................................................................................                            14 6.2 Thermal and hydraulic flow of steam generator secondary side ....................................                                                17
: 7. Methodology .............................................................................................................................            32 7.1 Fluid elastic vibration ......................................................................................................                    32 7.2 Calculation m odel ..........................................................................................................                    49
: 8. Com putation Results ........................................................................................................                      60 8.1 O ut of plane FEI analysis results ...................................................................................                            60 8.2 In-plane FEI analysis results ..........................................................................................                          65
: 9. Reference ..............................................................................................................................          95 Attachm ent-1        Com puter Input and O utput File List ..............................................................                                96  Evaluation of Liquid Film Thickness of Tube at AVB Support Point ..................... 106  Evaluation of the Effective Distance of Liquid Film of Tube from the Contact Point for Squeeze Film Dam ping ..............................................................................................................                    114 Attachm ent-4 Confirm ation of Flow Regim e ...............................................................................                            117  Case Study for Applying Split Stabilizers for TTW tube of Unit-2 at 70% Thermal Power .........................................................................................................................................        118 Attachm ent-6 Uncertainty of Calculated Stability Ratio ..............................................................                                  128 Attachm ent-7 Selection of Evaluated Tubes ...............................................................................                              145 MITSUBISHI HEAVY INDUSTRIES, LTD.
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At
: 1. Purpose The 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.
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At.
: 2. Conclusion By considering numbers of inactive support points as the parameter for the case study, the following results are obtained.
2.1 Stability ratio of out of plane FEI 2.1.1 Assuming all support points active With all AVB supports active, the stability ratios are less than 1.0 for all analyzed tubes, for the reactor power levels up to, and including, 100% with no plugging.
Table 2.1-1 Stabilitv Ratio with All Active Sunoort Points for 2A SG Case                              Thermal Power Row      Column                70                    100 (No Plug) 80        70 80          80 100        70 10011      80(*)
120        70 120        80 95(*)      85(*)
125        85 138        84 Note(*): Plugged tube with Type J stabilizer 2.1.2 Assuming 1 support points inactive With 1 AVB supports inactive, the stability ratios are less than 1.0 for all analyzed tubes, for the reactor power levels up to, and including, 70%
Table 2.1-2 Stability Ratio with I Inactive Su~oort Point for 2A SG Case                              Thermal Power Row      Column                70                    100 (No Plug) 80        70 80        80 100        70 100C)      80(*)
120        70 120        80 95(1)      85(*)
125        85 138        84 L                                        YI Note(*): Plugged tube with Type J stabilizer MITSUBISHI HEAVY INDUSTRIES, LTD.
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At 2.2 Stability ratio of in-plane FEI 2.2.1 Assuming 6 support points inactive With 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 SG Case                                          Thermal Power Row    Column          50          60        70          80        90          100        100 (No Plug) 80        70 80        80 100        70 1 00M      80(.)
120        70 120        80 95(')      85(*)
125        85 138        84 Note(*): Plugged tube with Type J stabilizer MITSUBISHI HEAVY INDUSTRIES, LTD.
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At 2.2.2 Assuming 8 support points inactive With 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 SG Case                                        Thermal Power 100 Row      Column      50            60        70          80          90        100      (Pu 80        70 80        80 100        70 1O0)      80()
120        70 120        80 95(*)    85(*)
125        85 138        84 Note(*): Plugged tube with Type J stabilizer MITSUBISHI HEAVY INDUSTRIES, LTD.
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At 2.2.3 Assuming 10 support points inactive With 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 SG Case                                          Thermal Power 100 50            60        70        80          90          100        (Pu Row    Column                                                                              (No Plug) 80        70 80        80 100        70 I O0)      80(')
120        70 120        80 95(")    85(*)
125        85 138        84 Note(*): Plugged tube with Type J stabilizer MITSUBISHI HEAVY INDUSTRIES, LTD.
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At 2.2.4 Assuming 12 support points inactive With 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 SG Case                                          Thermal Power Row    Column        50            60        70          80        90          100          100 (No Plug) 80        70 80        80 100        70 100(*)    80(*)
120        70 120        80 95()      85(')
125        85 138        84 Note(*): Plugged tube with Type J stabilizer 2.2.5 TTW tubes in Unit-2 The stability ratios of TTW (tube-to-tube wear) tubes with type J stabilizer (split stabilizers) in Unit-2 were evaluated and confirmed to be less than 1.0 as shown in Attachment-5.
MITSUBISHI HEAVY INDUSTRIES, LTD.
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At
: 3. Nomenclature Symbol            Unit                                        Definition E              psi    Modulus of elasticity of tube FEI                      Fluid elastic instability G              psi    Shear modulus of tube Tav              OF      Primary side average temperature TS              OF      Secondary side temperature D,              in    Tube inside diameter Do              in    Tube outside diameter P                in    Tube pitch 3
A            Ibm/ft      Density of water inside the tube 3
A_          Ibm/ft      Density of tube material 3
Po            Ibm/ft    Average density of water outside the tube t              in    Tube thickness m            Ibm/ft    Tube mass distribution per unit length my            Ibm/ft    Virtual added mass per unit length h                -      Damping ratio h-                      Structural damping ratio hTp                -    Two phase damping ratio h-                      Viscous damping ratio hSF                -      Squeeze film damping ratio K                -      Critical factor MHI                  -    Mitsubishi Heavy Industries M0            Ibm/ft    Average tube mass per unit length U,              ft/s    Critical flow velocity f              Hz      Tube natural frequency 6                -    Logarithmic decrement U"n              ft/s    Nth mode effective flow velocity O(x)-                      Vibration mode Tn(x)                -    Nth vibration mode 3
p,    p(x)        Ibm/ft    Fluid density distribution of water outside the tube in tube axis direction U, U(x)            ft/s    Flow velocity distribution orthogonal to tube axis in tube axis direction x                ft    Coordinate component along tube axis L                ft    Tube length SCE                        Southern California Edison SR, SR,                      (Nth mode) Stability ratio MITSUBISHI HEAVY INDUSTRIES, LTD.
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: 4. Assumption 4.1 Modeling assumption (1) Nominal tube thickness and nominal tube length are used in the evaluation model because the effect 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 supported condition at tubesheet is added.
(3) Contact condition between tube and active support points by the anti-vibration bar (AVB) is pin-supported.
of              2 (4) Modulus of elasticity of tube is interpolated based on the tube average temperature from table of ASME Boiler and Pressure Vessel Code, Sec II, Materials, 1998 Edition, 2000 addenda (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 virtual added 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).
f rD~po (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 effect
: p.        Average water density outside the tube of each region obtained from ATHOS analysis Do        :Tube outside diameter P          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 side are assumed for the evaluation of the stability ratio of in-plane FEI. All active support points and 1 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 and support span of each evaluated tube. The inactive support will be one of the 2 supports at the span with the highest amplitude, whichever that has a higher hydraulic pressure. The maximum stability ratio in each inactive support location is shown as the result of the stability ratio with 1 inactive support.
MITSUBISHI HEAVY INDUSTRIES, LTD.
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At (7) Type J stabilizers are assumed to be installed for all plugged tubes which have AVB wear indications. The additional structural damping ratio due to Type J stabilizer (split stabilizers installed 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 and Attachment-1 for details).
4.2 Open item There is no open item remaining.
MITSUBISHI HEAVY INDUSTRIES, LTD.
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At
: 5. Acceptance Criteria The stability ratio against fluid elastic instability shall be less than 1.0. The analysis is performed in accordance with the procedures given in ASME code section III Appendix N-1 330 (Ref.2).
MITSUBISHI HEAVY INDUSTRIES, LTD.
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At
: 6. Design Input 6.1 Geometry of tube bundle region Tube bundle consists of thermally treated Alloy 690 U-tubes which are supported in[  ]triangular pitch arrangement 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-240 Type 405 Stainless steel).
Nominal dimension of tube, TSPs and AVBs are listed in Table 6-1. The applicable design drawings to be referred are listed in Table 6-2.
MITSUBISHI HEAVY INDUSTRIES, LTD.
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Ak Table 6-1 Nominal dimensions of tubes, TSPs, and AVBs Part                Item                                Value Material                    Thermally treated SB-1 63 UNS N06690 Outside diameter                          0.75 in Thickness                                0.043 in Tubes Number of tubes                          9727 Tube pitch                                1.0 in Tube arrangement                          Triangular Material                                  SA-240 Type 405 Thickness Number of TSPs TSPs Tube support span (between TSP centrals)
Tube support span (from TS to No.1 TSP)    I Material                                  SA-479 Type 405 Type AVBs Thickness Width Stabilizer Unit weight MITSUBISHI HEAVY INDUSTRIES, LTD.
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At Table 6-2 A plicable design drawings (Ref.3 to 20)
Drawing No.                                      Title L5-04FU001                        COMPONENT AND OUTLINE DRAWING 1/3 L5-04FU002                        COMPONENT AND OUTLINE DRAWING 2/3 L5-04FU003                        COMPONENT AND OUTLINE DRAWING 3/3 L5-04FU021                        TUBE SHEET AND EXTENSION RING 1/3 L5-04FU022                        TUBE SHEET AND EXTENSION RING 2/3 L5-04FU023                        TUBE SHEET AND EXTENSION RING 3/3 L5-04FU051                        TUBE BUNDLE 1/3 L5-04FU052                        TUBE BUNDLE 2/3 L5-04FU053                        TUBE BUNDLE 3/3 L5-04FU111                        AVB ASSEMBLY 1/9 L5-04FU112                        AVB ASSEMBLY 2/9 L5-04FU1 13                        AVB ASSEMBLY 3/9 L5-04FU1 14                        AVB ASSEMBLY 4/9 L5-04FU115                        AVB ASSEMBLY 5/9 L5-04FU116                        AVB ASSEMBLY 6/9 L5-04FU117                        AVB ASSEMBLY 7/9 L5-04FU118                        AVB ASSEMBLY 8/9 L5-04FU119                        AVB ASSEMBLY 9/9 MITSUBISHI HEAVY INDUSTRIES, LTD.
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At 6.2 Thermal and hydraulic flow of steam generator secondary side The basic parameters for the thermal hydraulic analysis of unit-2 and 3 steam generators are shown in Table 6.2-1 to 6.2-4. As discussed in ATHOS analysis report (Ref. 22), the larger number of the plugged tubes of unit-2 (305 tubes for 2A) is used for the FEI evaluation. The flow characteristics of the tubes listed in Table 7.2-1 are obtained from ATHOS/SGAP analysis (See Ref.21 and 22 for detail) and used for the vibration analysis.
The distributions of flow gap velocity normal to the in-plane direction of the tube, flow density and void fraction are shown in Fig.6.2-3 to 6.2-11. Several of the flow gap velocity distributions indicate negative flow velocities at lower thermal power on the cold leg side since the water flow is more likely to go downward on the cold leg side because the circulation ratio is higher and the water flow rate compared with 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 flow velocity and mode shape in order to evaluate the actual tube vibration which is multi degrees of freedom system with beam type of vibration modes. Therefore, there is no adverse effect of negative flow velocity.
MITSUBISHI HEAVY INDUSTRIES, LTD.
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Table 6.2-1 Basic parameters for calculation for 2A SG evaluation after plugging 50%              60%              70%              80%              90%          100%        100%withno Case plugging Plugging                      305              305              305              305              305          305              0 869.5            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          209,880 z0 cj~              Thot (Tsg-in) (°F)
                                                                                                                                                                  '0 Tsg-out (°F)*2 2                                                                                                                                0)
TcoId ('F)*
z Saturation Steam Pressure (psia)                                                                                                                            CD 2
Fouling Factor (ft hr°F /Btu)                                                                                                                            CD)
Tfeedwater (OF)
C Circulation Ratio Steam Mass Flow (lb/hr) r:j~                                    3 Feed Water Mass Flow (lb/hr)*
Blowdown flow rate (gpm)
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 RV 0
C) inlet is caused by heat input from the reactor coolant pump.
C)
      *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.
0
      *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 the    c-I (A
address 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 column          41 of 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.
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Table 6.2-2 Basic parameters for calculation for 2B SG evaluation after plugging 60%              70%              80%              90%        100%        100 % with no Case                        50%
plugging Plugging*6                      205              205              205              205              205        205              0 869.5          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          209,880 z
0 C-,            Thot (Tsg-in) (°F)                                                                                                                                  7 Tsg-out (OF)"*2 Cd,                                                                                                                                                                0 2
TcoId (OF)*                                                                                                                                      0)
Saturation Steam Pressure (psia)        I                                                                                                                    CD Fouling Factor (ft 2 hr°F /Btu)
Cn.
0 Tfeedwater (°F)
C-,            Circulation Ratio Steam Mass Flow (lb/hr)
Feed Water Mass Flow (lb/hr) 3 C-,
Blowdown flow rate (gpm)
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 0
RV inlet is caused by heat input from the reactor coolant pump.                                                                                    0
    *3: Feedwater mass flow rate is the sum of the blowdown flow rate and the steam mass flow based on heat balance calculation.
z
    *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 the SC) address of the plugged tubes of 2A SG.
Page 19 of 149                                            S023-617-1-M1539, REV. 0
Table 6.2-3 Basic parameters for calculation for 3A SG evaluation after plugging 100%        100 % with no 50%              60%            70%              80%                90%
Case plugging Plugging*4                    387              387              387              387                387          387              0 Thermal power (MWt)                  869.5            1041.4          1213.3            1385.2            1557.1          1729            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-z 0
Thot (Tsg-in) (*F)                                                                                                                                  -7 2                                                                                                                              a
                                                                                                                                                                  '0 Tsg-.out (F)"
2 TcoId (°F).
z Saturation Steam Pressure (psia)        I 2                                                                                                                                  CD Fouling Factor (ft hr°F /Btu)
(n) 0 Tfeedwater (OF)                                                                                                                                  '-3 Circulation Ratio Steam Mass Flow (lb/hr)
Feed Water Mass Flow (lb/hr) 3 Blowdown flow rate (gpm)          -z F
Note
  *1: Obtained by interpolating the flow rate of 0% plugging and 8% plugging.                                                                                  C 0
  *2: RCS flow temperature at SG outlet is assumed to be 0.30 F lower than that at RV inlet. The 0.30 F temperature increase between the SG outlet and RV H
0 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: 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 the o
address of the plugged tubes of 2A SG.                                                                                                                  c~I (A  0 Page 20 of 149                                              S023-617-1-M1539, REV. 0
Table 6.2-4 Basic parameters for calculation for 3B SG evaluation after plugging 50%              60%            70%              80%              90%          100%        100 % with no Case plugging Plugging"4                    420              420              420            420              420            420              0 869.5            1041.4          1213.3          1385.2            1557.1          1729            1729 Thermal power (MWt)
Thermal power (M      ____          (50%)            (60%)          (70%)            (80%)            (90%)        (100%)            1729 RCS flow rate (gpm) .'              205,545          205,545        205,545          205,545          205,545      205,545          209,880 z
0 Thot (Tsg-in) (°F)                                                                                                                                  0 2
Tsg.out (°F)'
TcoId (°F)*2                                                                                                                                    CD Saturation Steam Pressure (psia)                                                                                                                              (n Fouling Factor (ft2hr°F /Btu)                                                                                                                              ChD 0
LD Tfeedwater (°F)
C,'            Circulation Ratio Steam Mass Flow (lb/hr) 3 Feed Water Mass Flow (lb/hr)"
~j)
Blowdown flow rate (gpm)
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 RV 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: 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 the address of the plugged tubes of 2A SG.                                                                                                                C.'
                                                                                                                                                              >I Page 21 of 149                                              S023-617-1-M1539, REV. 0
I        Non-proprietary Version                                  I ft                                                    ) (22/149)
Document No. L5-04GA567(6)
Tubes to be plugged of 2A SG 3      - 4,                    J, - j                                                          *.-
s          4      4...
121        A    1!.L                                                                                                                        -    L 51 1            _ -    -. - .      . - . - . .  .  . -3.  - .  .- .    .- . '- . .  -S .- - F.j-      -      -        "-    .    .  .        . ..,    . - _-
      " 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    .
COL Fig. 6.2-1 Plugging tubes of 2A SG I,-
Fig.6.2-2 Tube plugging model of ATHOS for 2A SG MITSUBISHI HEAVY INDUSTRIES, LTD.
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r z
Ca                                                                                      0 a
10 Ca CD Cn.
Y, C
Ca C
0 Ca                                                                                    0 r                                                                                      0 o
                                                                            -V Fig.6.2-3 Flow Characteristics of Row 80 Column 70 (2A SG)
Page 23 of 149                        S023-617-1-M1539, REV. 0
r z0 0
CD (1) 0 C)
                                                                                  >~
Fig.6.2-4 Flow Characteristics of Row 80 Column 80 (2A SG)
Page 24 of 149                        S023-617-1-M1539, REV. 0
C12 z0 0
CD (1) 2                                                                                        0 C,,
                                                                                      >H-Y, 41 Fig.6.2-5 Flow Characteristics of Row 100 Column 70 (2A SG)
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r z
_=                                                                                        o 0
C ,)
ri)
Y, C>
FER 0
CN Fig.6.2-6 Flow Characteristics of Row 100 Column 80 (2A SG)                      -&
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z 0
CA                                                                                        B 10 n.---
CICD                                                                                    0
                                                                                            °0 CD
                                                                                      > -F1 Fig.6.2-7 Flow Characteristics of Row 120 Column 70 (2A SG)                      **
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z 0
0 0
Fig.6.2-8 Flow Characteristics of Row 120 Column 80 (2A SG)
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z 0
r:j~
z CD CD Y,
0 C)
K                                                                      -I Fig.6.2-9 Flow Characteristics of Row 95 Column 85 (2A SG)
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K-z z                                                                      -(D 0,
CD Yl ofRow125ColunFow Fig..2-0                      8 Caraterstis (2 S0 Page 30 of 149                              S023-617-1-M1539, REV. 0
z 0
CD
,-                                                                                      0 CD 4n Fig.6.2-11 Flow Characteristics of Row 138 Column 84 (2A SG)                          -
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Document No. L5-04GA567(6)
: 7. Methodology 7.1 Fluid elastic vibration The term "fluid elastic vibrations" is generally used to refer to self-excited vibration of tube bundles due to 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 is greater than the amount that the tubes can dissipate. The measure of the fluid-elastic vibration threshold for any given tube in the bundle (tube stability) is the ratio of the actual velocity of the fluid surrounding the tube to the critical fluid flow velocity for this particular tube. The critical flow velocity Uc required to generate fluid-elastic vibration is obtained using Connor's formula (Ref.23).
r    11/2 U'    _ K [ m°* 2          ............................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .  .. ... .
(3)
Where, UV              Critical flow velocity f                Tube natural frequency D,            : Tube outside diameter K                Critical factor M0            :Average tube mass per unit length 5                Tube logarithmic decrement(= 2Trh) h                Damping ratio PO              Density of water outside the tube The critical flow velocity U, in eq. (3) is evaluated in case of tube vibration of single degree of freedom system with uniform cross flow along the tube axis. In actual tube, however, the vibration of the tube supported by the tube support plate is multi degrees of freedom system with beam type of vibration modes. Therefore, considering the vibration mode and fluid distribution, the effective flow velocity Ue, is evaluated in the following formula.
MITSUBISHI HEAVY INDUSTRIES, LTD.
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                                                                                                                        ]    (33/149)
Document No. L5-04GA567(6)
Ak p___ U(x) 2.
* 0 (X) dx        1 0  PC) u                          .                        ................................................................... (4 )
2 f L MW      04(x)    dx Where, Uen              Nth mode effective flow velocity (Pn(X)            Nth vibration mode p(x)              Fluid density distribution of water outside the tube in tube axis direction m(x)              Tube mass distribution per unit length in tube axis direction U(x)              Flow velocity distribution orthogonal to tube axis in tube axis direction x                Coordinate component along tube axis PO                Average density of water outside the tube m,              :Average tube mass per unit length L              : Tube length The stability ratio is determined as follows in each vibration mode by calculating the ratio of eq. (3) and eq. (4).
SR .                . . ......................................      ................................................. (5 )
Ucn where, 1/2
: f. 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 is simply expressed as SR. The uncertainty of SR calculated by the methodology of this section is evaluated in Attachment-6.
MITSUBISHI HEAVY INDUSTRIES, LTD.
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Document No. L5-04GA567(6)
A&
7.1.1 Damping ratio and Critical Factor Although the suggested value by ASME Sec. Ill Appendix N-1330 for damping ratio is 1.5% and the suggested value for critical factor is 2.4, the values based on recent experimental data are used in this evaluation as follows.
7.1.1.1 Damping ratio For U-bend tubes in two phase flow, there are four sources of damping: structural damping, two-phase damping, viscous damping and squeeze film damping.
          "    s + ýT +    "+ 's.  ...................................................................................      (7 )
: Where,
:s        :Structural damping ratio Two-phase damping ratio Viscous damping ratio
ýSF        : Squeeze film damping ratio MITSUBISHI HEAVY INDUSTRIES, LTD.
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Document No. L5-04GA567(6)
At (1) Structural damping The structural damping ratio is estimated with the following experimental equation developed by Pettigrew (Ref.25 and 27). In the case of plugged tubes with Type J stabilizers, the additional damping 0.6% is added s j= N -1 [ 5,L          in gas ........................................................................      (8)
          ,s = (N N- 1    0.5( Lgm 7  ,in liquid ................................................................ (9)
: Where, 4S        : Structural damping ratio N            Number of free spans at U-bend region N-1          AVB support points without assuming inactive AVB support points L'          AVB width Ira          Characteristic tube length: average of the longest three free spans lengths assuming 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).
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At (2) Two-phase damping The two-phase damping depends on the void fraction and fluid properties. Pettigrew's test result of the two 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 of homogeneous void fraction was obtained as shown in Figure 7.1.2.
The effective homogeneous void fraction is calculated by using the ATHOS outputs and following equation, considering vibration mode.
_  Jfg(x)¢ 2 dx SqZd2l=  ...........................................................................................                      (10)
: Where, Homogeneous void fraction
      @
* Vibration mode x                  Tube axis The two-phase damping along the tube length is calculated by using Pettigrew's data and the following equation Tp              )f(    )    1 (D                  I)                    ...........................................    ..    (11) f([3)=      P3/40                  for 13< 40%
1                        for              40% _<[3 _<70% ............................................. (12) 1 - (P3- 70) / 30                                  > 70%                                                              (for D , = ( 1+ 1 P/D &#xfd;o P ......................................................................................                      (13) m 0 = nzm, + n p + n , .........................................................................................                  (14 )
              = fD&deg;p&deg;  f(DOe/OD)2 + I...........................................(15 l(D  I/D  o)2 -I(5 4
Where,
        &#xfd;TP              Two-phase damping P3                Homogeneous void fraction D                  Tube outside diameter MITSUBISHI HEAVY INDUSTRIES, LTD.
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Document No. L5-04GA567(6) jAk P                  Tube pitch po Po                Density of secondary mixture flow (Calculated by ATHOS)
Pi                Density of secondary liquid flow Average tube mass per unit length mv                Virtual added mass per unit length Mass of primary coolant in tube per unit length mt                Mass of tube metal per unit length 1- 7 Ul  0' CM6                                                    0 E                            0                      0 123o 0 ca5                              00 (V4 co 4 t1=
A*
  .3                9 0            A                      A I--
_0      2    -'0      0:
A Air-Water          Stearn-Waler          Freon
                                                                            , Nomal Trangle    A Normal Triangle
* Frwn-22 (NTI)
E            w                                                          V  Rotated Triangle T Rotated Triangle  0 Froon-22 (RT) o0                                                                    0  NortndrSquare    N Normal Square      0 Froon-l I (RT) t*J  t
_,0                                                          0  RolaWed Squae 0            20      40        60          80        100 Void Fraction (%)
(VTO)D = CT-A(pD /m)-'
2        {[1 + (DID,)'))/[I - (DID,)2]2 }-'
Fig 7.1-2    Effect of void fraction on two-phase damping MITSUBISHI HEAVY INDUSTRIES, LTD.
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A (3) Viscous damping Since the viscous effects are negligibly small in high void fraction (homogeneous void fraction is 40% or greater) (Ref.27), it is not taken into account in this analysis.
(4) Squeeze film damping Squeeze film damping takes place at the supports and the following equation is based on the available experimental data. (Ref.26)
YSF =( N -    {  f
* mo )(. L., ' ......................................................................... (16)
: Where, SF        Squeeze film damping Secondary flow liquid density D            Tube outside diameter N                Number of free spans at U-bend region N-1            AVB support points without assuming inactive AVB support points f            Natural frequency L            AVB width Im            Characteristic tube length M0            Average tube mass per unit length MITSUBISHI HEAVY INDUSTRIES, LTD.
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Ai For unplugqed tubes The support damping (structural and squeeze film) depends on the void fraction. Since the structural damping 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. The effective wetness of supports is estimated to determine the damping ratio used for the SR evaluation by the following equations based on the assumptions listed below. (The basis of these assumptions is described 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 and squeeze film damping is effective.
When the void fraction is      [                    ]there is no liquid film on the surface of tube. The support is considered "dry," structural damping corresponds to the gas condition and squeeze film damping is not effective.
When the void fraction is between                                  )
                                                                        ) there is a discontinuous liquid film on the surface of tube and the support is considered partially wet. The approach to calculate damping in this void fraction range is described below.
N-1 s        a    ........    .........................................                                    ............... (17) a      i                                                    ...........................................................      (18 )
N DS      N......
N - I - N s ..........................................                  ....................................... (19)
Where, N              Number of free spans in U-bend N    -  1        Number of AVB support points in U-bend NWS            Number of effectively wet AVB supports NDS            Number of effectively dry AVB supports i              :AVB support points a:              Void fraction at AVB support points ai              Function of void fraction at AVB support points MITSUBISHI HEAVY INDUSTRIES, LTD.
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At By replacing the (N-i/N) term in equations 8 and 9 and combining, structural damping adjusted for void fraction becomes:
j.........                                  . . . . (20)
Similarly replacing the (N-i/N) term in equation 16 with (Nws/N), squeeze film damping adjusted for void fraction becomes:
2 Ni,'s  (2 460) plD      L
          &#xfd;SF      ,
Nf
* no .
(..              ............................................................... (21)
For pluaqed tubes The plugged tubes are assumed to be in wet condition despite the void fraction. Equations 7 and 16 are used for structural and squeeze film damping, respectively.
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At 7.1.1.2 Critical Factor The effect of void fraction, the effect of pitch to diameter ratio, the ratio between In-plane & Out-of-plane and the effect of flow direction are considered to estimate the Connor's constant as follows.
(1) Effect of the void fraction Based on MHI experimental data (Ref.28), the critical factor K is evaluated using the equation shown in Figure 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 the triangular 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 mode and using the following equation in the same manner as the two-phase damping. The obtained critical factor obtained is K1, when the value of P/D is 1.33.
K, =(                                                ) .................................................... (2 2 )
                    -f/3(x)O252cy
_= _'      _ . .........................................................    ..................... (23)
: Where, Homogeneous void fraction Vibration mode x                    Tube axis MITSUBISHI HEAVY INDUSTRIES, LTD.
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Ak
                                                                            -/
Fig.7.1-3 MHI Experimental Test Result (Relation between Critical Factor and Superficial Void Fraction)
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Table 7.1-1 MHI Test Condition Tube diameter Tube pitch Number of tubes                ii Flow condition Pressure Temperature Suoerficial void fraction Fig.7.1-4 MHI Test Equipment MITSUBISHI HEAVY INDUSTRIES, LTD.
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(2) Effect of P/D The greater the pitch is, the higher the critical velocity will be. Since the tube bundle has index and the nominal pitch depends on the number of tube Row, the effect of the tube pitch to diameter ratio (P/D) is added 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 to be evaluated.
P, -- P , + P + . ..................................................................................... (24 )
3 Where,                                    Evaluated tubes                                ,
Pe            Effective pitch P1,P2,P3      Pithes defined in Fig.7.1-5                                                    P, Fig.7.1-5 Effective pitch The effect of the tube pitch on the Connor's constant is calculated by using the following equation based on Pettigrew's experimental data (Ref.29).
Kp=4.76(P-D )/D+0.76 .................................................................................. (25)
KpI Ko =    K P' D    x K 1 ................................................................................      (26 )
: Where, KP            "Equation 21 K1              Critical Factor based on MHI experimental test results by taking into account of the effect of void fraction (P/D=1.33)
Kp.P/D        : Critical Factor based on Pettigrew's experimental test results by taking into account of the effect of P/D Kp.P/D=.33    "Critical  Factor based on Pettigrew's experimental test results when P/D is 1.33 Ko              Best estimated critical factor of out-of-plane FEI MITSUBISHI HEAVY INDUSTRIES, LTD.
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(3)Critical Factor of In-plane FEI In accordance with the experiments by T. Nakamura (Ref.30), FEI is observed in the in-plane direction in a single-phase air flow when the tube pitch-to-tube ratio (P/D) is small. The Connor's constant of In-plane FEI is estimated in accordance with the following equation based on Nakamura's experimental data. The ratio between the Connor's constant of in-plane FEI and out-of-plane FEI depends on P/D as shown in Figure 7.1-6. In order to reinforce the basis of Connor's constant used for In-plane FEI evaluation, MHI performed air flow test by using the straight tube bundle of the triangular pitch as shown in Fig. 7.1-7. The ratio of Connor's constant between in-plane and out-of-plane FEI obtained by MHI test result is consistent with Nakamura's experimental data as shown in Fig. 7.1-6. Therefore, the Connor's constant of in-plane FEI for SONGS RSGs is calculated based on the effective tube pitch calculated 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 FEI Ki          *Best estimated critical factor of In-plane FEI Ko          Best estimated critical factor of out-of-plane FEI Ratio K Vc(In-flow)/Vc(Out-of-flow)
Ratio ol              Note critical fl      &#xfd;J.city K=Vc(ln-plane) fVc(0ut-4*plane) 1.5    Air-            2.7              voletteetal Water                                (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)
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At I-(a) Test equipment r
k-.
(b) Test Results Fig.7.1-7 MHI air flow test MITSUBISHI HEAVY INDUSTRIES, LTD.
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Document No. L5-04GA567(6)
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(4) Effect of Flow Direction The 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 of the critical velocity will be.
The effect of the flow direction on the critical velocity (increase ratio"                        a(e)") is determined based on the test result shown in Fig.7.1-8 (Ref.31). "a(8)" is defined by the upstream critical flow velocity; not in-plane flow velocity a (O )    _=U c(_ )      . .  ....................................................................................        (28)
Uc(Odeg)
: Where, 0              Angle of Flow direction Uc            Critical velocity 0.41                                                                                    FLCW                          FLOW 000
    -6            &deg;-      ,              -
0                    .1              .      .      -
o*0oO.
* 000.@
00006 o 0 deg 0101                            20                    20                                                    00 PMALLflL                                                    NOOMA TALANGLE          FLOW DIRECTION        dcjrc)            "RII
        . Fig. 1O Ellectot Incident flOWdirection on critical Velocity Parallel (0 deg.)              Normal triangle (30 deg.)
Fig.7.1-8 Effect of the flow direction (Ref.31)
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Ak-Stability ratio is usually calculated by using in-plane flow velocity V. On the other hand, the function a( e) is defined by the magnitude of normal flow velocity Vn to the tube. Therefore, Ki or K0 are multiplied by the velocity ratio Vn/V and function a(O ) as shown in Fig.7.1-9, then K used for the analysis 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, a            Effect of Flow direction Vn          Average in-plane velocity V            Magnitude of flow velocity Best estimated critical factor of In-plane FEI K,
Best estimated critical factor of out of plane FEI K.
Best estimated critical factor used for the evaluation Row Magnitude of Flow Column Fig.7.1-9 Effect of flow direction MITSUBISHI HEAVY INDUSTRIES, LTD.
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A 7.2 Calculation model Stability analyses are carried out in the following manner.
(1) Tube row The tubes shown in Table 7.2-1 and Fig.7.2-1 are selected by SCE for the evaluation (see                        A Attachment-7 for details).
Table 7.2-1 Evaluated Tubes Row                  Column 80                      70 80                      80 100                      70 100                      80 120                      70 120                      80 95                      85 125                      85 138                      84
* Plugged tubes O  Representative tube for OA        -  ,--    --                -
140
                                      -                                            O      ..        135 130 O' 0.-
125 i                  ,*
* S i                  .                      S    S 120 115
                                                      -0                                              110 105 100 =
95 90 85 o------..0-*...                          --- i 80 t-75 70 60          65          70      75        80            85 COL Fig.7.2-1 Evaluated Tubes MITSUBISHI HEAVY INDUSTRIES, LTD.
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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 including node number and coordinate of TSP elevation are shown in Fig. 7.2-1 to 7.2-9.
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At r
Fig. 7.2-1 Calculation model for Row 80 Column 70 MITSUBISHI HEAVY INDUSTRIES, LTD.
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At Fig. 7.2-2 Calculation model for Row 80 Column 80 MITSUBISHI HEAVY INDUSTRIES, LTD.
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Aok Fig. 7.2-3 Calculation model for Row 100 Column 70 MITSUBISHI HEAVY INDUSTRIES, LTD.
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                                                    -At Fig. 7.2-4 Calculation model for Row 100 Column 80 MITSUBISHI HEAVY INDUSTRIES, LTD.
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At I-2 Fig. 7.2-5 Calculation model for Row 120 Column 70 MITSUBISHI HEAVY INDUSTRIES, LTD.
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At K-Fig. 7.2-6 Calculation model for Row 120 Column 80 MITSUBISHI HEAVY INDUSTRIES, LTD.
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At Fig. 7.2-7 Calculation model for Row 95 Column 85 MITSUBISHI HEAVY INDUSTRIES, LTD.
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A Fig. 7.2-8 Calculation model for Row 125 Column 85 MITSUBISHI HEAVY INDUSTRIES, LTD.
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At I-Fig. 7.2-9 Calculation model for Row 138 Column 84 MITSUBISHI HEAVY INDUSTRIES, LTD.
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: 8. Computation Results 8.1 Out of plane FEI analysis results The 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 SG Table 8.1.1-1  All support points are active and the thermal power is 70%
No olugging Table 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 SG Table 8.1.2-1  1 support point is inactive and the thermal power is 70%
No plugaina Table 8.1.2-2  1 support point is inactive and the thermal power is 100% with no plugging MITSUBISHI HEAVY INDUSTRIES, LTD.
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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              /*X Damping Ratio                      Critical        Average Average Maximum Critical      Effective Tube      Location          Tube natural h(%)                        coefficient          fluid      void  void      flow      flow    Stability of inactive        frequency density fraction fraction velocity  velocity    rati6 support Mode point              f(Hz)    Structural  Two    Squeeze Row Col                                      dal        phase      film    Total  K1    Ko      Ke  K    Po(ibfft 3 )  [-]    [-]  Uc(ft/sec) Ue(ft/sec) damping    damping  damping z
0 80    70 80    80 C,=
100    70                                                                                                                                                                  CD
                                                                                                                                                                            --n cn 1 0(*) 80(')
0 120    70 120    80 95(*) 85(')
125    85 138    84 Note(*): Plugged tube with Type J stabilizer C,
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Table 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 active      A Location of inactive      Tube natural              Damping Ratio                    Critical          Average Average Maximum Critical      Effective ponsupport    frequency                    h(%)                        coefficient          fluid    void    void      flow      flow    Stability point    Mode                                                                              density fraction fraction velocity    velocity    ratio Structural  Two    Squeeze                                            3 RowSrcCaol          phase      film    Total    K1    Ko      Ke  K    Po(lb/ft )  [-1      [-]  Uc(ftlsec) Ue(ftlsec) damping    damping  damping 80 70 80 80                                                                                                                                                                z 0
100 70                                                                                                                                                                0 CD n
100 80                                                                                                                                                                ,=-
                                                                                                                                                                          "o 120 70                                                                                                                                                                CD 0
120 80 C,'
95 85 C,' 125 85 138 84 I~
CD 41~  '-
0~\
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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 inactive Location of inactive                                      Damping                        Critical          Average Average Maximum      Critical  Effective Tube        support            Tube natural                  Ratio                      coefficient          fluid      void    void      flow      flow    Stability point      Mode                                h(%)                                            density  fraction fraction  velocity  velocity    ratio f(Hz)    Structural  Two      Squeeze                                      (Ib/ft)    [-]            Uc(ft/sec) Ue(ft/sec)
Row Col                                                  phase      film  Total    KI    Ko      Ke  K    PO I            I-                  damping    damping    damping 80    70      B03 C
c.4~  80    80      B03 100    70      B03 100(*) 80(*)    B03 C    120    70      B03 CI) 120    80      B03 CI) 95(') 85(')    B03 125    85      B03 138    84      B04                                                                                                                                                          Y0 C)
Note(*): Plugged tube with Type J stabilizer 0
                                                                                                                                                                                      '-I Page 63 of 149                                              S023-617-1-M1539, REV. 0
Table 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 inactive      A Location of inactive                                  Damping                          Critical        Average Average Maximum    Critical  Effective Tube  support        Tube natural                  Ratio                        coefficient          fluid    void    void      flow      flow    Stability point    Mode  frequency                    h(%)                                            density  fraction fraction  velocity  velocity    ratio f(Hz)    Structural  Two      Squeeze Row Col                                          phase      film    Total    K1    Ko      Ke  K    po(Ift3)    [-]      [-]  Uc(ft/sec) Ue(ftfsec)
RowCol                                damping damping      damping 80  70    B03 80  80    B03                                                                                                                                                          z0 10 100  70    B02 02 100  80    B02 120  70    B02 CD CO 120  80    B02                                                                                                                                                          0 95  85    B03 125  85    B02 138  84    B02 0
as K
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Document No. L5-04GA567(6)
At 8.2 In-plane FEI analysis results The 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 SG Table 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 pluaaina Table 8.2.1-7    6 consecutive support points are inactive and the thermal power is 100% with no plugging (2) Assuming 8 support points are inactive:
For 2A SG Table 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 plugging Table 8.2.2-7    8 consecutive support points are inactive and the thermal power is 100% with no plugging MITSUBISHI HEAVY INDUSTRIES, LTD.
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Document No. L5-04GA567(6)
A&
(3) Assuming 10 support points are inactive:
For 2A SG Table 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 plugging Table 8.2.3-7  10 consecutive support points are inactive and the thermal power is 100% with no plugging (4) Assuming All support points are inactive:
For 2A SG Table 8.2.4-1  All consecutive support point:s are inactive and the thermal power is 50%
Table 8.2.4-2  All consecutive support point:s are inactive and the thermal power is 60%
Table 8.2.4-3  All consecutive support point:s are inactive and the thermal power is 70%
Table 8.2.4-4  All consecutive support point:s are inactive and the thermal power is 80%
Table 8.2.4-5  All consecutive support point:s are inactive and the thermal power is 90%
Table 8.2.4-6  All consecutive support point:s are inactive and the thermal power is 100%
No plugging Table 8.2.4-7  All consecutive support poirnts are inactive and the thermal power is 100% with no plugging MITSUBISHI HEAVY INDUSTRIES, LTD.
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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 inactive Tube                      Damping                            Critical          Average Average Maximum      Critical  Effective Tube            natural                      Ratio                          coefficient            fluid      void    void      flow      flow    Stability Mode frequency                      h(%)                                                density    fraction fraction  velocity  velocity    ratio f(Hz)  Structural    Two    Squeezefilm                                        po(lb/ft3)    [-]      [-]  Uc(ft/sec) Ue(ft/sec)
Row    0Col                  dampin        phase              Total  Kf1    Ko      K      Ke  K damping    damping    damping                                                                                                          z 0
C,'  80    70 0
                                                                                                                                                                            'a 80    80 CD 100    70 C,
100(*) 80(.)                                                                                                                                                            0 C,'  120    70 120    80 95(*)  85(*)
125    85 Y0 138    84 IA&#xfd; Note(*): Plugged tube with Type J stabilizer Page 67 of 149                                                S023-617-1-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 inactive Tube                      Damping                                Critical        Average Average Maximum    Critical  Effective Tube              natural                      Ratio                              coefficient        fluid    void    void      flow      flow    Stability Mode frequency                      h(%)                                                density  fraction fraction  velocity  velocity    ratio Rwof(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    damping 80    70 z0 80    80 0
100    70                                                                                                                                                                  ,.-i CD 100(*' 80(')                                                                                                                                                      6 CD 120    70                                                                                                                                                                  Cn 0
120    80 95()  85(*)                                                                                                                                                      6 125    85 138    84                                                                                                                                                            tz 0
Note(*): Plugged tube with Type J stabilizer 1j4a
                                                                                                                                                                  )40 Y
                                                                                                                                                                          >0 Page 68 of 149                                          S023-617-1-M1539, REV. 0
Table 8.2.1-3 In-plane FEI Analysis Results for 2A SG when the thermal power is 70% and 6 consecutive support points are inactive Tube                      Damping                            Critical          Average Average Maximum    Critical  Effective Tube            natural                      Ratio                          coefficient            fluid    void    void    flow        flow    Stability Mode frequency                      h(%)                                                density  fraction fraction velocity    velocity    ratio Two                                                      po(b/f3)    [-]      [-]  Uc(ft/sec) Ue(ft/sec)
Row    Col          f(Hz)  Structural    phase  Squeeze film Total K1      Ko      Ki    Ke  K damping                damping 80    70                                                                                                                                                            Z 0
                                                                                                                                                                        "{3 80    80 0
100    70                                                                                                                                                            -6 z
1 00M 80M                                                                                                                                                              CD 120                                                                                                                                                                  0 70 120    80 W.(
95(*)  85(1)                                                                                                                                                      6 125    85 0
138    84 Note(*): Plugged tube with Type J stabilizer
                                                                                                                                                              &#xfd;k 4-I Page 69 of 149                                            S023-617-1-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 inactive Tube                      Damping                            Critical          Average Average Maximum      Critical  Effective Tube              natural                      Ratio                          coefficient            fluid      void    void    flow        flow    Stability Mode frequency                        h(%)                                                  density  fraction fraction velocity    velocity    ratio Row    ColRo    o    f(Hz)  Structural ig    Two phase    Squeeze apn film Total K1      Ko      Ki    Ke  K    po(lb/ft3)    [-1      [-]  Uc(ft/sec) Ue(ft/sec)
____ ____              damping_____damping    damping damingphase 80    70 z
80    80                                                                                                                                                                0
                                                                                                                                                                            '0 100    70 100M 80(1)
CD 120    70                                                                                                                                                                  W.
0 120    80                                                                                                                                                                "33 95(*)  85(*)
                                                                                                                                                                      /
125    85 138    84 Note(*): Plugged tube with Type J stabilizer                                                                                                                  [&#xfd;&#xfd;
                                                                                                                                                                      )100.
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Table 8.2.1-5 In-plane FEI Analysis Results for 2A SG when the thermal power is 90% and 6 consecutive support points are inactive Tube                      Damping                            Critical          Average Average Maximum Critical      Effective Tube            natural                    Ratio                            coefficient            fluid    void    void      flow      flow    Stability Mode frequency                      h(%)                                                  density  fraction fraction  velocity  velocity    ratio Two    Squeeze3film                                        p(Ib/ft3)    [-]            Uc(ft/sec) Ue(ft/sec)
Row    Col          f(Hz)  Structural phase                  Total  KI      Ko      Ki    Ke  K damping damping        damping 80    70                                                                                                                                                              Z 0
7
                                                                                                                                                                            '0 80    80 CD M"
100    70                                                                                                                                                              0) 100(') 80(*)
Mj 120    70 120    80 C-,
95(*)  85(*)                                                                                                                                                      6 125    85 C0 138    84 Note(*): Plugged tube with Type J stabilizer Page 71 of 149                                                S023-617-1-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 inactive Tube                      Damping                            Critical          Average Average Maximum        Critical  Effective Tube            natural                      Ratio                          coefficient            fluid      void    void      flow      flow    Stability Mode frequency                      h(%)                                                density    fraction fraction  velocity  velocity    ratio Row    Co Ro ~      f(Hz)  Structural apn          Two Squeeze phase    dmig film Total  K1    KO      Ki    Ke  K  po(lb/ft3 )    [-]      [-]  Uc(ft/sec) Ue(ft/sec) damping    damping    damping 80    70 z
80    80                                                                                                                                                              0
                                                                                                                                                                          ,0 100    70
                                                                                                                                                                          "(3 100(*)  80(*)                                                                                                                                                            CD 10 70                                                                                                                                                              5.
CD 120                                                                                                                                                                      C, 120    80 95(')  85(*)
125    85 138    84 Note(*): Plugged tube with Type J stabilizer k&#xfd;
                                                                                                                                                                    )10.
Page 72 of 149                                                S023-617-1-M1539, REV. 0
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 inactive Tube                  Damping                              Critical            Average Average Maximum Critical      Effective Tube              natural                  Ratio                              coefficient            fluid    void    void    flow        flow    Stability Mode frequency                    h(%)                                                    density fraction fraction velocity    velocity    ratio f(Hz)  Structural  Two Squeeze film                                              po(lb/ft3)  H[      [-]  Uc(ft/sec) Ue(ft/sec)
Row  Col                              phase                  Total  K1    K0      Ki    Ke damping damping    damping 80    70 z
80    80                                                                                                                                                            0 U)'
100    70 100    80                                                                                                                                                            0.n 0
:3 W,                                                                                                                                                                        _D 120    70 120    80 95    85 125    85 138    84 CD 0
Page 73 of 149                                              S023-617-1-M1539, REV. 0
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 inactive Tube                      Damping                            Critical          Average Average Maximum    Critical  Effective Tube            natural                    Ratio                            coefficient            fluid    void    void      flow        flow  Stability Mode frequency                      h(%)                                                  density  fraction fraction  velocity    velocity  ratio Two                                                        p(bf3        -        -    cf/e)U~tsc Row    0ol          f(Hz)  Structural phase    Squeeze film Total  K      Ko      K      Ke  KUc(fsec)                                  Ue(ftsec) damping dampin        damping 80    70 rj2 80    80                                                                                                                                                                I0 100    70 z
I 80()
100(')
120    70 6      &#xfd; 120    80 cj~
95(*)  85(*)
0 125    85 6
138    84 Note(*): Plugged tube with Type J stabilizer kR&#xfd;        0 Vh Page 74 of 149                                              S023-617-1-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 inactive Tube                      Damping                          Critical            Average Average Maximum          Critical  Effective Tube              natural                      Ratio                          coefficient            fluid      void      void      flow      flow    Stability Mode frequency                        h(%)                                                density    fraction  fraction  velocity  velocity    ratio Row    Col          f(Hz)  Structura      w Two    Squeezefilm Total                                                H    I    [-]
dampin dmi 9 ph        damping    Total K1      Ko      Ki    Ke  K    P&deg;(Ib/ft3 )                    Uc(ft/sec) Ue(ftlsec) damping    dmi 80    70 80    80                                                                                                                                                                    I0 100    70                                                                                                                                                                    CDl 100(*) 80(*)
120    70 120    80 95(.)  85(*)
0 125    85 6
138    84 Note(*): Plugged tube with Type J stabilizer V~~1 I
0h Page 75 of 149                                                    S023-617-1-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 inactive Tube                      Damping                            Critical          Average Average Maximum Critical        Effective Tube            natural                      Ratio                          coefficient            fluid      void    void      flow      flow    Stability Mode frequency                      h(%)                                                  density  fraction fraction  velocity  velocity    ratio f(Hz)  Structural            Squeeze film                                      po(lb/ft3)    [-]      [-]  Uc(ft/sec) Ue(ft/sec)
Row    Col                                phase                Total K1      Ko      Ki    KO  K damping damping        damping 80    70 80    80                                                                                                                                                              I0
                                                                                                                                                                          '0 100    70 CD 100(*)  80(*)
120    70 120    80 95(*)  85(*)
0 125    85 138    84                                                                                                                                                          0 Note(*): Plugged tube with Type J stabilizer
                                                                                                                                                              &#xfd;k~
C) 4zi Page 76 of 149                                                S023-617-1-M1539, REV. 0
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 inactive Tube                      Damping                            Critical          Average Average Maximum Critical        Effective Tube            natural                      Ratio                          coefficient            fluid      void    void      flow      flow    Stability Mode frequency                      h(%)                                                density    fraction fraction  velocity  velocity    ratio f(Hz)    Structural            Squeeze film                                      po(lb/ft3)    [-]      [    Uc(ft/sec) Ue(ft/sec)
Row    Col                  damping      phase                Total K1      Ko      Ki    Ke  K damping    damping    damping 80    70                                                                                                                                                              z 0,=
6 80    80 rj~
100    70
                                                                                                                                                                              =3 100(*) 80(*)
120    70                                                                                                                                                          6 C,)
120    80 0
C-,  95(*)  85(*)
125    85                                                                                                                                                            03 O
Y,,3 0
138    84
                                                                                                                                                                        -L.-
CD Note(*): Plugged tube with Type J stabilizer Page 77 of 149                                                S023-617-1-M1539, REV. 0
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 inactive Tube                    Damping                              Critical          Average Average Maximum Critical        Effective Tube              natural                    Ratio                            coefficient            fluid      void    void      flow      flow    Stability Mode frequency                      h(%)                                                  density    fraction fraction  velocity  velocity    ratio Row    Col                            n da  Pase    Squeezefilm lmpin    Total  Ki    Ko      K      Ke      po(lb/ft3)    [-]      [-]  Uc(ftlsec) Ue(ft/sec)
___            _______    damping    dapn 80    70 z
80    80                                                                                                                                                                0,=
C,'                                                                                                                                                                          .6 100    70                                                                                                                                                                0 rj~
z  100(      0(//
              &deg;                                                                                                                                                              CD
                                                                                                                                                                              =3 120    70                                                                                                                                                              CD O
_j.
120    80 C')
95(*) 85(*)
C" 125    85 138    84                                                                                                                                                          0 0
C Note(*): Plugged tube with Type J stabilizer 0
                                                                                                                                                                          >~0 Page 78 of 149                                                  S023-617-1-M1539, REV. 0
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 inactive Tube                      Damping                            Critical          Average Average Maximum Critical      Effective Tube            natural                    Ratio                            coefficient          fluid    void    void      flow      flow    Stability Mode frequency                      h(%)                                                  density fraction fraction velocity    velocity    ratio Row    Col Two                                                      po(Ib/ft3)  [-]    [-]  Uc(ft/sec) Ue(ft/sec) f(Hz)    Structural  phase Squeeze film  Total  K1    Ko      Ki    Ke  K damping damping damping 80    70 80    80                                                                                                                                                            z0 100    70                                                                                                                                                              0 100)    80(*)
6      CD 120    70                                                                                                                                                              (n.
0i 120    80 C,'
95(*)  85(*)
6 rj~
125    85 0
138    84 Note(*): Plugged tube with Type J stabilizer                                                                                                                        0 CD Y.,
Page 79 of 149                                              S023-617-1-M1539, REV. 0
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 inactive Tube                    Damping                              Critical            Average Average Maximum      Critical  Effective Tube            natural                    Ratio                            coefficient            fluid      void    void      flow      flow    Stability Mode frequency                      h(%)                                                    density  fraction fraction  velocity  velocity    ratio Two                                                          p(bf3)        -        -    cf/e)U~tsc Row    Col          f(Hz)    Structural  phase Squeeze film    T(lbft                                          )                  Uc(ftlsec) Ue(ftlsec) damping    damping    damping    Total  K1    Ko      Ki    K,  K 70 80                                                                                                                                                                          z 0
CI) 80    80
                                                                                                                                                                                '0 Cl, 100    70                                                                                                                                                                    0) 0-i 100    80 Cn 120    70 Cl, 120    80 95    85 125    85 138    84 1 0t o Y '-
                                                                                                                                                                          >    G8 Page 80 of 149                                              S023-617-1-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 inactive Tube                      Damping                              Critical          Average Average Maximum      Critical  Effective Tube            natural                      Ratio                            coefficient            fluid      void    void      flow      flow    Stability Mode frequency                      h(%)                                                  density  fraction fraction  velocity  velocity    ratio Row    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  K damping 80    70                                                                                                                                                          z0 80    80                                                                                                                                                            0 C,,
100    70 CD 100(o) 80(*)
CD.
0 120    70 120    80 95(*) 85(*)
125    85 138    84 Note(*): Plugged tube with Type J stabilizer oc Page 81 of 149                                                S023-617-1-M1539, REV. 0
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 inactive Tube                      Damping                              Critical          Average Average Maximum      Critical  Effective Tube            natural                    Ratio                            coefficient            fluid      void    void    flow        flow    Stability Mode frequency                      h(%)                                                  density  fraction fraction velocity    velocity    ratio Row    Col          f(z Cf(Hz)    trcualp Structural  phase Two      dmig film Squeeze      Total  K1      Ko      Ki    Ke  K    po(lb/ft3)    [-]      [-]  Uc(ft/sec) Ue(ftlsec) d  damping    damping 80    70 z
80    80                                                                                                                                                            0 CI) 100    70                                                                                                                                                            ")
CI)
CD 100M 80(*)
ZI 120    70                                                                                                                                                            CD.
0 120    80 95(*)  85(*)
CI) 125    85 138    84                                                                                                                                                          0 Note(*): Plugged tube with Type J stabilizer V, N Page 82 of 149                                                S023-617-1-M1539, REV. 0
Table 8.2.3-3 In-plane FEI Analysis Results for 2A SG when the thermal power is 70% and 10 consecutive support points are inactive Tube                      Damping                            Critical          Average Average Maximum      Critical  Effective Tube            natural                      Ratio                          coefficient            fluid    void    void    flow      flow    Stability Mode frequency                      h(%)                                                  density  fraction fraction velocity  velocity    ratio Row    Co            f(Hz)  Structural    Two    Squeezefilm                                        po(Ib/ft)                  Uc(ft/sec) Ue(ft/sec) tur damping      phase damping    d    ilm damping  Total  K1      Ko      Ki    Ke  K 80    70 Z
80    80                                                                                                                                                            0 C,,
100    70 C,,
CD 100(*) 80(*)                                                                                                                                                            10 120    70                                                                                                                                                            Cn.
0n 6
120    80 95(*)  85(*)
Cj2 125    85 138    84                                                                                                                                                          U 0
Note(*): Plugged tube with Type J stabilizer
                                                                                                                                                                &#xfd;k )
1111 CD C)
                                                                                                                                                                        >J ~
Page 83 of 149                                              S023-617-1-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 inactive Tube                      Damping                              Critical          Average Average Maximum        Critical  Effective Tube            natural                      Ratio                            coefficient            fluid      void    void    flow        flow    Stability Mode frequency                      h(%)                                                  density    fraction fraction velocity    velocity    ratio f(Hz)    Structural    Two Squeeze film                                          po(lb/ft3 )    [-]      [-]  Uc(ft/sec) Ue(ft/sec)
Row    Cola                                phase                Total  K1      Ko      Ki    Ke damping damping        damping 80    70 Z
0 80    80 100    70 100M) 80C)                                                                                                                                                            6L  :2.
0 120    70
:3 120    80 95(*)  85(*)
125    85 138    84                                                                                                                                                              C 0
Note(*): Plugged tube with Type J stabilizer 0
Page 84 of 149                                                S023-617-1-M1539, REV. 0
Table 8.2.3-5 In-plane FEI Analysis Results for 2A SG when the thermal power is 90% and 10 consecutive support points are inactive Tube                      Damping                              Critical          Average Average Maximum        Critical  Effective Tube            natural                    Ratio                            coefficient            fluid      void    void    flow        flow    Stability Mode frequency                      h(%)                                                  density    fraction fraction velocity    velocity  ratio f(Hz)    Structural          Squeeze film  T                                      po(Ib/ft3 )    [-]      [-1  Uc(ft/sec) Ue(ft/sec)
Row Ctrcdamping      phase dmigdamping    damping    Total  K1      Ko      Ki    Ke  K 80    70 z0 80    80 rj~
100    70 C,,
CD 100(') 80(')
k    (D 120    70                                                                                                                                                                  C,.
0 120    80 C,,
95(M  85(*)
C,,
125    85 F
138    84                                                                                                                                                              0E Note(*): Plugged tube with Type J stabilizer 0
Page 85 of 149                                                S023-617-1-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 inactive Tube                      Damping                            Critical          Average Average Maximum        Critical  Effective Tube            natural                      Ratio                          coefficient            fluid      void    void    flow        flow    Stability Mode frequency                      h(%)                                                  density    fraction fraction velocity    velocity    ratio f(Hz)  Structural            Squeeze film                                      po(lb/ft3 )    [-]      [-]  Uc(ft/sec) Ue(ft/sec)
Row    Col                    dal          phase    damping    Total  K1    KO      K      Ke damping damping        damping 80    70 Z
80    80                                                                                                                                                                0 100    70                                                                                                                                                                0D 100(*) 80(1)                                                                                                                                                          6    CD 120    70                                                                                                                                                                tn.
0 120    80 95(*)  85(*)
6 125    85                                                                                                                                                            CD 0
138    84                                                                                                                                                            0 Note(*): Plugged tube with Type J stabilizer 0
Y,J Page 86 of 149                                                S023-617-1-M1539, REV. 0
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 inactive Tube                  Damping                                Critical            Average Average Maximum      Critical  Effective Tube              natural                  Ratio                              coefficient            fluid      void    void    flow        flow    Stability Mode frequency                    h(%)                                                    density    fraction fraction velocity    velocity    ratio Row    Col            f(Hz)  Structural  Two    Squeeze film                                          po(Ib/ft3)    [-]    [-]  Uc(ft/sec) Ue(ft/sec) phase damping damping                  Total    K1    K      Ki    K    K damping 80    70 z
80    80                                                                                                                                                                0 r.j~                                                                                                                                                                          '0 0
100    70 rj, 100    80 CD 120    70                                                                                                                                                                Cn.
0 LO 120    80 95    85 r.j~
125    85 138    84 C)
Page 87 of 149                                              S023-617-1-M1539, REV. 0
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 inactive Tube                      Damping                              Critical          Average Average Maximum Critical      Effective Tube            natural                    Ratio                            coefficient            fluid    void    void      flow      flow    Stability Mode frequency                      h(%)                                                  density fraction  fraction  velocity  velocity    ratio f(Hz)    Structural    Two    Squeeze film                                        po(Ib/ft)  [-]      [-]  Uc(ft/sec) Ue(ft/sec)
Row    Col                                phaseToa damping damping        damping          K1      K        i    e  K z
0 80    70 0
X, 80    80 X,
CD 100    70 0)
C) 100(*)  80(*)
120    70 Y,
120    80                                                                                                                                                          N 95(*)  85(*)                                                                                                                                                          ('  0 125    85 138    84                                                                                                                                                          0 Note(*): Plugged tube with Type J stabilizer 49      0-\
Page 88 of 149                                                S023-617-1-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 inactive Tube                      Damping                              Critical          Average Average Maximum      Critical  Effective Tube              natural                    Ratio                            coefficient            fluid    void    void      flow      flow  Stability Mode frequency                      h(%)                                                  density  fraction fraction  velocity  velocity  ratio Two                                                        p0Ibf3)      [-]      [-]  Uc(ft/sec) Ue(ftsec)
Ki    Ke  K dampingfilm Row    Col          f(Hz)    Structural  phase Squeeze        Total  K1      Ko damping damping 80    70 Z
0 80    80 0
100    70 CD 100(*) 80(*'
0) 120    70 0
120    80 95()  85M' 6&#xfd; 125    85 138    84 Note(*): Plugged tube with Type J stabilizer Y0 Page 89 of 149                                                S023-617-1-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 inactive Tube                      Damping                            Critical          Average Average Maximum        Critical  Effective Tube            natural                      Ratio                          coefficient            fluid      void    void      flow      flow    Stability Mode frequency                      h(%)                                                  density    fraction fraction  velocity  velocity    ratio f(Hz)    Structural    Two    Squeeze film                                        po(lb/ft3 )    [-]      [-]  Uc(ft/sec) Ue(ft/sec)
Row    Col                  dal          phase damping damping        damping    Total K1      Ko      Ki    Ke  K 80    70 z
0 80    80 100    70                                                                                                                                                            3    3 100(*) 80(')
CD 120    70                                                                                                                                                                (n.
0 120    80 95(*)  85(*)
125    85 138    84 Note(*): Plugged tube with Type J stabilizer
                                                                                                                                                                      'z CDJ Page 90 of 149                                                  S023-617-1-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 inactive Tube                    Damping                                Critical          Average Average Maximum Critical        Effective Tube              natural                    Ratio                              coefficient            fluid      void    void      flow      flow    Stability Mode frequency                    h(%)                                                    density    fraction fraction  velocity  velocity    ratio f(Hz)    Structural    ose Squeeze film                                          po(lb/ft3 )    [-]      [-]  Uc(ft/sec) Ue(ft/sec) damping damping      damping 80      70 z
80      80                                                                                                                                                                  0 100    70 0
100(*) 80(')                                                                                                                                                                CD 0) 120    70 120    80 95(*)  85(*)
125    85 138    84                                                                                                                                                            I
* Note(*): Plugged tube with Type J stabilizer C)
                                                                                                                                                                        >~
(  'A!:7 Page 91 of 149                                                  S023-617-1-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 inactive z0 0
6 CD (n.
0 0
Note(*): Plugged tube with Type J stabilizer Y0 C~~-
                                                                                                                                                              >A Page 92 of 149                                              S023-617-1-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 inactive Tube                      Damping                              Critical          Average Average Maximum Critical      Effective Tube            natural                      Ratio                            coefficient            fluid    void    void      flow      flow    Stability Mode frequency                      h(%)                                                  density fraction fraction velocity    velocity    ratio Ro o    f(Hz)
(z      structural tutrlSqueezeTwo            film                                        po(Ib/f3 p(bf        [-]      [-]  Uc(ft/sec) Ue(ft/sec)
Row    Col                    damping    phase    damping    Total  K1    Ko      Ki    Ke  K dampinga 80    70 Z
80    80                                                                                                                                                                0 0
100    70                                                                                                                                                              'a
                                                                                                                                                                            ,0 0
1 00()  80(1) 120    70                                                                                                                                                                O 120    80 95(")  85(1) 125    85
                                                                                                                                                                      &#xa9; 138    84                                                                                                                                                          t-Note(*): Plugged tube with Type J stabilizer 0
_R&#xfd;
                                                                                                                                                                            'C Page 93 of 149                                              S023-617-1-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 inactive Tube                    Damping                              Critical            Average Average Maximum Critical        Effective Tube              natural                    Ratio                            coefficient            fluid      void    void    flow        flow    Stability Mode frequency                        h(%)                                                  density    fraction fraction velocity    velocity    ratio f(Hz)    Structural  Two    Squeezefilm                                          po(lb/ft3)    [-]      [-]  Uc(ft/sec) Ue(ft/sec)
Row    Col                      dal damping    phase damping    dampin damping    Total  K1    Ko      Ki    Ke    K 80    70 z
0 80    80 100    70                                                                                                                                                                '0 100    80                                                                                                                                                                CD 120    70                                                                                                                                                                CD.
0i
:3 120    80 95    85 125    85 138    84 C)
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: 9. Reference
: 1)  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 2000 addenda.
: 3)  L5-04FU001 the latest revision, Component and Outline Drawing 1/3
: 4)    L5-04FU002 the latest revision, Component and Outline Drawing 2/3
: 5)    L5-04FU003 the latest revision, Component and Outline Drawing 3/3
: 6)    L5-04FU021 the latest revision, Tube Sheet and Extension Ring 1/3
: 7)    L5-04FU022 the latest revision, Tube Sheet and Extension Ring 2/3
: 8)    L5-04FU023 the latest revision, Tube Sheet and Extension Ring 3/3
: 9)    L5-04FU051 the latest revision, Tube Bundle 1/3
: 10)  L5-04FU052 the latest revision, Tube Bundle 2/3
: 11)  L5-04FU053 the latest revision, Tube Bundle 3/3
: 12)  L5-04FU111 the latest revision, AVB assembly 1/9
: 13)  L5-04FU112 the latest revision, AVB assembly 2/9
: 14)  L5-04FU113 the latest revision, AVB assembly 3/9
: 15)  L5-04FU114 the latest revision, AVB assembly 4/9
: 16)  L5-04FU115 the latest revision, AVB assembly 5/9
: 17)  L5-04FU1 16 the latest revision, AVB assembly 6/9
: 18)  L5-04FU117 the latest revision, AVB assembly 7/9
: 19)  L5-04FU1 18 the latest revision, AVB assembly 8/9
: 20)  L5-04FU119 the latest revision, AVB assembly 9/9
: 21)  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 on internal SG thermal hydraulics parameters
: 23)  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 Design Guidelines,Journal of Pressure Vessel Technology Vol.133
: 26)  M.J. Pettigrew.,et.al.,2003,"Vibration analysis of shell-and-tube heat exchangers" Journal of Fluids and Structures 18 (2003) 469-483
: 27)  S. M. Fluit and M. J. Pettigrew, "Simplified method for predicting vibration and fretting-wear in nuclear steam generator U-bend tube bundle", ASME PVP 2001 Vol.420-1
: 28)  WJS16263, MHI Test Report of Fluid Elastic Vibration
: 29)  M.J. Pettigrew.,et.al.,2000, "The effects of tube bundle geometry on vibration in two-phase cross-flow",Flow      Induced    Vbration,  Ziada&Staubi(eds)    2000    Balkema,    Rotterdam ISBN9058091295
: 30)  Flow-Induced VibrationMeskell & Bennett (eds) ISBN 978-0-9548583-4-6, "Study on In-flow Fluid-elastic Instability of Circular Cylinder Arrays"], T.Nakamura, Y.Fujita, T.Oyakawa, Y.NI. July 2012
: 31)  H.C.Yeung, 1983, "The effect of Approach Flow Direction on the Flow-Induced Vibrations of a Triangular Tube Array", Transaction of ASME Vol.105
: 32)  L5-04GA587 the latest revision, Test result for damping ratio added by the stabilizer inserted for short length (Row No. 106)
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At Table I-1 Input and Output file name of out of plane FEI evaluation for 2A SG when all support points are active                                                                                            A Thermal        Row    Column                    Input 1)
Power(%)                                                                              Output 1) 80      70      _
80      80 100      70 100      80 70          120      70 120      80 95      85 125      85 138      84 80      70 80      80 100      70 100          100      80 120      70 (No Plug)        120      80 95      85 125      85 138      84    _____
Table 1-2 Input and Output file name of out of plane FEI evaluation for 2A SG when 1 support points are inactive Thermal        Row      Column                    Input 1)
Power(%)                                                                                  Output 1) 80      70 80      80 100      70 100      80 70          120      70 120      80 95      85 125      85 138      84 80      70 80      80 100      70 100          100      80 120      70 (No Plug)        120      80 95        85 125      85 138      84      ____
Notes:
: 1) All files are saved in the directory as below:
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At Table 1-3 Input and Output file name of in-plane FEI evaluation for 2A SG when 6 consecutive support points are inactive (1/2)
Thermal      Row      Column                    Input 1)                            Output 1)
Power(%)
80        70      ,
80        80 100        70 100        80 50          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 60          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 70          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 80          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 90          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 100          120        70 120        80 95        85  11 125        85 138        84                                                                          .-
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At Table 1-3 Input and Output file name of in-plane FEI evaluation for 2A SG when 6 consecutive support points are inactive (2/2)
Thermal      Row      Column                    Input 1)
Power(%)                                                                              Output 80        70 80        80 100        70 100          100        80 120        70 (No Plug)      120        80 95        85 125        85    11 138        84    1 Notes: 1) All files are saved in the directory as below:
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At Table 1-4 Input and Output file name of in-plane FEI evaluation for 2A SG when 8 consecutive support points are inactive (1/2)
Thermal Power(%)      Row      Column                    Input 1)                          Output 1) 80        70 80        80 100        70 100        80 50          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 60          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 70          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 80          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 90          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 100          120        70 120        80 95        85 125        85 138        84  1.
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Table 1-4 Input and Output file name of in-plane FEI evaluation for 2A SG when 8 consecutive support points are inactive (2/2)                                                                              A Thermal Power(%)      Row      Column                    Input )                            Output 1) 80        70 80        80 100        70 100          100        80 120        70 (No Plug)      120        80 95        85 125        85 138        84 Notes: 1) All files are saved in the directory as below:
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At Table I-5 Input and Output file name of in-plane FEI evaluation for 2A SG when 10 consecutive support points are inactive    (1/2)                                                                          14\
Thermal Poer(%)      Row      Column                      Input 1)
Power(%)                                                                                Output 1) 80          70                                              _
80          80 100        70 100        80 50          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 60          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 70          120        70 120        80 95        85 125        85 138        84 80        70 80        80    1 100        70 100        80 80          120        70 120        80 95        85 125        85 138        84    1 80        70 80        80 100        70 100        80 90          120        70 120          80 95          85 125          85 138          84 80          70 80          80 100          70 100          80 100          120          70 120          80 95          85 125          85 138          84      "-.
Notes: 1) All files are saved in the directory as below:
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At-Table I-5 Input and Output file name of in-plane FEt evaluation for 2A SG when 10 consecutive support points are inactive (2/2)                                                                              A Thermal      Row      Column                    Input 1)
Power(%)                                                                              Output 80        70      r 80        80 100        70 100          100        80 120        70 (No Plug)        120        80 95        85 125        85 138        84 Notes: 1) All files are saved in the directory as below:
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Ati Table 1-6 Input and Output file name of in-plane EIl evaluation for 2A SG when 12 consecutive support points are inactive (1/2)                                                                            Z6\
Thermal        Row      Column                    Input                            Output 1)
Power(%)
80        70 80        80 100        70 100        80 50          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 60          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 70          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 80          120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 90            120        70 120        80 95        85 125        85 138        84 80        70 80        80 100        70 100        80 100          120        70 120        80 95        85 125        85  1 138        84    t        A Notes: 1 ) All files are saved in the directory as below:
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At Table 1-6 Input and Output file name of in-plane FEI evaluation for 2A SG when 12 consecutive support points are inactive (2/2)
Thermal      Row      Column                    Input 1)
Power(%)                                                                              Output 80        70 80        80 100        70 100          100        80 120        70 (No Plug)      120        80 95        85 125        85 138        84 Notes: 1) All files are saved in the directory as below:
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80123-XXIV-37.0.26 Purchase Order No. 4500024051 Specification No. S023-617-01R3 HITUB8r1eer IUV' nlUnSTa., tIA.Page 1 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I 11(2/149)At Revision History Document No.L5-04GA567 No. Revision Date Approved Checked Prepared 0 Initial issue See cover sheet I -Revised in accordance with SCE comments of RSG-SCE/MHI-12-5722.-Added the evaluation of out of plane FEI.2 Revised in accordance with SCE comments of RSG-SCE/MHI-12-5729.
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3 -Revised the calculation method of the virtual added mass of tube in Sec. 4.1(5).4 -Added Attachment-5 to evaluate the stability ratio of the tube which has tube-to-tube wear at 70% thermal power 5 -Revised Attachment-5 to evaluate the effect of type J stabilizer on stability ratio of the tube which has tube-to-tube wear at 70% thermal power-Added Attachment-6 to evaluate the uncertainty of calculated stability ratio 6 -Revised in accordance with SCE comments of RSG-SCE/M HI-12-5769-Revised stability ratios due to the change of stabilizer type (Type J)-Revised out-of-plane FEI analysis results in Sec.2 and 8 _MITSUBISHI HEAVY INDUSTRIES, LTD.Page 2 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I) (3/149)Document No. L5-04GA567(6)
Document No. L5-04GA567(6)
At Table of Contents 1. Purpose ....................................................................................................................................
A,&
4 2. Conclusion
Attachment-2 Evaluation of Liquid Film Thickness of Tube at AVB Support Point
...............................................................................................................................
: 1. Summary In order to estimate the effect of void fraction on the squeeze film damping, the relation between the liquid film thickness of tube at each AVB support point and void fraction is evaluated as shown in Table-1.
5 2.1 Stability ratio of out of plane FEI .....................................................................................
Table-1 Relation between liquid film thickness of tube and void fraction Void fraction        Liquid Film          Condition              Figure No                Dry out              Fig.l-1 Discontinuous          Dry &Wet                Fig.1-2 Continuous              Wet                  Fig.1-3 Tube Droplet AVB                                      0                        Liquid film (Thickness :6)
5 2.2 Stability ratio of in-plane FEI ............................................................................................
S 0
6 3. Nom enclature
S                                                                                                        e from the S                                                                                                      point (1*)
.........................................................................................................................
S 0                                                                            0  **
10 4. Assum ption ............................................................................................................................
* 5     0 eS      S 0
11 4.1 M odeling assum ption .....................................................................................................
Fig.1-1 No film (Dry out)        Fig.1-2 Discontinuous (Dry & Wet)       Fig. 1-3 Continuous (Wet)
11 4.2 O pen item ............................................................................................................................
The boundary of void fraction is determined as follows and the flow regime is confirmed to be consistent with the figures above as described in Attachment-4.
12 5. Acceptance Criteria ..........................................................................................................
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13 6. Design Input ...........................................................................................................................
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14 6.1 G eom etry of tube bundle region .....................................................................................
14 6.2 Thermal and hydraulic flow of steam generator secondary side ....................................
17 7. M ethodology
.............................................................................................................................
32 7.1 Fluid elastic vibration
......................................................................................................
32 7.2 Calculation m odel ..........................................................................................................
49 8. Com putation Results ........................................................................................................
60 8.1 O ut of plane FEI analysis results ...................................................................................
60 8.2 In-plane FEI analysis results ..........................................................................................
65 9. Reference
..............................................................................................................................
95 Attachm ent-1 Com puter Input and O utput File List ..............................................................
96 Attachment-2 Evaluation of Liquid Film Thickness of Tube at AVB Support Point .....................
106 Attachment-3 Evaluation of the Effective Distance of Liquid Film of Tube from the Contact Point for Squeeze Film Dam ping ..............................................................................................................
114 Attachm ent-4 Confirm ation of Flow Regim e ...............................................................................
117 Attachment-5 Case Study for Applying Split Stabilizers for TTW tube of Unit-2 at 70% Thermal Power .........................................................................................................................................
118 Attachm ent-6 Uncertainty of Calculated Stability Ratio ..............................................................
128 Attachm ent-7 Selection of Evaluated Tubes ...............................................................................
145 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 3 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I I) (4/149)Document No. L5-04GA567(6)
At 1. Purpose The 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 S023-617-1-M1539, REV. 0 I Non-proprietary Version I) (5/149)Document No. L5-04GA567(6)
At.2. Conclusion By considering numbers of inactive support points as the parameter for the case study, the following results are obtained.2.1 Stability ratio of out of plane FEI 2.1.1 Assuming all support points active With all AVB supports active, the stability ratios are less than 1.0 for all analyzed tubes, for the reactor power levels up to, and including, 100% with no plugging.Table 2.1-1 Stabilitv Ratio with All Active Sunoort Points for 2A SG Case Thermal Power Row Column 70 100 (No Plug)80 70 80 80 100 70 10011 80(*)120 70 120 80 95(*) 85(*)125 85 138 84 Note(*): Plugged tube with Type J stabilizer


====2.1.2 Assuming====
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1 support points inactive With 1 AVB supports inactive, the stability ratios are less than 1.0 for all analyzed tubes, for the reactor power levels up to, and including, 70%Table 2.1-2 Stability Ratio with I Inactive Su~oort Point for 2A SG Case Thermal Power Row Column 70 100 (No Plug)80 70 80 80 100 70 1 00C) 80(*)120 70 120 80 95(1) 85(*)125 85 138 84 L YI Note(*): Plugged tube with Type J stabilizer MITSUBISHI HEAVY INDUSTRIES, LTD.Page 5 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I I) (6/149)Document No. L5-04GA567(6)
Document No. L5-04GA567(6)
At 2.2 Stability ratio of in-plane FEI 2.2.1 Assuming 6 support points inactive With 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 SG Case Thermal Power Row Column 50 60 70 80 90 100 100 (No Plug)80 70 80 80 100 70 1 00M 80(.)120 70 120 80 95(') 85(*)125 85 138 84 Note(*): Plugged tube with Type J stabilizer MITSUBISHI HEAVY INDUSTRIES, LTD.Page 6 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version j) (7/149)Document No. L5-04GA567(6)
A,&
At 2.2.2 Assuming 8 support points inactive With 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 SG Case Thermal Power 100 Row Column 50 60 70 80 90 100 (Pu 80 70 80 80 100 70 1 O0) 80()120 70 120 80 95(*) 85(*)125 85 138 84 Note(*): Plugged tube with Type J stabilizer MITSUBISHI HEAVY INDUSTRIES, LTD.Page 7 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I) (8/149)Document No. L5-04GA567(6)
: 2. Assumption of Liquid Film Thickness Fig.2 shows the relation between distance from the contact point (1*) and liquid film thickness      (a),
At 2.2.3 Assuming 10 support points inactive With 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 SG Case Thermal Power 100 Row Column 50 60 70 80 90 100 (Pu (No Plug)80 70 80 80 100 70 I O0) 80(')120 70 120 80 95(") 85(*)125 85 138 84 Note(*): Plugged tube with Type J stabilizer MITSUBISHI HEAVY INDUSTRIES, LTD.Page 8 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I II ) (9/149)Document No. L5-04GA567(6)
which is obtained by the following geometrical equation, where 0 and d are defined in Fig.3.
At 2.2.4 Assuming 12 support points inactive With 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 SG Case Thermal Power Row Column 50 60 70 80 90 100 100 (No Plug)80 70 80 80 100 70 100(*) 80(*)120 70 120 80 95() 85(')125 85 138 84 Note(*): Plugged tube with Type J stabilizer 2.2.5 TTW tubes in Unit-2 The stability ratios of TTW (tube-to-tube wear) tubes with type J stabilizer (split stabilizers) in Unit-2 were evaluated and confirmed to be less than 1.0 as shown in Attachment-5.
                      -(1- cos0)~=2S1                                        (1) 2 1*= dsin0                                                (2) 2 The thickness of the continuous liquid film is [                      ) which is obtained in Fig.2 by assuming the effective distance from the contact point for squeeze film damping is I
MITSUBISHI HEAVY INDUSTRIES, LTD.Page 9 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I) (10/149)Document No. L5-04GA567(6)
        )The basis of[            )of the effective distance is described in Attachment-3.
At 3. Nomenclature Symbol Unit Definition E psi Modulus of elasticity of tube FEI Fluid elastic instability G psi Shear modulus of tube Tav OF Primary side average temperature TS OF Secondary side temperature D, in Tube inside diameter Do in Tube outside diameter P in Tube pitch A Ibm/ft 3  Density of water inside the tube A_ Ibm/ft 3  Density of tube material Po Ibm/ft 3  Average density of water outside the tube t in Tube thickness m Ibm/ft Tube mass distribution per unit length my Ibm/ft Virtual added mass per unit length h -Damping ratio h- Structural damping ratio hTp -Two phase damping ratio h- Viscous damping ratio hSF -Squeeze film damping ratio K -Critical factor MHI -Mitsubishi Heavy Industries M0 Ibm/ft Average tube mass per unit length U, ft/s Critical flow velocity f Hz Tube natural frequency 6 -Logarithmic decrement U"n ft/s Nth mode effective flow velocity O(x)- Vibration mode Tn(x) -Nth vibration mode p, p(x) Ibm/ft 3  Fluid density distribution of water outside the tube in tube axis direction U, U(x) ft/s Flow velocity distribution orthogonal to tube axis in tube axis direction x ft Coordinate component along tube axis L ft Tube length SCE Southern California Edison SR, SR, (Nth mode) Stability ratio MITSUBISHI HEAVY INDUSTRIES, LTD.Page 10 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I) (11/149)Document No. L5-04GA567(6)
The minimum thickness of discontinuous liquid film is assumed to be[                        }whicl is comparable to the degree of surface roughness of tube.
: 4. Assumption
L        Fig.2 Relation between distance from the contact point and liquid film thickness MITSUBISHI HEAVY INDUSTRIES, LTD.
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===4.1 Modeling===
Non-proprietary Version   I J (108/149)
assumption (1) Nominal tube thickness and nominal tube length are used in the evaluation model because the effect of the tolerances of these dimensions on the natural frequency is negligible.
Document No. L5-04GA567(6)
(2) Contact condition between tube and tube support plate is pin-supported.
At Tube Liquid film Liquid 6                                                                 AVB 1*   I Fig.3 Distance from the contact point and liquid film thickness MITSUBISHI HEAVY INDUSTRIES, LTD.
Fixed supported condition at tubesheet is added.(3) Contact condition between tube and active support points by the anti-vibration bar (AVB) is pin-supported.
Page 108 of 149                     SO 23-617-1-M1539, REV. 0
(4) Modulus of elasticity of tube is interpolated based on the tube average temperature of 2 from table of ASME Boiler and Pressure Vessel Code, Sec II, Materials, 1998 Edition, 2000 addenda (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 virtual added 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 effect p. Average water density outside the tube of each region obtained from ATHOS analysis Do :Tube outside diameter P 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 side are assumed for the evaluation of the stability ratio of in-plane FEI. All active support points and 1 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 and support span of each evaluated tube. The inactive support will be one of the 2 supports at the span with the highest amplitude, whichever that has a higher hydraulic pressure.
The maximum stability ratio in each inactive support location is shown as the result of the stability ratio with 1 inactive support.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 11 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I I) (12/149)Document No. L5-04GA567(6)
At (7) Type J stabilizers are assumed to be installed for all plugged tubes which have AVB wear indications.
The additional structural damping ratio due to Type J stabilizer (split stabilizers installed 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 and Attachment-1 for details).4.2 Open item There is no open item remaining.
MITSUBISHI HEAVY INDUSTRIES, LTD.Page 12 of 149 S023-617-1-M1539, F REV. 0 I Non-proprietary Version I] (13/149)Document No. L5-04GA567(6)
At 5. Acceptance Criteria The stability ratio against fluid elastic instability shall be less than 1.0. The analysis is performed in accordance with the procedures given in ASME code section III Appendix N-1 330 (Ref.2).MITSUBISHI HEAVY INDUSTRIES, LTD.Page 13 of 149 S023-617-1-M1539, REV. 0
[Non-proprietary Version I II] (14/149)Document No. L5-04GA567(6)
At 6. Design Input 6.1 Geometry of tube bundle region Tube bundle consists of thermally treated Alloy 690 U-tubes which are supported in[ ]triangular pitch arrangement 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-240 Type 405 Stainless steel).Nominal dimension of tube, TSPs and AVBs are listed in Table 6-1. The applicable design drawings to be referred are listed in Table 6-2.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 14 of 149 S023-617-1-M1539, F REV. 0 11 Non-proprietary Version I) (15/149)Document No. L5-04GA567(6)
Ak Table 6-1 Nominal dimensions of tubes, TSPs, and AVBs Part Item Value Material Thermally treated SB-1 63 UNS N06690 Outside diameter 0.75 in Thickness 0.043 in Tubes Number of tubes 9727 Tube pitch 1.0 in Tube arrangement Triangular Material SA-240 Type 405 Thickness Number of TSPs TSPs Tube support span (between TSP centrals)Tube support span (from TS to No.1 TSP) I Material SA-479 Type 405 Type AVBs Thickness Width Stabilizer Unit weight MITSUBISHI HEAVY INDUSTRIES, LTD.Page 15 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I) (16/149)Document No. L5-04GA567(6)
At Table 6-2 A plicable design drawings (Ref.3 to 20)Drawing No. Title L5-04FU001 COMPONENT AND OUTLINE DRAWING 1/3 L5-04FU002 COMPONENT AND OUTLINE DRAWING 2/3 L5-04FU003 COMPONENT AND OUTLINE DRAWING 3/3 L5-04FU021 TUBE SHEET AND EXTENSION RING 1/3 L5-04FU022 TUBE SHEET AND EXTENSION RING 2/3 L5-04FU023 TUBE SHEET AND EXTENSION RING 3/3 L5-04FU051 TUBE BUNDLE 1/3 L5-04FU052 TUBE BUNDLE 2/3 L5-04FU053 TUBE BUNDLE 3/3 L5-04FU111 AVB ASSEMBLY 1/9 L5-04FU112 AVB ASSEMBLY 2/9 L5-04FU1 13 AVB ASSEMBLY 3/9 L5-04FU1 14 AVB ASSEMBLY 4/9 L5-04FU115 AVB ASSEMBLY 5/9 L5-04FU116 AVB ASSEMBLY 6/9 L5-04FU117 AVB ASSEMBLY 7/9 L5-04FU118 AVB ASSEMBLY 8/9 L5-04FU119 AVB ASSEMBLY 9/9 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 16 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version] (17/149)Document No. L5-04GA567(6)
At 6.2 Thermal and hydraulic flow of steam generator secondary side The basic parameters for the thermal hydraulic analysis of unit-2 and 3 steam generators are shown in Table 6.2-1 to 6.2-4. As discussed in ATHOS analysis report (Ref. 22), the larger number of the plugged tubes of unit-2 (305 tubes for 2A) is used for the FEI evaluation.
The flow characteristics of the tubes listed in Table 7.2-1 are obtained from ATHOS/SGAP analysis (See Ref.21 and 22 for detail) and used for the vibration analysis.The distributions of flow gap velocity normal to the in-plane direction of the tube, flow density and void fraction are shown in Fig.6.2-3 to 6.2-11. Several of the flow gap velocity distributions indicate negative flow velocities at lower thermal power on the cold leg side since the water flow is more likely to go downward on the cold leg side because the circulation ratio is higher and the water flow rate compared with 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 flow velocity and mode shape in order to evaluate the actual tube vibration which is multi degrees of freedom system with beam type of vibration modes. Therefore, there is no adverse effect of negative flow velocity.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 17 of 149 S023-617-1-M1539, REV. 0 cj~z C r:j~Table 6.2-1 Basic parameters for calculation for 2A SG evaluation after plugging Case 50% 60% 70% 80% 90% 100% 100%withno plugging Plugging 305 305 305 305 305 305 0 869.5 1041.4 1213.3 1385.2 1557.1 1729 (50%) (60%) (70%) (80%) (90%) (100%)RCS flow rate (gpm) *1  206,695 206,695 206,695 206,695 206,695 206,695 209,880 Thot (Tsg-in) (&deg;F)Tsg-out (&deg;F)*2 TcoId 2 Saturation Steam Pressure (psia)Fouling Factor (ft 2 hr&deg;F /Btu)Tfeedwater (OF)Circulation Ratio Steam Mass Flow (lb/hr)Feed Water Mass Flow (lb/hr)*3 Blowdown flow rate (gpm)z 0'0 0)CD CD)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&deg;F lower than that at RV inlet. The 0.3&deg;F temperature increase between the SG outlet and RV 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 the address 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 column of 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.
0 C)C)0 c-I (A 41 Page 18 of 149 S023-617-1-M1539, REV. 0 C-, Cd, C-, C-, Table 6.2-2 Basic parameters for calculation for 2B SG evaluation after plugging Case 50% 60% 70% 80% 90% 100% 100 % with no plugging Plugging*6 205 205 205 205 205 205 0 869.5 1041.4 1213.3 1385.2 1557.1 1729 (50%) (60%) (70%) (80%) (90%) (100%)RCS flow rate (gpm) 207,726 207,726 207,726 207,726 207,726 207,726 209,880 Thot (Tsg-in) (&deg;F)Tsg-out (OF)"*2 TcoId (OF)*2 Saturation Steam Pressure (psia) I Fouling Factor (ft 2 hr&deg;F /Btu)Tfeedwater
(&deg;F)Circulation Ratio Steam Mass Flow (lb/hr)Feed Water Mass Flow (lb/hr)3 Blowdown flow rate (gpm)z 0 7 0 CD 0)Cn.0 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&deg;F lower than that at RV inlet. The 0.3&deg;F temperature increase between the SG outlet and RV 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 the address of the plugged tubes of 2A SG.0 0 z SC)Page 19 of 149 S023-617-1-M1539, REV. 0 z F Table 6.2-3 Basic parameters for calculation for 3A SG evaluation after plugging 100 % with no Case 50% 60% 70% 80% 90% 100%plugging Plugging*4 387 387 387 387 387 387 0 869.5 1041.4 1213.3 1385.2 1557.1 1729 Thermal 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)" 2 TcoId (&deg;F).2 Saturation Steam Pressure (psia) I Fouling Factor (ft 2 hr&deg;F /Btu)Tfeedwater (OF)Circulation Ratio Steam Mass Flow (lb/hr)Feed Water Mass Flow (lb/hr)3 Blowdown flow rate (gpm) -z z 0-7'0 a CD (n)0'-3 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 0 F lower than that at RV inlet. The 0.3 0 F temperature increase between the SG outlet and RV 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: 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 the address of the plugged tubes of 2A SG.C 0 0 H o c~I (A 0 Page 20 of 149 S023-617-1-M1539, REV. 0 C,'~j)Table 6.2-4 Basic parameters for calculation for 3B SG evaluation after plugging Case 50% 60% 70% 80% 90% 100% 100 % with no plugging Plugging"4 420 420 420 420 420 420 0 869.5 1041.4 1213.3 1385.2 1557.1 1729 Thermal power (MWt) 1729 Thermal power (M ____ (50%) (60%) (70%) (80%) (90%) (100%) 1729 RCS flow rate (gpm) .' 205,545 205,545 205,545 205,545 205,545 205,545 209,880 Thot (Tsg-in) (&deg;F)Tsg.out (&deg;F)'2 TcoId (&deg;F)*2 Saturation Steam Pressure (psia)Fouling Factor (ft 2 hr&deg;F /Btu)Tfeedwater
(&deg;F)Circulation Ratio Steam Mass Flow (lb/hr)Feed Water Mass Flow (lb/hr)" 3 Blowdown flow rate (gpm)z 0 0 CD ChD (n 0 L D 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&deg;F temperature increase between the SG outlet and RV 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: 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 the address of the plugged tubes of 2A SG.C.'>I Page 21 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I ft ) (22/149)Document No. L5-04GA567(6)
Tubes to be plugged of 2A SG 3 -J, -j 4, -*...... ... ....s 4 4 121 A 1!.L -L 51 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 &#xfd;. U 40 41 36 31 N 21 1. 1I .COL Fig. 6.2-1 Plugging tubes of 2A SG I,-Fig.6.2-2 Tube plugging model of ATHOS for 2A SG MITSUBISHI HEAVY INDUSTRIES, LTD.S023-617-1-M1539, REV. 0 Page 22 of 149 r Ca a Ca C Ca Ca r z 0 10 CD Cn.Y,>C 0 0 0 o-V Fig.6.2-3 Flow Characteristics of Row 80 Column 70 (2A SG)Page 23 of 149 S023-617-1-M1539, REV. 0 r z 0 0 CD (1)0 C)>~Fig.6.2-4 Flow Characteristics of Row 80 Column 80 (2A SG)Page 24 of 149 S023-617-1-M1539, REV. 0 C12 2 C,, z 0 0 CD (1)0 Y,>H-41 Fig.6.2-5 Flow Characteristics of Row 100 Column 70 (2A SG)Page 25 of 149 S023-617-1-M1539, REV. 0 r z_= o 0 Y, C>C ,)ri)CN FER 0 Fig.6.2-6 Flow Characteristics of Row 100 Column 80 (2A SG) -&Page 26 of 149 S023-617-1-M1539, REV. 0 z 0 CA B 10 CICD---n.0&deg;0 CD> -F1 Fig.6.2-7 Flow Characteristics of Row 120 Column 70 (2A SG) Page 27 of 149 S023-617-1-M1539, REV. 0 z 0 0 0 Fig.6.2-8 Flow Characteristics of Row 120 Column 80 (2A SG)Page 28 of 149 S023-617-1-M1539, REV. 0 r:j~z z 0 CD CD 0 Y, C)>K-I Fig.6.2-9 Flow Characteristics of Row 95 Column 85 (2A SG)Page 29 of 149 S023-617-1-M1539, REV. 0 K-z z -(D 0, CD Yl Fig..2-0 Fow Caraterstis ofRow125Colun 8 (2 S0 Page 30 of 149 S023-617-1-M1539, REV. 0 z 0 ,-CD 0 CD 4n Fig.6.2-11 Flow Characteristics of Row 138 Column 84 (2A SG) -Page 31 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I] (32/149)Document No. L5-04GA567(6)
: 7. Methodology


===7.1 Fluid===
Non-proprietary Version j
elastic vibration The term "fluid elastic vibrations" is generally used to refer to self-excited vibration of tube bundles due to 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 is greater than the amount that the tubes can dissipate.
[]                                  (109/149)
The measure of the fluid-elastic vibration threshold for any given tube in the bundle (tube stability) is the ratio of the actual velocity of the fluid surrounding the tube to the critical fluid flow velocity for this particular tube. The critical flow velocity Uc required to generate fluid-elastic vibration is obtained using Connor's formula (Ref.23).r 11/2 U ' _ K [ m 2 ...............................
Document No. L5-04GA567(6)
........................................... ......(3)Where, UV Critical flow velocity f Tube natural frequency D, : Tube outside diameter K Critical factor M0 :Average tube mass per unit length 5 Tube logarithmic decrement(=
At
2Trh)h Damping ratio PO Density of water outside the tube The critical flow velocity U, in eq. (3) is evaluated in case of tube vibration of single degree of freedom system with uniform cross flow along the tube axis. In actual tube, however, the vibration of the tube supported by the tube support plate is multi degrees of freedom system with beam type of vibration modes. Therefore, considering the vibration mode and fluid distribution, the effective flow velocity Ue, is evaluated in the following formula.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 32 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I] (33/149)Document No. L5-04GA567(6)
: 3. Estimation of Void fraction Fig.4 shows the relation between void fraction and liquid film thickness, which is obtained from the following equations.
Ak p___ U(x) 2. 0 * (X) 1 dx 0 PC)u ....................................................................
Asub - (Af o*
(4 )f L MW 0 4(x) 2 dx Where, Uen Nth mode effective flow velocity (Pn(X) Nth vibration mode p(x) Fluid density distribution of water outside the tube in tube axis direction m(x) Tube mass distribution per unit length in tube axis direction U(x) Flow velocity distribution orthogonal to tube axis in tube axis direction x Coordinate component along tube axis PO Average density of water outside the tube m, : Average tube mass per unit length L : Tube length The stability ratio is determined as follows in each vibration mode by calculating the ratio of eq. (3) and eq. (4).SR .........................................
                                      + Ad)
.................................................
                                        =                                      (3)
(5 )Ucn where, 1/2 f. D -- ......................
Asub Af =      [(d + 2,)2 -d2]                                  (4) 4 Ad =  -4,f                                                (5)
(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 is simply expressed as SR. The uncertainty of SR calculated by the methodology of this section is evaluated in Attachment-6.
A,,,b =-      -        d                                    (6) 2        4
MITSUBISHI HEAVY INDUSTRIES, LTD.Page 33 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version] (34/149)Document No. L5-04GA567(6)
: Where, a              Void fraction Pt              Tube pitch d              Tube diameter Asub            Flow area of sub channel (See Fig.5)
A&7.1.1 Damping ratio and Critical Factor Although the suggested value by ASME Sec. Ill Appendix N-1330 for damping ratio is 1.5% and the suggested value for critical factor is 2.4, the values based on recent experimental data are used in this evaluation as follows.7.1.1.1 Damping ratio For U-bend tubes in two phase flow, there are four sources of damping: structural damping, two-phase damping, viscous damping and squeeze film damping." s + &#xfd; T + "+ 's. ...................................................................................
Ad              Sectional area of droplet (See Fig.5)
(7 )Where,:s :Structural damping ratio Two-phase damping ratio Viscous damping ratio&#xfd;SF : Squeeze film damping ratio MITSUBISHI HEAVY INDUSTRIES, LTD.Page 34 of 149 S023-617-1-M1539, REN/.0 I Non-proprietary Version) (35/149)Document No. L5-04GA567(6)
Af              Sectional area of liquid film, which is assumed to be a twice of the area of droplet (See Fig.5) and the basis of this assumption is described as follows.
At (1) Structural damping The structural damping ratio is estimated with the following experimental equation developed by Pettigrew (Ref.25 and 27). In the case of plugged tubes with Type J stabilizers, the additional damping 0.6% is added s j= N -1 [ 5,L in gas ........................................................................
The ratio between the flow rate of liquid film Gf and the flow rate of droplet GE  can be assumed to be 0.2 in accordance with the test results shown in Fig.6 (Ref.1).
(8),s = (N N- 1 0.5( Lg m 7 ,in liquid ................................................................
Fig.6 is the results of heating cylinder which indicates that the flow rate of liquid film, Gf, is approximately 20% of the flow rate of droplet,       GE, when the quality is 50%.(50% quality at SONGS RSG condition (steam pressure is 838 psia) corresponds to 91% of void fraction)..
(9)Where, 4S N N-1 L'Ira: Structural damping ratio Number of free spans at U-bend region AVB support points without assuming inactive AVB support points AVB width Characteristic tube length: average of the longest three free spans lengths assuming 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 149 S023-617-1-M1539, REV. 0 Non-proprietary Version) (36/149)Document No. L5-04GA567(6)
Gf        1 (7)
At (2) Two-phase damping The two-phase damping depends on the void fraction and fluid properties.
GE        5 On 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.
Pettigrew's test result of the two phase damping shown in Figure 7.1-2 (Ref.26) is used for this evaluation.
Fig.7 is the air-water flow test results of cylinder at atmospheric condition where the flow velocity of liquid film and the apparent gas velocity are measured in various conditions of the apparent liquid velocity, ji, and the hydraulic equivalent diameter (Ref.2). Since ratio between the flow velocity of liquid film and droplet does not depend on the pressure (Ref.3), these data are applicable to SONGS RSG MITSUBISHI HEAVY INDUSTRIES, LTD.
A semi-empirical expression was developed from the experimental data and the functional equation of homogeneous void fraction was obtained as shown in Figure 7.1.2.The effective homogeneous void fraction is calculated by using the ATHOS outputs and following equation, considering vibration mode._ Jfg(x)&#xa2;2 dx 2l= SqZd ...........................................................................................
Page 109 of 149                   S023-617-1-M1539, REV. 0
(10)Where, Homogeneous void fraction@
 
* Vibration mode x Tube axis The two-phase damping along the tube length is calculated by using Pettigrew's data and the following equation Tp )f( ) 1 (D I) ...........................................
Non-proprietary Version j L                                  ) (110/149)
..(11)f([3)= P3/40 for 13 < 40%1 for 40% _<[3 _< 70% .............................................
Document No. L5-04GA567(6)
(12)1 -(P3- 70) / 30 (for > 70%D , = ( 1+ 1 P /D &#xfd; o P ......................................................................................
(13)m 0  = nzm , + n p + n , .........................................................................................
(14 )= fD&deg;p&deg; f(DOe/OD)2
+ I...........................................(15 4 l(D I/D o)2 -I(5 Where,&#xfd;TP Two-phase damping P3 Homogeneous void fraction D Tube outside diameter MITSUBISHI HEAVY INDUSTRIES, LTD.Page 36 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I fi) (37/149)Document No. L5-04GA567(6) jAk P po Po Pi mv mt Tube pitch Density of secondary mixture flow (Calculated by ATHOS)Density of secondary liquid flow Average tube mass per unit length Virtual added mass per unit length Mass of primary coolant in tube per unit length Mass of tube metal per unit length 1- 7 CM6 E ca5 (V4 co 4 t1='-.3_0 I-- 2 E o0-'0 A w Ul 0'0 09 0: 0 123o 0  0 00 A A Air-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_,0 0t 20 40 60 80 100 Void Fraction (%)(VTO)D = CT-A(pD 2/m)-' {[1 + (DID,)']]/[I
-(DID,)2]2}-'Fig 7.1-2 Effect of void fraction on two-phase damping MITSUBISHI HEAVY INDUSTRIES, LTD.Page 37 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version) (38/149)Document No. L5-04GA567(6)
A (3) Viscous damping Since the viscous effects are negligibly small in high void fraction (homogeneous void fraction is 40% or greater) (Ref.27), it is not taken into account in this analysis.(4) Squeeze film damping Squeeze film damping takes place at the supports and the following equation is based on the available experimental data. (Ref.26)YSF = ( N -{ f m o )(. L., ' .........................................................................
(16)Where, SF D N N-1 f L Im M0 Squeeze film damping Secondary flow liquid density Tube outside diameter Number of free spans at U-bend region AVB support points without assuming inactive AVB support points Natural frequency AVB width Characteristic tube length Average tube mass per unit length MITSUBISHI HEAVY INDUSTRIES, LTD.Page 38 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version ( ] (39/149)Document No. L5-04GA567(6)
Ai For unplugqed tubes The support damping (structural and squeeze film) depends on the void fraction.
Since the structural damping 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.
The effective wetness of supports is estimated to determine the damping ratio used for the SR evaluation by the following equations based on the assumptions listed below. (The basis of these assumptions is described 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 and squeeze film damping is effective.
When the void fraction is [ ]there is no liquid film on the surface of tube. The support is considered "dry," structural damping corresponds to the gas condition and squeeze film damping is not effective.
When the void fraction is between ) ) there is a discontinuous liquid film on the surface of tube and the support is considered partially wet. The approach to calculate damping in this void fraction range is described below.N-1 s a ........ .........................................
...............
(17)a i ...........................................................
(18 )N DS N -I -N s ..........................................
N...... .......................................
(19)Where, N Number of free spans in U-bend N -1 Number of AVB support points in U-bend NWS Number of effectively wet AVB supports NDS Number of effectively dry AVB supports i :AVB support points a: Void fraction at AVB support points ai Function of void fraction at AVB support points MITSUBISHI HEAVY INDUSTRIES, LTD.Page 39 of 149 S023-617-1-M1539, REV. 0 t Non-proprietary Version I I (40/149)Document No. L5-04GA567(6)
At By replacing the (N-i/N) term in equations 8 and 9 and combining, structural damping adjusted for void fraction becomes: j.................................
....(20)Similarly replacing the (N-i/N) term in equation 16 with (Nws/N), squeeze film damping adjusted for void fraction becomes: Ni,'s (2 460) plD 2  L&#xfd;SF , Nf no .(.. ...............................................................
(21)For pluaqed tubes The plugged tubes are assumed to be in wet condition despite the void fraction.
Equations 7 and 16 are used for structural and squeeze film damping, respectively.
MITSUBISHI HEAVY INDUSTRIES, LTD.Page 40 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I] (41/149)Document No. L5-04GA567(6)
At 7.1.1.2 Critical Factor The effect of void fraction, the effect of pitch to diameter ratio, the ratio between In-plane & Out-of-plane and the effect of flow direction are considered to estimate the Connor's constant as follows.(1) Effect of the void fraction Based on MHI experimental data (Ref.28), the critical factor K is evaluated using the equation shown in Figure 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 the triangular 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 mode and using the following equation in the same manner as the two-phase damping. The obtained critical factor 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 fraction Vibration mode Tube axis MITSUBISHI HEAVY INDUSTRIES, LTD.Page 41 of 149 S023-617-1-M1539, REV. 0 I Non-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 Void Fraction)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 42 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version II j (43/149)Document No. L5-04GA567(6) is&Table 7.1-1 MHI Test Condition Tube diameter Tube pitch Number of tubes Flow condition Pressure Temperature i i Suoerficial void fraction Fig.7.1-4 MHI Test Equipment MITSUBISHI HEAVY INDUSTRIES, LTD.Page 43 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version[ ) (44/149)Document No. L5-04GA567(6)
A&(2) Effect of P/D The greater the pitch is, the higher the critical velocity will be. Since the tube bundle has index and the nominal pitch depends on the number of tube Row, the effect of the tube pitch to diameter ratio (P/D) is added to the value obtained in the previous section (K 1). 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 to be evaluated.
P , -- P , + P + ......................................................................................
(24 )3 Where, Evaluated tubes , Pe Effective pitch P1,P2,P3 Pithes defined in Fig.7.1-5 P, Fig.7.1-5 Effective pitch The effect of the tube pitch on the Connor's constant is calculated by using the following equation based on Pettigrew's experimental data (Ref.29).Kp=4.76(P-D
)/D +0.76 ..................................................................................
(25)KpI K o = K P' D x K 1 ................................................................................
(26 )Where, KP "Equation 21 K1 Critical Factor based on MHI experimental test results by taking into account of the effect of void fraction (P/D=1.33)
Kp.P/D : Critical Factor based on Pettigrew's experimental test results by taking into account of the effect of P/D Kp.P/D=.33 "Critical Factor based on Pettigrew's experimental test results when P/D is 1.33 Ko Best estimated critical factor of out-of-plane FEI MITSUBISHI HEAVY INDUSTRIES, LTD.Page 44 of 149 S023-617-1-M1539, RE\/.0 Non-proprietary Version j t ] (45/149)Document No. L5-04GA567(6)
A&-(3)Critical Factor of In-plane FEI In accordance with the experiments by T. Nakamura (Ref.30), FEI is observed in the in-plane direction in a single-phase air flow when the tube pitch-to-tube ratio (P/D) is small. The Connor's constant of In-plane FEI is estimated in accordance with the following equation based on Nakamura's experimental data. The ratio between the Connor's constant of in-plane FEI and out-of-plane FEI depends on P/D as shown in Figure 7.1-6. In order to reinforce the basis of Connor's constant used for In-plane FEI evaluation, MHI performed air flow test by using the straight tube bundle of the triangular pitch as shown in Fig. 7.1-7. The ratio of Connor's constant between in-plane and out-of-plane FEI obtained by MHI test result is consistent with Nakamura's experimental data as shown in Fig. 7.1-6. Therefore, the Connor's constant of in-plane FEI for SONGS RSGs is calculated based on the effective tube pitch calculated 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 FEI Ki *Best estimated critical factor of In-plane FEI Ko Best estimated critical factor of out-of-plane FEI Ratio K Vc(In-flow)/Vc(Out-of-flow)
Ratio ol Note critical fl &#xfd;J.city K=Vc(ln-plane) fVc(0ut-4*plane) 1.5 Air- 2.7 voletteetal Water (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 S023-617-1-M1539, REV. 0 Non-proprietary Version I I) (46/149)Document No. L5-04GA567(6)
At I-(a) Test equipment r k-.(b) Test Results Fig.7.1-7 MHI air flow test MITSUBISHI HEAVY INDUSTRIES, LTD.Page 46 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version) ](47/149)Document No. L5-04GA567(6)
A&(4) Effect of Flow Direction The 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 of the critical velocity will be.The effect of the flow direction on the critical velocity (increase ratio" a(e)") is determined based on the test result shown in Fig.7.1-8 (Ref.31). "a(8)" is defined by the upstream critical flow velocity; not in-plane flow velocity a (O ) _= U c(_ ) ......................................................................................
(28)Uc(Odeg)Where, 0 Uc Angle of Flow direction Critical velocity 0.41 0 .1 ..--6 &deg;- , -0101 20 20 PMALLflL NOOMA TALANGLE FLOW DIRECTION dcjrc) "RII.Fig. 1O Ellectot Incident flOWdirection on critical Velocity FLCW0 o deg Parallel (0 deg.)FLOW 000 00006 00* 000.@Normal triangle (30 deg.)Fig.7.1-8 Effect of the flow direction (Ref.31)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 47 of 149 S023-617-1-M1539, REV. 0 11 Non-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 function a( e) is defined by the magnitude of normal flow velocity Vn to the tube. Therefore, Ki or K 0 are multiplied by the velocity ratio Vn/V and function a(O ) as shown in Fig.7.1-9, then K used for the analysis 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, a Vn V K, K.Effect of Flow direction Average in-plane velocity Magnitude of flow velocity Best estimated critical factor of In-plane FEI Best estimated critical factor of out of plane FEI Best estimated critical factor used for the evaluation Row Magnitude of Flow Column Fig.7.1-9 Effect of flow direction MITSUBISHI HEAVY INDUSTRIES, LTD.Page 48 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I t) (49/149)Document No. L5-04GA567(6)
A 7.2 Calculation model Stability analyses are carried out in the following manner.(1) Tube row The tubes shown in Table Attachment-7 for details).7.2-1 and Fig.7.2-1 are selected by SCE for the evaluation (see A Table 7.2-1 Evaluated Tubes Row Column 80 70 80 80 100 70 100 80 120 70 120 80 95 85 125 85 138 84* Plugged tubes O Representative tube for OA ---,-- -O'
* 0.--O ..-0-- -. .--------i ,*
* S i .S S 140 135 130 125 120 115 110 105 100 =95 90 85 80 75 70
---i t-60 65 70 75 80 85 COL Fig.7.2-1 Evaluated Tubes MITSUBISHI HEAVY INDUSTRIES, LTD.Page 49 of 149 S023-617-1-M1539, REV. 0 I Non-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 including node 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 S023-617-1-M1539, REV. 0 I Non-proprietary Version I] (51/149)Document No. L5-04GA567(6)
At r Fig. 7.2-1 Calculation model for Row 80 Column 70 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 51 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I t) (52/149)Document No. L5-04GA567(6)
At Fig. 7.2-2 Calculation model for Row 80 Column 80 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 52 of 149 SO2Z 3-617-1-M1539, REV. 0 Non-proprietary Version () (53/149)Document No. L5-04GA567(6)
Aok Fig. 7.2-3 Calculation model for Row 100 Column 70 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 53 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version j t) (54/149)Document No. L5-04GA567(6)-At Fig. 7.2-4 Calculation model for Row 100 Column 80 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 54 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I] (55/149)Document No. L5-04GA567(6)
At I-2 Fig. 7.2-5 Calculation model for Row 120 Column 70 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 55 of 149 S023-617-1-M1539, REV. 0 Non-propr ietary Version] (56/149)Document No. L5-04GA567(6)
At K-Fig. 7.2-6 Calculation model for Row 120 Column 80 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 56 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I t] (57/149)Document No. L5-04GA567(6)
At_-Fig. 7.2-7 Calculation model for Row 95 Column 85 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 57 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I] (58/149)Document No. L5-04GA567(6)
A Fig. 7.2-8 Calculation model for Row 125 Column 85 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 58 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I 1 (59/149)Document No. L5-04GA567(6)
At I-Fig. 7.2-9 Calculation model for Row 138 Column 84 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 59 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version 1 (60/149)Document No. L5-04GA567(6)
A&8. Computation Results 8.1 Out of plane FEI analysis results The 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 SG Table 8.1.1-1 All support points are active and the thermal power is 70%No olugging Table 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 SG Table 8.1.2-1 1 support point is inactive and the thermal power is 70%No plugaina Table 8.1.2-2 1 support point is inactive and the thermal power is 100% with no plugging MITSUBISHI HEAVY INDUSTRIES, LTD.Page 60 of 149 S023-617-1-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 Effective of inactive frequency h(%) coefficient fluid void void flow flow Stability support Mode density fraction fraction velocity velocity rati6 point f(Hz) Structural Two Squeeze Row Col dal phase film Total K1 Ko Ke K Po(ibfft 3) [-] [-] Uc(ft/sec)
Ue(ft/sec) damping damping damping 80 70 80 80 100 70 1 0(*) 80(')120 70 120 80 95(*) 85(')125 85 138 84 z 0 CD cn C,=0--n Note(*): Plugged tube with Type J stabilizer C, Page 61 of 149 S023-617-1-M1539, REV. 0 A Table 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 active C,'C,'Location of inactive Tube natural Damping Ratio Critical Average Average Maximum Critical Effective ponsupport frequency h(%) coefficient fluid void void flow flow Stability point Mode density fraction fraction velocity velocity ratio Structural Two Squeeze 3 RowSrcCaol phase film Total K1 Ko Ke K Po(lb/ft ) [-1 [-] Uc(ftlsec)
Ue(ftlsec) damping damping damping 80 70 80 80 100 70 100 80 120 70 120 80 95 85 125 85 138 84 z 0 0 CD CD 0 n ,=-"o I ~CD 41~ '-0~\Page 62 of 149 S023-617-1-M1539, REV. 0 C c.4~C CI)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 inactive Location of inactive Damping Critical Average Average Maximum Critical Effective Tube support Tube natural Ratio coefficient fluid void void flow flow Stability point Mode h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeeze (Ib/ft) [-] Uc(ft/sec)
Ue(ft/sec)
Row Col phase film Total KI Ko Ke K PO I I- damping damping damping 80 70 B03 80 80 B03 100 70 B03 100(*) 80(*) B03 120 70 B03 120 80 B03 95(') 85(') B03 125 85 B03 138 84 B04 Note(*): Plugged tube with Type J stabilizer 0 Y0 C)>'-I Page 63 of 149 S023-617-1-M1539, REV. 0 A Table 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 inactive Location of inactive Damping Critical Average Average Maximum Critical Effective Tube support Tube natural Ratio coefficient fluid void void flow flow Stability point Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeeze Row Col phase film Total K1 Ko Ke K po(Ift 3) [-] [-] Uc(ft/sec)
Ue(ftfsec)
RowCol damping damping damping 80 70 B03 80 80 B03 100 70 B02 100 80 B02 120 70 B02 120 80 B02 95 85 B03 125 85 B02 138 84 B02 as z 0 10 02 CD CO 0 0 K Page 64 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I[ 1(65/149)Document No. L5-04GA567(6)
At 8.2 In-plane FEI analysis results The 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 SG Table 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 pluaaina Table 8.2.1-7 6 consecutive support points are inactive and the thermal power is 100% with no plugging (2) Assuming 8 support points are inactive: For 2A SG Table 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 plugging Table 8.2.2-7 8 consecutive support points are inactive and the thermal power is 100% with no plugging MITSUBISHI HEAVY INDUSTRIES, LTD.Page 65 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I II J (66/149)Document No. L5-04GA567(6)
A&(3) Assuming 10 support points are inactive: For 2A SG Table 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 plugging Table 8.2.3-7 10 consecutive support points are inactive and the thermal power is 100% with no plugging (4) Assuming All support points are inactive: For 2A SG Table 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 plugging Table 8.2.4-7 All consecutive support poir plugging s 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 no MITSUBISHI HEAVY INDUSTRIES, LTD.Page 66 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeezefilm po(lb/ft 3) [-] [-] Uc(ft/sec)
Ue(ft/sec)
Row 0Col dampin phase Total Kf1 Ko K Ke K damping damping damping 80 70 80 80 100 70 100(*) 80(.)120 70 120 80 95(*) 85(*)125 85 138 84 z 0 0'a CD C, 0 Note(*): Plugged tube with Type J stabilizer IA&#xfd;Y0>Page 67 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Rwof(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 damping 80 70 80 80 100 70 100(*' 80(')120 70 120 80 95() 85(*)125 85 138 84 6 6 z 0 ,.-i 0 CD CD Cn 0 tz 0 Note(*): Plugged tube with Type J stabilizer 1j4a)40 Y>0 Page 68 of 149 S023-617-1-M1539, REV. 0 z Table 8.2.1-3 In-plane FEI Analysis Results for 2A SG when the thermal power is 70% and 6 consecutive support points are inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Two po(b/f3) [-] [-] Uc(ft/sec)
Ue(ft/sec)
Row Col f(Hz) Structural phase Squeeze film Total K1 Ko Ki Ke K damping damping 80 70 80 80 100 70 1 00M 80M 120 70 120 80 95(*) 85(1)125 85 138 84 Z 0"{3-6 0 CD W.(0 6 0 4-I Note(*): Plugged tube with Type J stabilizer
&#xfd;k Page 69 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Col f(Hz) Structural Two Squeeze film po(lb/ft 3) [-1 [-] Uc(ft/sec)
Ue(ft/sec)
Ro o ig phase apn Total K1 Ko Ki Ke K daming phase____ ____ damping_____damping damping 80 70 80 80 100 70 1 00M 80(1)120 70 120 80 95(*) 85(*)125 85 138 84 z 0'0 CD W.0"33/Note(*): Plugged tube with Type J stabilizer
[&#xfd;&#xfd; ) 1 00.Page 70 of 149 S023-617-1-M1539, REV. 0 M" Mj Table 8.2.1-5 In-plane FEI Analysis Results for 2A SG when the thermal power is 90% and 6 consecutive support points are inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Two Squeeze3film p(Ib/ft3)
[-] Uc(ft/sec)
Ue(ft/sec)
Row Col f(Hz) Structural phase Total KI Ko K i  Ke K damping damping damping 80 70 80 80 100 70 100(') 80(*)120 70 120 80 95(*) 85(*)125 85 138 84 Z 0 7'0 CD 0)C-, 6 C0 Note(*): Plugged tube with Type J stabilizer Page 71 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Co f(Hz) Structural Two Squeeze film po(lb/ft 3) [-] [-] Uc(ft/sec)
Ue(ft/sec)
Ro ~ apn phase dmig Total K1 KO Ki Ke K damping damping damping 80 70 80 80 100 70 100(*) 80(*)120 70 120 80 95(') 85(*)125 85 138 84 z 0 ,0 CD"(3 10 CD C, 5.Note(*): Plugged tube with Type J stabilizer k&#xfd; ) 1 0.Page 72 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeeze film po(lb/ft 3) H[ [-] Uc(ft/sec)
Ue(ft/sec)
Row Col phase Total K1 K0 Ki Ke damping damping damping 80 70 80 80 100 70 100 80 120 70 120 80 95 85 125 85 138 84 z 0 0:3_D.n 0 CD 0 Page 73 of 149 S023-617-1-M1539, REV. 0 rj2 z cj~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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Two p(bf3 --cf/e)U~tsc Row 0ol f(Hz) Structural phase Squeeze film Total K Ko K Ke KUc(fsec)
Ue(ftsec)damping dampin damping 80 70 80 80 100 70 100(') I 80()120 70 120 80 95(*) 85(*)125 85 138 84 I0 6 &#xfd;0 6 0 Vh Note(*): Plugged tube with Type J stabilizer kR&#xfd;Page 74 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Col f(Hz) Structura w Two Squeezefilm Total H I [-]dampin h p damping Total K1 Ko Ki Ke K P&deg;(Ib/ft 3) Uc(ft/sec)
Ue(ftlsec) dmi 9 damping dmi 80 70 80 80 100 70 1 00(*) 80(*)120 70 120 80 95(.) 85(*)125 85 138 84 I0-'CDl 0 6>0h Note(*): Plugged tube with Type J stabilizer V~~1 I Page 75 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Squeeze film po(lb/ft3)
[-] [-] Uc(ft/sec)
Ue(ft/sec)
Row Col phase Total K1 Ko Ki KO K damping damping damping 80 70 80 80 100 70 100(*) 80(*)120 70 120 80 95(*) 85(*)125 85 138 84 I0'0 CD 0 0 C)4zi Note(*): Plugged tube with Type J stabilizer
&#xfd;k~Page 76 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Squeeze film po(lb/ft 3) [-] [ Uc(ft/sec)
Ue(ft/sec)
Row Col damping phase Total K1 Ko Ki Ke K damping damping damping 80 70 80 80 100 70 100(*) 80(*)120 70 120 80 95(*) 85(*)125 85 138 84 z 0 ,=6 6 0=3 0 CD Y,,3 O 03-L .-Note(*): Plugged tube with Type J stabilizer Page 77 of 149 S023-617-1-M1539, REV. 0 C,'rj~z C')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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Col da n Pase lmpin Total Ki Ko K Ke Squeezefilm po(lb/ft3)
[-] [-] Uc(ftlsec)
Ue(ft/sec)
_____ ___ _______ damping dapn 80 70 80 80 100 70 1 00( &deg; 0(//120 70 120 80 95(*) 85(*)125 85 138 84 z 0 ,=.6 0 CD=3_j.O CD 0 0 C Note(*): Plugged tube with Type J stabilizer 0>~0 Page 78 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Two po(Ib/ft3)
[-] [-] Uc(ft/sec)
Ue(ft/sec)
Row Col f(Hz) Structural phase Squeeze film Total K1 Ko Ki Ke K damping damping damping 80 70 80 80 100 70 10 0) 80(*)120 70 120 80 95(*) 85(*)125 85 138 84 6 6 z 0 0 CD (n.0i 0 Note(*): Plugged tube with Type J stabilizer CD 0 Y., Page 79 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Two p(bf3) --cf/e)U~tsc Row Col f(Hz) Structural phase Squeeze film T(lbft ) Uc(ftlsec)
Ue(ftlsec) damping damping damping Total K1 Ko Ki K, K 80 70 80 80 100 70 100 80 120 70 120 80 95 85 125 85 138 84 z 0'0 0)Cn 0-i 1 0 t o '- Y> G8 Page 80 of 149 S023-617-1-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 inactive C,, Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Col f(Hz) Structural Two Squeeze film po(lb/ft 3) [-1 [-] Uc(ft/sec)
Ue(ft/sec) damping phase damping Total K1 Ko Ki KO K damping 80 70 80 80 100 70 100(o) 80(*)120 70 120 80 95(*) 85(*)125 85 138 84 z 0 0 CD CD.0 Note(*): Plugged tube with Type J stabilizer oc Page 81 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Cf(Hz) Structural Two Squeeze film po(lb/ft 3) [-] [-] Uc(ft/sec)
Ue(ftlsec)
Row Col f(z trcualp phase dmig Total K1 Ko Ki Ke K d damping damping 80 70 80 80 100 70 1 00M 80(*)120 70 120 80 95(*) 85(*)125 85 138 84 z 0 CD")CD.0 ZI 0 Note(*): Plugged tube with Type J stabilizer V, N Page 82 of 149 S023-617-1-M1539, REV. 0 C,, C,, Cj2 Table 8.2.3-3 In-plane FEI Analysis Results for 2A SG when the thermal power is 70% and 10 consecutive support points are inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Co f(Hz) Structural Two Squeezefilm po(Ib/ft)
Uc(ft/sec)
Ue(ft/sec) tur phase d ilm Total K1 Ko Ki Ke K damping damping damping 80 70 80 80 100 70 100(*) 80(*)120 70 120 80 95(*) 85(*)125 85 138 84 Z 0 CD Cn.0n 10 6 Note(*): Plugged tube with Type J stabilizer
&#xfd;k ) 1111 U 0 CD C)>J ~Page 83 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeeze film po(lb/ft 3) [-] [-] Uc(ft/sec)
Ue(ft/sec)
Row Cola phase Total K1 Ko Ki Ke damping damping damping 80 70 80 80 100 70 1 00M) 80C)120 70 120 80 95(*) 85(*)125 85 138 84 6L Z 0:2.0:3 C 0 Note(*): Plugged tube with Type J stabilizer 0 Page 84 of 149 S023-617-1-M1539, REV. 0 rj~C,, C,, C,, F Table 8.2.3-5 In-plane FEI Analysis Results for 2A SG when the thermal power is 90% and 10 consecutive support points are inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Squeeze film T po(Ib/ft 3) [-] [-1 Uc(ft/sec)
Ue(ft/sec)
Row Ctrcdamping phase Total K1 Ko Ki Ke K dmigdamping damping 80 70 80 80 100 70 100(') 80(')120 70 120 80 95(M 85(*)125 85 138 84 k z 0 CD (D C,.0 0 E Note(*): Plugged tube with Type J stabilizer 0 Page 85 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Squeeze film po(lb/ft 3) [-] [-] Uc(ft/sec)
Ue(ft/sec)
Row Col dal phase damping Total K1 KO K Ke damping damping damping 80 70 80 80 100 70 100(*) 80(1)120 70 120 80 95(*) 85(*)125 85 138 84 6 6 CD 0 0 Y,J 0 Z 0 0D CD tn.0 Note(*): Plugged tube with Type J stabilizer Page 86 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Col f(Hz) Structural Two Squeeze film po(Ib/ft3)
[-] [-] Uc(ft/sec)
Ue(ft/sec) damping phase Total K1 K Ki K K damping damping 80 70 80 80 100 70 100 80 120 70 120 80 95 85 125 85 138 84 z 0'0 0 CD Cn.0 LO C)> -Page 87 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeeze film po(Ib/ft)
[-] [-] Uc(ft/sec)
Ue(ft/sec)
Row Col phaseToa K1 K i e K damping damping damping 80 70 80 80 100 70 100(*) 80(*)120 70 120 80 95(*) 85(*)125 85 138 84 z 0 0 CD 0)Y, C)0>N (' 0 0*-\Note(*): Plugged tube with Type J stabilizer 49 Page 88 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Two p0Ibf3) [-] [-] Uc(ft/sec)
Ue(ftsec)Row Col f(Hz) Structural phase Squeeze film Total K1 Ko Ki Ke K damping damping damping 80 70 80 80 100 70 100(*) 80(*'120 70 120 80 95() 85M'125 85 138 84 6&#xfd;Z 0 0 CD 0)0 Note(*): Plugged tube with Type J stabilizer Y0>-Page 89 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeeze film po(lb/ft 3) [-] [-] Uc(ft/sec)
Ue(ft/sec)
Row Col dal phase Total K1 Ko Ki Ke K damping damping damping 80 70 80 80 100 70 100(*) 80(')120 70 120 80 95(*) 85(*)125 85 138 84 z 0 3 3 CD (n.0 Note(*): Plugged tube with Type J stabilizer
'z CDJ Page 90 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural ose Squeeze film po(lb/ft 3) [-] [-] Uc(ft/sec)
Ue(ft/sec) damping damping damping 80 70 80 80 100 70 100(*) 80(')120 70 120 80 95(*) 85(*)125 85 138 84 z 0 0 CD 0)I Note(*): Plugged tube with Type J stabilizer C)>~( 'A!:7 Page 91 of 149 S023-617-1-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 inactive z 0 0 6 CD (n.0 0 Y0 C~~->A Note(*): Plugged tube with Type J stabilizer Page 92 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) structural Two po(Ib/f [-] [-] Uc(ft/sec)
Ue(ft/sec)
Ro o (z tutrlSqueeze film p(bf 3 Row Col damping phase damping Total K1 Ko Ki Ke K dampinga 80 70 80 80 100 70 1 00() 80(1)120 70 120 80 95(") 85(1)125 85 138 84 Z 0 0'a 0 O ,0&#xa9;t-Note(*): Plugged tube with Type J stabilizer
_R&#xfd; 0'C Page 93 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeezefilm po(lb/ft 3) [-] [-] Uc(ft/sec)
Ue(ft/sec)
Row Col dal phase dampin Total K1 Ko Ki Ke K damping damping damping 80 70 80 80 100 70 100 80 120 70 120 80 95 85 125 85 138 84 z 0'0 CD CD.0i:3 C)Page 94 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I[ 3 (95/149)Document No. L5-04GA567(6)
At 9. Reference 1) 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 2000 addenda.3) L5-04FU001 the latest revision, Component and Outline Drawing 1/3 4) L5-04FU002 the latest revision, Component and Outline Drawing 2/3 5) L5-04FU003 the latest revision, Component and Outline Drawing 3/3 6) L5-04FU021 the latest revision, Tube Sheet and Extension Ring 1/3 7) L5-04FU022 the latest revision, Tube Sheet and Extension Ring 2/3 8) L5-04FU023 the latest revision, Tube Sheet and Extension Ring 3/3 9) L5-04FU051 the latest revision, Tube Bundle 1/3 10) L5-04FU052 the latest revision, Tube Bundle 2/3 11) L5-04FU053 the latest revision, Tube Bundle 3/3 12) L5-04FU111 the latest revision, AVB assembly 1/9 13) L5-04FU112 the latest revision, AVB assembly 2/9 14) L5-04FU113 the latest revision, AVB assembly 3/9 15) L5-04FU114 the latest revision, AVB assembly 4/9 16) L5-04FU115 the latest revision, AVB assembly 5/9 17) L5-04FU1 16 the latest revision, AVB assembly 6/9 18) L5-04FU117 the latest revision, AVB assembly 7/9 19) L5-04FU1 18 the latest revision, AVB assembly 8/9 20) L5-04FU119 the latest revision, AVB assembly 9/9 21) 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 on internal SG thermal hydraulics parameters
: 23) 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 Design Guidelines,Journal of Pressure Vessel Technology Vol.133 26) M.J. Pettigrew.,et.al.,2003,"Vibration analysis of shell-and-tube heat exchangers" Journal of Fluids and Structures 18 (2003) 469-483 27) S. M. Fluit and M. J. Pettigrew, "Simplified method for predicting vibration and fretting-wear in nuclear steam generator U-bend tube bundle", ASME PVP 2001 Vol.420-1 28) WJS16263, MHI Test Report of Fluid Elastic Vibration 29) M.J. Pettigrew.,et.al.,2000, "The effects of tube bundle geometry on vibration in two-phase cross-flow",Flow Induced Vbration, Ziada&Staubi(eds) 2000 Balkema, Rotterdam ISBN9058091295
: 30) Flow-Induced VibrationMeskell
& Bennett (eds) ISBN 978-0-9548583-4-6, "Study on In-flow Fluid-elastic Instability of Circular Cylinder Arrays"], T.Nakamura, Y.Fujita, T.Oyakawa, Y.NI. July 2012 31) H.C.Yeung, 1983, "The effect of Approach Flow Direction on the Flow-Induced Vibrations of a Triangular Tube Array", Transaction of ASME Vol.105 32) L5-04GA587 the latest revision, Test result for damping ratio added by the stabilizer inserted for short length (Row No. 106)Page 95 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I) (96/149)Document No. L5-04GA567(6)
Ak Attachment-1 Computer Input and Output File List Page 96 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version (97/149)Document No. L5-04GA567(6)
At Table I-1 Input and Output file name of out of plane FEI evaluation for 2A SG when all support points are active A Thermal Row Column Input 1) Output 1)Power(%)80 70 _80 80 100 70 100 80 70 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 100 80 120 70 (No Plug) 120 80 95 85 125 85 138 84 _____Table 1-2 Input and Output file name of out of plane FEI evaluation for 2A SG when 1 support points are inactive Thermal Row Column Input 1) Output 1)Power(%)80 70 80 80 100 70 100 80 70 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 100 80 120 70 (No Plug) 120 80 95 85 125 85 138 84 ____Notes: 1) All files are saved in the directory as below: Page 97 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I J (98/149)Document No. L5-04GA567(6)
At Table 1-3 Input and Output file name of in-plane FEI evaluation for 2A SG when 6 consecutive support points are inactive (1/2)Thermal Row Column Input 1) Output 1)Power(%)80 70 , 80 80 100 70 100 80 50 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 60 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 70 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 80 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 90 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 100 120 70 120 80 95 85 1 1 125 85 138 84 .-Notes: 1) All files are saved in the directory as below: I A Page 98 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version[ 3(99/149)Document No. L5-04GA567(6)
At Table 1-3 Input and Output file name of in-plane FEI evaluation for 2A SG when 6 consecutive support points are inactive (2/2)Thermal Row Column Input 1) Output Power(%)80 70 80 80 100 70 100 100 80 120 70 (No Plug) 120 80 95 85 125 85 11 138 84 1 Notes: 1) All files are saved in the directory as below: Page 99 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I II) (100/149)Document No. L5-04GA567(6)
At Table 1-4 Input and Output file name of in-plane FEI evaluation for 2A SG when 8 consecutive support points are inactive (1/2)Thermal Power(%) Row Column Input 1) Output 1)80 70 80 80 100 70 100 80 50 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 60 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 70 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 80 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 90 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 100 120 70 120 80 95 85 125 85 138 84 1.Notes: 1) All files are saved in the directory as below: Page 100 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I 3 (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 support points are inactive (2/2) A Thermal Power(%) Row Column Input ) Output 1)80 70 80 80 100 70 100 100 80 120 70 (No Plug) 120 80 95 85 125 85 138 84 Notes: 1) All files are saved in the directory as below: I I IA Page 101 of 149 S023-617-1-M1539, REV. 0 (Non-proprietary Version I) (102/149)Document No. L5-04GA567(6)
At Table I-5 Input and Output file name of in-plane FEI evaluation for 2A SG when 10 consecutive support points are inactive (1/2) 14\Thermal Poer(%) Row Column Input 1) Output 1)Power(%)80 70 _80 80 100 70 100 80 50 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 60 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 70 120 70 120 80 95 85 125 85 138 84 80 70 80 80 1 100 70 100 80 80 120 70 120 80 95 85 125 85 138 84 1 80 70 80 80 100 70 100 80 90 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 100 120 70 120 80 95 85 125 85 138 84 "-.Notes: 1) All files are saved in the directory as below: Page 102 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I I J (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 support points are inactive (2/2) A Thermal Row Column Input 1) Output Power(%)80 70 r 80 80 100 70 100 100 80 120 70 (No Plug) 120 80 95 85 125 85 138 84 Notes: 1) All files are saved in the directory as below: Page 103 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I) (104/149)Document No. L5-04GA567(6)
Ati Table 1-6 Input and Output file name of in-plane EIl evaluation for 2A SG when 12 consecutive support points are inactive (1/2) Z6\Thermal Row Column Input Output 1)Power(%)80 70 80 80 100 70 100 80 50 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 60 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 70 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 80 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 90 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 100 120 70 120 80 95 85 125 85 1 138 84 A t Notes: 1 ) All files are saved in the directory as below: MITSUBISHI HEAVY INDUSTRIES, LTD.Page 104 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version j I) (105/149)Document No. L5-04GA567(6)
At Table 1-6 Input and Output file name of in-plane FEI evaluation for 2A SG when 12 consecutive support points are inactive (2/2)Thermal Row Column Input 1) Output Power(%)80 70 80 80 100 70 100 100 80 120 70 (No Plug) 120 80 95 85 125 85 138 84 Notes: 1) All files are saved in the directory as below: MITSUBISHI HEAVY INDUSTRIES, LTD.Page 105 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I) (106/149)Document No. L5-04GA567(6)
A,&Attachment-2 Evaluation of Liquid Film Thickness of Tube at AVB Support Point 1. Summary In order to estimate the effect of void fraction on the squeeze film damping, the relation between the liquid film thickness of tube at each AVB support point and void fraction is evaluated as shown in Table-1.Table-1 Relation between liquid film thickness of tube and void fraction Void fraction Liquid Film Condition Figure No Dry out Fig.l-1 Discontinuous Dry & Wet Fig.1-2 Continuous Wet Fig.1-3 Tube AVB 0 Droplet Liquid film (Thickness
:6)S S S 0 e from the point (1*)0 S 0 *** 5 0 eS S 0 Fig.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 be consistent with the figures above as described in Attachment-4.
MITSUBISHI HEAVY INDUSTRIES, LTD.Page 106 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I) (107/149)Document No. L5-04GA567(6)
A,&2. Assumption of Liquid Film Thickness Fig.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)~ =2S1 2 1*= dsin 0 2 (1)(2)The thickness of the continuous liquid film is [ ) which is obtained in Fig.2 assuming 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[ }whicl comparable to the degree of surface roughness of tube.by I is L Fig.2 Relation between distance from the contact point and liquid film thickness MITSUBISHI HEAVY INDUSTRIES, LTD.Page 107 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I J (108/149)Document No. L5-04GA567(6)
At Tube Liquid film Liquid AVB 6 1* I Fig.3 Distance from the contact point and liquid film thickness MITSUBISHI HEAVY INDUSTRIES, LTD.Page 108 of 149 SO 23-617-1-M1539, REV. 0 Non-proprietary Version j[] (109/149)Document No. L5-04GA567(6)
At 3. Estimation of Void fraction Fig.4 shows the relation between void fraction and liquid film thickness, which is obtained from the following equations.
Asub -(Af + Ad)= (3)Asub Af = [(d + 2,)2 -d2] (4)4 Ad = -4,f (5)A,,,b =- -d (6)2 4 Where, a Void fraction Pt Tube pitch d Tube diameter Asub 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 (See Fig.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 0.2 in 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, is approximately 20% of the flow rate of droplet, GE, when the quality is 50%.(50% quality at SONGS RSG condition (steam pressure is 838 psia) corresponds to 91% of void fraction)..
Gf 1 (7)GE 5 On 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 of liquid film and the apparent gas velocity are measured in various conditions of the apparent liquid velocity, ji, and the hydraulic equivalent diameter (Ref.2). Since ratio between the flow velocity of liquid film and droplet does not depend on the pressure (Ref.3), these data are applicable to SONGS RSG MITSUBISHI HEAVY INDUSTRIES, LTD.Page 109 of 149 S023-617-1-M1539, REV. 0 L Non-proprietary Version j) (110/149)Document No. L5-04GA567(6)
At evaluation.
At evaluation.
Assuming the velocity of the droplet, Ue, is identical to the apparent gas velocity, jg, the flow velocity of droplet, Ue, is approximately ten times the flow velocity of liquid film, Uf, at all conditions.
Assuming the velocity of the droplet,   Ue, is identical to the apparent gas velocity, jg, the flow velocity of droplet, Ue, is approximately ten times the flow velocity of liquid film, Uf, at all conditions. The flow velocity of the liquid film does not depend on the condition of the apparent liquid velocity or the hydraulic equivalent diameter.
The flow velocity of the liquid film does not depend on the condition of the apparent liquid velocity or the hydraulic equivalent diameter.'l _= 10 (8)11f Uf*~lf *~lf From the equation of continuity (9), the ratio of sectional area between liquid film and droplet can be derived as follows. (Equation (10) is identical to Equation (5))Gf = PfQf _ -Af ,,f GE PsQE QE Ad 1 1 E Af Qf "E -= =2 Ad QE Uf MITSUBISHI HEAVY INDUSTRIES, LTD.Page 110 of 149 (9)(10)S023-617-1-M1539, REV. 0 I Non-proprietary Version J (111/149)Document No. L5-04GA567(6)
                  'l       _= 10                                               (8)
At-Fig.4 indicates; When void fraction is lower than 95%, there is a continuous liquid film on the tube since the thickness of liquid film is larger than( ]When void fraction is higher than 98%, there is no liquid film on the tube since the thickness of liquid film is smaller than[ ]which is the assumed minimum thickness of the discontinuous liquid film on the tube.Fig.4 Relation between void fraction and liquid film thickness 4. References
                *~lf 11f    *~lf Uf From the equation of continuity (9), the ratio of sectional area between liquid film and droplet can be derived as follows. (Equation (10) is identical to Equation (5))
: 1) Akagawa,"Gas and liquid Two-phase Flow" p.150 2) "Fluid characteristics of annular mist flow of gas and liquid" p.395-495, 49-438 3) Nakazatomi, et.al, Experimental study of vertical upward gas-liquid two-phase annular flow (2 nd report, effects of system pressure on characteristics of waves)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 111 of 149 S023-617-1-M1539, RE\/.0 Non-proprietary Version I) (112/149)Document No. L5-04GA567(6)
Gf = PfQf _           - Af ,,f 11                                (9)
A~k 6 Droplet (Sectional area Ad)Liquid film (Sectional area Af)Fig. 5 Sectional area of droplet and liquid film 1.0 Gf is approximately 20 % of GE when the quality is 0.5 0 0)N E 0 z Test condition-Two-phase flow (steam/water) in heating cylinder (heat flix is 8.6 x 104 W/ft 2)film -At high pressure (427psia)o 0.6 0 Quality Fig.6 Flow rate of liquid film and droplet (Ref.1)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 112 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version j II] (113/149)Document No. L5-04GA567(6)
GE     PsQE         QE   Ad     E Af     Qf     "E =2
A&Shearer &Hall -Taylor et al.Uf is approximately 10 % of Jg in all cases, which does not depend on J, and the hydraulic equivalent diameter E E Er 0 0&deg;-LL Test condition-Water/air flow in a cylinder-At atmospheric pressure and room temperature Definition of symbols J~m 8 12 18 25126 0.04 *10~i oA v 0.06 14) 1 A AV 0.1
                                  =-
* 11 A V ot14 Al V 8 10 15 20 30 Hydraulic equivalent diameter Fig.7 Flow rate of liquid film and droplet (Ref.2)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 113 of 149 S 023-617-1-M1539, REV. 0 I Non-proprietary Version I] (114/149)Document No. L5-04GA567(6)
(10)
Ath for Squeeze Film Damping The effective distance of liquid film of tube from the contact point for squeeze film damping is evaluated to be[ ] as calculated below.The calculation model of tube and AVB is shown in Fig.l. When the amplitude of gap velocity vibration in normal direction of AVB is v 0 , the velocity at x in horizontal direction is defined as equation (1) since the liquid volume pushed out by the tube is the same as the liquid volume which flows in the horizontal direction.
Ad     QE     Uf MITSUBISHI HEAVY INDUSTRIES, LTD.
V(v) = v.5(x)(1)Tube{I'0 r~AVB~I Fig.1 Calculation model MITSUBISHI HEAVY INDUSTRIES, LTD.Page 114 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I[ j (115/149)Document No. L5-04GA567(6)
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A On 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) v 2 dx v- + -_ + (2)2 p 2 p 25 Where, p :Pressure p :Liquid density A :Tube friction factor defined by equation (3).{48/Re if Re < 1300 0.26 Re 2 4 if Re > 1300 (3)The equation (4) represents the pressure gradient, which is derived by differentiating the equation (3).dp p dv 2 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 is negligibly small, P 0 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 width I" Effective distance of liquid film of tube from the contact point Therefore, 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 the maximum value obtained by using the equations above and the conditions listed in Tablel.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 115 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version[ ) (116/149)Document No. L5-04GA567(6)
 
At Fig.2 indicates a trend that when the distance from the contact point is greater thani damping coefficient will be saturated.
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Ithe Table 1 Conditions Initial gap Tube diameter AVB width Amplitude of displacement Frequency of vibration Liquid density Kinetic viscosity Note *: Values at BOL design condition (Th=598 deg.F)-11 Distance from the contact point (mm)Fig.2 The damping coefficient and the distance from the contact point MITSUBISHI HEAVY INDUSTRIES, LTD.Page 116 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version II 3(117/149)
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At-Fig.4 indicates; When void fraction is lower than 95%, there is a continuous liquid film on the tube since the thickness of liquid film is larger than(                   ]
When void fraction is higher than 98%, there is no liquid film on the tube since the thickness of liquid film is smaller than[                   ]which   is the assumed minimum thickness of the discontinuous liquid film on the tube.
Fig.4 Relation between void fraction and liquid film thickness
: 4. References
: 1) Akagawa,"Gas and liquid Two-phase Flow" p.150
: 2) "Fluid characteristics of annular mist flow of gas and liquid" p.395-495, 49-438
: 3) Nakazatomi, et.al, Experimental study of vertical upward gas-liquid two-phase annular flow ( 2 nd report, effects of system pressure on characteristics of waves)
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A~k 6
Droplet (Sectional area Ad)
Liquid film (Sectional area Af)
Fig. 5 Sectional area of droplet and liquid film 1.0 Gf is approximately 20 % of GE when the quality is 0.5 0
Test condition
: 0)                                         -   Two-phase flow (steam/water) in N
E heating cylinder (heat flix is 8.6 0                                                x 104 W/ft2 )
z film   -   At high pressure (427psia) o                 0.6 0       Quality Fig.6 Flow rate of liquid film and droplet (Ref.1)
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A&
Shearer           &                   Uf is approximately 10 % of Jg in all cases, Hall -Taylor et              al.      which does not depend on J, and the hydraulic equivalent diameter Test condition E                                      -     Water/air flow in a cylinder
                                        -     At atmospheric pressure and E
room temperature Er 0
0                                          Definition of symbols
&deg;-
LL J~m         8 12 18 25126 0.04     *10~i oA v 0.06           114) A AV 0.1
* 11 A V ot14                   Al V 8 10     15   20     30 Hydraulic equivalent diameter Fig.7 Flow rate of liquid film and droplet (Ref.2)
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Ath for Squeeze Film Damping The effective distance of liquid film of tube from the contact point for squeeze film damping is evaluated to be[             ] as calculated below.
The calculation model of tube and AVB is shown in Fig.l. When the amplitude of gap velocity vibration in normal direction of AVB is v0 , the velocity at x in horizontal direction is defined as equation (1) since the liquid volume pushed out by the tube is the same as the liquid volume which flows in the horizontal direction.
V(v) = v                                                                                       (1)
            .5(x)
Tube I'
{      0 r
                        ~AVB~
I Fig.1   Calculation model MITSUBISHI HEAVY INDUSTRIES, LTD.
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A On 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)   v 2 dx
              +  v-             -   _     +                                           (2) 2     p         2               p         25
: Where, p           :Pressure p           :Liquid density A           :Tube friction factor defined by equation (3).
{48/Re               if   Re < 1300 24 0.26 Re           if   Re > 1300                                             (3)
The equation (4) represents the pressure gradient, which is derived by differentiating the equation (3).
dp       p dv 2     p*,(x) 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 is negligibly small, P 0 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 width I"           Effective distance of liquid film of tube from the contact point Therefore, 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         the maximum value obtained by using the equations above and the conditions listed in Tablel.
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At Fig.2 indicates a trend that when the distance from the contact point is greater thani               Ithe damping coefficient will be saturated.
Table 1 Conditions Initial gap Tube diameter AVB width Amplitude of displacement Frequency of vibration Liquid density Kinetic viscosity Note *: Values at BOL design condition (Th=598 deg.F)
                                                                                            -11 Distance from the contact point (mm)
Fig.2 The damping coefficient and the distance from the contact point MITSUBISHI HEAVY INDUSTRIES, LTD.
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A&
Attachment-4 Confirmation of Flow Regime
: 1. Flow regime MHI has calculated the Grant flow regime map as shown in Figurel by using ATHOS computer code outputs of BOL design conditionI                      ] in accordance with Reference 1.12 tubes shown in Figure 1 are selected as representatives and each tube has 19 evaluation points in U-bend (10 degrees pitch 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 side are 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) 469-483 r
                                                                                                            )
Note *: The points at 90 degrees are included in the hot side.
Figure 1 Flow Regime of Representative Tubes at BOL Design Condition MITSUBISHI HEAVY INDUSTRIES, LTD.
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A&Attachment-4 Confirmation of Flow Regime 1. Flow regime MHI has calculated the Grant flow regime map as shown in Figurel by using ATHOS computer code outputs of BOL design conditionI
A Attachment-5 Case Study for Applying Split Stabilizers for TTW tube of Unit-2 at 70%
] in accordance with Reference 1.12 tubes shown in Figure 1 are selected as representatives and each tube has 19 evaluation points in U-bend (10 degrees pitch 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 side are in the spray flow regime, which is consistent with the methodology of the squeeze film evaluation.
Thermal Power
: 2. Reference[1] M. Pettigrew and C. Taylor, "Vibration Analysis of shell-and-tube heat exchangers:
: 1. Purpose The 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 cases shown in Table 2-1 are studied.
an overview-Part I: Flow, Damping, Fluidelastic Instability," Journal of Fluids and Structures 18 (2003) 469-483 r)Note *: The points at 90 degrees are included in the hot side.Figure 1 Flow Regime of Representative Tubes at BOL Design Condition MITSUBISHI HEAVY INDUSTRIES, LTD.Page 117 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version 1 I ) (118/149)Document No. L5-04GA567(6)
: 2. Conclusion The results of case study for applying type J stabilizer are shown in Table 2-1 and Figure 2-1. Type J stabilizers are split stabilizers that extend approximately 60' into the U-bend, inserted on the hot and cold side of the tube. It has been confirmed that stability ratio of TTW tubes with type J stabilizer is less than 1.0.
A Attachment-5 Case Study for Applying Split Stabilizers for TTW tube of Unit-2 at 70%Thermal Power 1. Purpose The 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 cases shown in Table 2-1 are studied.2. Conclusion The results of case study for applying type J stabilizer are shown in Table 2-1 and Figure 2-1. Type J stabilizers are split stabilizers that extend approximately 60' into the U-bend, inserted on the hot and cold side of the tube. It has been confirmed that stability ratio of TTW tubes with type J stabilizer is less than 1.0.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 118 of 149 S023-617-1-M1539, RE\/. 0 Table 2-1 Natural Frequency and Stability Ratio 6 W, 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 I Additional damping ratio Additional damping ratio Additional damping ratio Additional damping ratio SI I I I Natural Stability Natural Stability Natural Stability Natural Stability Natural Stability Ratio Frequency Ratio Frequency Ratio Frequency Ratio Frequency Ratio Frequency (Hz) (Hz) (Hz) (Hz) (Hz)R111C81 R113C81 Z 0 CD 0/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 ratio Page 119 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version] (120/149)Document No. L5-04GA567(6)
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At 3. Assumption (1) Representative tube Representative tubes (Row1 13 Col.81 and Row1 11 Col.81) are TTW tubes of Unit-2 (2 tubes).(2) AVB support points In this evaluation, all AVB support points are assumed to be inactive for conservatism because the stability ratios of the tubes obtained from the evaluation will be the maximum possible values.(3)Plugging and Stabilizer The representative tubes are assumed to be plugged with or without split stabilizers.
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In the cases with split stabilizers, the stabilizers are assumed to be installed to 60 degrees in the U-bend region at the both of hot and cold side to maximize the structural damping. As shown in Table 3-1, the additional damping ratio by the split stabilizers (Type J) is assumed to be the difference between the damping ratio of tube with and without split stabilizers based on the report of the damping test (Ref.32).
 
Table 3-1 was derived for Row 106 but can be applied to all rows.Ak Table 3-1 Additional dampina due to split stabilizers Amplitude Damping ratio (%)Without stabilizer With split stabilizers Additional damping ratio Small I I Mediumi I Large I I Very large I _(4) Effect of primary water entering into the TTW tubes The effect of primary water entering into the TTW tubes is not taken into account by assuming there in no leakage through the plugging.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 120 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version[ 1(121/149)
Table 2-1 Natural Frequency and Stability Ratio Tube         Without Stabilizer                                                         With split Stabilizers                                                   6 (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       I Additional damping ratio         Additional damping ratio SI                                              I Additional damping I ratio           Additional damping ratio I                     Z 0
Natural     Stability     Natural       Stability       Natural       Stability       Natural     Stability       Natural     Stability Ratio W,
Frequency       Ratio     Frequency         Ratio       Frequency         Ratio         Frequency       Ratio       Frequency (Hz)                       (Hz)                         (Hz)                           (Hz)                         (Hz)                             CD R111C81 0
R113C81
  /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 ratio Page 119 of 149                                                 S023-617-1-M1539, REV. 0
 
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At 4. Acceptance criteria There are no criteria because of parametric case study.5. Design inputs 5.1 Geometry The tube bundle consists ofi diameter, thermally treated Alloy 690 U-tubes that are arranged in a I 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 nominal dimension of tube, TSPs and AVBs are listed in Table 5-1.5.2 Thermal and Hydraulic flow of steam generator secondary side The ATHOS thermal hydraulic analysis program was used to determine the distributions of fluid gap velocity in the normal direction to tube in-plane and fluid density. Table 5-2 and Fig 5-1, 5-2 show the flow characteristic that are applied to the tubes for the evaluation at 70% thermal power of Unit-2 with plugging.6. Methodology The analysis is performed in accordance with the same procedures provided in main report to evaluate the best estimated stability ratio for in-plane FEI.7" Results The analysis results are shown in Table 7-1 and 7-2.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 121 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version) (122/149)Document No. L5-04GA567(6)
At
A&Table 5-1 Nominal dimensions of tubes, TSPs, and AVBs Part Item Value Material Thermally treated SB-163 UNS N06690 Outside diameter 0.75 in Thickness 0.043 in Tubes Number of tubes 9727 Tube pitch 1.0 in Tube arrangement Triangular Material SA-240 Type 405 Thickness TSPs Number of TSPs Tube support span (between TSP centers)Tube support span (from tubesheet to TSP-1)Material SA-479 Type 405 Type AVBs Thickness Width Stabilizer Unit weight A MITSUBISHI HEAVY INDUSTRIES, LTD.Page 122 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version) (123/149)Document No. L5-04GA567(6)
: 3. Assumption (1) Representative tube Representative tubes (Row1 13 Col.81 and Row1 11 Col.81) are TTW tubes of Unit-2 (2 tubes).
At Table 5-2 Basic parameters for calculation for 2A SG evaluation after plugging Plugging 305 Thermal power (MWt) 1213.3 (70%)RCS flow rate (gpm) 206,695 Thot (Tsg-in) (*F)Tsg..out (*F)TCOlId (F)Saturation Steam Pressure (psia)Fouling Factor (ft 2 hr&deg;F /Btu)Tfeedwater
(2) AVB support points In this evaluation, all AVB support points are assumed to be inactive for conservatism because the stability ratios of the tubes obtained from the evaluation will be the maximum possible values.
('F)Circulation Ratio Steam Mass Flow (lb/hr)Feed Water Mass Flow (lb/hr)Blowdown flow rate (gpm)MITSUBISHI HEAVY INDUSTRIES, LTD.Page 123 of 149 S023-617-1-M1539, REV. 0 r C Cl)z 0'0 CD Cn)0 Y,-I Fig. 5-1 Flow Characteristics of Row1 11 Col81 Page 124 of 149 S023-617-1-M1539, REV. 0 7--N Cl)z 0 CD 0)0r,__S023-617-1-M1539, REV. 0 Fig. 5-2 Flow Characteristic of Row 113 CoI.81 Page 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 Effective Additional natural Ratio coefficient fluid void void flow flow Stability Structural Mode frequencyh()
(3)Plugging and Stabilizer The representative tubes are assumed to be plugged with or without split stabilizers.
density fraction fraction velocity velocity ratio Tubeing cSqueeze dmi Structural Two phase film Total Ki Ko Ki Ke K f(Hz) damping damping damping po(Ib/ft3)
In the cases with split stabilizers, the stabilizers are assumed to be installed to 60 degrees in the U-bend region at the both of hot and cold side to maximize the structural damping. As shown in Table 3-1, the additional damping ratio by the split stabilizers (Type J) is assumed to be the difference between the damping ratio of tube with and without split stabilizers based on the report of the damping test (Ref.32). Table 3-1 was derived for Row 106 but can be applied to all rows.
[-] [-] Uc(ft/sec)
Table 3-1 Additional dampina due to split stabilizers   Ak Amplitude                                    Damping ratio (%)
Ue(ftlsec)
Without stabilizer   With split stabilizers   Additional damping ratio Small I          I Mediumi          I Large I          I Very large    I    _
Plugged without stabilizer Plugged with split stabilizers when tube amplitude is small Plugged with split stabilizers when tube amplitude is medium Plugged with split stabilizers when tube amplitude is large Plugged with split stabilizers when tube amplitude is very large ___z 0'0 M..CD 0)CD 0.0 0 :>Page 126 of 149 S023-617-1-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 Effective Additional natural Ratio coefficient fluid void void flow flow Stability Tube condi sti n sructural Mo ef q enyh )Tube condition damping Mode frequency h(%) density fraction fraction velocity velocity ratio N%) Structural Two phase Squeeze Hi film Total KS KK Ke K po(ib/ft 3) [_] [-] Uc(ft/sec)
(4) Effect of primary water entering into the TTW tubes The effect of primary water entering into the TTW tubes is not taken into account by assuming there in no leakage through the plugging.
Ue(ftlsec) f(Hz) damping damping damping Plugged without stabilizer Plugged with standard stabilizer Plugged with split stabilizers when tube amplitude is small _Plugged with split stabilizers when tube amplitude is medium Plugged with split stabilizers when tube amplitude is large Plugged with split stabilizers when tube amplitude is very large _ _z 0 0 0)CD Cn.0 '> t Page 127 of 149 S023-617-1-M1539, REV. 0 Non-propr ietary Version) (128/149)Document No. L5-04GA567(6)
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At Attachment-6 Uncertainty of Calculated Stability Ratio 1. Purpose The purpose of this attachment is to evaluate the uncertainty of stability ratio evaluation based on MHI methodology.
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: 2. Summary The uncertainty of the stability ratio (SR) evaluation based on MHI methodology is evaluated by summing the uncertainties of critical parameters.
 
As a result, the uncertainty of SR evaluation is calculated to be in the range between -5 % and -57%. Therefore, the stability ratios are calculated conservatively based on MHI methodology.
Non-proprietary Version
Table 1 Difference between SR based on MHI evaluation method and best estimated Relative stability Best estimated Uncertainty of MHI's SR ratio based on evaluation MHI evaluation, Upper bound Lower bound R 1 H 1 MS Mean +/-20 SRmax SRmin value deviation,o SR .Hr SRAHI 3. Evaluation method In this evaluation, the standard deviation of SR evaluation multiplied by 2 is regarded as an uncertainty.
[                                 1(121/149)
Table 2 shows the parameters used in the SR calculation and includes which parameters should be taken into account. The methodology of the uncertainty evaluation is shown as follows.3.1 Uncertainty of Each Parameter The uncertainty of each parameter is estimated by the following equation.
In this equation, it is assumed that the uncertainty of each parameter is equal to two times as large as standard deviation of relative error.i Xir f J ...................................................................
(1)Where, MITSUBISHI HEAVY INDUSTRIES, LTD.Page 128 of 149 S023-617-1-M1539, R EV. 0 Non-proprietary Version[ ](129/149)
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A Xref :Reference value of each test data X : test data 0" N: Standard deviation of relative error of each test data: Number of data According to error propagation law, the effect of the standard deviation of each parameter on that of SR is evaluated with the following equations (See Ref. 3) and 2 O-SR is regarded as an uncertainty of SR evaluation.
At
S p TH -Ay 2-)T..........................................................
: 4. Acceptance criteria There are no criteria because of parametric case study.
(2 )-(sr s + (7TpATP + CFSF&#xfd;SF -OrT rP + C+/-ASF SF. ...............................................
: 5. Design inputs 5.1 Geometry The tube bundle consists ofi          diameter, thermally treated Alloy 690 U-tubes that are arranged in a I        1equilateral 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.
(3)&#xfd;ST + TP + SF 2K + a 7.2 ..............................................................................................
All the contacting support structures above the tubesheet are made of 405 stainless steel. The nominal dimension of tube, TSPs and AVBs are listed in Table 5-1.
(4 )Where, C-sR Standard deviation of SR uncertainty a 7 r,, Standard deviation of SR due to thermal hydraulic parameters evaluation UP Standard deviation of parameters used for SR evaluation Total damping ratio&#xfd;ST Structural damping&#xfd;Tp Two phase damping&#xfd;SF Squeeze film damping IA: Standard deviation of 1" CYST Standard deviation of &#xfd;ST Gr : Standard deviation of &#xfd;Tp a's Standard deviation of ;SF a7K Standard deviation of K'KI :Standard deviation of KI Ca : Standard deviation of a(O)X- Standard deviation noted above ( used parameter (dimensionless) for SR evaluationeviation of relative error of each MITSUBISHI HEAVY INDUSTRIES, LTD.Page 129 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I[ )(130/149)
5.2 Thermal and Hydraulic flow of steam generator secondary side The ATHOS thermal hydraulic analysis program was used to determine the distributions of fluid gap velocity in the normal direction to tube in-plane and fluid density. Table 5-2 and Fig 5-1, 5-2 show the flow characteristic that are applied to the tubes for the evaluation at 70% thermal power of Unit-2 with plugging.
: 6. Methodology The analysis is performed in accordance with the same procedures provided in main report to evaluate the best estimated stability ratio for in-plane FEI.
7"Results The analysis results are shown in Table 7-1 and 7-2.
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Table 5-1 Nominal dimensions of tubes, TSPs, and AVBs Part                Item                                Value Material              Thermally treated SB-163 UNS N06690 Outside diameter                          0.75 in Thickness                              0.043 in Tubes Number of tubes                            9727 Tube pitch                              1.0 in Tube arrangement                          Triangular Material                        SA-240 Type 405 Thickness TSPs          Number of TSPs Tube support span (between TSP centers)
Tube support span (from tubesheet to TSP-1)
Material                        SA-479 Type 405 Type AVBs Thickness Width Stabilizer        Unit weight                                                          A MITSUBISHI HEAVY INDUSTRIES, LTD.
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At 3.2 Difference between SR based on MHI method and that based on the best estimated parameters In MHI method, the Connor's constant and damping ratio are evaluated conservatively because lower bounded data are used for some parameters.
At Table 5-2 Basic parameters for calculation for 2A SG evaluation after plugging Plugging                                  305 Thermal power (MWt)                          1213.3 (70%)
The difference between the stability ratio based on MHI method and that based on the best estimated parameters is evaluated by the following equation.S SR. Rm R *,H, 7 7*-m K K ,'q m_ KBE [. &#xfd;BE .S
RCS flow rate (gpm)                            206,695 Thot  (Tsg-in) (*F)
* n._. ...................................
Tsg..out (*F)
(5)A SRBE 1 HS* K V M AI l SR(KBE SS Where, R,*HI : Relative stability ratio based on MHI evaluation method SRAfH: Stability ratio based on MHI evaluation method SRBE Mean stability ratio based on the best estimated parameters KMH : Connor's constant based on MHI evaluation method KBE Mean Connor's constant based on the best estimated parameters MAMH: Damping ratio based on MHI evaluation method&#xfd;BE Mean damping ratio based on the best estimated parameters SR* Average of normalized SR based on three different TH codes (See Sec. 4.2)SR 11Average 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 ........................................................................................................
TCOlId (F)
(6 )KBE R , ..........................................................................................................
Saturation Steam Pressure (psia)
(7 )&#xfd;BE SR .T H I .I. ... ...........................................................................................
Fouling Factor (ft2 hr&deg;F /Btu)
(8 )SR" R'M,="IT -R ....................................................................
Tfeedwater ('F)
(9)RAIll -T R K R 4&#xfd;MITSUBISHI HEAVY INDUSTRIES, LTD.Page 130 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version[ 3(131/149)
Circulation Ratio Steam Mass Flow (lb/hr)
Feed Water Mass Flow (lb/hr)
Blowdown flow rate (gpm)
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r z0
                                                                                '0 CD Cn) 0 C
Cl)
Y,
                                                            -I Fig. 5-1 Flow Characteristics of Row1 11 Col81 Page 124 of 149                S023-617-1-M1539, REV. 0
 
7-                                                          -N z0 Cl)
CD 0) 0 It*r,__
Fig. 5-2 Flow Characteristic of Row 113 CoI.81 Page 125 of 149                S023-617-1-M1539, REV. 0
 
Thble 7-1 Analv.*is results for case study of solit stabilizers (Row 111 Column 81)      /
Tube                    Damping                              Critical        Average Average Maximum Critical Effective Additional        natural                    Ratio                            coefficient          fluid    void    void    flow      flow    Stability Structural Mode frequencyh()                                                                       density fraction fraction velocity velocity      ratio Tubeing                      cSqueeze dmi                      Structural Two phase      film  Total  Ki    Ko      Ki    Ke K f(Hz)    damping    damping    damping                                      po(Ib/ft3)  [-]      [-]  Uc(ft/sec) Ue(ftlsec)
Plugged without                                                                                                                                                                  z 0
stabilizer
                                                                                                                                                                                      '0 Plugged with split                                                                                                                                                                M..
CD stabilizers when                                                                                                                                                                0) tube amplitude is small                                                                                                                                                                      CD C,'
0.
Plugged with split                                                                                                                                                                0 stabilizers when tube amplitude is medium Plugged with split stabilizers when tube amplitude is large Plugged with split stabilizers when tube amplitude is very large                      ___
0  :
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Table 7-2 Analysis results for case study of stabilizer (Row 113 Column 81)    A.
Tube                  Damping                          Critical        Average Average Maximum Critical    Effective Tube condi  n Additional sructural Mo ef natural sti                  q enyh                  Ratio
                                                                      )                        coefficient        fluid    void  void    flow        flow    Stability Tube condition damping N%)    Mode frequency                  h(%)                                           density fraction fraction velocity    velocity    ratio Hi    Structural Two phase Squeeze film    Total  KS          KK Ke    K  po(ib/ft3 )  [_]    [-]  Uc(ft/sec) Ue(ftlsec) f(Hz)  damping    damping  damping Plugged without stabilizer z0 0
Plugged with standard                                                                                                                                                                0) stabilizer M,
Plugged with split stabilizers when                                                                                                                                                            CD Cn.
tube amplitude is small Plugged with split                                                                                                              _
stabilizers when tube amplitude is medium Plugged with split stabilizers when tube amplitude is large Plugged with split stabilizers when                                                                                                                                                        0  '
tube amplitude is very large    _          _
                                                                                                                                                                            >    t Page 127 of 149                                             S023-617-1-M1539, REV. 0
 
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Document No. L5-04GA567(6)
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At Based on Table 2, the relative ratios of Connor's constant and damping ratio are converted to Equation (10) and (11).R K K 1 a( ) .... ..... .............  
At Attachment-6 Uncertainty of Calculated Stability Ratio
............................................
: 1. Purpose The purpose of this attachment is to evaluate the uncertainty of stability ratio evaluation based on MHI methodology.
(10)KBE KlBE a(O)BE&#xfd; 1P &#xfd;TP-MHIf +&#xfd;SF 4SF-AIHf-&#xfd; &#xfd;1MHI -TP-BE 4SF-BE..............................()
: 2. Summary The uncertainty of the stability ratio (SR) evaluation based on MHI methodology is evaluated by summing the uncertainties of critical parameters. As a result, the uncertainty of SR evaluation is calculated to be in the range between -5 % and - 57%. Therefore, the stability ratios are calculated conservatively based on MHI methodology.
&#xfd;BE Where, K1 Afi Connor's constant based on MHI evaluation KIBE Mean Connor's constant based on the experimental data a(O)MHI" The effect of flow direction based on MHI evaluation method a(O)BE Mean effect of flow direction based on the experimental data&#xfd;SF-MHI Squeeze film damping ratio based on MHI evaluation method 4SFB-E Mean squeeze film damping ratio based on the experimental data&#xfd;TP-AIHI Two phase damping ratio based on MHI evaluation method&#xfd;TP-BE Mean two phase damping ratio based on the experimental data 3.3 Uncertainty of SR Based on the standard deviation and the relative stability ratio, the uncertainty of stability ratio based on the MHI method is obtained from the following equations.
Table 1 Difference between SR based on MHI evaluation method and best estimated Relative stability              Best estimated                        Uncertainty of MHI's SR ratio based on                                                               evaluation MHI evaluation,                                                    Upper bound        Lower bound R 1 H1          MS                          Mean +/-20            SRmax              SRmin value      deviation,o                          SR .Hr              SRAHI
For the upper bound, SRmax I+ 2crsR .SRAfH...........................................................................
: 3. Evaluation method In this evaluation, the standard deviation of SR evaluation multiplied by 2 is regarded as an uncertainty. Table 2 shows the parameters used in the SR calculation and includes which parameters should be taken into account. The methodology of the uncertainty evaluation is shown as follows.
(12)For the lower bound, SRmin 1 -2rsR.(13)SR A H RM(13 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 131 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I[ ) (132/149)Document No. L5-04GA567(6),Ak-Table 2 Parameters used for SR calculation U, Effective flow Yes velocity Ul Critical flow Yes The uncertainty of these parameters velocity due to thermal-hydraulic parameters f Tube natural Yes analysis error is evaluated by the frequency comparison of three independent Average tube Yes analyses as shown in Section 4.2.mass P 0  Fluid density Yes Connors's The uncertainty of KI is estimated K1 constant based Yes based on MHI test data.on MHI test ecoefficient to Lower limit of Pettigrew's test data is used for SR calculation. (Ref. 4)Kp consider the effect No It is not necessary to consider of tube pitch on K uncertainty of Kp K The ratio of K The result of MHI air flow test was (See in the in-plane consistent with the public test data Sec.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 not FEI necessary to consider.Lower limit of Yeung's test data is Th cons eeffcint ts used for SR calculation. (Ref. 1)a(9) consider the effect Yes Teucranyo
3.1 Uncertainty of Each Parameter The uncertainty of each parameter is estimated by the following equation. In this equation, it is assumed that the uncertainty of each parameter is equal to two times as large as standard deviation of relative error.
()i of flow angle on K The uncertainty ofa(O) is estimated based on test data.Structural 4 IST is relatively small compared to 4'sT damping ratio No 'SF Two-Phase Yes The uncertainty OfisF is estimated (e damping ratio based on Prof. Pettigrew's test data.(SeeVicu Sec.4.1 (2)) ;'v Viscous No ;, is not used for SR calculation damping ratio II msF Squeezerfilm Yes The uncertainty of 4;s is estimated damping ratio Ibased on Prof. Pettigrew's test data.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 132 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version j[~ 1(133/149)
J ...................................................................
(1) i Xir    f Where, MITSUBISHI HEAVY INDUSTRIES, LTD.
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At-4. Evaluation Result 4.1Parameters Used for SR Evaluation (1) Connors' constant Connor's constant based on MHI test Standard Deviation of Connors' constant K is estimated based on MHI's steam water two phase flow test data to investigate the fluid elastic vibration in the out of plane direction.
A Xref      :Reference value of each test data X        : test data 0"        : Standard deviation of relative error of each test data N          : Number of data According to error propagation law, the effect of the standard deviation of each parameter on that of SR is evaluated with the following equations (See Ref. 3) and 2 O-SR is regarded as an uncertainty of SR evaluation.
S    p -)T TH      -                Ay          2
                                                                                                ..........................................................        (2 )
Cy* - (sr    s + (7TpATP +              CFSF&#xfd;SF -              OrT rP +                C+/-ASFSF.            ............................................... (3)
                    &#xfd;ST +      TP +        SF a 2K +    7.2      ..............................................................................................
(4 )
Where, C-sR            Standard deviation of SR uncertainty a7r,,          Standard deviation of SR due to thermal hydraulic parameters evaluation UP              Standard deviation of parameters used for SR evaluation Total damping ratio
              &#xfd;ST            Structural damping                                                                                                                        IA
              &#xfd;Tp            Two phase damping
              &#xfd;SF            Squeeze film damping
(*y*          : Standard deviation of 1" CYST            Standard deviation of                                &#xfd;ST Gr            : Standard deviation of                                &#xfd;Tp a's            Standard deviation of ;SF a7K            Standard deviation of K
                  'KI        :Standard              deviation of KI Ca            : Standard deviation of a(O)
X- Standard deviation noted above ( used for SR evaluationeviation of relative error of each parameter (dimensionless)
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At 3.2 Difference between SR based on MHI method and that based on the best estimated parameters In MHI method, the Connor's constant and damping ratio are evaluated conservatively because lower bounded data are used for some parameters. The difference between the stability ratio based on MHI method and that based on the best estimated parameters is evaluated by the following equation.
R*,H,              S  K    ,'q      m_ 7Rm  7*-m        KKBE      [. &#xfd;BE    .SSR. *n._....................................    (5)
A        SRBE                  1                        K M HS*  V  l  AI      SR(
KBE                SS Where, R,*HI : Relative stability ratio based on MHI evaluation method SRAfH: Stability ratio based on MHI evaluation method SRBE      Mean stability ratio based on the best estimated parameters KMH      : Connor's constant based on MHI evaluation method KBE        Mean Connor's constant based on the best estimated parameters MAMH:  Damping ratio based on MHI evaluation method
              &#xfd;BE        Mean damping ratio based on the best estimated parameters SR*          Average of normalized SR based on three different TH codes (See Sec. 4.2)
SR 1* 1 *, Average 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).
RK    K A H ........................................................................................................              (6 )
KBE R, .        .  ........................................................................................................          (7 )
            &#xfd;BE SR .
T H I. SR" I.... .            ..........................................................................................          (8 )
R'M,="IT  -          R ....................................................................                                      (9)
RAIll  -                  T RK    R4&#xfd; MITSUBISHI HEAVY INDUSTRIES, LTD.
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At Based on Table 2, the relative ratios of Connor's constant and damping ratio are converted to Equation (10) and (11).
R    K              K1              a( )          ....      .....        .............    ............................................ (10)
KBE        KlBE            a(O)BE
                        &#xfd; 1P &#xfd;TP-MHIf        +&#xfd;SF        4SF-AIHf
        -&#xfd;  &#xfd;1MHI  -            TP-BE                    4SF-BE..............................()
            &#xfd;BE Where, K1 Afi          Connor's constant based on MHI evaluation KIBE            Mean Connor's constant based on the experimental data a(O)MHI" The effect of flow direction based on MHI evaluation method a(O)BE          Mean effect of flow direction based on the experimental data
              &#xfd;SF-MHI        Squeeze film damping ratio based on MHI evaluation method 4SFB-E          Mean squeeze film damping ratio based on the experimental data
              &#xfd;TP-AIHI        Two phase damping ratio based on MHI evaluation method
              &#xfd;TP-BE          Mean two phase damping ratio based on the experimental data 3.3 Uncertainty of SR Based on the standard deviation and the relative stability ratio, the uncertainty of stability ratio based on 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 AH          RM(13 MITSUBISHI HEAVY INDUSTRIES, LTD.
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                                                                                ,Ak-Table 2 Parameters used for SR calculation U,          Effective flow            Yes velocity Ul            Critical flow            Yes      The uncertainty of these parameters velocity                      due to thermal-hydraulic parameters f          Tube natural              Yes      analysis error is evaluated by the frequency                        comparison of three independent Average tube              Yes      analyses as shown in Section 4.2.
mass P0          Fluid density            Yes Connors's                        The uncertainty of KI is estimated K1    constant based              Yes      based on MHI test data.
on MHI test ecoefficient to              Lower limit of Pettigrew's test data is used for SR calculation. (Ref. 4)
Kp    consider the effect        No      It is not necessary to consider of tube pitch on K                  uncertainty of Kp K              The ratio of K                      The result of MHI air flow test was (See              in the in-plane                    consistent with the public test data Sec.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 not FEI                          necessary to consider.
Lower limit of Yeung's test data is Thcons eeffcintts                  used for SR calculation. (Ref. 1) a(9)    consider the effect        Yes      Teucranyo ()i of flow angle on K                  The uncertainty ofa(O) is estimated based on test data.
Structural                        4 IST  is relatively small compared to 4
                'sT  damping ratio              No        'SF Two-Phase                Yes      The uncertainty OfisF is estimated (e
(SeeVicu          damping ratio                      based on Prof. Pettigrew's test data.
Sec.4.1 (2))  ;'v      Viscous                No      ;,    is not used for SR calculation damping ratio        II msF Squeezerfilm              Yes      The uncertainty of 4;s is estimated damping ratio                    Ibased on Prof. Pettigrew's test data.
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At-
: 4. Evaluation Result 4.1Parameters Used for SR Evaluation (1) Connors' constant Connor's constant based on MHI test Standard Deviation of Connors' constant K is estimated based on MHI's steam water two phase flow 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
Figure 1 shows Connors' constant data obtained by MHr's test (black points
* in Figure 1). However Connors' constant data include the error due to estimating it without considering measuring error of ratio of volume flow rate, flow velocity and fluid density. Therefore it is necessary to consider the error of both ratio of volume flow rate ,/ and Connors' constant K which are horizontal and vertical axis (these data are indicated as red points N in Figure 1). Equations for calculating the error are as follows. Here the effect of error of damping ratio on Connors' constant K is neglected.
* in Figure 1). However Connors' constant data include the error due to estimating it without considering measuring error of ratio of volume flow rate, flow velocity and fluid density. Therefore it is necessary to consider the error of both ratio of volume flow rate ,/ and Connors' constant K which are horizontal and vertical axis (these data are indicated as red points N in Figure 1). Equations for calculating the error 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 that estimation of damping ratio is not affected by measuring error.-Error of Connors' constant 2e= ic + 6 .0) + ( 6 0 ......................................................................
Because damping ratio is determined with shape of the spectrum, therefore it is assumed that estimation of damping ratio is not affected by measuring error.
(14)Where, Equation of Connors' constant : K = ) oD2 EK Relative error of Connors' constant K cuc Relative error of critical flow velocity 6 m0 Relative error of tube density considered added mass of outside water 0,0 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  
    - Error of Connors' constant ic 2e=+   6 .0)   +(     6 0       ...................................................................... (14)
+U2(EiU 1)2  .(15)U 9 + U l f U 9 + U X1 U .Where, Equation of ratio of volume flow rate : 8 = Ug Ug + UI Ug: flow velocity of vapor (gas)U,: flow velocity of water (liquid)Ep Relative error of ratio of volume flow rate 6 ug : 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 S023-617-1-M1539, REV. 0 I Non-proprietary Version I] (134/149)Document No. L5-04GA567(6)
                                                                        )    oD2 Equation of Connors' constant : K
At According to MHI's test data, measuring error ( ug, E'l, .0 and c.0 is as follows: E= I Euc =1 (max value of measuring error of flow velocity; max( 6 ug', CCU))-.6 0 = 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 result according to GUM (Guide to the expression of Uncertainty in Measurement, ASME).Table 3 Measuring error of each parameter steam water measuring error of pressure (%)fluid density at reference pressure;6MPa (kg/mA3)fluid density at the pressure considering error; 6.02MPa (kg/mA3)measuring error of fluid density (%)measuring error of flow rate (%) IL X 1 X 2 measuring error of cross section (%)3 X 1 Relative error between fluid density ati landl I steam I water I X-2 Proof reading result of flow rate measurement X-3 Measuring error of cross section is estimated by dimensional inspection result and measuring error of digital vernier calipers I I X-4 Measuring error of flow velocity is calculated by following equation in accordance with GUM E26 ~2 C 2 ELI = 2 x 3+ 3 + 3 3 3 3 Where EL measuring error of flow velocity EQ measuring error of flow rate CA measuring error of cross section 6,p :measuring error of fluid density steam : MITSUBISHI HEAVY INDUSTRIES, LTD.Page 134 of 149 S023-617-1-M1539, 4. 0 Non-proprietary Version[ 3(135/149)
                                                              =
Where, EK     Relative error of Connors' constant K cuc     Relative error of critical flow velocity 6
m0   Relative error of tube density considered added mass of outside water 0,0   Relative error of fluid density         Em.0)
Error of ratio of volume flow rate UUU9+ U l 2
          -                 U2   _2(Ug 2                      +U)2       4U/(ugUg)2           +U2(EiU1 )               .(15) f       U 9 + U X1                 U                                     .
Where,     Equation of ratio of volume flow rate : 8             =     Ug Ug + UI Ug: flow velocity of vapor (gas)
U,: flow velocity of water (liquid)
Ep     Relative error of ratio of volume flow rate 6
ug : Relative error of flow velocity of vapor (gas) cut     Relative error of flow velocity of water (liquid)
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At water Therefore 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 calculation result is shown in Table 4. Both relative error of cK and e. are calculated according to error propagation law.Table 4 Calculation of relative error of 13 P jg+jl'&#xfd;&#xfd;(M/s) jg,*(mls) jlm, (mis) (%0.7 0.98_____0.93____ _X-1 Critical flow velocity obtained by MHI testCritical flow velocity of vapor and water calculated by test condition (linear interpolation)
At According to MHI's test data, measuring error     (  ug, E'l,   .0 and c.0 is as follows:
Then the uncertainty of KI is estimated from the measuring error of test data by calculating the maximum 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 ) and ratio 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'l There 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 maximum relative error from fitting curve.K ma .........
E=              I Euc =1        (max value of measuring error of flow velocity; max( 6  ug', CCU))
..............
    -. 0 = EP0 =1 6
(16)Where Ki each data for uncertainty evaluation; K1 k 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 S023-617-1-M1539, RE'V. 0 Non-proprietary Version[ 3(136/149)
I(maximum value of measuring error of fluid density)
Measuring error of each parameter is estimated based on proof reading result and inspection result according to GUM (Guide to the expression of Uncertainty in Measurement, ASME).
Table 3  Measuring error of each parameter steam      water measuring error of pressure (%)
fluid density at reference pressure; 6MPa (kg/mA3) fluid density at the pressure considering error; 6.02MPa (kg/mA3) measuring error of fluid density (%)                               X1 measuring error of flow rate (%)       IL                          X2 measuring error of cross section (%)3 X 1 Relative error between fluid density ati        landl                            I steam      I water        I X-2 Proof reading result of flow rate measurement X-3 Measuring error of cross section is estimated by dimensional inspection result and measuring error of digital vernier calipers I            I X-4 Measuring error of flow velocity is calculated by following equation in accordance with GUM ELI= 2 x      E26 3+ ~23  + 3 C2 3 3      3 Where EL    measuring error of flow velocity EQ    measuring error of flow rate CA    measuring error of cross section 6,p  :measuring error of fluid density steam :
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At (4) at each ratio of volume flow rate ; 2-K =KI= I (UK =1 I)' Because measuring error of KI and 61 are estimated as 2 times as large as standard deviation
At water Therefore relative error of Connors' constant is estimated to be              6
: 2a, it is assumed that K1 Since the mean data is used for the SR evaluation, the relative ratio of K1, KImH , isI I KIBE K -Figure 1 Experimental data of Connors's constant based on MHI test; KI MITSUBISHI HEAVY INDUSTRIES, LTD.Page 136 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I[ )(137/149)
                                                                                ,K=      fby using equation (14).
Also E. is calculated with measuring error eug & E                      by using equation (15), the calculation result is shown in Table 4. Both relative error of cK and e. are calculated according to error propagation law.
Table 4     Calculation of relative error of 13 P          jg+jl'&#xfd;&#xfd;(M/s)  jg,*(mls)       jlm, (mis)          (%
0.7 0.98_____
0.93____                              _
X-1    Critical flow velocity obtained by MHI test X-*2    Critical 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 the maximum 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 ) and ratio 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'l There 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 maximum relative error from fitting curve.
K      ma            .........                                                      ..............      (16)
Where Ki    each data for uncertainty evaluation; K1 k      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)-
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At Effect of flow direction Figure 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 than 20 degrees; the flow directions are smaller than 20 degrees in the center of the bundle (FEI susceptible region) as shown in Figure 3.In accordance with Figure 2, the standard deviation below 20 degrees is obtained to bel land the mean line is added, which isi larger than the lower limit used for the SR evaluation.
At (4) at each ratio of volume flow rate ; 2-K =KI=  I      (UK =1      I)' Because measuring error of KI and 61 are estimated as 2 times as large as standard deviation : 2a, it is assumed that K1 Since the mean data is used for the SR evaluation, the relative ratio of K1, KImH  , isI  I KIBE K                                                                                    -
a(o)AfH ii, Therefore, the relative ratio, a(O),E isl I Connor's constant Therefore, 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.&#xfd;, 2, + I" 07 KI a I=RK = ______ a(9)Aff.KIBE a(O)BE MITSUBISHI HEAVY INDUSTRIES, LTD.Page 137 of 149 S023-617-1-M1539, RE\/.0 I Non-proprietary Version I) (138/149)Document No. L5-04GA567(6)
Figure 1    Experimental data of Connors's constant based on MHI test; KI MITSUBISHI HEAVY INDUSTRIES, LTD.
A Figure 2 Experimental data of a(O)Figure 3 Region where the flow direction is greater than 20 degrees from the tube in-plane direction to out-of-plane direction MITSUBISHI HEAVY INDUSTRIES, LTD.Page 138 of 149 S023-617-1-M1539, RE'V. 0 I Non-proprietary Version [)1(139/149)
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At Effect of flow direction Figure 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 than 20 degrees; the flow directions are smaller than 20 degrees in the center of the bundle (FEI susceptible region) as shown in Figure 3.
In accordance with Figure 2, the standard deviation below 20 degrees is obtained to bel               land the mean line is added, which isi                     than the lower limit used for the SR evaluation.
a(o)AfH ii, larger Therefore, the relative ratio,     a(O),E isl       I Connor's constant Therefore, 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.
                      &#xfd;, 2, +       I" 07     KI   a     I=
RK =   ______   a(9)Aff.
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A Figure 2     Experimental data of a(O)
Figure 3 Region where the flow direction is greater than 20 degrees from the tube in-plane direction to out-of-plane direction MITSUBISHI HEAVY INDUSTRIES, LTD.
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At (2) Damping Ratio Squeeze film dampinq Uncertainty of squeeze film damping &#xfd;SF is estimated based on Pettigrew's test data as shown in the Figure 4 (See Ref. 2). According to this figure, the squeeze film damping ratio depends on the vibration frequency and the bounded line of 4-SF, with 9 0 th percentile ( = 50 / f ) is used for the OA evaluation in accordance with Pettigrew's guideline.
At (2) Damping Ratio Squeeze film dampinq Uncertainty of squeeze film damping &#xfd;SF is estimated based on Pettigrew's test data as shown in the Figure 4 (See Ref. 2). According to this figure, the squeeze film damping ratio depends on the vibration frequency and the bounded line of 4-SF, with 9 0 th percentile ( = 50 / f ) is used for the OA evaluation in accordance with Pettigrew's guideline.
As shown in Figure 4, the bounded line based on 9 0 th percentile ( = 50 / f) is used for MHI's SR evaluation.
As shown in Figure 4, the bounded line based on           9 0 th percentile ( = 50 / f) is used for MHI's SR evaluation. In order to obtain the standard deviation and the relative ratio, the lower bounded line with 9 5 th percentile (= 43.5 / f) and the average line ( = 100 / f )are added.
In order to obtain the standard deviation and the relative ratio, the lower bounded line with 9 5 th percentile
2 0 Since the difference between         9 5 th percentile and the average line is considered as               SF, the standard deviation is Iand                                         the ratio between   90 th percentile and the average line is the relative ratio of squeeze film damping,         7SF-Aff , which is]
(= 43.5 / f) and the average line ( = 100 / f )are added.Since the difference between 9 5 th percentile and the average line is considered as 2 0 SF, the standard deviation is Iand the ratio between 9 0 th percentile and the average line is the relative ratio of squeeze film damping, 7SF-Aff , which is]9SF-BE MITSUBISHI HEAVY INDUSTRIES, LTD.Page 139 of 149 S023-617-1-M1539, R EV. 0 Non-proprietary Version I I] (140/149)Document No. L5-04GA567(6)
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At/-Note) because there are 20 points below the Pettigrew's guideline with 9 0 th percentile, the lower bounded line with 9 5 th percentile is determined such that there are 10 plot points below this line Figure 4 Experimental data of squeeze film damping MITSUBISHI HEAVY INDUSTRIES, LTD.Page 140 of 149 S023-617-1-M1539, RI EV. 0 Non-proprietary Version[ 3(141/149)
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At Two phase dampingq Uncertainty of two phase damping is estimated based on Pettigrew's test data as shown in Figure 5 (See Ref. 5). In order to obtain the standard deviation and the relative ratio, the lower bounded line of all the data, which is assumed to show 99. 7 th percentile ( = -3 aTp), is added. Since the difference between the gradient of the 9 9.7th percentile I and the gradient of the average linel I is considered as 3 STp, the standard deviation is I The ratio between the gradient of guide line used for SR evaluation I and the gradient of the average line is the relative ratio of two phase damping, !which isTP-BE Figure 5 Experimental data of two phase damping MITSUBISHI HEAVY INDUSTRIES, LTD.Page 141 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version) (142/149)Document No. L5-04GA567(6)
At
At Total dampinq ratio According to equation (3), in order to estimate the standard deviation of total damping ratio 4,it is necessary to consider absolute value of each damping ratio. According to damping ratio data used in analysis shown in Table 5, it is found that &#xfd;4 SF / =1 land Tp/IL=I ITherefore the standard deviation of total damping ratio, c,, Iis estimated to bel Ias follows.a "- = S "F+ Tp The relative damping ratio is obtained to bel 4'SF -H + 4"T &#xfd;'TP-MHIf R= SF-BE qTP-BE 4-Iby using Equation (11) as follows.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 142 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I[ )(143/149)
/-
Note) because there are 20 points below the Pettigrew's guideline with  9 0 th percentile, the lower bounded line with 9 5 th percentile is determined such that there are 10 plot points below this line Figure 4    Experimental data of squeeze film damping MITSUBISHI HEAVY INDUSTRIES, LTD.
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At Two phase dampingq Uncertainty of two phase damping *TP          is estimated based on Pettigrew's test data as shown in Figure 5 (See Ref. 5). In order to obtain the standard deviation and the relative ratio, the lower 3
bounded line of all the data, which is assumed to show 99.         7 th percentile ( = - aTp), is added. Since the difference between the gradient of the         9 9 .7th percentile I               and the gradient of the 3
average linel         I is considered as       STp, the standard deviation is                             I The ratio between the gradient of guide line used for SR evaluation                       Iand the gradient of the average line           is the relative ratio of two phase damping,               !which   is
* TP-BE Figure 5   Experimental data of two phase damping MITSUBISHI HEAVY INDUSTRIES, LTD.
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At Total dampinq ratio According to equation (3), in order to estimate the standard deviation of total damping ratio 4,it is necessary to consider absolute value of each damping ratio. According to damping ratio data used in analysis shown in Table 5, it is found that &#xfd;4 SF / =1         land Tp/IL=I         ITherefore the standard deviation of total damping ratio, c,, Iis estimated to bel     Ias follows.
a   ="- S         "F+Tp The relative damping ratio is obtained to bel     Iby using Equation (11) as follows.
4'SF -H   + 4 "T &#xfd;'TP-MHIf R=SF-BE           qTP-BE 4-MITSUBISHI HEAVY INDUSTRIES, LTD.
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At 4.2 SR due to Thermal-Hydraulic Parameters Evaluation In order to evaluate the standard deviation of SR due to the thermal-hydraulic (TH) parameters evaluation, stability ratios for representative 8 tubes are calculated by using 3 independent TH analysis codes (MHI-ATHOS, CAFCA and WEC-ATHOS)
At 4.2 SR due to Thermal-Hydraulic Parameters Evaluation In order to evaluate the standard deviation of SR due to the thermal-hydraulic (TH) parameters evaluation, stability ratios for representative 8 tubes are calculated by using 3 independent TH analysis codes (MHI-ATHOS, CAFCA and WEC-ATHOS)
Table 5 shows the results of SR calculation and the normalized values, which are the ratio between the 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 land the average relative stability ratio based on MHI ATHOS isi I A 1 ............................
Table 5 shows the results of SR calculation and the normalized values, which are the ratio between the calculated SRs based on each TH analysis and the average of SRs based on 3 analysis codes.
N.................................................
A The standard deviation of normalized stability ratios obtained by the following equation isi                                       land the average relative stability ratio based on MHI ATHOS isi                                         I 1                                           .         ...........................
(17 )Where,-TTH Standard deviation of SR based on each TH code SR* : Normalized SR (= each analysis result / average value of 3 analysis code result)SR* Average of normalized SR N :Number of data Table 5 Comparison of Stability Ratio based on MHI-ATHOS, CAFCA and WEC-ATHOS MHI-ATHOS CAFCA WEC-ATHOS Average Row Column SR Normalized Normalized SR Normalized SR Normalized SR SR SR SR SR 81 69 r 81 89 101 69 101 89 121 69 121 89 125 85 105 69 Average t, MITSUBISHI HEAVY INDUSTRIES, LTD.Page 143 of 149 S023-617-1-M1539, REV. 0 I Non-proprietary Version I) ](144/149)
N.................................................                                                           (17 )
Where,
          -TTH Standard deviation of SR based on each TH code SR* : Normalized SR (= each analysis result / average value of 3 analysis code result)
SR*     Average of normalized SR N     :Number of data Table 5 Comparison of Stability Ratio based on MHI-ATHOS, CAFCA and WEC-ATHOS MHI-ATHOS                                             CAFCA               WEC-ATHOS             Average Row   Column       SR               Normalized                                   Normalized     SR   Normalized     SR     Normalized SR                       SR             SR                   SR                   SR 81       69 r 81       89 101       69 101       89 121       69 121       89 125       85 105       69 Average   t, MITSUBISHI HEAVY INDUSTRIES, LTD.
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Document No. L5-04GA567(6) 4.3 Uncertainty of SR Table 6 shows the standard deviation and the relative ratio of each parameter. According to                    V6 equation (2), the standard deviation of stability ratio is calculated to bel      Ias follows.
U'S, = 0"* +      O"_  + O'7n2=
The upper bounded and lower bounded of stability ratios are -5% and -57%, which are obtained by Equation (12) and (13).
Table 6 Uncertainty of Stability Ratio Best estimated            Uncertainty of MHI's SR evaluation Relative Ratio                                Upper bound              Lower bound Parameters                based on        Mean          (              Skax                      SRkin MHI method SRMIII                  SRAfH, K1 Connor's constant        a(O)
K
                *SF Damping Ratio            TP Thermal-Hydraulic Parameters Stability Ratio
: 5. References
[1]  "The Effect of Approach Flow Direction on the Flow-Induced Vibrations of a Triangular Tube Array" , 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 ( 3 rd Report, Advanced Estimated Method)St, 2002, T. Nakamura et al, Journal of The Japan Society of 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) &#xa9; 2000 Balkema, Rotterdam, ISBN 90 5809 129 5, 561-568
[5] "Vibration analysis of shell-and-tube heat exchangers : an overview - Part1: flow, damping, fluid elastic instability ", 2003, M.J. Pettigrew et al, Journal of Fluids and Structures 18 469-483 MITSUBISHI HEAVY INDUSTRIES, LTD.
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Document No. L5-04GA567(6)
At Attachment-7 Selection of Evaluated Tubes As shown in Table 1, 28 tubes are selected for thermal hydraulic analysis by ATHOS/SGAP (see Ref.21 for detail). Among these tubes, 8 tubes (#2,#3,#6,#7,#l0,#11,#14,#16) selected by SCE (See the emails shown in Appendix-I) and an additional tube (#28), which stability ratio of out-of-plane FEI was the maximum when all AVB support points are active, are evaluated in the main report.
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At Table 1 Evaluated Tubes (See Ref.22 for details)
Tube #      Row      Column 1        80        60 2"1      80        70 3"1      80        80 4        80        88 5      100        60 6*1      100        70 7*1      100        80 8      100        88 9      120        60 10*1      120        70 11"1      120        80 12      120        88 13      80        84 14*1      95        85 15      110        84 16*1      125        85 17      135        85 18      40        30 19      74        80 20        95        69 21      105        69 22      111        69 23      127        73 24      138        80 25        86        80 26        95        75 27      124        76 282      138        84 Notes:
(*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 is the maximum when all AVB support points are active MITSUBISHI HEAVY INDUSTRIES, LTD.
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===4.3 Uncertainty===
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Appendix-1 E-mails from SCE MITSUBISHI HEAVY INDUSTRIES, LTD.
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of SR Table 6 shows the standard deviation and the relative ratio of each parameter.
Non-proprietary Version I 3(148/149)
According to V6 equation (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 by Equation (12) and (13).Table 6 Uncertainty of Stability Ratio Best estimated Uncertainty of MHI's SR evaluation Relative Ratio Upper bound Lower bound Parameters based on Mean ( Skax SRkin MHI method SRMIII SRAfH, K1 Connor's constant a(O)K Damping Ratio TP Thermal-Hydraulic Parameters Stability Ratio 5. References
                                                    )
[1] "The Effect of Approach Flow Direction on the Flow-Induced Vibrations of a Triangular Tube Array" , 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 (3 rd Report, Advanced Estimated Method)St, 2002, T. Nakamura et al, Journal of The Japan Society of 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) &#xa9; 2000 Balkema, Rotterdam, ISBN 90 5809 129 5, 561-568[5] "Vibration analysis of shell-and-tube heat exchangers
: an overview -Part1: flow, damping, fluid elastic instability
", 2003, M.J. Pettigrew et al, Journal of Fluids and Structures 18 469-483 MITSUBISHI HEAVY INDUSTRIES, LTD.Page 144 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I) 3(145/149)
Document No. L5-04GA567(6)
Document No. L5-04GA567(6)
At Attachment-7 Selection of Evaluated Tubes As shown in Table 1, 28 tubes are selected for thermal hydraulic analysis by ATHOS/SGAP (see Ref.21 for detail). Among these tubes, 8 tubes (#2,#3,#6,#7,#l0,#11,#14,#16) selected by SCE (See the emails shown in Appendix-I) and an additional tube (#28), which stability ratio of out-of-plane FEI was the maximum when all AVB support points are active, are evaluated in the main report.MITSUBISHI HEAVY INDUSTRIES, LTD.Page 145 of 149 S023-617-1-M1539, RE'V. 0 Non-propr rietary Version I (146/149)Document No. L5-04GA567(6)
A&
At Table 1 Evaluated Tubes (See Ref.22 for details)Tube # Row Column 1 80 60 2"1 80 70 3"1 80 80 4 80 88 5 100 60 6*1 100 70 7*1 100 80 8 100 88 9 120 60 10*1 120 70 11"1 120 80 12 120 88 13 80 84 14*1 95 85 15 110 84 16*1 125 85 17 135 85 18 40 30 19 74 80 20 95 69 21 105 69 22 111 69 23 127 73 24 138 80 25 86 80 26 95 75 27 124 76 282 138 84 Notes: (*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 is the maximum when all AVB support points are active MITSUBISHI HEAVY INDUSTRIES, LTD.Page 146 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I I) (147/149)Document No. L5-04GA567(6)
MITSUBISHI HEAVY INDUSTRIES, LTD.
A&Appendix-1 E-mails from SCE MITSUBISHI HEAVY INDUSTRIES, LTD.Page 147 of 149 S023-617-1-M1539, REV. 0 Non-proprietary Version I) 3(148/149)
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At r
At r-I MITSUBISHI HEAVY INDUSTRIES, LTD.Page 149 of 149 S023-617-1-M1539, REV. 0}}
                                                          -I MITSUBISHI HEAVY INDUSTRIES, LTD.
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Latest revision as of 08:44, 20 March 2020

Enclosure 4, L5-04GA567, Rev. 6, Evaluation of Stability Ratio for Return to Service
ML13051A192
Person / Time
Site: San Onofre Southern California Edison icon.png
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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Text

ENCLOSURE 4 MHI Non-Proprietary Document L5-04GA567, Evaluation of Stability Ratio for Return to Service (Non-Proprietary)

I Non-proprietary Version

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San Onofre Nuclear Generating Station, Unit 2 & 3 REPLACEMENT STEAM GENERATORS Evaluation of Stability Ratio for Return to Service Supplier Status Stamp VPL No: S023-617-1-M1539 Reo

  • I QCN/A R-DESIGN DOCUMENT ORDER NO. _

REFERENCE DOCUMENT-INFORMIATION ONLY EIIVIRP 10M MANUAL 8008734135 MFG MAY PROCEED: [YES []NO EN/A STATUS - A status Is required for design documents and Is optional for reference documents. Drawings are reviewed and approved for arrangements and conformance to specification only. Approval does not relieve the submilttr from the responsibility of adequacy and suitability of design, materials, and/or equipment represented.

E-1, APPROVED

-]2. APPROVED EXCEPT AS NOTED - Make changes and resubmit 013. NOT APPROVED . Correct and resubmit for review. NOT for field use.

APPROVAL: (PRINT/ SIGN / ATE),

RE: J FLS:

Other.

SCE DE(123) 6 REV. 3 07t11

REFERENCE:

80123-XXIV-37.0.26 Purchase Order No. 4500024051 Specification No. S023-617-01R3 HITUB8r1eer IUV' nlUnSTa., tIA.

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At Revision History Document No.L5-04GA567 No. Revision Date Approved Checked Prepared 0 Initial issue See cover sheet I -Revised in accordance with SCE comments of RSG-SCE/MHI-12-5722.

-Added the evaluation of out of plane FEI.

2 Revised in accordance with SCE comments of RSG-SCE/MHI-12-5729.

3 -Revised the calculation method of the virtual added mass of tube in Sec. 4.1(5).

4 - Added Attachment-5 to evaluate the stability ratio of the tube which has tube-to-tube wear at 70% thermal power 5 - Revised Attachment-5 to evaluate the effect of type J stabilizer on stability ratio of the tube which has tube-to-tube wear at 70% thermal power

- Added Attachment-6 to evaluate the uncertainty of calculated stability ratio 6 -Revised in accordance with SCE comments of RSG-SCE/M HI-12-5769

-Revised stability ratios due to the change of stabilizer type (Type J)

-Revised out-of-plane FEI analysis results in Sec.2 and 8 _

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At Table of Contents

1. Purpose .................................................................................................................................... 4
2. Conclusion ............................................................................................................................... 5 2.1 Stability ratio of out of plane FEI ..................................................................................... 5 2.2 Stability ratio of in-plane FEI ............................................................................................ 6
3. Nom enclature ......................................................................................................................... 10
4. Assum ption ............................................................................................................................ 11 4.1 Modeling assum ption ..................................................................................................... 11 4.2 O pen item ............................................................................................................................ 12
5. Acceptance Criteria .......................................................................................................... 13
6. Design Input ........................................................................................................................... 14 6.1 G eom etry of tube bundle region ..................................................................................... 14 6.2 Thermal and hydraulic flow of steam generator secondary side .................................... 17
7. Methodology ............................................................................................................................. 32 7.1 Fluid elastic vibration ...................................................................................................... 32 7.2 Calculation m odel .......................................................................................................... 49
8. Com putation Results ........................................................................................................ 60 8.1 O ut of plane FEI analysis results ................................................................................... 60 8.2 In-plane FEI analysis results .......................................................................................... 65
9. Reference .............................................................................................................................. 95 Attachm ent-1 Com puter Input and O utput File List .............................................................. 96 Evaluation of Liquid Film Thickness of Tube at AVB Support Point ..................... 106 Evaluation of the Effective Distance of Liquid Film of Tube from the Contact Point for Squeeze Film Dam ping .............................................................................................................. 114 Attachm ent-4 Confirm ation of Flow Regim e ............................................................................... 117 Case Study for Applying Split Stabilizers for TTW tube of Unit-2 at 70% Thermal Power ......................................................................................................................................... 118 Attachm ent-6 Uncertainty of Calculated Stability Ratio .............................................................. 128 Attachm ent-7 Selection of Evaluated Tubes ............................................................................... 145 MITSUBISHI HEAVY INDUSTRIES, LTD.

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1. Purpose The 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.

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At.

2. Conclusion By considering numbers of inactive support points as the parameter for the case study, the following results are obtained.

2.1 Stability ratio of out of plane FEI 2.1.1 Assuming all support points active With all AVB supports active, the stability ratios are less than 1.0 for all analyzed tubes, for the reactor power levels up to, and including, 100% with no plugging.

Table 2.1-1 Stabilitv Ratio with All Active Sunoort Points for 2A SG Case Thermal Power Row Column 70 100 (No Plug) 80 70 80 80 100 70 10011 80(*)

120 70 120 80 95(*) 85(*)

125 85 138 84 Note(*): Plugged tube with Type J stabilizer 2.1.2 Assuming 1 support points inactive With 1 AVB supports inactive, the stability ratios are less than 1.0 for all analyzed tubes, for the reactor power levels up to, and including, 70%

Table 2.1-2 Stability Ratio with I Inactive Su~oort Point for 2A SG Case Thermal Power Row Column 70 100 (No Plug) 80 70 80 80 100 70 100C) 80(*)

120 70 120 80 95(1) 85(*)

125 85 138 84 L YI Note(*): Plugged tube with Type J stabilizer MITSUBISHI HEAVY INDUSTRIES, LTD.

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At 2.2 Stability ratio of in-plane FEI 2.2.1 Assuming 6 support points inactive With 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 SG Case Thermal Power Row Column 50 60 70 80 90 100 100 (No Plug) 80 70 80 80 100 70 1 00M 80(.)

120 70 120 80 95(') 85(*)

125 85 138 84 Note(*): Plugged tube with Type J stabilizer MITSUBISHI HEAVY INDUSTRIES, LTD.

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At 2.2.2 Assuming 8 support points inactive With 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 SG Case Thermal Power 100 Row Column 50 60 70 80 90 100 (Pu 80 70 80 80 100 70 1O0) 80()

120 70 120 80 95(*) 85(*)

125 85 138 84 Note(*): Plugged tube with Type J stabilizer MITSUBISHI HEAVY INDUSTRIES, LTD.

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At 2.2.3 Assuming 10 support points inactive With 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 SG Case Thermal Power 100 50 60 70 80 90 100 (Pu Row Column (No Plug) 80 70 80 80 100 70 I O0) 80(')

120 70 120 80 95(") 85(*)

125 85 138 84 Note(*): Plugged tube with Type J stabilizer MITSUBISHI HEAVY INDUSTRIES, LTD.

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At 2.2.4 Assuming 12 support points inactive With 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 SG Case Thermal Power Row Column 50 60 70 80 90 100 100 (No Plug) 80 70 80 80 100 70 100(*) 80(*)

120 70 120 80 95() 85(')

125 85 138 84 Note(*): Plugged tube with Type J stabilizer 2.2.5 TTW tubes in Unit-2 The stability ratios of TTW (tube-to-tube wear) tubes with type J stabilizer (split stabilizers) in Unit-2 were evaluated and confirmed to be less than 1.0 as shown in Attachment-5.

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3. Nomenclature Symbol Unit Definition E psi Modulus of elasticity of tube FEI Fluid elastic instability G psi Shear modulus of tube Tav OF Primary side average temperature TS OF Secondary side temperature D, in Tube inside diameter Do in Tube outside diameter P in Tube pitch 3

A Ibm/ft Density of water inside the tube 3

A_ Ibm/ft Density of tube material 3

Po Ibm/ft Average density of water outside the tube t in Tube thickness m Ibm/ft Tube mass distribution per unit length my Ibm/ft Virtual added mass per unit length h - Damping ratio h- Structural damping ratio hTp - Two phase damping ratio h- Viscous damping ratio hSF - Squeeze film damping ratio K - Critical factor MHI - Mitsubishi Heavy Industries M0 Ibm/ft Average tube mass per unit length U, ft/s Critical flow velocity f Hz Tube natural frequency 6 - Logarithmic decrement U"n ft/s Nth mode effective flow velocity O(x)- Vibration mode Tn(x) - Nth vibration mode 3

p, p(x) Ibm/ft Fluid density distribution of water outside the tube in tube axis direction U, U(x) ft/s Flow velocity distribution orthogonal to tube axis in tube axis direction x ft Coordinate component along tube axis L ft Tube length SCE Southern California Edison SR, SR, (Nth mode) Stability ratio MITSUBISHI HEAVY INDUSTRIES, LTD.

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4. Assumption 4.1 Modeling assumption (1) Nominal tube thickness and nominal tube length are used in the evaluation model because the effect 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 supported condition at tubesheet is added.

(3) Contact condition between tube and active support points by the anti-vibration bar (AVB) is pin-supported.

of 2 (4) Modulus of elasticity of tube is interpolated based on the tube average temperature from table of ASME Boiler and Pressure Vessel Code, Sec II, Materials, 1998 Edition, 2000 addenda (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 virtual added 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).

f rD~po (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 effect

p. Average water density outside the tube of each region obtained from ATHOS analysis Do :Tube outside diameter P 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 side are assumed for the evaluation of the stability ratio of in-plane FEI. All active support points and 1 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 and support span of each evaluated tube. The inactive support will be one of the 2 supports at the span with the highest amplitude, whichever that has a higher hydraulic pressure. The maximum stability ratio in each inactive support location is shown as the result of the stability ratio with 1 inactive support.

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At (7) Type J stabilizers are assumed to be installed for all plugged tubes which have AVB wear indications. The additional structural damping ratio due to Type J stabilizer (split stabilizers installed 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 and Attachment-1 for details).

4.2 Open item There is no open item remaining.

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At

5. Acceptance Criteria The stability ratio against fluid elastic instability shall be less than 1.0. The analysis is performed in accordance with the procedures given in ASME code section III Appendix N-1 330 (Ref.2).

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At

6. Design Input 6.1 Geometry of tube bundle region Tube bundle consists of thermally treated Alloy 690 U-tubes which are supported in[ ]triangular pitch arrangement 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-240 Type 405 Stainless steel).

Nominal dimension of tube, TSPs and AVBs are listed in Table 6-1. The applicable design drawings to be referred are listed in Table 6-2.

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Ak Table 6-1 Nominal dimensions of tubes, TSPs, and AVBs Part Item Value Material Thermally treated SB-1 63 UNS N06690 Outside diameter 0.75 in Thickness 0.043 in Tubes Number of tubes 9727 Tube pitch 1.0 in Tube arrangement Triangular Material SA-240 Type 405 Thickness Number of TSPs TSPs Tube support span (between TSP centrals)

Tube support span (from TS to No.1 TSP) I Material SA-479 Type 405 Type AVBs Thickness Width Stabilizer Unit weight MITSUBISHI HEAVY INDUSTRIES, LTD.

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At Table 6-2 A plicable design drawings (Ref.3 to 20)

Drawing No. Title L5-04FU001 COMPONENT AND OUTLINE DRAWING 1/3 L5-04FU002 COMPONENT AND OUTLINE DRAWING 2/3 L5-04FU003 COMPONENT AND OUTLINE DRAWING 3/3 L5-04FU021 TUBE SHEET AND EXTENSION RING 1/3 L5-04FU022 TUBE SHEET AND EXTENSION RING 2/3 L5-04FU023 TUBE SHEET AND EXTENSION RING 3/3 L5-04FU051 TUBE BUNDLE 1/3 L5-04FU052 TUBE BUNDLE 2/3 L5-04FU053 TUBE BUNDLE 3/3 L5-04FU111 AVB ASSEMBLY 1/9 L5-04FU112 AVB ASSEMBLY 2/9 L5-04FU1 13 AVB ASSEMBLY 3/9 L5-04FU1 14 AVB ASSEMBLY 4/9 L5-04FU115 AVB ASSEMBLY 5/9 L5-04FU116 AVB ASSEMBLY 6/9 L5-04FU117 AVB ASSEMBLY 7/9 L5-04FU118 AVB ASSEMBLY 8/9 L5-04FU119 AVB ASSEMBLY 9/9 MITSUBISHI HEAVY INDUSTRIES, LTD.

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At 6.2 Thermal and hydraulic flow of steam generator secondary side The basic parameters for the thermal hydraulic analysis of unit-2 and 3 steam generators are shown in Table 6.2-1 to 6.2-4. As discussed in ATHOS analysis report (Ref. 22), the larger number of the plugged tubes of unit-2 (305 tubes for 2A) is used for the FEI evaluation. The flow characteristics of the tubes listed in Table 7.2-1 are obtained from ATHOS/SGAP analysis (See Ref.21 and 22 for detail) and used for the vibration analysis.

The distributions of flow gap velocity normal to the in-plane direction of the tube, flow density and void fraction are shown in Fig.6.2-3 to 6.2-11. Several of the flow gap velocity distributions indicate negative flow velocities at lower thermal power on the cold leg side since the water flow is more likely to go downward on the cold leg side because the circulation ratio is higher and the water flow rate compared with 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 flow velocity and mode shape in order to evaluate the actual tube vibration which is multi degrees of freedom system with beam type of vibration modes. Therefore, there is no adverse effect of negative flow velocity.

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Table 6.2-1 Basic parameters for calculation for 2A SG evaluation after plugging 50% 60% 70% 80% 90% 100% 100%withno Case plugging Plugging 305 305 305 305 305 305 0 869.5 1041.4 1213.3 1385.2 1557.1 1729 (50%) (60%) (70%) (80%) (90%) (100%)

RCS flow rate (gpm) *1 206,695 206,695 206,695 206,695 206,695 206,695 209,880 z0 cj~ Thot (Tsg-in) (°F)

'0 Tsg-out (°F)*2 2 0)

TcoId ('F)*

z Saturation Steam Pressure (psia) CD 2

Fouling Factor (ft hr°F /Btu) CD)

Tfeedwater (OF)

C Circulation Ratio Steam Mass Flow (lb/hr) r:j~ 3 Feed Water Mass Flow (lb/hr)*

Blowdown flow rate (gpm)

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 RV 0

C) inlet is caused by heat input from the reactor coolant pump.

C)

  • 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.

0

  • 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 the c-I (A

address 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 column 41 of 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.

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Table 6.2-2 Basic parameters for calculation for 2B SG evaluation after plugging 60% 70% 80% 90% 100% 100 % with no Case 50%

plugging Plugging*6 205 205 205 205 205 205 0 869.5 1041.4 1213.3 1385.2 1557.1 1729 (50%) (60%) (70%) (80%) (90%) (100%)

RCS flow rate (gpm) 207,726 207,726 207,726 207,726 207,726 207,726 209,880 z

0 C-, Thot (Tsg-in) (°F) 7 Tsg-out (OF)"*2 Cd, 0 2

TcoId (OF)* 0)

Saturation Steam Pressure (psia) I CD Fouling Factor (ft 2 hr°F /Btu)

Cn.

0 Tfeedwater (°F)

C-, Circulation Ratio Steam Mass Flow (lb/hr)

Feed Water Mass Flow (lb/hr) 3 C-,

Blowdown flow rate (gpm)

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 0

RV inlet is caused by heat input from the reactor coolant pump. 0

  • 3: Feedwater mass flow rate is the sum of the blowdown flow rate and the steam mass flow based on heat balance calculation.

z

  • 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 the SC) address of the plugged tubes of 2A SG.

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Table 6.2-3 Basic parameters for calculation for 3A SG evaluation after plugging 100% 100 % with no 50% 60% 70% 80% 90%

Case plugging Plugging*4 387 387 387 387 387 387 0 Thermal power (MWt) 869.5 1041.4 1213.3 1385.2 1557.1 1729 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-z 0

Thot (Tsg-in) (*F) -7 2 a

'0 Tsg-.out (F)"

2 TcoId (°F).

z Saturation Steam Pressure (psia) I 2 CD Fouling Factor (ft hr°F /Btu)

(n) 0 Tfeedwater (OF) '-3 Circulation Ratio Steam Mass Flow (lb/hr)

Feed Water Mass Flow (lb/hr) 3 Blowdown flow rate (gpm) -z F

Note

  • 1: Obtained by interpolating the flow rate of 0% plugging and 8% plugging. C 0
  • 2: RCS flow temperature at SG outlet is assumed to be 0.30 F lower than that at RV inlet. The 0.30 F temperature increase between the SG outlet and RV H

0 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: 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 the o

address of the plugged tubes of 2A SG. c~I (A 0 Page 20 of 149 S023-617-1-M1539, REV. 0

Table 6.2-4 Basic parameters for calculation for 3B SG evaluation after plugging 50% 60% 70% 80% 90% 100% 100 % with no Case plugging Plugging"4 420 420 420 420 420 420 0 869.5 1041.4 1213.3 1385.2 1557.1 1729 1729 Thermal power (MWt)

Thermal power (M ____ (50%) (60%) (70%) (80%) (90%) (100%) 1729 RCS flow rate (gpm) .' 205,545 205,545 205,545 205,545 205,545 205,545 209,880 z

0 Thot (Tsg-in) (°F) 0 2

Tsg.out (°F)'

TcoId (°F)*2 CD Saturation Steam Pressure (psia) (n Fouling Factor (ft2hr°F /Btu) ChD 0

LD Tfeedwater (°F)

C,' Circulation Ratio Steam Mass Flow (lb/hr) 3 Feed Water Mass Flow (lb/hr)"

~j)

Blowdown flow rate (gpm)

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 RV 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: 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 the address of the plugged tubes of 2A SG. C.'

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Tubes to be plugged of 2A SG 3 - 4, J, - j *.-

s 4 4...

121 A 1!.L - L 51 1 _ - -. - . . - . - . . . . -3. - . .- . .- . '- . . -S .- - F.j- - - "- . . . . .., . - _-

" 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 .

COL Fig. 6.2-1 Plugging tubes of 2A SG I,-

Fig.6.2-2 Tube plugging model of ATHOS for 2A SG MITSUBISHI HEAVY INDUSTRIES, LTD.

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r z

Ca 0 a

10 Ca CD Cn.

Y, C

Ca C

0 Ca 0 r 0 o

-V Fig.6.2-3 Flow Characteristics of Row 80 Column 70 (2A SG)

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r z0 0

CD (1) 0 C)

>~

Fig.6.2-4 Flow Characteristics of Row 80 Column 80 (2A SG)

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C12 z0 0

CD (1) 2 0 C,,

>H-Y, 41 Fig.6.2-5 Flow Characteristics of Row 100 Column 70 (2A SG)

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r z

_= o 0

C ,)

ri)

Y, C>

FER 0

CN Fig.6.2-6 Flow Characteristics of Row 100 Column 80 (2A SG) -&

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z 0

CA B 10 n.---

CICD 0

°0 CD

> -F1 Fig.6.2-7 Flow Characteristics of Row 120 Column 70 (2A SG) **

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z 0

0 0

Fig.6.2-8 Flow Characteristics of Row 120 Column 80 (2A SG)

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z 0

r:j~

z CD CD Y,

0 C)

K -I Fig.6.2-9 Flow Characteristics of Row 95 Column 85 (2A SG)

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K-z z -(D 0,

CD Yl ofRow125ColunFow Fig..2-0 8 Caraterstis (2 S0 Page 30 of 149 S023-617-1-M1539, REV. 0

z 0

CD

,- 0 CD 4n Fig.6.2-11 Flow Characteristics of Row 138 Column 84 (2A SG) -

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7. Methodology 7.1 Fluid elastic vibration The term "fluid elastic vibrations" is generally used to refer to self-excited vibration of tube bundles due to 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 is greater than the amount that the tubes can dissipate. The measure of the fluid-elastic vibration threshold for any given tube in the bundle (tube stability) is the ratio of the actual velocity of the fluid surrounding the tube to the critical fluid flow velocity for this particular tube. The critical flow velocity Uc required to generate fluid-elastic vibration is obtained using Connor's formula (Ref.23).

r 11/2 U' _ K [ m°* 2 ............................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. ... .

(3)

Where, UV Critical flow velocity f Tube natural frequency D,  : Tube outside diameter K Critical factor M0 :Average tube mass per unit length 5 Tube logarithmic decrement(= 2Trh) h Damping ratio PO Density of water outside the tube The critical flow velocity U, in eq. (3) is evaluated in case of tube vibration of single degree of freedom system with uniform cross flow along the tube axis. In actual tube, however, the vibration of the tube supported by the tube support plate is multi degrees of freedom system with beam type of vibration modes. Therefore, considering the vibration mode and fluid distribution, the effective flow velocity Ue, is evaluated in the following formula.

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Ak p___ U(x) 2.

  • 0 (X) dx 1 0 PC) u . ................................................................... (4 )

2 f L MW 04(x) dx Where, Uen Nth mode effective flow velocity (Pn(X) Nth vibration mode p(x) Fluid density distribution of water outside the tube in tube axis direction m(x) Tube mass distribution per unit length in tube axis direction U(x) Flow velocity distribution orthogonal to tube axis in tube axis direction x Coordinate component along tube axis PO Average density of water outside the tube m, :Average tube mass per unit length L  : Tube length The stability ratio is determined as follows in each vibration mode by calculating the ratio of eq. (3) and eq. (4).

SR . . . ...................................... ................................................. (5 )

Ucn where, 1/2

f. 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 is simply expressed as SR. The uncertainty of SR calculated by the methodology of this section is evaluated in Attachment-6.

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7.1.1 Damping ratio and Critical Factor Although the suggested value by ASME Sec. Ill Appendix N-1330 for damping ratio is 1.5% and the suggested value for critical factor is 2.4, the values based on recent experimental data are used in this evaluation as follows.

7.1.1.1 Damping ratio For U-bend tubes in two phase flow, there are four sources of damping: structural damping, two-phase damping, viscous damping and squeeze film damping.

" s + ýT + "+ 's. ................................................................................... (7 )

Where,
s :Structural damping ratio Two-phase damping ratio Viscous damping ratio

ýSF  : Squeeze film damping ratio MITSUBISHI HEAVY INDUSTRIES, LTD.

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At (1) Structural damping The structural damping ratio is estimated with the following experimental equation developed by Pettigrew (Ref.25 and 27). In the case of plugged tubes with Type J stabilizers, the additional damping 0.6% is added s j= N -1 [ 5,L in gas ........................................................................ (8)

,s = (N N- 1 0.5( Lgm 7 ,in liquid ................................................................ (9)

Where, 4S  : Structural damping ratio N Number of free spans at U-bend region N-1 AVB support points without assuming inactive AVB support points L' AVB width Ira Characteristic tube length: average of the longest three free spans lengths assuming 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).

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At (2) Two-phase damping The two-phase damping depends on the void fraction and fluid properties. Pettigrew's test result of the two 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 of homogeneous void fraction was obtained as shown in Figure 7.1.2.

The effective homogeneous void fraction is calculated by using the ATHOS outputs and following equation, considering vibration mode.

_ Jfg(x)¢ 2 dx SqZd2l= ........................................................................................... (10)

Where, Homogeneous void fraction

@

  • Vibration mode x Tube axis The two-phase damping along the tube length is calculated by using Pettigrew's data and the following equation Tp )f( ) 1 (D I) ........................................... .. (11) f([3)= P3/40 for 13< 40%

1 for 40% _<[3 _<70% ............................................. (12) 1 - (P3- 70) / 30 > 70% (for D , = ( 1+ 1 P/D ýo P ...................................................................................... (13) m 0 = nzm, + n p + n , ......................................................................................... (14 )

= fD°p° f(DOe/OD)2 + I...........................................(15 l(D I/D o)2 -I(5 4

Where,

ýTP Two-phase damping P3 Homogeneous void fraction D Tube outside diameter MITSUBISHI HEAVY INDUSTRIES, LTD.

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Document No. L5-04GA567(6) jAk P Tube pitch po Po Density of secondary mixture flow (Calculated by ATHOS)

Pi Density of secondary liquid flow Average tube mass per unit length mv Virtual added mass per unit length Mass of primary coolant in tube per unit length mt Mass of tube metal per unit length 1- 7 Ul 0' CM6 0 E 0 0 123o 0 ca5 00 (V4 co 4 t1=

A*

.3 9 0 A A I--

_0 2 -'0 0:

A Air-Water Stearn-Waler Freon

, Nomal Trangle A Normal Triangle

  • Frwn-22 (NTI)

E w V Rotated Triangle T Rotated Triangle 0 Froon-22 (RT) o0 0 NortndrSquare N Normal Square 0 Froon-l I (RT) t*J t

_,0 0 RolaWed Squae 0 20 40 60 80 100 Void Fraction (%)

(VTO)D = CT-A(pD /m)-'

2 {[1 + (DID,)'))/[I - (DID,)2]2 }-'

Fig 7.1-2 Effect of void fraction on two-phase damping MITSUBISHI HEAVY INDUSTRIES, LTD.

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A (3) Viscous damping Since the viscous effects are negligibly small in high void fraction (homogeneous void fraction is 40% or greater) (Ref.27), it is not taken into account in this analysis.

(4) Squeeze film damping Squeeze film damping takes place at the supports and the following equation is based on the available experimental data. (Ref.26)

YSF =( N - { f

  • mo )(. L., ' ......................................................................... (16)
Where, SF Squeeze film damping Secondary flow liquid density D Tube outside diameter N Number of free spans at U-bend region N-1 AVB support points without assuming inactive AVB support points f Natural frequency L AVB width Im Characteristic tube length M0 Average tube mass per unit length MITSUBISHI HEAVY INDUSTRIES, LTD.

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Ai For unplugqed tubes The support damping (structural and squeeze film) depends on the void fraction. Since the structural damping 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. The effective wetness of supports is estimated to determine the damping ratio used for the SR evaluation by the following equations based on the assumptions listed below. (The basis of these assumptions is described 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 and squeeze film damping is effective.

When the void fraction is [ ]there is no liquid film on the surface of tube. The support is considered "dry," structural damping corresponds to the gas condition and squeeze film damping is not effective.

When the void fraction is between )

) there is a discontinuous liquid film on the surface of tube and the support is considered partially wet. The approach to calculate damping in this void fraction range is described below.

N-1 s a ........ ......................................... ............... (17) a i ........................................................... (18 )

N DS N......

N - I - N s .......................................... ....................................... (19)

Where, N Number of free spans in U-bend N - 1 Number of AVB support points in U-bend NWS Number of effectively wet AVB supports NDS Number of effectively dry AVB supports i :AVB support points a: Void fraction at AVB support points ai Function of void fraction at AVB support points MITSUBISHI HEAVY INDUSTRIES, LTD.

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At By replacing the (N-i/N) term in equations 8 and 9 and combining, structural damping adjusted for void fraction becomes:

j......... . . . . (20)

Similarly replacing the (N-i/N) term in equation 16 with (Nws/N), squeeze film damping adjusted for void fraction becomes:

2 Ni,'s (2 460) plD L

ýSF ,

Nf

  • no .

(.. ............................................................... (21)

For pluaqed tubes The plugged tubes are assumed to be in wet condition despite the void fraction. Equations 7 and 16 are used for structural and squeeze film damping, respectively.

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At 7.1.1.2 Critical Factor The effect of void fraction, the effect of pitch to diameter ratio, the ratio between In-plane & Out-of-plane and the effect of flow direction are considered to estimate the Connor's constant as follows.

(1) Effect of the void fraction Based on MHI experimental data (Ref.28), the critical factor K is evaluated using the equation shown in Figure 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 the triangular 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 mode and using the following equation in the same manner as the two-phase damping. The obtained critical factor obtained is K1, when the value of P/D is 1.33.

K, =( ) .................................................... (2 2 )

-f/3(x)O252cy

_= _' _ . ......................................................... ..................... (23)

Where, Homogeneous void fraction Vibration mode x Tube axis MITSUBISHI HEAVY INDUSTRIES, LTD.

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Ak

-/

Fig.7.1-3 MHI Experimental Test Result (Relation between Critical Factor and Superficial Void Fraction)

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Table 7.1-1 MHI Test Condition Tube diameter Tube pitch Number of tubes ii Flow condition Pressure Temperature Suoerficial void fraction Fig.7.1-4 MHI Test Equipment MITSUBISHI HEAVY INDUSTRIES, LTD.

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(2) Effect of P/D The greater the pitch is, the higher the critical velocity will be. Since the tube bundle has index and the nominal pitch depends on the number of tube Row, the effect of the tube pitch to diameter ratio (P/D) is added 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 to be evaluated.

P, -- P , + P + . ..................................................................................... (24 )

3 Where, Evaluated tubes ,

Pe Effective pitch P1,P2,P3 Pithes defined in Fig.7.1-5 P, Fig.7.1-5 Effective pitch The effect of the tube pitch on the Connor's constant is calculated by using the following equation based on Pettigrew's experimental data (Ref.29).

Kp=4.76(P-D )/D+0.76 .................................................................................. (25)

KpI Ko = K P' D x K 1 ................................................................................ (26 )

Where, KP "Equation 21 K1 Critical Factor based on MHI experimental test results by taking into account of the effect of void fraction (P/D=1.33)

Kp.P/D  : Critical Factor based on Pettigrew's experimental test results by taking into account of the effect of P/D Kp.P/D=.33 "Critical Factor based on Pettigrew's experimental test results when P/D is 1.33 Ko Best estimated critical factor of out-of-plane FEI MITSUBISHI HEAVY INDUSTRIES, LTD.

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(3)Critical Factor of In-plane FEI In accordance with the experiments by T. Nakamura (Ref.30), FEI is observed in the in-plane direction in a single-phase air flow when the tube pitch-to-tube ratio (P/D) is small. The Connor's constant of In-plane FEI is estimated in accordance with the following equation based on Nakamura's experimental data. The ratio between the Connor's constant of in-plane FEI and out-of-plane FEI depends on P/D as shown in Figure 7.1-6. In order to reinforce the basis of Connor's constant used for In-plane FEI evaluation, MHI performed air flow test by using the straight tube bundle of the triangular pitch as shown in Fig. 7.1-7. The ratio of Connor's constant between in-plane and out-of-plane FEI obtained by MHI test result is consistent with Nakamura's experimental data as shown in Fig. 7.1-6. Therefore, the Connor's constant of in-plane FEI for SONGS RSGs is calculated based on the effective tube pitch calculated 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 FEI Ki *Best estimated critical factor of In-plane FEI Ko Best estimated critical factor of out-of-plane FEI Ratio K Vc(In-flow)/Vc(Out-of-flow)

Ratio ol Note critical fl ýJ.city K=Vc(ln-plane) fVc(0ut-4*plane) 1.5 Air- 2.7 voletteetal Water (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)

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At I-(a) Test equipment r

k-.

(b) Test Results Fig.7.1-7 MHI air flow test MITSUBISHI HEAVY INDUSTRIES, LTD.

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(4) Effect of Flow Direction The 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 of the critical velocity will be.

The effect of the flow direction on the critical velocity (increase ratio" a(e)") is determined based on the test result shown in Fig.7.1-8 (Ref.31). "a(8)" is defined by the upstream critical flow velocity; not in-plane flow velocity a (O ) _=U c(_ ) . . .................................................................................... (28)

Uc(Odeg)

Where, 0 Angle of Flow direction Uc Critical velocity 0.41 FLCW FLOW 000

-6 °- , -

0 .1 . . -

o*0oO.

  • 000.@

00006 o 0 deg 0101 20 20 00 PMALLflL NOOMA TALANGLE FLOW DIRECTION dcjrc) "RII

. Fig. 1O Ellectot Incident flOWdirection on critical Velocity Parallel (0 deg.) Normal triangle (30 deg.)

Fig.7.1-8 Effect of the flow direction (Ref.31)

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Ak-Stability ratio is usually calculated by using in-plane flow velocity V. On the other hand, the function a( e) is defined by the magnitude of normal flow velocity Vn to the tube. Therefore, Ki or K0 are multiplied by the velocity ratio Vn/V and function a(O ) as shown in Fig.7.1-9, then K used for the analysis 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, a Effect of Flow direction Vn Average in-plane velocity V Magnitude of flow velocity Best estimated critical factor of In-plane FEI K,

Best estimated critical factor of out of plane FEI K.

Best estimated critical factor used for the evaluation Row Magnitude of Flow Column Fig.7.1-9 Effect of flow direction MITSUBISHI HEAVY INDUSTRIES, LTD.

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A 7.2 Calculation model Stability analyses are carried out in the following manner.

(1) Tube row The tubes shown in Table 7.2-1 and Fig.7.2-1 are selected by SCE for the evaluation (see A Attachment-7 for details).

Table 7.2-1 Evaluated Tubes Row Column 80 70 80 80 100 70 100 80 120 70 120 80 95 85 125 85 138 84

  • Plugged tubes O Representative tube for OA - ,-- -- -

140

- O .. 135 130 O' 0.-

125 i ,*

  • S i . S S 120 115

-0 110 105 100 =

95 90 85 o------..0-*... --- i 80 t-75 70 60 65 70 75 80 85 COL Fig.7.2-1 Evaluated Tubes MITSUBISHI HEAVY INDUSTRIES, LTD.

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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 including node number and coordinate of TSP elevation are shown in Fig. 7.2-1 to 7.2-9.

MITSUBISHI HEAVY INDUSTRIES, LTD.

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At r

Fig. 7.2-1 Calculation model for Row 80 Column 70 MITSUBISHI HEAVY INDUSTRIES, LTD.

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At Fig. 7.2-2 Calculation model for Row 80 Column 80 MITSUBISHI HEAVY INDUSTRIES, LTD.

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Aok Fig. 7.2-3 Calculation model for Row 100 Column 70 MITSUBISHI HEAVY INDUSTRIES, LTD.

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-At Fig. 7.2-4 Calculation model for Row 100 Column 80 MITSUBISHI HEAVY INDUSTRIES, LTD.

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At I-2 Fig. 7.2-5 Calculation model for Row 120 Column 70 MITSUBISHI HEAVY INDUSTRIES, LTD.

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At K-Fig. 7.2-6 Calculation model for Row 120 Column 80 MITSUBISHI HEAVY INDUSTRIES, LTD.

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At Fig. 7.2-7 Calculation model for Row 95 Column 85 MITSUBISHI HEAVY INDUSTRIES, LTD.

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A Fig. 7.2-8 Calculation model for Row 125 Column 85 MITSUBISHI HEAVY INDUSTRIES, LTD.

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At I-Fig. 7.2-9 Calculation model for Row 138 Column 84 MITSUBISHI HEAVY INDUSTRIES, LTD.

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8. Computation Results 8.1 Out of plane FEI analysis results The 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 SG Table 8.1.1-1 All support points are active and the thermal power is 70%

No olugging Table 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 SG Table 8.1.2-1 1 support point is inactive and the thermal power is 70%

No plugaina Table 8.1.2-2 1 support point is inactive and the thermal power is 100% with no plugging MITSUBISHI HEAVY INDUSTRIES, LTD.

Page 60 of 149 S023-617-1-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 /*X Damping Ratio Critical Average Average Maximum Critical Effective Tube Location Tube natural h(%) coefficient fluid void void flow flow Stability of inactive frequency density fraction fraction velocity velocity rati6 support Mode point f(Hz) Structural Two Squeeze Row Col dal phase film Total K1 Ko Ke K Po(ibfft 3 ) [-] [-] Uc(ft/sec) Ue(ft/sec) damping damping damping z

0 80 70 80 80 C,=

100 70 CD

--n cn 1 0(*) 80(')

0 120 70 120 80 95(*) 85(')

125 85 138 84 Note(*): Plugged tube with Type J stabilizer C,

Page 61 of 149 S023-617-1-M1539, REV. 0

Table 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 active A Location of inactive Tube natural Damping Ratio Critical Average Average Maximum Critical Effective ponsupport frequency h(%) coefficient fluid void void flow flow Stability point Mode density fraction fraction velocity velocity ratio Structural Two Squeeze 3 RowSrcCaol phase film Total K1 Ko Ke K Po(lb/ft ) [-1 [-] Uc(ftlsec) Ue(ftlsec) damping damping damping 80 70 80 80 z 0

100 70 0 CD n

100 80 ,=-

"o 120 70 CD 0

120 80 C,'

95 85 C,' 125 85 138 84 I~

CD 41~ '-

0~\

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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 inactive Location of inactive Damping Critical Average Average Maximum Critical Effective Tube support Tube natural Ratio coefficient fluid void void flow flow Stability point Mode h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeeze (Ib/ft) [-] Uc(ft/sec) Ue(ft/sec)

Row Col phase film Total KI Ko Ke K PO I I- damping damping damping 80 70 B03 C

c.4~ 80 80 B03 100 70 B03 100(*) 80(*) B03 C 120 70 B03 CI) 120 80 B03 CI) 95(') 85(') B03 125 85 B03 138 84 B04 Y0 C)

Note(*): Plugged tube with Type J stabilizer 0

'-I Page 63 of 149 S023-617-1-M1539, REV. 0

Table 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 inactive A Location of inactive Damping Critical Average Average Maximum Critical Effective Tube support Tube natural Ratio coefficient fluid void void flow flow Stability point Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeeze Row Col phase film Total K1 Ko Ke K po(Ift3) [-] [-] Uc(ft/sec) Ue(ftfsec)

RowCol damping damping damping 80 70 B03 80 80 B03 z0 10 100 70 B02 02 100 80 B02 120 70 B02 CD CO 120 80 B02 0 95 85 B03 125 85 B02 138 84 B02 0

as K

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At 8.2 In-plane FEI analysis results The 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 SG Table 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 pluaaina Table 8.2.1-7 6 consecutive support points are inactive and the thermal power is 100% with no plugging (2) Assuming 8 support points are inactive:

For 2A SG Table 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 plugging Table 8.2.2-7 8 consecutive support points are inactive and the thermal power is 100% with no plugging MITSUBISHI HEAVY INDUSTRIES, LTD.

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(3) Assuming 10 support points are inactive:

For 2A SG Table 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 plugging Table 8.2.3-7 10 consecutive support points are inactive and the thermal power is 100% with no plugging (4) Assuming All support points are inactive:

For 2A SG Table 8.2.4-1 All consecutive support point:s are inactive and the thermal power is 50%

Table 8.2.4-2 All consecutive support point:s are inactive and the thermal power is 60%

Table 8.2.4-3 All consecutive support point:s are inactive and the thermal power is 70%

Table 8.2.4-4 All consecutive support point:s are inactive and the thermal power is 80%

Table 8.2.4-5 All consecutive support point:s are inactive and the thermal power is 90%

Table 8.2.4-6 All consecutive support point:s are inactive and the thermal power is 100%

No plugging Table 8.2.4-7 All consecutive support poirnts are inactive and the thermal power is 100% with no plugging MITSUBISHI HEAVY INDUSTRIES, LTD.

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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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeezefilm po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)

Row 0Col dampin phase Total Kf1 Ko K Ke K damping damping damping z 0

C,' 80 70 0

'a 80 80 CD 100 70 C,

100(*) 80(.) 0 C,' 120 70 120 80 95(*) 85(*)

125 85 Y0 138 84 IAý Note(*): Plugged tube with Type J stabilizer Page 67 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Rwof(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 damping 80 70 z0 80 80 0

100 70 ,.-i CD 100(*' 80(') 6 CD 120 70 Cn 0

120 80 95() 85(*) 6 125 85 138 84 tz 0

Note(*): Plugged tube with Type J stabilizer 1j4a

)40 Y

>0 Page 68 of 149 S023-617-1-M1539, REV. 0

Table 8.2.1-3 In-plane FEI Analysis Results for 2A SG when the thermal power is 70% and 6 consecutive support points are inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Two po(b/f3) [-] [-] Uc(ft/sec) Ue(ft/sec)

Row Col f(Hz) Structural phase Squeeze film Total K1 Ko Ki Ke K damping damping 80 70 Z 0

"{3 80 80 0

100 70 -6 z

1 00M 80M CD 120 0 70 120 80 W.(

95(*) 85(1) 6 125 85 0

138 84 Note(*): Plugged tube with Type J stabilizer

ýk 4-I Page 69 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row ColRo o f(Hz) Structural ig Two phase Squeeze apn film Total K1 Ko Ki Ke K po(lb/ft3) [-1 [-] Uc(ft/sec) Ue(ft/sec)

____ ____ damping_____damping damping damingphase 80 70 z

80 80 0

'0 100 70 100M 80(1)

CD 120 70 W.

0 120 80 "33 95(*) 85(*)

/

125 85 138 84 Note(*): Plugged tube with Type J stabilizer [ýý

)100.

Page 70 of 149 S023-617-1-M1539, REV. 0

Table 8.2.1-5 In-plane FEI Analysis Results for 2A SG when the thermal power is 90% and 6 consecutive support points are inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Two Squeeze3film p(Ib/ft3) [-] Uc(ft/sec) Ue(ft/sec)

Row Col f(Hz) Structural phase Total KI Ko Ki Ke K damping damping damping 80 70 Z 0

7

'0 80 80 CD M"

100 70 0) 100(') 80(*)

Mj 120 70 120 80 C-,

95(*) 85(*) 6 125 85 C0 138 84 Note(*): Plugged tube with Type J stabilizer Page 71 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Co Ro ~ f(Hz) Structural apn Two Squeeze phase dmig film Total K1 KO Ki Ke K po(lb/ft3 ) [-] [-] Uc(ft/sec) Ue(ft/sec) damping damping damping 80 70 z

80 80 0

,0 100 70

"(3 100(*) 80(*) CD 10 70 5.

CD 120 C, 120 80 95(') 85(*)

125 85 138 84 Note(*): Plugged tube with Type J stabilizer ký

)10.

Page 72 of 149 S023-617-1-M1539, REV. 0

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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeeze film po(lb/ft3) H[ [-] Uc(ft/sec) Ue(ft/sec)

Row Col phase Total K1 K0 Ki Ke damping damping damping 80 70 z

80 80 0 U)'

100 70 100 80 0.n 0

3 W, _D 120 70 120 80 95 85 125 85 138 84 CD 0

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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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Two p(bf3 - - cf/e)U~tsc Row 0ol f(Hz) Structural phase Squeeze film Total K Ko K Ke KUc(fsec) Ue(ftsec) damping dampin damping 80 70 rj2 80 80 I0 100 70 z

I 80()

100(')

120 70 6 ý 120 80 cj~

95(*) 85(*)

0 125 85 6

138 84 Note(*): Plugged tube with Type J stabilizer kRý 0 Vh Page 74 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Col f(Hz) Structura w Two Squeezefilm Total H I [-]

dampin dmi 9 ph damping Total K1 Ko Ki Ke K P°(Ib/ft3 ) Uc(ft/sec) Ue(ftlsec) damping dmi 80 70 80 80 I0 100 70 CDl 100(*) 80(*)

120 70 120 80 95(.) 85(*)

0 125 85 6

138 84 Note(*): Plugged tube with Type J stabilizer V~~1 I

0h Page 75 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Squeeze film po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)

Row Col phase Total K1 Ko Ki KO K damping damping damping 80 70 80 80 I0

'0 100 70 CD 100(*) 80(*)

120 70 120 80 95(*) 85(*)

0 125 85 138 84 0 Note(*): Plugged tube with Type J stabilizer

ýk~

C) 4zi Page 76 of 149 S023-617-1-M1539, REV. 0

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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Squeeze film po(lb/ft3) [-] [ Uc(ft/sec) Ue(ft/sec)

Row Col damping phase Total K1 Ko Ki Ke K damping damping damping 80 70 z 0,=

6 80 80 rj~

100 70

=3 100(*) 80(*)

120 70 6 C,)

120 80 0

C-, 95(*) 85(*)

125 85 03 O

Y,,3 0

138 84

-L.-

CD Note(*): Plugged tube with Type J stabilizer Page 77 of 149 S023-617-1-M1539, REV. 0

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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Col n da Pase Squeezefilm lmpin Total Ki Ko K Ke po(lb/ft3) [-] [-] Uc(ftlsec) Ue(ft/sec)

___ _______ damping dapn 80 70 z

80 80 0,=

C,' .6 100 70 0 rj~

z 100( 0(//

° CD

=3 120 70 CD O

_j.

120 80 C')

95(*) 85(*)

C" 125 85 138 84 0 0

C Note(*): Plugged tube with Type J stabilizer 0

>~0 Page 78 of 149 S023-617-1-M1539, REV. 0

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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Col Two po(Ib/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec) f(Hz) Structural phase Squeeze film Total K1 Ko Ki Ke K damping damping damping 80 70 80 80 z0 100 70 0 100) 80(*)

6 CD 120 70 (n.

0i 120 80 C,'

95(*) 85(*)

6 rj~

125 85 0

138 84 Note(*): Plugged tube with Type J stabilizer 0 CD Y.,

Page 79 of 149 S023-617-1-M1539, REV. 0

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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Two p(bf3) - - cf/e)U~tsc Row Col f(Hz) Structural phase Squeeze film T(lbft ) Uc(ftlsec) Ue(ftlsec) damping damping damping Total K1 Ko Ki K, K 70 80 z 0

CI) 80 80

'0 Cl, 100 70 0) 0-i 100 80 Cn 120 70 Cl, 120 80 95 85 125 85 138 84 1 0t o Y '-

> G8 Page 80 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row 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 K damping 80 70 z0 80 80 0 C,,

100 70 CD 100(o) 80(*)

CD.

0 120 70 120 80 95(*) 85(*)

125 85 138 84 Note(*): Plugged tube with Type J stabilizer oc Page 81 of 149 S023-617-1-M1539, REV. 0

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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Col f(z Cf(Hz) trcualp Structural phase Two dmig film Squeeze Total K1 Ko Ki Ke K po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ftlsec) d damping damping 80 70 z

80 80 0 CI) 100 70 ")

CI)

CD 100M 80(*)

ZI 120 70 CD.

0 120 80 95(*) 85(*)

CI) 125 85 138 84 0 Note(*): Plugged tube with Type J stabilizer V, N Page 82 of 149 S023-617-1-M1539, REV. 0

Table 8.2.3-3 In-plane FEI Analysis Results for 2A SG when the thermal power is 70% and 10 consecutive support points are inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Co f(Hz) Structural Two Squeezefilm po(Ib/ft) Uc(ft/sec) Ue(ft/sec) tur damping phase damping d ilm damping Total K1 Ko Ki Ke K 80 70 Z

80 80 0 C,,

100 70 C,,

CD 100(*) 80(*) 10 120 70 Cn.

0n 6

120 80 95(*) 85(*)

Cj2 125 85 138 84 U 0

Note(*): Plugged tube with Type J stabilizer

ýk )

1111 CD C)

>J ~

Page 83 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeeze film po(lb/ft3 ) [-] [-] Uc(ft/sec) Ue(ft/sec)

Row Cola phase Total K1 Ko Ki Ke damping damping damping 80 70 Z

0 80 80 100 70 100M) 80C) 6L :2.

0 120 70

3 120 80 95(*) 85(*)

125 85 138 84 C 0

Note(*): Plugged tube with Type J stabilizer 0

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Table 8.2.3-5 In-plane FEI Analysis Results for 2A SG when the thermal power is 90% and 10 consecutive support points are inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Squeeze film T po(Ib/ft3 ) [-] [-1 Uc(ft/sec) Ue(ft/sec)

Row Ctrcdamping phase dmigdamping damping Total K1 Ko Ki Ke K 80 70 z0 80 80 rj~

100 70 C,,

CD 100(') 80(')

k (D 120 70 C,.

0 120 80 C,,

95(M 85(*)

C,,

125 85 F

138 84 0E Note(*): Plugged tube with Type J stabilizer 0

Page 85 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Squeeze film po(lb/ft3 ) [-] [-] Uc(ft/sec) Ue(ft/sec)

Row Col dal phase damping Total K1 KO K Ke damping damping damping 80 70 Z

80 80 0 100 70 0D 100(*) 80(1) 6 CD 120 70 tn.

0 120 80 95(*) 85(*)

6 125 85 CD 0

138 84 0 Note(*): Plugged tube with Type J stabilizer 0

Y,J Page 86 of 149 S023-617-1-M1539, REV. 0

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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Row Col f(Hz) Structural Two Squeeze film po(Ib/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec) phase damping damping Total K1 K Ki K K damping 80 70 z

80 80 0 r.j~ '0 0

100 70 rj, 100 80 CD 120 70 Cn.

0 LO 120 80 95 85 r.j~

125 85 138 84 C)

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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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeeze film po(Ib/ft) [-] [-] Uc(ft/sec) Ue(ft/sec)

Row Col phaseToa damping damping damping K1 K i e K z

0 80 70 0

X, 80 80 X,

CD 100 70 0)

C) 100(*) 80(*)

120 70 Y,

120 80 N 95(*) 85(*) (' 0 125 85 138 84 0 Note(*): Plugged tube with Type J stabilizer 49 0-\

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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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Two p0Ibf3) [-] [-] Uc(ft/sec) Ue(ftsec)

Ki Ke K dampingfilm Row Col f(Hz) Structural phase Squeeze Total K1 Ko damping damping 80 70 Z

0 80 80 0

100 70 CD 100(*) 80(*'

0) 120 70 0

120 80 95() 85M' 6ý 125 85 138 84 Note(*): Plugged tube with Type J stabilizer Y0 Page 89 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeeze film po(lb/ft3 ) [-] [-] Uc(ft/sec) Ue(ft/sec)

Row Col dal phase damping damping damping Total K1 Ko Ki Ke K 80 70 z

0 80 80 100 70 3 3 100(*) 80(')

CD 120 70 (n.

0 120 80 95(*) 85(*)

125 85 138 84 Note(*): Plugged tube with Type J stabilizer

'z CDJ Page 90 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural ose Squeeze film po(lb/ft3 ) [-] [-] Uc(ft/sec) Ue(ft/sec) damping damping damping 80 70 z

80 80 0 100 70 0

100(*) 80(') CD 0) 120 70 120 80 95(*) 85(*)

125 85 138 84 I

  • Note(*): Plugged tube with Type J stabilizer C)

>~

( 'A!:7 Page 91 of 149 S023-617-1-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 inactive z0 0

6 CD (n.

0 0

Note(*): Plugged tube with Type J stabilizer Y0 C~~-

>A Page 92 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio Ro o f(Hz)

(z structural tutrlSqueezeTwo film po(Ib/f3 p(bf [-] [-] Uc(ft/sec) Ue(ft/sec)

Row Col damping phase damping Total K1 Ko Ki Ke K dampinga 80 70 Z

80 80 0 0

100 70 'a

,0 0

1 00() 80(1) 120 70 O 120 80 95(") 85(1) 125 85

© 138 84 t-Note(*): Plugged tube with Type J stabilizer 0

_Rý

'C Page 93 of 149 S023-617-1-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 inactive Tube Damping Critical Average Average Maximum Critical Effective Tube natural Ratio coefficient fluid void void flow flow Stability Mode frequency h(%) density fraction fraction velocity velocity ratio f(Hz) Structural Two Squeezefilm po(lb/ft3) [-] [-] Uc(ft/sec) Ue(ft/sec)

Row Col dal damping phase damping dampin damping Total K1 Ko Ki Ke K 80 70 z

0 80 80 100 70 '0 100 80 CD 120 70 CD.

0i

3 120 80 95 85 125 85 138 84 C)

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9. Reference
1) 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 2000 addenda.
3) L5-04FU001 the latest revision, Component and Outline Drawing 1/3
4) L5-04FU002 the latest revision, Component and Outline Drawing 2/3
5) L5-04FU003 the latest revision, Component and Outline Drawing 3/3
6) L5-04FU021 the latest revision, Tube Sheet and Extension Ring 1/3
7) L5-04FU022 the latest revision, Tube Sheet and Extension Ring 2/3
8) L5-04FU023 the latest revision, Tube Sheet and Extension Ring 3/3
9) L5-04FU051 the latest revision, Tube Bundle 1/3
10) L5-04FU052 the latest revision, Tube Bundle 2/3
11) L5-04FU053 the latest revision, Tube Bundle 3/3
12) L5-04FU111 the latest revision, AVB assembly 1/9
13) L5-04FU112 the latest revision, AVB assembly 2/9
14) L5-04FU113 the latest revision, AVB assembly 3/9
15) L5-04FU114 the latest revision, AVB assembly 4/9
16) L5-04FU115 the latest revision, AVB assembly 5/9
17) L5-04FU1 16 the latest revision, AVB assembly 6/9
18) L5-04FU117 the latest revision, AVB assembly 7/9
19) L5-04FU1 18 the latest revision, AVB assembly 8/9
20) L5-04FU119 the latest revision, AVB assembly 9/9
21) 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 on internal SG thermal hydraulics parameters
23) 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 Design Guidelines,Journal of Pressure Vessel Technology Vol.133
26) M.J. Pettigrew.,et.al.,2003,"Vibration analysis of shell-and-tube heat exchangers" Journal of Fluids and Structures 18 (2003) 469-483
27) S. M. Fluit and M. J. Pettigrew, "Simplified method for predicting vibration and fretting-wear in nuclear steam generator U-bend tube bundle", ASME PVP 2001 Vol.420-1
28) WJS16263, MHI Test Report of Fluid Elastic Vibration
29) M.J. Pettigrew.,et.al.,2000, "The effects of tube bundle geometry on vibration in two-phase cross-flow",Flow Induced Vbration, Ziada&Staubi(eds) 2000 Balkema, Rotterdam ISBN9058091295
30) Flow-Induced VibrationMeskell & Bennett (eds) ISBN 978-0-9548583-4-6, "Study on In-flow Fluid-elastic Instability of Circular Cylinder Arrays"], T.Nakamura, Y.Fujita, T.Oyakawa, Y.NI. July 2012
31) H.C.Yeung, 1983, "The effect of Approach Flow Direction on the Flow-Induced Vibrations of a Triangular Tube Array", Transaction of ASME Vol.105
32) L5-04GA587 the latest revision, Test result for damping ratio added by the stabilizer inserted for short length (Row No. 106)

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At Table I-1 Input and Output file name of out of plane FEI evaluation for 2A SG when all support points are active A Thermal Row Column Input 1)

Power(%) Output 1) 80 70 _

80 80 100 70 100 80 70 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 100 80 120 70 (No Plug) 120 80 95 85 125 85 138 84 _____

Table 1-2 Input and Output file name of out of plane FEI evaluation for 2A SG when 1 support points are inactive Thermal Row Column Input 1)

Power(%) Output 1) 80 70 80 80 100 70 100 80 70 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 100 80 120 70 (No Plug) 120 80 95 85 125 85 138 84 ____

Notes:

1) All files are saved in the directory as below:

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At Table 1-3 Input and Output file name of in-plane FEI evaluation for 2A SG when 6 consecutive support points are inactive (1/2)

Thermal Row Column Input 1) Output 1)

Power(%)

80 70 ,

80 80 100 70 100 80 50 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 60 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 70 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 80 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 90 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 100 120 70 120 80 95 85 11 125 85 138 84 .-

Notes: 1) All files are saved in the directory as below: IA Page 98 of 149 S023-617-1-M1539, REV. 0

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At Table 1-3 Input and Output file name of in-plane FEI evaluation for 2A SG when 6 consecutive support points are inactive (2/2)

Thermal Row Column Input 1)

Power(%) Output 80 70 80 80 100 70 100 100 80 120 70 (No Plug) 120 80 95 85 125 85 11 138 84 1 Notes: 1) All files are saved in the directory as below:

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At Table 1-4 Input and Output file name of in-plane FEI evaluation for 2A SG when 8 consecutive support points are inactive (1/2)

Thermal Power(%) Row Column Input 1) Output 1) 80 70 80 80 100 70 100 80 50 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 60 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 70 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 80 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 90 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 100 120 70 120 80 95 85 125 85 138 84 1.

Notes: 1) All files are saved in the directory as below:

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Table 1-4 Input and Output file name of in-plane FEI evaluation for 2A SG when 8 consecutive support points are inactive (2/2) A Thermal Power(%) Row Column Input ) Output 1) 80 70 80 80 100 70 100 100 80 120 70 (No Plug) 120 80 95 85 125 85 138 84 Notes: 1) All files are saved in the directory as below:

I I IA Page 101 of 149 S023-617-1-M1539, REV. 0

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At Table I-5 Input and Output file name of in-plane FEI evaluation for 2A SG when 10 consecutive support points are inactive (1/2) 14\

Thermal Poer(%) Row Column Input 1)

Power(%) Output 1) 80 70 _

80 80 100 70 100 80 50 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 60 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 70 120 70 120 80 95 85 125 85 138 84 80 70 80 80 1 100 70 100 80 80 120 70 120 80 95 85 125 85 138 84 1 80 70 80 80 100 70 100 80 90 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 100 120 70 120 80 95 85 125 85 138 84 "-.

Notes: 1) All files are saved in the directory as below:

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At-Table I-5 Input and Output file name of in-plane FEt evaluation for 2A SG when 10 consecutive support points are inactive (2/2) A Thermal Row Column Input 1)

Power(%) Output 80 70 r 80 80 100 70 100 100 80 120 70 (No Plug) 120 80 95 85 125 85 138 84 Notes: 1) All files are saved in the directory as below:

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Ati Table 1-6 Input and Output file name of in-plane EIl evaluation for 2A SG when 12 consecutive support points are inactive (1/2) Z6\

Thermal Row Column Input Output 1)

Power(%)

80 70 80 80 100 70 100 80 50 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 60 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 70 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 80 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 90 120 70 120 80 95 85 125 85 138 84 80 70 80 80 100 70 100 80 100 120 70 120 80 95 85 125 85 1 138 84 t A Notes: 1 ) All files are saved in the directory as below:

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At Table 1-6 Input and Output file name of in-plane FEI evaluation for 2A SG when 12 consecutive support points are inactive (2/2)

Thermal Row Column Input 1)

Power(%) Output 80 70 80 80 100 70 100 100 80 120 70 (No Plug) 120 80 95 85 125 85 138 84 Notes: 1) All files are saved in the directory as below:

MITSUBISHI HEAVY INDUSTRIES, LTD.

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Attachment-2 Evaluation of Liquid Film Thickness of Tube at AVB Support Point

1. Summary In order to estimate the effect of void fraction on the squeeze film damping, the relation between the liquid film thickness of tube at each AVB support point and void fraction is evaluated as shown in Table-1.

Table-1 Relation between liquid film thickness of tube and void fraction Void fraction Liquid Film Condition Figure No Dry out Fig.l-1 Discontinuous Dry &Wet Fig.1-2 Continuous Wet Fig.1-3 Tube Droplet AVB 0 Liquid film (Thickness :6)

S 0

S e from the S point (1*)

S 0 0 **

  • 5 0 eS S 0

Fig.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 be consistent with the figures above as described in Attachment-4.

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2. Assumption of Liquid Film Thickness Fig.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)~=2S1 (1) 2 1*= dsin0 (2) 2 The thickness of the continuous liquid film is [ ) which is obtained in Fig.2 by assuming the effective distance from the contact point for squeeze film damping is I

)The basis of[ )of the effective distance is described in Attachment-3.

The minimum thickness of discontinuous liquid film is assumed to be[ }whicl is comparable to the degree of surface roughness of tube.

L Fig.2 Relation between distance from the contact point and liquid film thickness MITSUBISHI HEAVY INDUSTRIES, LTD.

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At Tube Liquid film Liquid 6 AVB 1* I Fig.3 Distance from the contact point and liquid film thickness MITSUBISHI HEAVY INDUSTRIES, LTD.

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3. Estimation of Void fraction Fig.4 shows the relation between void fraction and liquid film thickness, which is obtained from the following equations.

Asub - (Af o*

+ Ad)

= (3)

Asub Af = [(d + 2,)2 -d2] (4) 4 Ad = -4,f (5)

A,,,b =- - d (6) 2 4

Where, a Void fraction Pt Tube pitch d Tube diameter Asub 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 (See Fig.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 0.2 in 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, is approximately 20% of the flow rate of droplet, GE, when the quality is 50%.(50% quality at SONGS RSG condition (steam pressure is 838 psia) corresponds to 91% of void fraction)..

Gf 1 (7)

GE 5 On 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 of liquid film and the apparent gas velocity are measured in various conditions of the apparent liquid velocity, ji, and the hydraulic equivalent diameter (Ref.2). Since ratio between the flow velocity of liquid film and droplet does not depend on the pressure (Ref.3), these data are applicable to SONGS RSG MITSUBISHI HEAVY INDUSTRIES, LTD.

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Assuming the velocity of the droplet, Ue, is identical to the apparent gas velocity, jg, the flow velocity of droplet, Ue, is approximately ten times the flow velocity of liquid film, Uf, at all conditions. The flow velocity of the liquid film does not depend on the condition of the apparent liquid velocity or the hydraulic equivalent diameter.

'l _= 10 (8)

  • ~lf 11f *~lf Uf From the equation of continuity (9), the ratio of sectional area between liquid film and droplet can be derived as follows. (Equation (10) is identical to Equation (5))

Gf = PfQf _ - Af ,,f 11 (9)

GE PsQE QE Ad E Af Qf "E =2

=-

(10)

Ad QE Uf MITSUBISHI HEAVY INDUSTRIES, LTD.

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At-Fig.4 indicates; When void fraction is lower than 95%, there is a continuous liquid film on the tube since the thickness of liquid film is larger than( ]

When void fraction is higher than 98%, there is no liquid film on the tube since the thickness of liquid film is smaller than[ ]which is the assumed minimum thickness of the discontinuous liquid film on the tube.

Fig.4 Relation between void fraction and liquid film thickness

4. References
1) Akagawa,"Gas and liquid Two-phase Flow" p.150
2) "Fluid characteristics of annular mist flow of gas and liquid" p.395-495,49-438
3) Nakazatomi, et.al, Experimental study of vertical upward gas-liquid two-phase annular flow ( 2 nd report, effects of system pressure on characteristics of waves)

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A~k 6

Droplet (Sectional area Ad)

Liquid film (Sectional area Af)

Fig. 5 Sectional area of droplet and liquid film 1.0 Gf is approximately 20 % of GE when the quality is 0.5 0

Test condition

0) - Two-phase flow (steam/water) in N

E heating cylinder (heat flix is 8.6 0 x 104 W/ft2 )

z film - At high pressure (427psia) o 0.6 0 Quality Fig.6 Flow rate of liquid film and droplet (Ref.1)

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Shearer & Uf is approximately 10 % of Jg in all cases, Hall -Taylor et al. which does not depend on J, and the hydraulic equivalent diameter Test condition E - Water/air flow in a cylinder

- At atmospheric pressure and E

room temperature Er 0

0 Definition of symbols

°-

LL J~m 8 12 18 25126 0.04 *10~i oA v 0.06 114) A AV 0.1

  • 11 A V ot14 Al V 8 10 15 20 30 Hydraulic equivalent diameter Fig.7 Flow rate of liquid film and droplet (Ref.2)

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Ath for Squeeze Film Damping The effective distance of liquid film of tube from the contact point for squeeze film damping is evaluated to be[ ] as calculated below.

The calculation model of tube and AVB is shown in Fig.l. When the amplitude of gap velocity vibration in normal direction of AVB is v0 , the velocity at x in horizontal direction is defined as equation (1) since the liquid volume pushed out by the tube is the same as the liquid volume which flows in the horizontal direction.

V(v) = v (1)

.5(x)

Tube I'

{ 0 r

~AVB~

I Fig.1 Calculation model MITSUBISHI HEAVY INDUSTRIES, LTD.

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A On 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) v 2 dx

+ v- - _ + (2) 2 p 2 p 25

Where, p :Pressure p :Liquid density A :Tube friction factor defined by equation (3).

{48/Re if Re < 1300 24 0.26 Re if Re > 1300 (3)

The equation (4) represents the pressure gradient, which is derived by differentiating the equation (3).

dp p dv 2 p*,(x) 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 is negligibly small, P 0 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 width I" Effective distance of liquid film of tube from the contact point Therefore, 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 the maximum value obtained by using the equations above and the conditions listed in Tablel.

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At Fig.2 indicates a trend that when the distance from the contact point is greater thani Ithe damping coefficient will be saturated.

Table 1 Conditions Initial gap Tube diameter AVB width Amplitude of displacement Frequency of vibration Liquid density Kinetic viscosity Note *: Values at BOL design condition (Th=598 deg.F)

-11 Distance from the contact point (mm)

Fig.2 The damping coefficient and the distance from the contact point MITSUBISHI HEAVY INDUSTRIES, LTD.

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Attachment-4 Confirmation of Flow Regime

1. Flow regime MHI has calculated the Grant flow regime map as shown in Figurel by using ATHOS computer code outputs of BOL design conditionI ] in accordance with Reference 1.12 tubes shown in Figure 1 are selected as representatives and each tube has 19 evaluation points in U-bend (10 degrees pitch 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 side are 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) 469-483 r

)

Note *: The points at 90 degrees are included in the hot side.

Figure 1 Flow Regime of Representative Tubes at BOL Design Condition MITSUBISHI HEAVY INDUSTRIES, LTD.

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A Attachment-5 Case Study for Applying Split Stabilizers for TTW tube of Unit-2 at 70%

Thermal Power

1. Purpose The 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 cases shown in Table 2-1 are studied.
2. Conclusion The results of case study for applying type J stabilizer are shown in Table 2-1 and Figure 2-1. Type J stabilizers are split stabilizers that extend approximately 60' into the U-bend, inserted on the hot and cold side of the tube. It has been confirmed that stability ratio of TTW tubes with type J stabilizer is less than 1.0.

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Table 2-1 Natural Frequency and Stability Ratio Tube Without Stabilizer With split Stabilizers 6 (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 I Additional damping ratio Additional damping ratio SI I Additional damping I ratio Additional damping ratio I Z 0

Natural Stability Natural Stability Natural Stability Natural Stability Natural Stability Ratio W,

Frequency Ratio Frequency Ratio Frequency Ratio Frequency Ratio Frequency (Hz) (Hz) (Hz) (Hz) (Hz) CD R111C81 0

R113C81

/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 ratio Page 119 of 149 S023-617-1-M1539, REV. 0

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3. Assumption (1) Representative tube Representative tubes (Row1 13 Col.81 and Row1 11 Col.81) are TTW tubes of Unit-2 (2 tubes).

(2) AVB support points In this evaluation, all AVB support points are assumed to be inactive for conservatism because the stability ratios of the tubes obtained from the evaluation will be the maximum possible values.

(3)Plugging and Stabilizer The 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 the U-bend region at the both of hot and cold side to maximize the structural damping. As shown in Table 3-1, the additional damping ratio by the split stabilizers (Type J) is assumed to be the difference between the damping ratio of tube with and without split stabilizers based on the report of the damping test (Ref.32). Table 3-1 was derived for Row 106 but can be applied to all rows.

Table 3-1 Additional dampina due to split stabilizers Ak Amplitude Damping ratio (%)

Without stabilizer With split stabilizers Additional damping ratio Small I I Mediumi I Large I I Very large I _

(4) Effect of primary water entering into the TTW tubes The effect of primary water entering into the TTW tubes is not taken into account by assuming there in no leakage through the plugging.

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4. Acceptance criteria There are no criteria because of parametric case study.
5. Design inputs 5.1 Geometry The tube bundle consists ofi diameter, thermally treated Alloy 690 U-tubes that are arranged in a I 1equilateral 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 nominal dimension of tube, TSPs and AVBs are listed in Table 5-1.

5.2 Thermal and Hydraulic flow of steam generator secondary side The ATHOS thermal hydraulic analysis program was used to determine the distributions of fluid gap velocity in the normal direction to tube in-plane and fluid density. Table 5-2 and Fig 5-1, 5-2 show the flow characteristic that are applied to the tubes for the evaluation at 70% thermal power of Unit-2 with plugging.

6. Methodology The analysis is performed in accordance with the same procedures provided in main report to evaluate the best estimated stability ratio for in-plane FEI.

7"Results The analysis results are shown in Table 7-1 and 7-2.

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A&

Table 5-1 Nominal dimensions of tubes, TSPs, and AVBs Part Item Value Material Thermally treated SB-163 UNS N06690 Outside diameter 0.75 in Thickness 0.043 in Tubes Number of tubes 9727 Tube pitch 1.0 in Tube arrangement Triangular Material SA-240 Type 405 Thickness TSPs Number of TSPs Tube support span (between TSP centers)

Tube support span (from tubesheet to TSP-1)

Material SA-479 Type 405 Type AVBs Thickness Width Stabilizer Unit weight A MITSUBISHI HEAVY INDUSTRIES, LTD.

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At Table 5-2 Basic parameters for calculation for 2A SG evaluation after plugging Plugging 305 Thermal power (MWt) 1213.3 (70%)

RCS flow rate (gpm) 206,695 Thot (Tsg-in) (*F)

Tsg..out (*F)

TCOlId (F)

Saturation Steam Pressure (psia)

Fouling Factor (ft2 hr°F /Btu)

Tfeedwater ('F)

Circulation Ratio Steam Mass Flow (lb/hr)

Feed Water Mass Flow (lb/hr)

Blowdown flow rate (gpm)

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r z0

'0 CD Cn) 0 C

Cl)

Y,

-I Fig. 5-1 Flow Characteristics of Row1 11 Col81 Page 124 of 149 S023-617-1-M1539, REV. 0

7- -N z0 Cl)

CD 0) 0 It*r,__

Fig. 5-2 Flow Characteristic of Row 113 CoI.81 Page 125 of 149 S023-617-1-M1539, REV. 0

Thble 7-1 Analv.*is results for case study of solit stabilizers (Row 111 Column 81) /

Tube Damping Critical Average Average Maximum Critical Effective Additional natural Ratio coefficient fluid void void flow flow Stability Structural Mode frequencyh() density fraction fraction velocity velocity ratio Tubeing cSqueeze dmi Structural Two phase film Total Ki Ko Ki Ke K f(Hz) damping damping damping po(Ib/ft3) [-] [-] Uc(ft/sec) Ue(ftlsec)

Plugged without z 0

stabilizer

'0 Plugged with split M..

CD stabilizers when 0) tube amplitude is small CD C,'

0.

Plugged with split 0 stabilizers when tube amplitude is medium Plugged with split stabilizers when tube amplitude is large Plugged with split stabilizers when tube amplitude is very large ___

0  :

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Table 7-2 Analysis results for case study of stabilizer (Row 113 Column 81) A.

Tube Damping Critical Average Average Maximum Critical Effective Tube condi n Additional sructural Mo ef natural sti q enyh Ratio

) coefficient fluid void void flow flow Stability Tube condition damping N%) Mode frequency h(%) density fraction fraction velocity velocity ratio Hi Structural Two phase Squeeze film Total KS KK Ke K po(ib/ft3 ) [_] [-] Uc(ft/sec) Ue(ftlsec) f(Hz) damping damping damping Plugged without stabilizer z0 0

Plugged with standard 0) stabilizer M,

Plugged with split stabilizers when CD Cn.

tube amplitude is small Plugged with split _

stabilizers when tube amplitude is medium Plugged with split stabilizers when tube amplitude is large Plugged with split stabilizers when 0 '

tube amplitude is very large _ _

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At Attachment-6 Uncertainty of Calculated Stability Ratio

1. Purpose The purpose of this attachment is to evaluate the uncertainty of stability ratio evaluation based on MHI methodology.
2. Summary The uncertainty of the stability ratio (SR) evaluation based on MHI methodology is evaluated by summing the uncertainties of critical parameters. As a result, the uncertainty of SR evaluation is calculated to be in the range between -5 % and - 57%. Therefore, the stability ratios are calculated conservatively based on MHI methodology.

Table 1 Difference between SR based on MHI evaluation method and best estimated Relative stability Best estimated Uncertainty of MHI's SR ratio based on evaluation MHI evaluation, Upper bound Lower bound R 1 H1 MS Mean +/-20 SRmax SRmin value deviation,o SR .Hr SRAHI

3. Evaluation method In this evaluation, the standard deviation of SR evaluation multiplied by 2 is regarded as an uncertainty. Table 2 shows the parameters used in the SR calculation and includes which parameters should be taken into account. The methodology of the uncertainty evaluation is shown as follows.

3.1 Uncertainty of Each Parameter The uncertainty of each parameter is estimated by the following equation. In this equation, it is assumed that the uncertainty of each parameter is equal to two times as large as standard deviation of relative error.

J ...................................................................

(1) i Xir f Where, MITSUBISHI HEAVY INDUSTRIES, LTD.

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A Xref :Reference value of each test data X  : test data 0"  : Standard deviation of relative error of each test data N  : Number of data According to error propagation law, the effect of the standard deviation of each parameter on that of SR is evaluated with the following equations (See Ref. 3) and 2 O-SR is regarded as an uncertainty of SR evaluation.

S p -)T TH - Ay 2

.......................................................... (2 )

Cy* - (sr s + (7TpATP + CFSFýSF - OrT rP + C+/-ASFSF. ............................................... (3)

ýST + TP + SF a 2K + 7.2 ..............................................................................................

(4 )

Where, C-sR Standard deviation of SR uncertainty a7r,, Standard deviation of SR due to thermal hydraulic parameters evaluation UP Standard deviation of parameters used for SR evaluation Total damping ratio

ýST Structural damping IA

ýTp Two phase damping

ýSF Squeeze film damping

(*y*  : Standard deviation of 1" CYST Standard deviation of ýST Gr  : Standard deviation of ýTp a's Standard deviation of ;SF a7K Standard deviation of K

'KI :Standard deviation of KI Ca  : Standard deviation of a(O)

X- Standard deviation noted above ( used for SR evaluationeviation of relative error of each parameter (dimensionless)

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At 3.2 Difference between SR based on MHI method and that based on the best estimated parameters In MHI method, the Connor's constant and damping ratio are evaluated conservatively because lower bounded data are used for some parameters. The difference between the stability ratio based on MHI method and that based on the best estimated parameters is evaluated by the following equation.

R*,H, S K ,'q m_ 7Rm 7*-m KKBE [. ýBE .SSR. *n._.................................... (5)

A SRBE 1 K M HS* V l AI SR(

KBE SS Where, R,*HI : Relative stability ratio based on MHI evaluation method SRAfH: Stability ratio based on MHI evaluation method SRBE Mean stability ratio based on the best estimated parameters KMH  : Connor's constant based on MHI evaluation method KBE Mean Connor's constant based on the best estimated parameters MAMH: Damping ratio based on MHI evaluation method

ýBE Mean damping ratio based on the best estimated parameters SR* Average of normalized SR based on three different TH codes (See Sec. 4.2)

SR 1* 1 *, Average 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).

RK K A H ........................................................................................................ (6 )

KBE R, . . ........................................................................................................ (7 )

ýBE SR .

T H I. SR" I.... . .......................................................................................... (8 )

R'M,="IT - R .................................................................... (9)

RAIll - T RK R4ý MITSUBISHI HEAVY INDUSTRIES, LTD.

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At Based on Table 2, the relative ratios of Connor's constant and damping ratio are converted to Equation (10) and (11).

R K K1 a( ) .... ..... ............. ............................................ (10)

KBE KlBE a(O)BE

ý 1P ýTP-MHIf +ýSF 4SF-AIHf

-ý ý1MHI - TP-BE 4SF-BE..............................()

ýBE Where, K1 Afi Connor's constant based on MHI evaluation KIBE Mean Connor's constant based on the experimental data a(O)MHI" The effect of flow direction based on MHI evaluation method a(O)BE Mean effect of flow direction based on the experimental data

ýSF-MHI Squeeze film damping ratio based on MHI evaluation method 4SFB-E Mean squeeze film damping ratio based on the experimental data

ýTP-AIHI Two phase damping ratio based on MHI evaluation method

ýTP-BE Mean two phase damping ratio based on the experimental data 3.3 Uncertainty of SR Based on the standard deviation and the relative stability ratio, the uncertainty of stability ratio based on 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 AH RM(13 MITSUBISHI HEAVY INDUSTRIES, LTD.

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,Ak-Table 2 Parameters used for SR calculation U, Effective flow Yes velocity Ul Critical flow Yes The uncertainty of these parameters velocity due to thermal-hydraulic parameters f Tube natural Yes analysis error is evaluated by the frequency comparison of three independent Average tube Yes analyses as shown in Section 4.2.

mass P0 Fluid density Yes Connors's The uncertainty of KI is estimated K1 constant based Yes based on MHI test data.

on MHI test ecoefficient to Lower limit of Pettigrew's test data is used for SR calculation. (Ref. 4)

Kp consider the effect No It is not necessary to consider of tube pitch on K uncertainty of Kp K The ratio of K The result of MHI air flow test was (See in the in-plane consistent with the public test data Sec.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 not FEI necessary to consider.

Lower limit of Yeung's test data is Thcons eeffcintts used for SR calculation. (Ref. 1) a(9) consider the effect Yes Teucranyo ()i of flow angle on K The uncertainty ofa(O) is estimated based on test data.

Structural 4 IST is relatively small compared to 4

'sT damping ratio No 'SF Two-Phase Yes The uncertainty OfisF is estimated (e

(SeeVicu damping ratio based on Prof. Pettigrew's test data.

Sec.4.1 (2))  ;'v Viscous No  ;, is not used for SR calculation damping ratio II msF Squeezerfilm Yes The uncertainty of 4;s is estimated damping ratio Ibased on Prof. Pettigrew's test data.

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At-

4. Evaluation Result 4.1Parameters Used for SR Evaluation (1) Connors' constant Connor's constant based on MHI test Standard Deviation of Connors' constant K is estimated based on MHI's steam water two phase flow 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). However Connors' constant data include the error due to estimating it without considering measuring error of ratio of volume flow rate, flow velocity and fluid density. Therefore it is necessary to consider the error of both ratio of volume flow rate ,/ and Connors' constant K which are horizontal and vertical axis (these data are indicated as red points N in Figure 1). Equations for calculating the error 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 that estimation of damping ratio is not affected by measuring error.

- Error of Connors' constant ic 2e=+ 6 .0) +( 6 0 ...................................................................... (14)

) oD2 Equation of Connors' constant : K

=

Where, EK Relative error of Connors' constant K cuc Relative error of critical flow velocity 6

m0 Relative error of tube density considered added mass of outside water 0,0 Relative error of fluid density Em.0)

Error of ratio of volume flow rate UUU9+ U l 2

- U2 _2(Ug 2 +U)2 4U/(ugUg)2 +U2(EiU1 ) .(15) f U 9 + U X1 U .

Where, Equation of ratio of volume flow rate : 8 = Ug Ug + UI Ug: flow velocity of vapor (gas)

U,: flow velocity of water (liquid)

Ep Relative error of ratio of volume flow rate 6

ug : Relative error of flow velocity of vapor (gas) cut Relative error of flow velocity of water (liquid)

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At According to MHI's test data, measuring error ( ug, E'l, .0 and c.0 is as follows:

E= I Euc =1 (max value of measuring error of flow velocity; max( 6 ug', CCU))

-. 0 = EP0 =1 6

I(maximum value of measuring error of fluid density)

Measuring error of each parameter is estimated based on proof reading result and inspection result according to GUM (Guide to the expression of Uncertainty in Measurement, ASME).

Table 3 Measuring error of each parameter steam water measuring error of pressure (%)

fluid density at reference pressure; 6MPa (kg/mA3) fluid density at the pressure considering error; 6.02MPa (kg/mA3) measuring error of fluid density (%) X1 measuring error of flow rate (%) IL X2 measuring error of cross section (%)3 X 1 Relative error between fluid density ati landl I steam I water I X-2 Proof reading result of flow rate measurement X-3 Measuring error of cross section is estimated by dimensional inspection result and measuring error of digital vernier calipers I I X-4 Measuring error of flow velocity is calculated by following equation in accordance with GUM ELI= 2 x E26 3+ ~23 + 3 C2 3 3 3 Where EL measuring error of flow velocity EQ measuring error of flow rate CA measuring error of cross section 6,p :measuring error of fluid density steam :

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At water Therefore 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 calculation result is shown in Table 4. Both relative error of cK and e. are calculated according to error propagation law.

Table 4 Calculation of relative error of 13 P jg+jl'ýý(M/s) jg,*(mls) jlm, (mis) (%

0.7 0.98_____

0.93____ _

X-1 Critical flow velocity obtained by MHI test X-*2 Critical 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 the maximum 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 ) and ratio 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'l There 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 maximum relative error from fitting curve.

K ma ......... .............. (16)

Where Ki each data for uncertainty evaluation; K1 k 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)-

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At (4) at each ratio of volume flow rate ; 2-K =KI= I (UK =1 I)' Because measuring error of KI and 61 are estimated as 2 times as large as standard deviation : 2a, it is assumed that K1 Since the mean data is used for the SR evaluation, the relative ratio of K1, KImH , isI I KIBE K -

Figure 1 Experimental data of Connors's constant based on MHI test; KI MITSUBISHI HEAVY INDUSTRIES, LTD.

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At Effect of flow direction Figure 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 than 20 degrees; the flow directions are smaller than 20 degrees in the center of the bundle (FEI susceptible region) as shown in Figure 3.

In accordance with Figure 2, the standard deviation below 20 degrees is obtained to bel land the mean line is added, which isi than the lower limit used for the SR evaluation.

a(o)AfH ii, larger Therefore, the relative ratio, a(O),E isl I Connor's constant Therefore, 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)BE MITSUBISHI HEAVY INDUSTRIES, LTD.

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A Figure 2 Experimental data of a(O)

Figure 3 Region where the flow direction is greater than 20 degrees from the tube in-plane direction to out-of-plane direction MITSUBISHI HEAVY INDUSTRIES, LTD.

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At (2) Damping Ratio Squeeze film dampinq Uncertainty of squeeze film damping ýSF is estimated based on Pettigrew's test data as shown in the Figure 4 (See Ref. 2). According to this figure, the squeeze film damping ratio depends on the vibration frequency and the bounded line of 4-SF, with 9 0 th percentile ( = 50 / f ) is used for the OA evaluation in accordance with Pettigrew's guideline.

As shown in Figure 4, the bounded line based on 9 0 th percentile ( = 50 / f) is used for MHI's SR evaluation. In order to obtain the standard deviation and the relative ratio, the lower bounded line with 9 5 th percentile (= 43.5 / f) and the average line ( = 100 / f )are added.

2 0 Since the difference between 9 5 th percentile and the average line is considered as SF, the standard deviation is Iand the ratio between 90 th percentile and the average line is the relative ratio of squeeze film damping, 7SF-Aff , which is]

9SF-BE MITSUBISHI HEAVY INDUSTRIES, LTD.

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At

/-

Note) because there are 20 points below the Pettigrew's guideline with 9 0 th percentile, the lower bounded line with 9 5 th percentile is determined such that there are 10 plot points below this line Figure 4 Experimental data of squeeze film damping MITSUBISHI HEAVY INDUSTRIES, LTD.

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At Two phase dampingq Uncertainty of two phase damping *TP is estimated based on Pettigrew's test data as shown in Figure 5 (See Ref. 5). In order to obtain the standard deviation and the relative ratio, the lower 3

bounded line of all the data, which is assumed to show 99. 7 th percentile ( = - aTp), is added. Since the difference between the gradient of the 9 9 .7th percentile I and the gradient of the 3

average linel I is considered as STp, the standard deviation is I The ratio between the gradient of guide line used for SR evaluation Iand the gradient of the average line is the relative ratio of two phase damping, !which is

  • TP-BE Figure 5 Experimental data of two phase damping MITSUBISHI HEAVY INDUSTRIES, LTD.

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At Total dampinq ratio According to equation (3), in order to estimate the standard deviation of total damping ratio 4,it is necessary to consider absolute value of each damping ratio. According to damping ratio data used in analysis shown in Table 5, it is found that ý4 SF / =1 land Tp/IL=I ITherefore the standard deviation of total damping ratio, c,, Iis estimated to bel Ias follows.

a ="- S "F+Tp The relative damping ratio is obtained to bel Iby using Equation (11) as follows.

4'SF -H + 4 "T ý'TP-MHIf R=SF-BE qTP-BE 4-MITSUBISHI HEAVY INDUSTRIES, LTD.

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At 4.2 SR due to Thermal-Hydraulic Parameters Evaluation In order to evaluate the standard deviation of SR due to the thermal-hydraulic (TH) parameters evaluation, stability ratios for representative 8 tubes are calculated by using 3 independent TH analysis codes (MHI-ATHOS, CAFCA and WEC-ATHOS)

Table 5 shows the results of SR calculation and the normalized values, which are the ratio between the calculated SRs based on each TH analysis and the average of SRs based on 3 analysis codes.

A The standard deviation of normalized stability ratios obtained by the following equation isi land the average relative stability ratio based on MHI ATHOS isi I 1 . ...........................

N................................................. (17 )

Where,

-TTH Standard deviation of SR based on each TH code SR* : Normalized SR (= each analysis result / average value of 3 analysis code result)

SR* Average of normalized SR N :Number of data Table 5 Comparison of Stability Ratio based on MHI-ATHOS, CAFCA and WEC-ATHOS MHI-ATHOS CAFCA WEC-ATHOS Average Row Column SR Normalized Normalized SR Normalized SR Normalized SR SR SR SR SR 81 69 r 81 89 101 69 101 89 121 69 121 89 125 85 105 69 Average t, MITSUBISHI HEAVY INDUSTRIES, LTD.

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Document No. L5-04GA567(6) 4.3 Uncertainty of SR Table 6 shows the standard deviation and the relative ratio of each parameter. According to V6 equation (2), the standard deviation of stability ratio is calculated to bel Ias follows.

U'S, = 0"* + O"_ + O'7n2=

The upper bounded and lower bounded of stability ratios are -5% and -57%, which are obtained by Equation (12) and (13).

Table 6 Uncertainty of Stability Ratio Best estimated Uncertainty of MHI's SR evaluation Relative Ratio Upper bound Lower bound Parameters based on Mean ( Skax SRkin MHI method SRMIII SRAfH, K1 Connor's constant a(O)

K

  • SF Damping Ratio TP Thermal-Hydraulic Parameters Stability Ratio
5. References

[1] "The Effect of Approach Flow Direction on the Flow-Induced Vibrations of a Triangular Tube Array" , 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 ( 3 rd Report, Advanced Estimated Method)St, 2002, T. Nakamura et al, Journal of The Japan Society of 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, ISBN 90 5809 129 5, 561-568

[5] "Vibration analysis of shell-and-tube heat exchangers : an overview - Part1: flow, damping, fluid elastic instability ", 2003, M.J. Pettigrew et al, Journal of Fluids and Structures 18 469-483 MITSUBISHI HEAVY INDUSTRIES, LTD.

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At Attachment-7 Selection of Evaluated Tubes As shown in Table 1, 28 tubes are selected for thermal hydraulic analysis by ATHOS/SGAP (see Ref.21 for detail). Among these tubes, 8 tubes (#2,#3,#6,#7,#l0,#11,#14,#16) selected by SCE (See the emails shown in Appendix-I) and an additional tube (#28), which stability ratio of out-of-plane FEI was the maximum when all AVB support points are active, are evaluated in the main report.

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At Table 1 Evaluated Tubes (See Ref.22 for details)

Tube # Row Column 1 80 60 2"1 80 70 3"1 80 80 4 80 88 5 100 60 6*1 100 70 7*1 100 80 8 100 88 9 120 60 10*1 120 70 11"1 120 80 12 120 88 13 80 84 14*1 95 85 15 110 84 16*1 125 85 17 135 85 18 40 30 19 74 80 20 95 69 21 105 69 22 111 69 23 127 73 24 138 80 25 86 80 26 95 75 27 124 76 282 138 84 Notes:

(*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 is the maximum when all AVB support points are active MITSUBISHI HEAVY INDUSTRIES, LTD.

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A&

Appendix-1 E-mails from SCE MITSUBISHI HEAVY INDUSTRIES, LTD.

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At r

-I MITSUBISHI HEAVY INDUSTRIES, LTD.

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