ML11215A059

WCAP-17345-NP, Rev 2, H*: Resolution of NRC Technical Issue Regarding Tubesheet Bore Eccentricity (3-Loop Model 44F/ Model 51F), Attachment 5 to 11-403

ML11215A059
Person / Time
Site:	Surry
Issue date:	06/30/2011
From:	Bedont W, Cassino C, Roslund A, Whiteman G Westinghouse
To:	Office of Nuclear Reactor Regulation
References
11-403 WCAP-17345-NP, Rev 2
Download: ML11215A059 (145)

Text

Serial No.11-403 Docket Nos. 50-280/281 ATTACHMENT 5 WESTINGHOUSE ELECTRIC COMPANY LLC WCAP-17345-NP, "H*: RESOLUTION OF NRC TECHNICAL ISSUE REGARDING TUBESHEET BORE ECCENTRICITY (3-LOOP MODEL 44F/MODEL 51 F)"

(NON-PROPRIETARY), REVISION 2, JUNE 2011 VIRGINIA ELECTRIC AND POWER COMPANY (DOMINION)

SURRY POWER STATION UNITS I AND 2

Westinghouse Non-Proprietary Class 3 WCAP-1 7345-NP June 20 11 Revision 2 H*: Resolution of NRC Technical Issue Regarding Tubesheet Bore Eccentricity (3-Loop Model 44F/Model 51 F)

Westinghouse

WESTINGHOUSE NON-PROPRIETARY CLASS 3 WCAP-17345-NP Revision 2 H*: Resolution of NRC Technical Issue Regarding Tubesheet Bore Eccentricity (3-Loop Model 44F/Model 51F)

W. J. Bedont*

SG Design and Analysis C. D. Cassino*

SG Design and Analysis A. 0. Roslund*

SG Design and Analysis G W. Whiteman*

SG Design and Analysis June 2011 Reviewer: H. 0. Lagally*

SG Management Programs Approved: D. A. Testa*, Manager SG Management Programs

• Electronically approved records are authenticated in the electronic document management system.

Westinghouse Electric Company LLC 1000 Westinghouse Drive Cranberry Township, PA 16066, USA

© 2011 Westinghouse Electric Company LLC All Rights Reserved WCAP-17345-NP.doc-061711

ii REVISION RECORD Revision Date of No. Issue 0 Original Issue 11/10 I Revised to correct page numbering inconsistency. 01/11 2 Section 1; editorial modifications, added Section 1.3 to summarize independent 06/11 review Section 2.1; editorial changes Section 2.3.1; modified third paragraph Section 2.5; expanded meshing discussion, added convergence criteria and added discussion on artificial stiffness Section 3; tables and figures for axial distributions referenced to top of tubesheet Section 3.2.2; expanded discussion on SLB analysis; editorial changes in discussion of divider plate Section 3.2.4; expanded discussion on divider plate modeling Section 3.2.5; editorial changes only Section 3.2.8; editorial changes only Section 3.3.3, 3.3.4; editorial changes only Section 3.3.9; now includes prior Section 3.3.11 Section 3.3.10; now includes prior Section 3.3.12 Tables 3-14 through 3-19; data added for additional elevations Figures 3-24 through 3-29; data added for additional elevations Section 3.3.11; replaces prior Section 3.3.13, added discussion on calculation process and effect of Poisson contraction Section 3.3.12; new section: "Axial Location of Departure from Zero Contact Pressure" Section 3.3.13; new section: "Circumferential Contact Pressure" Added Table 3-22 Added Figure 3-30 through 3-35; Circumferential Contact Pressure for Model 44F and Model 51F Section 3.4; re-written in its entirety Section 3.5; modified to reflect minor process change to account for added axial Section 3.6; new section for crevice pressure adjustment length; replaces discussion in Section 3.4 in Rev. 1 Section 3.7; new summary section; replaces discussion in Section 3.4 in Rev. 0 Table 5-1; updated values WCAP-17345-NP June 2011 Revision 2

iii TABLE OF CONTENTS L IST OF TA B LE S ........................................................................................................................................ v L IST OF F IGU RES ................................................................................................................................... viii IN TRO DU C T ION ........................................................................................................................ 1-1 1.1 ORIGINAL NRC RAI RESOLUTION ACTION PLAN DISCUSSION ....................... 1-1 1.2 REVISED NRC RAI RESOLUTION ACTION PLAN DISCUSSION .......................... 1-2 1.2.1 Road Map to Final Response to 14 NRC RAI Except RAI #5 and RA I # 12 .................................................................................................... 1-2 1.2.2 Need for Alternate Leakage Factor Approach ................................................. 1-2 1.2.3 C2 Model Contact Pressures Results ................................................................ 1-3 1.2.4 Process for Determining the Limiting H* Value ............................................. 1-3 1.3

SUMMARY

OF THE IMPACT OF INDEPENDENT REVIEW ON H* ....................... 1-5 1.4 REF ERE N C E S ................................................................................................................. 1-6 2 SQUARE CELL (C) MODEL ANALYSIS ................................................................................. 2-1 2.1 PURPOSE OF THE C 2 ANALYSIS ................................................................................ 2-1 2

2.2 DEFINITION OF THE C MODEL ................................................................................ 2-3 2.3 APPLICATION OF BOUNDARY CONDITIONS ......................................................... 2-7 2.3.1 Deformation of Tubesheet Cell Edges ............................................................. 2-7 2.3.2 Applying the Internal and Crevice Pressures in the Square Cell Model ......... 2-8 2.4 MATERIAL PROPERTIES ............................................................................................. 2-9 2.5 CONTACT MODELING DISCUSSION ...................................................................... 2-10 2.6 DISCUSSION OF BENCHMARK MODEL FOR C 2 MODEL COMPARISON ......... 2-12 2.6.1 Thick Shell Model to Describe Finite Element Model .................................. 2-12 2.7 RE FERE N C E S ............................................................................................................. 2-19 3 STRUCTURAL CALCULATIONS FOR H* ............................................................................... 3-1 3.1 OVERVIEW OF THE STRUCTURAL ANALYSIS FOR H* ........................................ 3-1 3.2 STRUCTURAL ANALYSES (3-D FEA MODEL) ......................................................... 3-2 3.2.1 M ethod D iscussion .......................................................................................... 3-2 3.2.2 A ssum ptions .................................................................................................... 3-3 3 .2 .3 In p u t ................................................................................................................. 3 -4 3.2 .4 G eom etry ......................................................................................................... 3-4 3.2.5 M esh D iscussion .............................................................................................. 3-5 3.2.6 Tubesheet Equivalent Properties ..................................................................... 3-5 3.2.7 B oundary C onditions ....................................................................................... 3-5 3.2.8 Tubesheet Complex 3-D FEA Analysis Results .............................................. 3-6 3.3 CALCULATION OF MEAN H* FROM C 2 MODEL .................................................. 3-16 3.3.1 M ethod D iscussion ........................................................................................ 3-16 3.3.2 Development of Displacements for Square Cell ........................................... 3-16 3.3.3 A ssum ptions .................................................................................................. 3-18 3 .3 .4 In p u t ............................................................................................................... 3 -18 3.3.5 G eom etry ....................................................................................................... 3-18 3.3.6 M esh Discussion ............................................................................................ 3-18 WCAP-17345-NP June 2011 Revision 2

iv TABLE OF CONTENTS (cont.)

3.3.7 B oundary C onditions..................................................................................... 3-20 3.3.8 C 2 FEA R esults .............................................................................................. 3-2 1 3.3.9 Model 44F (Turkey Point Units 3 & 4) Square Cell Model Results ............. 3-21 3.3.10 Model 5IF (Surry Units 1 & 2) Square Cell Model Results ......................... 3-22 3.3.11 M ean H

• C alculations ................................................................................... 3-41 3.3.12 Axial Location of Departure from Zero Contact Pressure ............................. 3-41 3.3.13 Circumferential Contact Pressure .................................................................. 3-42 3.4 CALCULATIONS OF PROBABILISTIC H* USING THE C2 MODEL ..................... 3-51 3.4.1 Assum ptions .................................................................................................. 3-52 3.4.2 M ethods D iscussion ....................................................................................... 3-52 3.4.3 Application to Bounding Model 44F SG (Turkey Point Units 3 & 4) ........... 3-57 3.4.4 Application to Bounding Model 5IF SGs (Surry Unit 1).............................. 3-58 3.5 POISSON CONTRACTION EFFECT ON H* ............................................................. 3-71 3.5.1 M ethods D iscussion ....................................................................................... 3-71 3.5.2 Inp ut ............................................................................................................... 3-7 1 3.5.3 Calculation of Radial Dilation ....................................................................... 3-71 3.5.4 Calculation of Contact Pressure Reduction from Poisson Effect .................. 3-72 3.6 CREVICE PRESSURE ADJUSTMENT LENGTH ...................................................... 3-89 3.7 CALCULATION OF FINAL H* ................................................................................... 3-91 3.8 RE FERE NC E S .............................................................................................................. 3-92 4 C 2 MODEL LEAKAGE INTEGRITY DISCUSSION ................................................................. 4-1 4.1 RE FERE NC E S ................................................................................................................ 4-3 5 REPORT

SUMMARY

AND CONCLUSIONS ............................................................................ 5-1 5.1 RE F ERE NC E S ................................................................................................................ 5-4 WCAP-17345-NP June 2011 Revision 2

v LIST OF TABLES Table 2-1F Free Radial Expansion of a Tube ................................................................................... 2-16 Table 2-2 Difference between Radial Dilation of the Tube Bore and Tube ................................... 2-16 Table 2-3 Rigid Collar Model Input Parameters (Tube) ................................................................ 2-16 Table 2-4 Rigid Collar Model Input Parameters (Tubesheet) ........................................................ 2-17 Table 2-5 Rigid Collar Model Contact Pressure Results ................................................................ 2-17 Table 2-6 Calculated Tubesheet Inner Diameter Dilation ............................................................. 2-17 Table 2-7 Comparison of C 2 and Thick Shell Results .................................................................... 2-18 Table 3-1 Input Boundary Conditions for Model 44F (Turkey Point Units 3 & 4) ......................... 3-7 Table 3-2 Input Boundary Conditions for Model 5IF (Surry Units 1 & 2) ..................................... 3-7 Table 3-3 Modulus of Elasticity for M aterials ................................................................................. 3-8 Table 3-4 Coefficient of Thermal Expansion for Materials ............................................................. 3-8 Table 3-5 Interpolated Ratios of Equivalent Material Properties for Analysis of P erforated P late ................................................................................................................ 3-8 Table 3-6 Equivalent Properties for Tubesheet for Model 44F SG (Turkey Point Units 3 & 4) ...... 3-9 Table 3-7 Equivalent Properties for Tubesheet for Model 5 IF SG (Surry Units 1 & 2) .................. 3-9 Table 3-8 Model 44F Turkey Points Units 3 & 4 Inputs and Results, 2.655 in. Radius ................ 3-23 Table 3-9 Model 44F Turkey Point Units 3 & 4 Inputs and Results, 7.219 in. Radius .................. 3-24 Table 3-10 Model 44F Turkey Point Units 3 & 4 Inputs and Results, 18.171 in. Radius ................ 3-25 Table 3-11 Model 44F Turkey Point Units 3 &4 Inputs and Results, 28.21 in. Radius ................... 3-26 Table 3-12 Model 44F Turkey Point Units 3 & 4 Inputs and Results, 34.598 in. Radius ................ 3-27 Table 3-13 Model 44F Turkey Points Units 3 & 4 Inputs and Results, 48.288 in. Radius .............. 3-28 Table 3-14 Model 5IF Surry Units 1 & 2 Inputs and Results, 4.016 in. Radius .............................. 3-29 Table 3-15 Model 51F Surry Units 1 & 2 Inputs and Results, 11.772 in. Radius ........................... 3-30 Table 3-16 Model 51F Surry Units 1 & 2 Inputs and Results, 20.498 in. Radius ............................ 3-31 Table 3-17 Model 5IF Surry Units 1 & 2 Inputs and Results, 30.193 in. Radius ............................ 3-32 Table 3-18 Model 5IF Surry Units 1 & 2 Inputs and Results, 48.613 in. Radius ............................ 3-33 Table 3-19 Model 5IF Surry Units 1 & 2 Inputs and Results, 58.308 in. Radius ............................ 3-34 Table 3-20 H

• Input Summ ary ......................................................................................................... 3-43 Table 3-21 Summary of H* Mean Values before Poisson Correction ............................................. 3-43 Table 3-22 Summary of H* Mean Values after Poisson Correction ................................................ 3-44

. WCAP-17345-NP June 2011 Revision 2

vi LIST OF TABLES (cont.)

Table 3-23 Typical Monte Carlo Result Output ............................................................................... 3-60 Table 3-24 Positive Variations About the Mean TS CTE Used for FEA ......................................... 3-60 Table 3-25 Negative Variations About the Mean Tube CTE Used for FEA .................................... 3-61 Table 3-26 Required Probabilistic Estimate for H* ......................................................................... 3-61 Table 3-27 Monte Carlo Data Used in Comparative Probabilistic Analysis .................................... 3-62 Table 3-28 Typical Variation of CTEs Over a Range of Rank Order Statistics R ef. Model F C2 Results) .............................................................................................. 3-63 Table 3-29 Variation of H* for Adjacent Rank Order Variables (Ref. Model F C 2 Results) ............ 3-63 Table 3-30 Model 44F and Model 5IF H* Results .......................................................................... 3-64 Table 3-31 Calculation of Radial Dilation Due to Poisson Effects .................................................. 3-75 Table 3-32 - Calculation of Elastic Constants .................................................................................... 3-75 Table 3-33 Calculation of Reduction in Contact Pressure from Poisson Effects ............................. 3-76 Table 3-34 Baseline and Adjusted Mean H* Calculation for Model 44F (Turkey Point Units 3 & 4) ............................................................................................ 3-76 Table 3-35 Baseline and Adjusted Mean H* Calculation for Model 5 IF (Surry Units 1 & 2) ........ 3-77 Table 3-36 Distance for Poisson Effect to Attenuate ....................................................................... 3-77 Table 3-37 Adjusted Mean H* Including Poisson Attenuation for Model 44F (Turkey Point U nits 3 & 4) ............................................................................................ 3-78 Table 3-38 Adjusted Mean H* Including Poisson Attenuation for Model 51F (Surry U nits 1 & 2) ....................................................................................................... 3-79 Table 3-39 Comparison of Mean H* Values .................................................................................... 3-79 Table 3-40 Baseline and Adjusted Probabilistic H* Calculation for Model 44F ....................... :..... 3-80 Table 3-41 Baseline and Adjusted Probabilistic H* Calculation for Model 51F ............................. 3-81 Table 3-42 Baseline and Adjusted Probabilistic H* Calculation for Model 44F ............................. 3-82 Table 3-43 Baseline and Adjusted Probabilistic H* Calculation for Model 51F ............................. 3-83 Table 3-44 Distance for Poisson Effect to Attenuate Probabilistic H* Values ................................. 3-83 Table 3-45 H* Calculation Including Poisson Attenuation Model 44F (Turkey Point U nits 3 & 4) ............................................................................................ 3-84 Table 3-46 H* Calculation Including Poisson Attenuation Model 44F (Turkey Point U nits 3 & 4) ............................................................................................ 3-85 Table 3-47 H* Calculation Including Poisson Attenuation Model 5 IF (Surry U nits 1 & 2) ........................................................................................................ 3-86 WCAP-17345-NP June 2011 Revision 2

vii LIST OF TABLES (cont.)

Table 3-48 H* Calculation Including Poisson Attenuation Model 5IF (Surry Units 1 & 2) ........... 3-87 Table 3-49 Comparison of Model 44F and Model 5IF SG Probabilistic H* Values (inches) ......... 3-88 Table 3-50 Summary of Model 44F Probabilistic Estimates ........................................................... 3-91 Table 3-51 Summary of Model 51F Probabilistic Estimates ........................................................... 3-91 Table 5-1 Results of Probabilistic Comparison Study for the Limiting Plants for M odels 44F and 5IF ........................................................................................................ 5-3 WCAP-17345-NP June 2011 Revision 2

viii LIST OF FIGURES Figure 2-1 Current Licensing Basis Tubesheet Bore Displacements ................................................ 2-2 Figure 2-2 C 2 Model Tubesheet Bore Displacements ........................................................................ 2-2 Figure 2-3 Typical Lower SG Complex M odel ................................................................................. 2-4 Figure 2-4 Square Cell M odel "Core Sample". ................................................................................. 2-4 Figure 2-5 Square C ell Model ........................................................................................................... 2-4 Figure 2-6 Typical Square Cell Coordinate System .......................................................................... 2-5 Figure 2-7 Typical Square Model without Symmetry Conditions ..................................................... 2-5 Figure 2-8 Typical Mesh Square Cell with Quarter Symmetry Conditions ....................................... 2-6 Figure 2-9 Sketches of Possible C 2 Model Response to Applied Displacement ............................... 2-8 Figure 2-10 Tube and TS Collar A ssembly ....................................................................................... 2-13 Figure 2-11 Constant Tubesheet Bore Dilation Model .............................. 2-13 Figure 3-1 Typical Representation of Severed Divider Plate Condition; Model 5IF ...................... 3-10 Figure 3-2 Typical Solid Model for Intact Divider Plate; Model 44F ............................................. 3-10 Figure 3-3 Model 5IF (Surry Unit 1) Mesh, View Down Z-Axis .............................................. 3-11 Figure 3-4 Model 5IF (Surry Unit 1) Mesh, View Down Y-Axis ................................................... 3-11 Figure 3-5 Model 51F (Surry Unit 1) Mesh, View Down X-Axis ................................................... 3-12 Figure 3-6 Model 5IF (Surry Unit 1) Results of NOP Thermal Analysis ....................................... 3-12 Figure 3-7 Model 5 IF (Surry Unit 1) Results of Thermal-Structural Analysis, Y D eform ation ............................................................................................................... 3-13 Figure 3-8 Model 5IF (Surry Unit 1) Results of Thermal-Structural Analysis, X Deform ation on H ot Leg Face ................................................................................... 3-13 Figure 3-9 Model 5IF (Surry Unit 1) Results of Thermal-Structural Analysis, Z Deform ation on Hot Leg ............................................................................................ 3-14 Figure 3-10 Model 5 IF (Surry Unit 1) Results of SLB Thermal Analysis ........................................ 3-14 Figure 3-11 Model 5 IF (Surry Unit 1) Results of SLB Thermal-Structural Analysis, X D eform ation on H ot Leg Face ................................................................................... 3-15 Figure 3-12 Model 5IF (Surry Unit 1) Results of SLB Thermal-Structural Analysis, Z Deform ation on Hot Leg ............................................................................................ 3-15 Figure 3-13 Sub-Model for Computational Analysis ........................................................................ 3-16 Figure 3-14 R epresentative Solid M odel ........................................................................................... 3-19 Figure 3-15 Representative Dimensions for All Models ................................................................... 3-19 WCAP- 17345-NP June 2011 Revision 2

ix LIST OF FIGURES (cont.)

Figure 3-16 Implemented M odel M esh, View Down Z-Axis ............................................................ 3-20 Figure 3-17 Boundary Conditions for A ll Models ............................................................................. 3-21 Figure 3-18 M odel 44F Contact Pressure Results, 2.655 in. Radius ................................................ 3-35 Figure 3-19 Model 44F Contact Pressure Results, 7.219 in. Radius. ....................... 3-35 Figure 3-20 Model 44F Contact Pressure Results, 18.171 in. Radius ............................................... 3-36 Figure 3-21 M odel 44F Contact Pressure Results, 28.21 in. Radius ............................................... 3-36 Figure 3-22 Model 44F Contact Pressure Results, 34.598 in. Radius ............................................... 3-37 Figure 3-23 Model 44F Contact Pressure Results, 48.288 in. Radius ............................................... 3-37 Figure 3-24 Model 4IF Contact Pressure Results, 4.0216 in. Radius ............................................... 3-38 Figure 3-25 Model 51F Contact Pressure Results, 11.772 in. Radius ............................................... 3-38 Figure 3-26 Model 51F Contact Pressure Results, 20.498 in. Radius ............................................... 3-39 Figure 3-27 Model 51F Contact Pressure Results, 30.193 in. Radius ............................................... 3-39 Figure 3-28 Model 51F Contact Pressure Results, 48.613 in. Radius ............................................... 3-40 Figure 3-29 Model 5IF Contact Pressure Results, 58.308 in. Radius ............................................... 3-40 Figure 3-30 Model 44F: Circumferential Contact Pressure at the Critical Radius ............. 3-45 Figure 3-31 Model 44F: Circumferential Contact Pressure at the Minimum Radius........................ 3-46 Figure 3-32 Model 44F: Circumferential Contact Pressure at the Maximum Radius ....................... 3-47 Figure 3-33 Model 5 IF: Circumferential Contact Pressure at the Critical Radius ....................... 3-48 Figure 3-34 Model 51 F: Circumferential Contact Pressure at the Minimum Radius........................ 3-49 Figure 3-35 Model 5 IF: Circumferential Contact Pressure at the Maximum Radius ........... 3-50 Figure 3-36 Typical Result for Plotting the Combined Tube and Tubesheet CTE Values vs. H* from the Licensing Basis Analysis (Ref. Model D5 NOP) ..................... 3-65 Figure 3-37 Typical Result of Combined Tube and Tubesheet CTE Values vs. Monte Carlo Rank Order from the Licensing Basis Analysis (Ref. Model D5 SLB) ......................... 3-65 Figure 3-38 H* Curves from Response Surface (Ref. M odel F) ....................................................... 3-66 Figure 3-39 Variation in H* from a Linear Fit of H* Results in a Range of Order Statistics Required to Meet Probabilistic H* Goals (Ref. Model 44F NOP) ................................ 3-66 Figure 3-40 Variation in H* from a Linear Fit of H* Results in a Range of Order Statistics Required to Meet Probabilistic H* Goals (Ref. Model 51F NOP) ................................ 3-67 Figure 3-41 Model 5 IF NOP Combined CTET and CTETs vs. Monte Carlo Rank Order ................. 3-67 Figure 3-42 Model 5IF NOP Combined CTET and CTETS vs. H* Value .......................................... 3-68 WCAP- 17345-NP June 2011 Revision 2

x LIST OF FIGURES (cont.)

Figure 3-43 Model 5 IF H* Summary Showing Linear Fit Results ................................................. 3-68 Figure 3-44 Model 44F NOP Combined CTET and CTETS vs. Monte Carlo Rank Order ................ 3-69 Figure 3-45 Model 44F NOP Combined CTET and CTETS vs. H* Value......................................... 3-69 Figure 3-46 Model 44F H* Summary Showing Linear Fit Results ................................................. 3-70 Figure 3-47 Effect of Poisson Contraction on Contact Pressure; Model 44F ................................... 3-88 Figure 3-48 Model 44F Crevice Pressure Adjustment Curve ......................................................... 3-90 Figure 3-49 Model 5IF Crevice Pressure Adjustment Curve ........................................................... 3-90 WCAP-1 7345-NP June 2011 Revision 2

1-1 1 INTRODUCTION The purpose of H* is to replace the tube-end weld with the hydraulic expansion joint as the primary pressure boundary in the SG There are two principal requirements for H*:

1. Assure that the tube(s) do not pull out of the tubesheet under the most limiting loads during normal operating or accident conditions.

2. Assure that the primary coolant leakage through the tube-to-tubesheet crevice is no greater than the leakage assumed in the final safety analysis report (FSAR) for the most limiting accident.

After withdrawal of the first permanent license amendment requests in 2008, the industry addressed the questions posed by the U.S. Nuclear Regulatory Commission (NRC) about the technical analysis, and in September 2009, the NRC issued its first of several approvals of H* that recognizes the hydraulic expansion joint as the primary pressure boundary (Reference 1-1, typical). The approval in each case was limited to the operating period until the plant's next scheduled inspection because, as stated by the NRC, one technical issue remained to be resolved. The technical issue revolves around the relationship between tubesheet bore eccentricity and the tube-to-tubesheet contact pressure. This issue was identified in Reference 1-2, which provided 14 questions related to this issue. (Although Reference 1-2 is not a formal request for additional information (RAI), it will be referred to in this report as an RAI.) The purpose of this report, in conjunction with References 1-6 and 1-7, is to provide final resolution of the remaining questions in support of the permanent application of the H* criterion. The remaining eccentricity issue impacts both the structural and leakage analysis aspects of the H* analysis.

In this report, reference to the "current licensing basis" means the basis on which the temporary licenses were provided to the Model 44F and Model 5 IF plants. Principally, the technical basis for the current licensing basis is contained in WCAP- 17091 -P, Rev. 2 (Reference 1-3) and WCAP- 17092-P (Reference 1-4), but also includes other documents included in the respective License Amendment Requests (LARs) from various plants with different models of SGs.

1.1 ORIGINAL NRC RAI RESOLUTION ACTION PLAN DISCUSSION Westinghouse initially interpreted the thrust of the NRC questions as follows:

The H* structural justification includes an analysis that determines the contact pressure between the tubes and the tubesheet. The reference model for this calculation, the "Scale Factor Model" (SF) is a previously documented model (Reference 1-5) developed to determine the contact pressure for various values of dilation and eccentricity of the tubesheet bore. The output of this model is a multiplier to be applied to the calculated value of contact pressure due to tubesheet bore dilation, which is subtracted from the contact pressure generated due to tube-to-tubesheet differential thermal and pressure expansions. Because the transient conditions for one model (D5) of the affected steam generators required application of this model for conditions outside of the applicability of the reference model, a second model, the "Square-Cell Model" (C2), a two-dimensional (2-D) finite element analysis (FEA), was utilized to directly determine the contact loads between the tubes and the tubesheet for these conditions.

WCAP-17345-NP June 2011 Revision 2

1-2 Both models are based on conservative analysis and assumptions; however, Westinghouse believes that the C 2 model more accurately represents the physical structure. Originally, the principal purpose of the C 2 model was to demonstrate that adequate contact pressure exists around the circumference of the tube under significant tubesheet bore eccentricity conditions. The two models, SF and C 2, are entirely different approaches; thus it is not expected that the results from both models provide the same results.

Westinghouse believed that, in aggregate, the NRC unresolved issue questions requested a comparison of the models and rationalization of the conservatism of the current licensing basis.

During a meeting in January 2010 with the NRC and the industry participants, Westinghouse proposed a plan to resolve all of the NRC questions through an approach believed to minimize the potential for additional questions. The NRC staff did not reject the recommended approach but stated that the 14 questions provided by Reference 1-2 must be clearly, if not directly, addressed. The target date established for a permanent H* license was the Spring 2011 outages. It was expected at the time that the contact pressures developed using the C2 model would be of such a magnitude that the conservatism of the original licensing basis from both a structural and leakage integrity basis would be readily demonstrated.

1.2 REVISED NRC RAI RESOLUTION ACTION PLAN DISCUSSION The Westinghouse action plan to respond to the 14 RAI questions, presented at the January 2010 meeting, was revised as discussed below.

1.2.1 Road Map to Final Response to 14 NRC RAI Except RAI #5 and RAI #12 It was determined by the NRC staff that the issues related to the SF model were resolved and that within the context of the SF model, eccentricity does not appear to be a significant variable affecting the tube-to-tubesheet contact pressure or calculated H* distances. This conclusion is based largely on the information provided in References 1-6 and 1-7 (LTR-SGMP-10-78 P-Attachment and LTR-SGMP-10-33 P-Attachment). From this information, the NRC staff concluded in Reference 1-8 that several of the NRC questions no longer require specific answers. Reference 1-7 provides a final response for each of the 14 remaining questions except RAI Questions #5 and #12, which address the C 2 model specifically. A more detailed description of the C 2 model, necessary to complete this remaining action, is provided by this report.

1.2.2 Need for Alternate Leakage Factor Approach The Darcy formulation was used in References 1-3 and 1-4 to develop the ratio of leak rates between postulated accident induced conditions (SLB) and normal operating conditions (NOP). The driving heads (Ap) at both of these conditions are known, as are the temperatures and pressures to define the fluid viscosity (it). In References 1-3 and 1-4, because the physical length of the leak path was the same under both normal operating and accident conditions, the length of the leak path was not a factor. The only remaining factor was the loss coefficient (K). Based on the analyses using the C2 model, the length of the leak paths under normal operating conditions and accident conditions may differ; therefore, the SLB to NOP leak rate ratio is re-evaluated in Section 4 of this report.

WCAP-17345-NP June 2011 Revision 2

1-3 The available data for hydraulically expanded tubes in tubesheet simulants (References 1-9 and 1-10),

both at room temperature and at elevated temperature, were used in References 1-3 and 1-4 to show that no correlation exists between loss coefficient and contact pressure. However, because the data exhibit considerable scatter, confidence in this data analysis was low. Engineering judgment could suggest that loss coefficient might be related to the absolute contact pressure between the tubes and the tubesheet.

Hence, a requirement was applied to the H* leakage analysis by the regulatory authorities that it is necessary to show that the contact pressure at accident induced conditions exceeds the contact pressure at normal operating conditions (PCsLB:PCNoP> 1).

The limiting accident leakage condition for H* for the Model 44F and Model 5IF SGs is the steam line break (SLB) condition. The Model 44F and Model 5IF SGs do not have a feedline break transient condition in their licensing basis. The contact pressure in the Model 44F and Model 5IF SGs during SLB meets or exceeds the contact pressure during NOR The criterion for contact pressure (PCSLB:PCNop>I) is met in application of the C2 model as well as the SF model.

1.2.3 C2 Model Contact Pressures Results Although in general, the C2 model contact pressure results exceed those based on the scale factor (SF) model results, the contact pressure results based on the C2 model are not always greater than the SF model results. Using the C2 Model, it was determined that the magnitude of contact pressures did not increase at all tubesheet radii at all elevations relative to the SF analysis results during normal operating and SLB conditions. As a result of the change in contact pressures, re-calculation of the probabilistic H* value was required for each model SG in the H* fleet.

1.2.4 Process for Determining the Limiting H* Value The final H* depth recommended is the 95% probability at 50% confidence (95/50) estimate of H*.

Consistent with prior practice, the 95% probability at 95% confidence (95/95) estimate of H* is also provided for information. The probabilistic H* depth is based on the mean H* value for the limiting tubesheet radius. When applying the C2 model, the definition of the mean H* must include an adjustment for Poisson contraction because the model does not inherently include it. The thick shell model inherently included the effect of Poisson contraction. Poisson contraction is a real physical response of the material and, therefore, must be accounted for in the calculation of the H* values. Calculation of the mean H*

value is required to determine the radial location on the tubesheet at which to calculate the probabilistic values of H*; however, the calculation of the probabilistic H* is independent of the mean value of H*.

Including the Poisson contraction when determining the mean value of H* is important insofar as the radial location of the limiting mean value of H* may depend on application of the Poisson correction.

As discussed in detail in References 1-3 and 1-4, the principal variables affecting the probabilistic value of H* are the coefficients of thermal expansion of the tube and tubesheet materials. The specific values of these variables that define probabilistic analysis of H* based on the C2 model are determined from the 2 variability surface described in Figure 8-5 of References 1-3 and 1-4. Application of these values in the C model is discussed in Section 3.4 of this report. The probabilistic estimate of H* is further adjusted by the addition of a factor to account for the Poisson contraction of the tubes due to end cap loading, and a further adjustment of the length to account for the effect of the crevice pressure distribution which is dependent on the initially predicted length of H*. The adjustment for crevice pressure distribution is WCAP-17345-NP June 2011 Revision 2

1-4 discussed in References 1-3 and 1-4 and Section 3.6 of this report. The adjustment for Poisson contraction is discussed in Section 3.5 of this report.

The limiting H* estimate for NOP and SLB is determined for the worst-case sector of the tubesheet, which is the region of the tubesheet perpendicular to the tube lane, plus or minus five degrees azimuthally (see Section 6.2.3 of References 1-3 and 1-4). The H* estimate is determined using TS displacements from the worst-case sector calculated using a three-dimensional (3-D) half-symmetry finite element model of the lower SG complex described in Section 6.2.1 of References 1-3 and 1-4 and further discussed in Section 3.2 of this report. The tubesheet displacements are input to the calculation of contact pressure between the tube and the tubesheet at multiple elevations at each tubesheet radius in the limiting sector. The distribution of contact pressure as a function of elevation at a given tubesheet (TS) radius (see Section 3.3) defines the pull out resistance of a SG tube to an applied end cap load at that radius. The required H* length is defined by the integration of the cumulative pull out resistance as a function of depth in the tubesheet. The structural model used to calculate the contact pressures between the tubesheet and the tube is a pseudo sub-model to the 3-D FEA model, called the square cell model (C2 in this report).

The C 2 model is a quarter symmetry model of the tube and tubesheet material in a single tube pitch subjected to applied pressure and temperature in addition to the applied displacements from the tubesheet.

A separate C 2 model is developed for each elevation at a single TS radius. The radial location of the worst case H* estimate is the TS radius with the longest required engagement length to balance an end cap load of 3APNOP or 1. 4 APDBA (whichever condition results in a greater H* value) assuming mean material properties. See Section 3.3 of this report for a detailed description.

The probabilistic estimate of H* is based on a Monte Carlo simulation for determining the effect of varying the TS coefficient of thermal expansion (CTE) and the tube (T) CTE on the contact pressure based on the limiting operating condition from the mean material estimate of H*. The final result of the simulation is the combination of TS and T CTE that defines the 95 percentile probability at a 50 percent or greater confidence estimate for increasing H* during the limiting operating condition at the limiting TS radius. The predicted combination of CTEs from the simulation is input to the C 2 model to calculate the value of H* at the required probabilistic estimate. See Section 3.4 of this report for a detailed description.

The distribution of contact pressure for the limiting operating condition, at the limiting TS radius, at the required probabilistic estimate, is used to determine the effect of Poisson contraction on the probabilistically defined H* value. The effect of Poisson contraction is determined by using standard thick shell equations (see Section 3.5) to calculate the reduction in contact pressure from a corresponding reduction in the outer diameter of the tube due to an applied axial end cap load on a closed thick walled pressure vessel. The net result is added to the probabilistic H* value to increase the required engagement length of the tube portion within the tubesheet. The Poisson contraction is based on the probabilistic contact pressure profile because the probabilistic value of H* is the basis of the requested license amendment.

The crevice pressure effect is added to H* after the probabilistic value of H* with the Poisson effect is determined. The effect of crevice pressure on the structural analysis is described in Sections 6.4.8 and 8.1.2 of References 1-3 and 1-4 and in Section 3.6 of this report. The crevice pressure adjustment is applied after the adjustment for Poisson contraction because the Poissoncontraction is an adjustment for a loading condition that is independent of the crevice pressure correction.

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1-5 As a result of the issues discussed above, the action plan shifted from demonstrating the conservatism of the current licensing basis to the following:

1. Using the more accurate C 2 model to confirm that the contact pressures at accident conditions exceed those at normal operating conditions, and to demonstrate that the criterion for contact pressure (SLB:NOP>1) for each of the model SGs in the H* fleet is met at all tubesheet bundle radii. For the Model D5 SG and for the 2-loop Model 44F SG, it was determined that the requirement PCSLB:PCNoP>I could not be met; therefore, two alternate means were developed to demonstrate that the leakage factors in place in the current licensing basis remain conservative for these model SGs.

2. Using the more accurate C 2 model, calculation of revised probabilistic H* values for each of the models of steam generators in the H* fleet.

Three reports are provided for the entire population of H* candidate plants:

WCAP-17330-P, Rev. 1; a combined report for the Model F and D5 SGs.

WCAP-17345-P, Rev. 2, a combined report for the 3-loop Model 44F and 51F plants (this report).

This report addresses the C 2 model results for the 3-loop Model 44F and 5IF SGs and provides a final response to RAI Question Numbers 5 and 12. The remainder of the NRC RAIs have been answered in previous submittals as discussed in Section 1.2.1 above.

• WCAP-17378-P, Rev. 0, a separate report for the single Model 44F 2-loop plant.

1.3

SUMMARY

OF THE IMPACT OF INDEPENDENT REVIEW ON H*

The H* utilities contracted MPR Associates to perform an independent review of the H* analysis that serves as the bases for the permanent alternate repair criteria (PARC). The MPR review recommended three significant changes to the document:

" Westinghouse should update the Poisson contraction calculation process.

" Westinghouse should provide an improved justification of the simplified C 2 model probabilistic analysis ("breakline" concept).

• Westinghouse should add a discussion of the method to transform the 95/50 to 95/95 H*value to the report.

Item number 1 is discussed in Section 3.5.4, "Calculation of Contact Pressure Reduction from Poisson Effect" of this report. Items 2 and 3 are discussed in Section 3.4.2, "Methods Discussion" of this report.

Also, two new references were included in the report as a result of the MPR review, References 3-15 and 3-16. These references provide an alternate method of justifying the "breakline" concept and an improved statistical analysis of the coefficient of thermal expansion data used in the H* analysis. It is important to note that the recommendations by MPR Associates did not alter the H* distances or leakage factors identified by Westinghouse in the H* licensing basis documents.

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1-6

1.4 REFERENCES

1-1. USNRC Letter, "Vogtle Electric Generating Plant, Units 1 and 2, Issuance of Amendments Regarding Technical Specifications (TS) Section 5.5.9, "Steam Generator Program," and TS 5.6.10, "Tube Inspection Report," for Interim Alternate Repair Criteria (TAC Nos. ME1339 and ME 1340)," September 24, 2009. (typical for H* participants).

1-2. USNRC Letter, "Vogtle Electric Generating Plant, Units 1 and 2 - Transmittal of Unresolved Issues Regarding Permanent Alternate Repair Criteria for Steam Generators (TAC Nos. ME1339 and ME 1340)," November 23, 2009.

1-3. WCAP-17091-P, Rev. 0, "H*: Alternate Repair Criteria for the Tubesheet Expansion Region in Steam Generators with Hydraulically Expanded Tubes (Model 44F)," June 2009.

1-4. WCAP- 17092-P, Rev. 0, "H*: Alternate Repair Criteria for the Tubesheet Expansion Region in Steam Generators with Hydraulically Expanded Tubes (Model 5 IF)," June 2009.

1-5. SM-94-58, Rev. 1, "Doel 4 Elevated Tubesheet Sleeve -ASME Code Evaluation and Effect of Tubesheet Rotations on Contact Pressures," December 1995. (Proprietary) 1-6. LTR-SGMP-10-78 P-Attachment, "Effects of Tubesheet Bore Eccentricity and Dilation on Tube-to-Tubesheet Contact Pressure and their Relative Importance to H*," September 2010.

1-7. LTR-SGMP-10-33 P-Attachment, "H*: Response to NRC Questions Regarding Tubesheet Bore Eccentricity," September 2010.

1-8. USNRC Letter, "Vogtle Electric Generating Plant - Audit of Steam Generator H* Amendment Reference Documents (TAC Numbers ME3003 and ME3004)," July 9, 2010.

1-9. CN-SGDA-03-119, Rev. 1, "Calculation of Loss Coefficient for Model D5 Steam Generators,"

Westinghouse Electric Company LLC, June 2004.

1-10. STD-MCE-03-49, "Determination of Model D5 Tube-to-Tubesheet Leakage Resistance for H-Star Program for CBE/CDE/DDP/TCX," November 4, 2003.

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2-1 2 SQUARE CELL (C2) MODEL ANALYSIS This section provides a generic description of the C2 model. Although there are SG model-specific applications of the C 2 model, the description of the C2 model is based principally on the application for the Model D5 steam generators because the model was initially developed for the Model D5 steam generators. The entire generic description of the C 2 model applies equally to the Model 44F and Model 5 IF steam generators.

2.1 PURPOSE OF THE C 2 ANALYSIS Figure 1-1 in the current licensing basis (Reference 2-1) defines the calculation process for H*. The foundation for all of the structural analyses is a global model of the lower tubesheet complex (called the 3-D FEA model) that provides the tubesheet displacements that are used to calculate tube-to-tubesheet contact pressures. In the current licensing basis for H*, based on the thick shell equations, tubesheet displacements generated by the bending of the tubesheet from the primary-to-secondary pressure differential in the global 3-D model are applied directly to the inner diameter of the tubesheet tube bore.

This is a conservative assumption that does not accurately represent the real physical condition.

The deflections of the tubesheet tube bore surfaces occur due to the radial thermal growth, radial pressure growth and the primary-to-secondary pressure differential acting on the tubesheet. The thermal growth of the tubesheet itself and the distortion of the tubesheet tube bore due to bending of the tubesheet under the primary-to-secondary pressure differential are transmitted to the tube bore through the tubesheet material to the ligament surrounding a given tube. The square cell model analysis (C2) is a more accurate approach to modeling the process by which the tubesheet deformations are transferred to an individual tube bore.

Figure 2-1 and Figure 2-2 illustrate the differences between the approach utilized in the thick shell model and that used in the square cell model in applying the displacement calculated with the 3-D FEA lower tubesheet complex model.

In Figure 2-1, the calculated local displacements are applied to the inner diameter of the tubesheet tube bore. In Figure 2-2, the calculated local displacements are applied to the outer edges of the tubesheet cell material, and the displacements at the inner diameter of the tubesheet tube bore evolve from the local structural model (the C2 model). The analysis method in Figure 2-2 is physically more realistic because it mimics the process by which the gross tubesheet displacements are transferred to the circumference of the tubesheet tube bore. The analysis method in Figure 2-1 is the simplest option for comparing the finite element model to analytical equations, i.e., the classical thick shell equations. Also, if the geometry of the model is circular, the simplest way to apply a postulated load or displacement on the collars is to a surface which includes the inner diameter. However, because the global model does not include a distinct representation of the individual tube bore, additional assumptions must be made to determine what displacements should be applied to the boundaries of a local model (as shown in Figure 2-2) so that the tubesheet tube bore deflects in a realistic fashion.

The issue of how tubesheet tube bore deflection affects the tube-to-tubesheet contact pressure is the same regardless of the method chosen to apply displacements from the large scale model (3-D FEA) to the local sub-model. The basic problem is defined by how the large scale tubesheet deflections are transferred (or "mapped") to the local scale of a single tubesheet tube bore and tube. For the purposes of this report, the terms large scale and global scale refer to the 3-D finite element model of the channelhead, tubesheet, WCAP-17345-NP June 2011 Revision 2

2-2 divider plate and lower shell (a.k.a., "stub barrel") that make up a typical Westinghouse designed steam generator in the existing domestic fleet (see Figure 2-3). In the case of the prior H* analysis (Reference 2-1), the sub-modeling is complicated by the fact that the presence of the perforations in the tubesheet are smeared throughout the perforated region in the tubesheet using the method of Slot (Reference 2-2). This means that in the global model of the lower steam generator complex the tube bores do not exist although the effect of the perforations on the structure is accounted for with respect to pressure and temperature. This is a complication for the square cell model approach because the exact displacements around a tube pitch cannot be directly taken from the 3-D finite element model of the lower SG complex.

Figure 2-1 Current Licensing Basis Tubesheet Bore Displacements (Local displacement applied directly to tubesheet bore) 1 4

Figure 2-2 C2 Model Tubesheet Bore Displacements (Local displacement applied to surrounding tubesheet material)

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2-3 The effect of the perforations in the non-perforated model with the effective material properties includes the expansion of the tubesheet with respect to temperature and pressure, assuming that all the tubes in the bundle are pressurized. The elastic modulus and Poisson's ratio of the perforated material are altered so that the isotropic material becomes orthotropic. This means that the stiffness of the tubesheet along different axes is different so that the expansion of the tubesheet due to the combined pressure and temperature loads is conserved without the perforations being modeled. The question remains as to how to include the effect of the individual tube bores interacting locally. That question can be accommodated using different sub-models which, in general, are not necessary to calculate the tube-to-tubesheet contact pressure. Section 6.2.3 in Reference 2-1 describes one approach to bridging the gap between a single tubesheet tube bore in an isolated model and including effects for the presence of other linked tubesheet tube bore at a local scale due to pressure at a given operating temperature. The reason they are not necessary is that along any given radial line from the center of the tubesheet it is possible to determine what the displacement is over that entire distance. This means that the displacement of a unit section can be determined but the displacement of a specific tube bore cannot be determined from the global model.

In the case of H*, the displacement of specific tubes at key radii is used in determining the average tube-to-tubesheet contact pressure.

Figure 2-3 shows a general model of the lower steam generator complex which is the source of the displacements used in the square cell analysis. The intent of the C 2 model is to simulate a limited thickness "core sample" of a single tube at a given radius as shown in Figure 2-4. The square cell model, shown in Figure 2-5, Figure 2-7, and Figure 2-8, is a local model consisting of plane stress solid elements that approximate the tube and tubesheet material defined by a one-half tube pitch around a single tubesheet tube bore through the thickness of the tubesheet (typically 21.03 inches). This is the definition of the unit "square cell" model of the local tubesheet tube bore. The intent of this model is to provide a physically more realistic estimate of the contact pressure between the tube and the tubesheet at various elevations through the thickness of the tubesheet during the operating condition of interest.

2.2 DEFINITION OF THE C2 MODEL The square cell model is based on a unit cell of tubesheet material surrounding a single tubesheet tube bore in various models of Westinghouse steam generators. Each SG model is represented by a separate square cell model. The square cell is defined by taking one-half of the nominal tube pitch around a tube as the limit of the material in the model. The initial dimensions for the square cell model are based on the room temperature unpressurized condition. For example, in a Westinghouse Model D5 SG, the tube pitch is ]a,,c,, inches. The outer nominal tube radius is [ ]a..c. inch. The inner nominal tube radius is

]a~c~e inch. The resulting square cell is shown in Figure 2-7 below, with typical boundary conditions applied on the model. A quarter section of the model is typically used for analysis.

The square cell model is oriented in the X-Z plane of the tubesheet as defined in the lower SG complex shown in Figure 2-3. (For clarity, the square cell model is in the plane of the tubesheet but, for convenience, the square cell model is imported to ANSYS in an X-Y plane as noted in Figure 2-6.) The applied displacements, or forces, representing the net strain over the cell in the global X direction (formerly referred to in prior RAI responses as "e-bar") and the global Z direction (formerly referred to in prior RAI responses as "z-bar"). These net displacements are now referred to as AX and AZ.

WCAP- 17345-NP June 2011 Revision 2

2-4 a,c.e Figure 2-3 Typical Lower SG Complex Model Figure 2-4 Square Cell Model "Core Sample" a,c,e Figure 2-5 Square Cell Model WCAP-17345-NP June 2011 Revision 2

2-5 a,c,e Figure 2-6 Typical Square Cell Coordinate System a,c,e Figure 2-7 Typical Square Model without Symmetry Conditions WCAP- 17345-NP June 2011 Revision 2

2-6 a,c,e (a) Coarse Mesh a,c,e (b) Fine Mesh Figure 2-8 Typical Mesh Square Cell with Quarter Symmetry Conditions WCAP-17345-NP June 2011 Revision 2

2-7 2.3 APPLICATION OF BOUNDARY CONDITIONS There are three categories of boundary conditions that are applied in the square cell model: thermal, pressure and displacement. All components in the square cell model are assumed to be at a uniform temperature, depending on the operating condition, with the tube in equilibrium with the primary fluid temperature. The approaches taken in this analysis were selected because they are consistent with the current licensing basis for H*. The discussion below summarizes the issues with each approach to applying the pressure and displacement loads to the square cell model. The impact of any installation effects from the hydraulic expansion of the tube into the tubesheet tube bore is ignored in this analysis in order to be consistent with the licensing basis used for H*. The potential effect of any strain-hardening from the expansion process can be ignored because the calculated elastic stresses in the tubes do not exceed the elastic limit of the tube material (see Section 6.2.5 of Reference 2-1).

2.3.1 Deformation of Tubesheet Cell Edges Displacement based boundary conditions are used in the C2 approach in a pseudo sub-model approach because the global model dictates how the sub-model should behave at the nodal level. For example, if the displacements due to the effect of temperature and pressure around the entire boundary of the sub-model are known, then those displacements can be directly applied to the sub-model. The square cell analysis is not a true sub-model analysis because the nodal displacement is not used as the applied boundary conditions. Instead, the average displacements over a tube pitch at a specified location and elevation are used. Loads which lead to additional displacements in the C2 model (such as the thermal expansion of the tubesheet tube bore inner diameter) are not additive with the displacements from the initial conditions taken from the global SG model. This is because the applied displacements on the boundaries of the square cell model already account for the expansion of the tubesheet material due to pressure and temperature.

The preferred approach in the square cell analysis is to specify displacements at the boundaries of the tubesheet material as taken from the 3-D finite element model of the lower SG complex. Figure 2-9 illustrates the potential responses to the applied displacement that can occur in the square cell model.

It is important to understand that from the perspective of calculating the tube bore eccentricity based on the deflection of the major and minor axes of the tube bore all of the possibilities in Figure 2-9 (a through c) are equal. The reaction of the model to those displacements is different based on how the nodal constraints are applied. For example, in Figure 2-9a, all nodes on the boundaries are assumed to expand equally along the different axes. In Figure 2-9b, nodal constraints are used so that the end points of the tubesheet material deform the entire distance and the remainder is linearly related to the maximum displacement. In Figure 2-9c, the displacement of the two surfaces in the model develops naturally based on the applied displacement with no constraints on the nodal behavior. Figure 2-9a is the most conservative application of the displacement because it minimizes contact forces. Figure 2-9b tends to maximize the eccentricity in the tubesheet tube bore. It is not physically possible for the outer edges of the tubesheet material to deform in this manner because a stress discontinuity will result at the intersections of the orthogonal boundaries. Further, the growth from adjacent pressurized tubesheet tube bore will also act to prevent such a deformation in the majority of the bundle. Figure 2-9c has no assumptions on the deformation of the tubesheet tube bore material and allows a non-uniform displacement to develop on either edge in response to the applied displacement. However, the majority of WCAP- 17345-NP June 2011 Revision 2

2-8 the deformation in the tubesheet is due to thermal effects, which means that the tubesheet material should deform in a mostly uniform manner. Therefore, the approach shown in Figure 2-9c is not used.

Figure 2-9a is the preferred approach to applying the displacement taken from the lower SG complex model because it is the most conservative for calculating H*.

(a) (b) (c)

Figure 2-9 Sketches of Possible C2 Model Response to Applied Displacement 2.3.2 Applying the Internal and Crevice Pressures in the Square Cell Model Two pressure loads must be accounted for in the square cell model. The first is the internal pressure acting on the inner diameter of the tube representing the reactor coolant pressure. The second is the crevice pressure that the outer diameter of the tube and the inner diameter of the tube bore are exposed to assuming a through-wall flaw in the tube. The distribution of the crevice pressure varies according to the elevation of the tube in the tubesheet relative to the location of the flaw that allows the primary coolant into the crevice (References 2-3 and 2-4).

The internal pressure and crevice pressure can be included in the square cell model in two ways: First, the difference in the pressure acting on the outer diameter of the tube and the inner diameter of the tube can be applied as a pressure load that varies according to the elevation within the tubesheet. In this case, both the internal pressure acting on the tube and the crevice pressure are combined into the single differential pressure applied on the inner diameter of the tube. Second, the full internal pressure is applied to the inner diameter of the tube and the full crevice pressure (as a function of elevation) is applied to the outer diameter of the tube and the inner diameter of the tubesheet tube bore. The first option is the preferred approach in the square cell model because it conservatively minimizes the growth of the tube at the lower elevations of the tubesheet. This leads to a reduced contact pressure at the bottom of the tubesheet. This option is also simple to resolve with the contact options available in the structural analysis code, ANSYS, because a uniform pressure is pushing the outer surface of the tube into the inner surface of the tubesheet.

The second crevice pressure option is difficult to resolve with the contact options in ANSYS.

The crevice pressure is assumed to act on 100% of the circumference of the outer diameter of the tube surface and inner diameter of the tubesheet tube bore. It is also simpler to account for the effect of the crevice pressure over the entire tubesheet tube bore as opposed to limited regions of the tube outer diameter. This assumption is conservative because test data (References 2-1 and 2-4) shows that this cannot occur. The observed leakage during the tests was more aptly characterized as "weepage,"

i.e., dropwise leakage. Also, recent work reported in the literature (Reference 2-5) based on fluid structure interaction shows that fluid blanketing of the entire crevice cannot occur. Both point to evidence that WCAP-17345-NP June 2011 Revision 2

2-9 supports the assumption in the analysis of record for H* of a "tortuous path" that the liquid must take as it diffuses through the porous medium of the tube-to-tubesheet crevice. However, the nature of the test specimens, used in References 2-1 and 2-4, make it impossible to ascertain what portion of the tube outer diameter constitutes a wetted surface. Limited sensitivity studies have been performed to determine the effect of applying the crevice pressure over a smaller portion of the tube. In these studies, "bubbles" of crevice pressure were applied to the tube bore inner diameter and the tube outer diameter while the full internal pressure was applied to the inner diameter of the tube. The "bubbles" varied in circumferential extent from 10 to 75 percent of the tube outer diameter. The effect of limiting the crevice pressure to less than 100 percent of the outer tube diameter was an increase in the average tube-to-tubesheet contact pressure of at least 10 percent.

2.4 MATERIAL PROPERTIES The manufacturing process used to assemble a steam generator creates a strain-hardened condition in the tubes. The tubes are initially inserted into the steam generator tubesheet tube bores, "tack" expanded into the tubesheet near the tube end by hydraulic (urethane plug) expansion or mechanical hard rolling over approximately a 0.75 inch length, and welded to the tubesheet. Each tube is then hydraulically expanded into contact with the tubesheet tube bore over the full depth of the tubesheet. This means that each of the tubes in the tube bundle begins in contact with the tubesheet tube bore. It also means that the tubes create a material non-linearity with respect to the contact pressure analysis because they are strain-hardened to a small percentage (1 to 3 percent on average) and typically thinned to a small extent (- 1% wall thinning)

[Reference 2-1]. No non-linear material effects are present in the tubesheet tube bore material. Consistent with the basis of the current licensing basis, the square cell model ignores any effects that could benefit the contact pressure analysis that come from the tube installation and steam generator manufacturing process, including any strain-hardening effect, residual contact pressure, wall thinning or other material non-linearity.

Test data has shown that the installation and tube expansion process develops sufficient pull out resistance between the tube and the tubesheet at room temperature and at elevated temperature conditions (Reference 2-1) to resist any applied pull out loads during normal and accident conditions. Any additional contact pressure dueto tubesheet deformation or applied pressure is above what is already sufficient to prevent pull out of the tube portion within the tubesheet. Therefore, it is conservative and convenient to ignore strain-hardening resulting from initial tube expansion as an initial condition. No elastic-plastic effects are included in the analysis. The displacements and pressures acting on the tubes are applied in an elastic analysis. This is appropriate provided that the average radial stress in the tube material due to the applied loads is less than [ ]apce ksi. None of the contact pressure results in the tube material for the square cell model described in this report approached an average radial stress of 30 ksi.

The material properties used for the tube and the tubesheet materials in square cell model are the same as originally used in the licensing basis analysis, Reference 2-1. The properties used for the Alloy 600 thermally treated tubing and SA-508 tubesheet materials are provided in Table 3-3 and Table 3-4.

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2-10 The Poisson's Ratio used for the tube material is 0.28'. The Poisson's Ratio used for the tubesheet material is 0.30.

2.5 CONTACT MODELING DISCUSSION The only boundary conditions that limit the displacement of the tube in the square cell model are the symmetry conditions on the edges of the model. This means that in the square cell model the contact between the tube and the tubesheet is what limits the potential displacement of the tube. If the contact relationship between the tube and the tubesheet is modeled inappropriately, the tube in the model could slide past the tubesheet and experience rigid body translation. Another possibility is that the tube deformations could lead to inter-penetration of the tube material into the tubesheet material which would generate unrealistically high contact pressures. Conversely, if the contact law is determined to resist node-to-node contact too strongly, the results of the analysis would be an unrealistically low contact pressure. While the ANSYS solver is capable of using different numerical schemes to resolve these difficulties, it is up to the user to make sure that the results which are obtained are appropriate. In the application of the square cell model, the contact pressure results using different contact modeling options were compared to determine the best approach. The final contact model used in the square cell analysis is a frictional model which is consistent with the assumptions in the H* analysis (e.g., =- [ ]*",).

In FEA structural modeling, the simplest way to prevent difficulties with a contact law is to construct a properly converged mesh. The metric used for mesh convergence in the C 2 analysis is the average contact pressure (radial stress) between the tube and the tubesheet. A mesh is typically considered properly converged when the change in the average contact pressure from a model with an increased mesh density is less than a defined percentage (i.e., 2%) different from the prior mesh density. It is difficult for nodal interpenetration to occur if a mesh is fine enough, because the nodes on either side of the contact surface will be aligned and cannot "slip" past each other. The symmetric boundary conditions also help to maintain the nodal positions on either side of the contact surface so that the nodes remain aligned properly throughout the analysis. Several mesh designs were evaluated in the C 2 analysis. Figure 2-8 shows the coarsest and the finest meshing schemes used in the analysis. The coarse mesh (shown in Figure 2-8a) has approximately [ ]a,,,, contact elements along the tube-to-tube bore interface. The fine mesh (shown in Figure 2-8b) has approximately [ ]ace contact elements along the tube-to-tube bore interface. 2 The finer meshing schemes tend to predict an increase in the tube-to-tubesheet contact pressure relative to the coarser meshes and can resolve the contact pressure closest to the boundaries in a quarter symmetry model with a higher degree of accuracy. However, the contact pressures nearest the displacement boundary conditions on the tube in the quarter symmetry model are not significant to the problem and lower contact pressures are conservative. Therefore, for conservatism, the preferred meshing scheme in the square cell analysis is a slightly more coarse mesh. Tests of the coarser mesh showed that it

1. The 2007 Edition of the ASME Code gives a value of Poisson's Ratio for Alloy 600 as 0.31. This is used in the Poisson's Ratio contraction calculation (Section 3.5) because that calculation focuses solely on the tube material. A Poisson's ratio of 0.28, a 10% reduction in the Code value and within the stated potential variation of the ASME Code properties, is used for the tube in the square cell analysis in order to facilitate the finite element analysis. Reducing the Poisson's ratio of the tube in this case increases the difference in the stiffness coefficients between the tube and the tubesheet which reduces the likelihood of numerical complications due to stress singularities in the model. The net effect on the calculations from using a Poisson's ratio of 0.28 for the tube is a slight reduction (conservative) in contact pressure, on the order of 10 psi, compared to using the ASME Code value of 0.31 for Poisson's ratio.

2

2. The final meshing scheme used in the C results described in this report for the calculation of H* has approximately [ ]*,ce contact elements along the tube and tubesheet interface.

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2-11 was sufficiently fine to prevent nodal interpenetration. The actual mesh used in the final analysis is shown in Figure 3-13.

The C 2 model mesh was converged to within a 2% difference of the previous model, at which point it was judged that additional refinement of the mesh would not yield a sufficient increase to merit the additional computational effort to solve the model. At that point, the model mesh refinement was reduced to the level of a 5% difference (equating to a roughly 3% reduction in contact pressure from the fine mesh model results) in the average radial stress along the outer diameter of the tube in order to reduce the amount of time necessary to perform each analysis. The alignment of the nodes on both the tubesheet surface and the tube surface was maintained by the boundary conditions in the model so that regardless of what level of mesh refinement was used they would line up appropriately and prevent fictitious material interpenetration.

The potential for an artificially stiff interface between the tube and the tubesheet was addressed in the square cell model. In the ANSYS model used for the analysis, the augmented Lagrangian contact model allows a user to specify the interfacial normal stiffness (any value between 0.01 and 10) or to have the computer determine it automatically in the course of calculating the solution to the model. In the square cell analysis, a sensitivity study was done using the converged mesh in which the solution for the interfacial stiffhess was determined by the computer. The result of that study showed that the initial interfacial normal stiffness began at 1.0 and varied between 0.7 and 1.2 at the end of the solution. These values resulted in material penetrations on the order of 10-9 to 10-13 inch, with very little change in the resulting contact pressure. A non-varying value of 0.7 is used for the interfacial normal stiffness in the square cell analysis which results in interpenetrations on the order of 10-9 to 10-'0 inches. This small level of interpenetration is not a significant issue and is within the bounds of calculated error in the solution process using the ANSYS solver. The interfacial normal stiffness is fixed in order to facilitate the numerical solution of the model.

The tubesheet is defined as the contact target body because the deformation of the tubesheet material is more controlled. The tube is defined as the contact body because the tube is expanding into the tubesheet material and its deformation is poorly controlled in the model. The contact relationship between the tube and the tubesheet is defined as symmetric and rough (e.g., with friction). The contact is symmetric for numerical expediency and because, in the range of deformations under consideration, the tube may lose contact with the tubesheet or the tubesheet may lose contact with the tube. The friction interface allows two-dimensional sliding between the tube and the tubesheet. Shear stresses can develop due to "stick-slip" behavior because the coefficient of friction between the tube and the tubesheet in this model is greater than zero. However, these shear stresses are separate from the calculated contact pressures in ANSYS and do not affect the final results used to calculate H*.

The augmented Lagrangian solver in ANSYS is used to resolve the contact so that the contact pressure results have a smaller variation around the circumference of the tube bore and because the extra degree of freedom helps the solver to calculate the contact interactions quickly. The tube and tubesheet are initially adjusted to be "just touching" using the contact options in ANSYS. The geometry defined in the model is such that the tube and tubesheet begin in line on line contact at the tube-to-tubesheet interface. However, the possibility exists for a small geometric inconsistency to lead to an interpenetration of the tube and tubesheet materials. Therefore, the tube outer surface and tubesheet inner surface are separated by an WCAP- 17345-NP June 2011 Revision 2

2-12 initial offset of +0E00 inch in ANSYS to set the initial gap to zero and to assure that no interpenetration occurs.

There are two options used in the analysis for managing the stiffness of the interface in the square cell model. The first option assumes that the stiffness of the interface is constant and does not need to be updated as the analysis proceeds to completion. This first option is th6 most similar to an analytical model using thick shell equations to solve for the contact pressure between the tube and the tubesheet. The second option assumes that the stiffness must be constantly updated to prevent interpenetration of the tube and tubesheet and adjust the contact law as the deformation of the nodes at the interface shift during the analysis. The "pinball" radius was set to [ ]a,c,c inch to reflect the surface roughness of the post-expanded tube. The pinball radius is the distance about a node on a defined contact surface which, if another existing node on a defined contact surface is equal to or closer than, the two surfaces are recognized to be in contact with each other.

2.6 DISCUSSION OF BENCHMARK MODEL FOR C2 MODEL COMPARISON The contact pressure results for the square cell analysis were benchmarked against classical thick shell equations. The thick shell model for the composite tube and tubesheet collar was developed to accept the displacement of the tubesheet inner diameter surface as input. The benchmark model used the Model D5 tube and tubesheet geometry. The benchmark model used a different thick shell model (see below) than described in the existing licensing basis for the calculation of the H* analysis contact pressures because the goal of the model was to provide an independent check on the square cell model results and the H*

methodology.

2.6.1 Thick Shell Model to Describe Finite Element Model The tube and tubesheet cylinders can be represented as two concentric, open cylinders. The tube material is thermally-treated Alloy 600. The tubesheet material is SA-508 Class 2. Neither cylinder has an applied axial load. There is no internal pressure within the tube. The coefficient of friction between the inner diameter of the tubesheet and the outer diameter of the tube is zero. The tube and the tubesheet are held at the same constant temperature during the simulation of the operating condition although the tubesheet is assumed to have a coefficient of thermal expansion equal to zero. The tube bore dilation, or expansion of the inner tubesheet collar diameter, is specified in the analysis and assumed to be constant regardless of any applied loading for the tube. The tube and tubesheet cylinders are assumed to have a zero stress, or a constant stress condition, along the tube axis (e.g., Gzz = 0 psi). The assembled model geometry appears in Figure 2-10.

WCAP-1 7345-NP June 2011 Revision 2

2-13 TS CollarN Tube*,,.

C Figure 2-10 Tube and TS Collar Assembly In Figure 2-10, a is the inner radius of the tube, b is the outer radius of the tube and also the inner radius of the tubesheet tube bore, and c is the outer radius of the tubesheet collar.

The free radial expansion of the tube, due to a change in temperature, is given by:

• AT = OD *aTUBE OD (t - IREF) (Equation 2-1) 2 Where OD is the outer diameter of the tube, aTUBE is the coefficient of thermal expansion of the tube, t is the temperature of the tube and tREF is the reference temperature in the analysis for the material of interest (typically 70'F). Several values of constant tubesheet tube bore inner diameter displacements were selected for the purposes of this sensitivity study. It is assumed that the tubesheet is essentially rigid with respect to any applied loading from the tube in excess of the initial dilation. The tube bore is assumed to deform (or dilate) as a perfect circular surface without any non-uniformities around the circumference of the tube. The difference between the specified tubesheet tube bore dilation and the amount that the tube wants to expand will create a contact stress between the tube and the tubesheet. See Figure 2-11.

Calculated Tube OD Growth 7,

Z _ m Specified TS ID Dilation Figure 2-11 Constant Tubesheet Bore Dilation Model WCAP-17345-NP June 2011 Revision 2

2-14 In Figure 2-11, P1 is the internal pressure applied to the inner surface of the tube, P2 is the external pressure applied to the outer surface of the tube, P3 is the internal pressure applied to the inner surface of the tubesheet collar, and P4 is the external pressure applied to the outer surface of the tubesheet collar. In the tube and tubesheet assembly, the contact pressure between the two cylinders is taken at the inner surface of the tubesheet collar and the outer surface of the tubesheet such that they are both equivalent (e.g., P2 = P3). There are no other applied pressures on the system so P1 = P4 = 0 psi.

The differential free radial expansion of the tube at normal operating conditions (NOP, t = [ 'OF) and steam line break conditions (SLB, t = [ ] .... 'F), calculated using Equation 2-1 and the material properties defined in Table 3-3 and Table 3-4. The NOP operating temperature of [ ]ace 'F was chosen to better compare to previous results in Reference 2-1 and is still representative of typical NOP conditions. The results are summarized in Table 2-1.

The difference between the inward radial dilation of the tubesheet tube bore and the outer diameter of the tube will change based on the temperatures during operation. The difference between the specified radial dilation of the tubesheet tube bore and the radial growth of the tube for each operating condition is shown in Table 2-2.

Column (1) in Table 2-2 is the assumed inner radius of the tubesheet tube bore and Column (2) in Table 2-2 is the amount that the tubesheet tube bore is allowed to dilate in the analysis. Column (3) and Column (4) in Table 2-2 are the difference between the allowed dilation in Column (2) and the results in Table 2-2 for each operating condition (e.g., AUNOP = Tube Growth - Tubesheet Growth). The difference between the deformations is taken so that a positive value means that the tube deformation exceeds the growth allowed by the tubesheet collar.

The equation for the radial deformation (either positive or negative) of the tube as an open thick walled cylinder at a constant temperature due to pressure loading is:

2 AlTUBE _Ew rb a2 (1-vuEXPla2 -p 2b2) )a 2 b 2 (l+v.E rEquation (P 2-2) 2 ATB= TB(b2-a21( - VTL B pa~ r2j PI-P Where r is the radial location within the tube material, b is the outer radius of the tube, a is the inner radius of the tube, ETUBE is the Young's modulus of the tube at the given operating condition and VTUBE is the Poisson's Ratio for the tube material. The equation for the radial deformation (either positive or negative) of the tubesheet collar as an open thick walled cylinder at a constant temperature due to pressure loading is:

ARs=Esr (I(- VTsXp~b2-_pc2)+ (I+ VTS )b c2((p3 -P4 (Equation 2-3)

Ts=Es c-bh~ ~T~Pb r Where r is the radial location within the tubesheet material, c is the outer radius of the tubesheet collar, b is the inner radius of the tubesheet collar, ETs is the Young's modulus of the tubesheet at the given operating condition and VTS is the Poisson's Ratio for the tubesheet material.

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2-15 The deformation of the tube is limited by the specified deformation of the tubesheet collar, as shown in Table 2-2, Columns (3) and (4). The values in Columns (3) and (4) are all positive; therefore, the final state of the tube outer surface and the tubesheet inner surface is positive contact. The magnitude of the contact pressure between the tube and the tubesheet will be the result of the additional growth that the tube cannot release due to the "rigid" tubesheet collar. The equation for the change in radial position of the contact surface between the tube and the tubesheet is:

AU = [ARTs ]=b -[ [ARTUBE Lb (Equation 2-4)

Where AU is the condition specific result from Table 2-2 for the appropriate value of tubesheet collar dilation in Column (2). Setting P1 and P4 equal to zero and P2=P3 in Equation 2-2 and Equation 2-3 yields the following for r = b, AU = s- b L(1-V sV)(P 2b2)+ (I+v 2 TS)bzc

• .ET S cb 2 - 2 ba (1+vTS ) c2a2 b

E [(1 VTUBX P 2 b2) + (1 + VTUI)a2b (2 P2) (Equation 2-5)

Rearranging to solve forp2 gives the final result.

b b -6) 7:AU[ 2_ [( "X2)+( ETUB C 2

[(+1 _VTUBE)bl)+(I+ VTUE)a2))(Equation2 Solving Equation 2-6 for each value in Column (3) and Column (4) in Table 2-2 with the properties in Table 2-3 and Table 2-4 yields the results shown in Table 2-5.

The results in Table 2-6 exclude any effect of non-uniform deformation around the circumference of the tubesheet tube bore. The loss of contact pressure between the tube and the tubesheet is due solely to the expansion (or dilation) of the tubesheet tube bore relative to the expansion of the tube due to thermal effects. Real deformations applied to the tubesheet tube bore are not perfectly uniform. Therefore, the displacement of the inner tubesheet tube bore was used in order to benchmark the model to compare directly against the C 2 model. Only the average tube-to-tubesheet contact pressure around the circumference of the tube can be calculated using the thick shell equation. This is an acceptable comparison to the finite element results because only the average contact pressure around the circumference of the tube is used in the calculation of H*. This benchmark was performed for the Model D5 NOP condition. The expansion of the inner surface of the tubesheet tube bore due to a pressure differential across the tube wall (i.e., the pressure of the primary fluid minus the assumed circumferentially uniform pressure in the tube/tubesheet crevice) and an applied temperature is shown in Table 2-6. This result was then applied to the inner diameter of the tubesheet surface in the C 2 model. The tube bore displacement in Table 2-6 varies as a function of elevation due to the change in the crevice pressure distribution. The result of using the calculated tubesheet tube bore displacements in the square cell and analytical models is given in Table 2-7. The average contact pressure between the tube and the tubesheet in the C 2 approach with the contact law as described is a very close approximation of the thick WCAP-17345-NP June 2011 Revision 2

2-16 shell equation for the same uniform tubesheet tube bore displacement. Based on the comparison with the thick shell equation models, the C 2 approach and the modeling described in this section are reasonable and appropriate.

Table 2-1 Free Radial Expansion of a Tube Nominal Tube OR CTUBE T tREF AR Condition in in/in-*F OF OF in a,c,e NOP F SLB Table 2-2 Difference between Radial Dilation of the Tube Bore and Tube (1) (2) (3) (4)

Avg TS IR Change in TS IR AUNOP AUSLB in in in in a,c,e 0.3810 0.3811I 0.3813 0.3815 Table 2-3 Rigid Collar Model Input Parameters (Tube)

Nominal Tube Properties Variable Description Value Units b OR in a IR in E (NOP) psi E (SLB) psi a (NOP) in/in-0 F a (SLB) iniin-0 F Poisson's Ratio WCAP-17345-NP June 2011 Revision 2

2-17 Table 2-4 Rigid Collar Model Input Parameters (Tubesheet)

Nominal TS Properties Variable Description Valuea,cjc Units c OR F in b IR in E (NOP) psi E (SLB) psi a (NOP) in/in-0 F (x (SLB) iniin-0 F Poisson's Ratio Table 2-5 Rigid Collar Model Contact Pressure Results (1) (2) (3)

Avg. TS IR P2 NOP P2 SLB

-In Psi psi a,c,e In Psi + psi

-i Table 2-6 Calculated Tubesheet Inner Diameter Dilation Thermal Expansion of TS ID (in.) [ ]a.c.

APcRuEv Expansion Tubesheet Elevation (in.) Combined Expansion (in.) a,c,e BTS Neutral Axis (NA)

TTS WCAP-17345-NP June 2011 Revision 2

2-18 Table 2-7 Comparison of C 2 and Thick Shell Results Contact Pressure Results TTS NA BTS a,c,e Max (psi)

Min (psi)

Average (psi)

Thick Shell WCAP-17345-NP June 2011 Revision 2

2-19

2.7 REFERENCES

2-1. WCAP-17072-P, "H*: Alternate Repair Criteria for the Tubesheet Expansion Region in Steam Generators with Hydraulically Expanded Tubes (Model D5)," May 2009.

2-2. Stress Analysis of Thick PerforatedPlates, T. Slot, Technomic Publishing Co.,

Westport, Conn., 1972.

2-3. LTR-SGDA-07-4 (Proprietary), "Letter Summary of Changes to B* and H* Analysis due to New Crevice Pressure and Divider Plate Data," Westinghouse Electric Company LLC, Pittsburgh, PA, January 17, 2007.

2-4. STD-MC 1-P, Rev. 1, "Pressure Profile Measurements during Tube-to-Tubesheet Leakage Tests of Hydraulically Expanded Steam Generator Tubing," Westinghouse Electric Company LLC, Pittsburgh, PA, August 30, 2007.

2-5. Journalof Pressure Vessel Technology, August 2006, Volume 128, Issue 3, pp. 408-413.

June2011 WCAP- 7345-NP WCAP-117345-NP June 2011 Revision 2

3-1 3 STRUCTURAL CALCULATIONS FOR H*

Section 2 of this report provided a description of the C 2 model, its intent, its design, how it fits in the overall process for calculating the H* distance and what its capabilities are relative to the model based on the thick shell equations. This section summarizes the actual analyses performed for the Model 44F and Model 51 F SGs. Sections 3.1 through 3.3 summarize the significant assumptions in the application of the C 2 model, and the interface between the C 2 model and the 3-D FEA model of the lower tubesheet complex. Section 3.2 discusses the boundary conditions applied for the only Model 51F plant, Surry Units 1 & 2, and the boundary conditions applied for the limiting Model 44F plant, Turkey Point Units 3 & 4. Section 3.3 discusses the solution for the mean value of H*, including the displacement inputs from the 3-D FEA model and the axial contact pressure profiles each tubesheet radius for both the Model 51 F and Model 44F SGs in both tabular and graphical form. Section 3.4 provides the probabilistic analysis based on the C 2 model for the Model 5 IF and Model 44F SGs. By its design and its interface with the 3-D FEA model of the lower tubesheet complex, the C 2 model cannot directly include the effect of Poisson contraction on H*; however, Section 3.5 provides the analysis of Poisson contraction on H*

predicted using the C 2 model. In this section, Turkey Point Units 3 & 4 and Surry Units 1 & 2 are frequently discussed. Turkey Point Units 3 & 4 are the limiting plants for the Model 44F 3-Loop SG plants and Surry Units 1 & 2 are the only Model 51F SG plants. The criteria for defining the limiting plants are discussed in the current licensing basis (i.e., Reference 3-1 and 3-2). Section 3.6 discusses the inclusion of the crevice pressure adjustment to H* result. Section 3.7 provides a summary of the H*

calculations and presents the final H* values.

3.1 OVERVIEW OF THE STRUCTURAL ANALYSIS FOR H*

As noted in Section 2 of this report, the C 2 model is a planar model of a tube in a tubesheet segment. The tubesheet segment can be visualized as a square local segment of the tubesheet that is defined by a single tube pitch ([ ]acC inches for the Model 44F, [ ]acC inches for the Model 5 IF) centered on the location of a tube (see Figure 2-4). The model includes the tubesheet bore and a tube in its expanded diameter but without any residual contact pressure from the hydraulic expansion process. Thus, in its unloaded state, the tube is in zero-pressure line-on-line contact with the tubesheet bore.

The loading conditions applied to the square cell model are:

• Temperature, which varies axially through the tubesheet

• The internal tube pressure modified by the axially-dependent crevice pressure Planar displacements at the model boundaries, which are taken from the 3-D FEA model of the tubesheet complex when it is loaded by temperature increase and differential pressures applicable to the operating conditions of interest In the licensing basis analysis, when applying the thick shell model, similar displacements were applied directly to the tubesheet bore; however, in the C2 model application, the displacement conditions are applied to the boundaries of the model and the model determines the conditions at the actual tube-to-tubesheet interface. This is a key difference between the C 2 model and the thick shell model.

WCAP-17345-NP June 2011 Revision 2

3-2 To calculate the axial contact pressure profile for a tube at the tubesheet radius of interest, the temperatures and displacements appropriate to the number of points considered through the thickness of the tubesheet are input separately to the model along with the tube wall pressure differential between the internal pressure of the tube, and the crevice pressure acting on the outer diameter of the tube wall and inner diameter of the tubesheet applicable to each elevation to determine the contact pressure between the tube and the tubesheet at each elevation. The elevations through the thickness of the tubesheet are consistent with the elevations utilized in the current licensing basis for H*. Application of the C2 model assumes that the centerline of the tube remains straight, e.g., that no bending of the tubesheet occurs. The displacement input conditions, taken from the 3-D FEA model of the tubesheet complex, include the total effects of temperature and pressure loading in the continuum of the thickness of the tubesheet. Ignoring the coupling due to tubesheet bending in applying the C2 model is a conservative application of this model because the introduction of tubesheet bore and tube bending would be expected to result in higher contact pressures between the tube and tubesheet.

The input boundary conditions include displacements in both axes of the plane. Conceptually, this is similar to the original analysis using the thick shell equations, but the application details are different.

Previously, the radial displacement was taken directly from the 3-D FEA model, and the circumferential displacement was derived from the radial displacement (see Section 6.3 of WCAP-17091-P) and applied directly to the tubesheet bore. For application of the C2 model, which is driven by the cell boundary displacements, it was desired that the radial displacements be calculated directly in the 3-D FEA model of the tubesheet complex. To facilitate this, the 3-D FEA model was modified by adding the same mesh used on the tubesheet centerline face perpendicular to the divider plate one and two pitches into the depth (not thickness) of the tubesheet. This permitted obtaining the displacements in the direction parallel to the divider plate directly from the 3-D FEA model for application to the C2 model boundaries instead of direct application to the tubesheet bore.

2 The 3-D FEA model mesh was also modified for other reasons not directly related to application of the C model. For example, to avoid applying a factor to account for a non-functional divider plate, the model was changed to directly reflect that the upper 5.0 inches of the divider plate were assumed to be non-existent (see Section 3.2.2 and Section 3.2.4). Further, changes were made to the 3-D FEA model, mesh to properly represent the axial thermal profile through the thickness of the tubesheet (see Section 3.2.5).

3.2 STRUCTURAL ANALYSES (3-D FEA MODEL) 3.2.1 Method Discussion The structural finite element analysis is based on a three-dimensional (3-D) model of the lower steam generator complex consisting of the channelhead, divider plate, tubesheet, and lower shell. The model uses Slot's effective material properties to model the perforated tubesheet section as an orthotropic material, as discussed in References 3-1 and 3-2. The plants are analyzed for low Tavg normal operating conditions (NOP) and steam line break (SLB), which have been determined to be limiting conditions in References 3-1 and 3-2. Note that these conditions represent the bounding pressure and temperature values specified by the design basis transients and represent the design limits of the plant operating conditions but not the current actual plant operating conditions.

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3-3 3.2.2 Assumptions The assumptions below, with the exception of the thermal temperature profile through the tubesheet, are copied from References 3-1 and 3-2. For each analysis condition, a thermal and a combined thermal-structural analysis were performed to determine the deformations in the tubesheet. All of the.

finite element analysis (FEA) results assume a static, steady-state, linear, and elastic system.

An analysis performed in Reference 3-3 concludes that, in general, the tubesheet is approximately at the primary side temperature through its thickness, except for a sharp thermal gradient that exists in approximately the top one (1.00) inch. In the thermal analysis, the secondary side of the tubesheet was assumed to be at a temperature equal to the average of the steam temperature and the feedwater temperature. The tubesheet portion of the 3-D FEA model used in this analysis was partitioned two inches from the top of the tubesheet. From the bottom of the tubesheet to the top of this partition in the tubesheet, an approximately uniform temperature equal to the hot leg temperature was applied. This produced a temperature gradient in the top two inches of the tubesheet from a value of 10 degrees cooler than the primary fluid temperature to the average of the coldest allowable condition-specific feedwater and steam outlet temperatures as specified by the applicable Performance Capability Working Group (PCWG). See Section 5 of References 3-1, 3-2, and Reference 3-17 for details. For the SLB case, the primary fluid and the average of the secondary fluids (steam and feedwater) were applied to the primary and secondary surfaces of the tubesheet, respectively, so that a linear temperature gradient developed through the thickness of the tubesheet. This is a reasonable assumption because the long-term portion of the transient specifies that flow will be reduced to natural circulation through the affected loop when the reactor coolant pumps are off.

Where a range of feedwater temperatures was specified in the PCWG parameters, the condition most conservative for H* was used. Since H* values are negatively impacted (i.e., greater H* values result) by large radial deformations of the tubesheet, a higher overall temperature of the tubesheet will result in a lower modulus, and thus a conservative H* value. Therefore the higher feedwater temperature was used.

The structural analyses for the SLB transient are performed statically. The analysis inputs for the SLB condition include the maximum pressure differential over the entire transient definition and the asymptotic temperature reached long after the initiation of the event. In the component hardware design transient, even though the plant is initially at no-load conditions, it is assumed that the steam line break results in an immediate reactor trip and actuation of the safety injection system. The transient also assumes that off-site power is ,lost at the time of the break and all reactor coolant pumps are de-energized so that coolant flow coasts down to the natural circulation value. The maximum pressure differential occurs because the safety injection system operates at design capacity and re-pressurizes the system in a relatively short time. It is conservative to use the stated conditions because the more realistic scenario would be that a reduction in pressure would occur across the tubes and tubesheet over the long-term duration of the event due to operator actions consistent with the plant Emergency Operator Procedures (EOPs). The EOPs, for an event which includes safety injection, provide for reduction/termination of safety injection flow and for the initiation of cool-down and depressurization of the reactor coolant system to the point that the residual heat removal system can be placed in operation for continued cooling of the RCS.

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3-4 The finite element model did not include the nozzles or manways. This is reasonable because the deformations of interest are in the tubesheet, which is well removed from the channelhead penetrations, and thus, would not be expected to have a significant effect on tubesheet deflections (Reference 3-7).

Prior analysis has shown that including the larger channeihead penetrations, such as the manways, tends to decrease displacements in the tubesheet. Decreasing tubesheet displacements will produce shorter H*

distances; therefore, the current approach is conservative. The model did not consider the tubes or any of the structure above the tubesheet except the lower shell (stub barrel). Including the portion of the tube within the tubesheet decreases the tubesheet displacement because it stiffens the tubesheet with respect to the bending caused by the primary-to-secondary pressure differential (Reference 3-4).

References 3-1 and 3-2 show that it is conservative to neglect the structural support that the divider plate provides to the tubesheet. Therefore, in the 3-D finite element model of the Model 44F SG and the Model 51 F SQ the divider plate is severed from the tubesheet and provides no direct structural support to the tubesheet in this analysis. This is discussed in Section 3.2.4. Consistent with previous applications, it is noted that the Model 44F SG and the Model 5 IF SGs considered in the structural analysis are model specific, e.g., the dimensions of the divider plate, channel head and lower shell are specific to the model of SG considered.

3.2.3 Input The input for this analysis consists of steam generator dimensions for the plants to be analyzed, material properties from the ASME Code, and pressure and temperature conditions from the PCWG parameters and transients.

The input boundary conditions for the limiting plants are shown in Table 3-1 and Table 3-2 for the Model 44F plants and Model 5IF plants, respectively. The modulus of elasticity and coefficients of thermal expansion are provided in Table 3-3 and Table 3-4. The tubesheet is SA-508 Class 2A, the divider plate is Alloy 600 (SB-168), the channelhead is SA-216 Grade WCC, and the lower shell is SA-533 Grade A Class 2. These are the same values included in References 3-1 and 3-2.

3.2.4 Geometry The structural model geometry analyzed for the Model 44F and 5 IF SGs is essentially identical to that considered in the baseline analyses in References 3-1 and 3-2. The only modifications were the addition of several model partitions in the tubesheet region and truncating the divider plate. The first partition in the tubesheet model is at two inches from the secondary surface to accommodate a non-linear temperature profile. Additional solid body partitions were made through the tubesheet at distances equal to one and two pitches behind the half-symmetry plane to facilitate the post-processing of displacements for the square cell model. The typical solid models used are shown in Figure 3-1 for the Model 5IF SG (Surry Units 1 & 2), showing the truncated divider plate, and Figure 3-2 for the Model 44F SG (Turkey Point Units 3 & 4), showing the model with the intact divider plate.

In References 3-1 and 3-2, concerns regarding the potential for divider plate cracking were addressed by applying a "divider plate factor" to represent whether, or not, the divider plate provides structural support.

This condition is discussed in Reference 3-4, which details the assessment of a fully degraded divider plate-to-tubesheet weld in terms of the divider plate factors discussed in Reference 3-1, Section 6.2.6. In WCAP-17345-NP June 2011 Revision 2

3-5 the current analysis, the 3-D FEA lower tubesheet complex model was modified to exclude the upper five inches of the divider plate to decouple it from the tubesheet; however, the divider plate was still included in the channelhead. This structural model variant eliminated the need to apply the divider plate factor because the structural model directly addresses the presumed degraded divider plate. Application of this model confirmed the conclusions of References 3-1 and 3-2 that this assumption is conservative relative to H*. Figure 3-1 shows a representation of the solid body with the upper five inches of the divider plate and attached materials suppressed. Eliminating this material in the model does not change the application or values of the applied boundary conditions nor does it change the results of the thermal analysis. The only effect that truncating the divider plate has is that the tubesheet has less resistance to the applied pressure loads than if it were connected to the divider plate. However, in all other respects, the steam generator model with the severed divider plate is the same model as the steam generator with an intact divider plate.

3.2.5 Mesh Discussion The model meshes for all models of SGs among the H* candidate population are similar but are adjusted to accommodate the specific geometry of each model of SG. The model meshes used in the analyses for the Models 44F and 51 F SGs are essentially the same as the meshes documented in References 3-1 and 3-2. Additional constraints were added to the current mesh to accommodate the vertical partition through the tubesheet. The typical mesh used is shown in Figure 3-3, Figure 3-4, and Figure 3-5 for the principal axes. Although the Model 5 1F mesh is shown, the mesh for the Model 44F is similar to that shown in Figure 3-3, Figure 3-4 and Figure 3-5.

3.2.6 Tubesheet Equivalent Properties Modeling of the equivalent properties of the perforated plate (tubesheet) by the method of Slot is discussed in Section 6.2.1 of References 3-1 and 3-2. The same equivalent properties used in References 3-1 and 3-2 were used in the current analysis. Information from those references is included here for completeness. Interpolated ratios of equivalent properties are in Table 3-5, where the "*"

indicates the properties of the equivalent tubesheet. The ratios are then multiplied by the material properties for SA-508 Class 2A in Table 3-3 to obtain the temperature-dependent equivalent properties.

The equivalent properties for the tubesheet are in Table 3-6 and Table 3-7 for the Model 44F SG and Model 5IF SG, respectively.

3.2.7 Boundary Conditions The application of the boundary conditions to the models is consistent with those included in the current licensing basis in References 3-1 and 3-2. Table 3-land Table 3-2 summarize the specific boundary conditions and how they are applied to the 3-D FEA model. Two different analyses were performed with the 3-D FEA model of the lower SG tubesheet complex to support application of the C 2 model:

1. Thermal Analysis: The absolute operating temperature conditions were applied to the SG, as opposed to a difference in temperature with a reference temperature of 70'F. The result from this analysis is purely a temperature profile through the tubesheet.

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3-6

2. Deflection Analysis: In this analysis, the non-uniform temperature profile from the first analysis and the pressure loads are simultaneously applied to the model. The results from this analysis, with the severed divider plate condition, are used in the final H* analysis, instead of accounting for the absence of the divider plate by application of a divider plate factor, as in the licensing basis analysis. All of the required displacements and effects are directly accounted for by ANSYS.

The results of the second analysis provide the input for subsequent analysis with the square cell model which replaces the thick shell model in the current licensing basis. The approach in the deflection analysis is beneficial because it eliminates the need to separately post-process and calculate the different displacements required for the H* analysis, as was done in the licensing basis.

The applied loads and temperatures in each analysis are shown in Table 3-1 and Table 3-2. The analysis was applied only to the limiting conditionsrequired for H*; that is, if a plant's limiting H* distance is controlled by the normal operating (NOP) condition, the NOP pressures and temperature loads were used in the analysis and the SLB conditions were not considered and vice versa (see Section 3.3.11 for the limiting operating conditions for the Model 44F and Model 5 IF SGs).

3.2.8 Tubesheet Complex 3-D FEA Analysis Results Typical results of the thermal analysis for Surry for normal operating conditions are shown in Figure 3-6. The thermal profile shown in Figure 3-6 is more accurate than that shown in Reference 3-2 (and, as appropriate, in Reference 3-1) due to the direct application of temperature loads to the tubesheet partition. Figure 3-7 through Figure 3-9 show the results of the thermal-structural analysis for Surry Unit 1 for 100% power. Figure 3-10 shows the results of the SLB thermal analysis for Surry Unit 1.

Figure 3-11 and Figure 3-12 show the X- and Z-deformations for SLB for Surry Unit 1. The results of the current 3-D FEA are taken from Reference 3-6.

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3-7 Table 3-1 Input Boundary Conditions for Model 44F (Turkey Point Units 3 & 4)

Parameter Low Ta.g SLB a,c,e Hot Leg Pressure (psia)

SG Outlet Pressure (psia)

Secondary Pressure (psia)

Hot Leg Temperature (OF)

SG Outlet Temperature (°F)

Steam Temperature (°F)

Feedwater Temperature (OF)

Mean Shell Radius rm (inches)

Shell Thickness t (inches)

Calculated Values a,c,e Secondary Fluid Temperature ('F) F Vessel End Cap Pressure (psia)

I Table 3-2 Input Boundary Conditions for Model 51F (Surry Units 1 & 2)

Parameter Low Tavg SLB a,c,e Hot Leg Pressure (psia)

SG Outlet Pressure (psia)

Secondary Pressure (psia)

Hot Leg Temperature (OF)

SG Outlet Temperature (OF)

Steam Temperature (OF)

Feedwater Temperature (OF)

Mean Shell Radius rm (inches)

Shell Thickness t (inches)

Calculated Values a~ce Secondary Fluid Temperature (OF) r Vessel End Cap Pressure (psia)

WCAP-17345-NP June 2011 Revision 2

3-8 Table 3-3 Modulus of Elasticity for Materials SA-216 Grade Temperature SA-508 Class 2A Alloy 600 WCC SA-533 Grade A Class 2 (OF) (Msi) (Msi) (Msi) (Msi) 70 29.2 31.0 29.5 29.2 200 28.5 30.2 28.8 28.5 300 28.0 29.9 28.3 28.0 400 27.4 29.5 27.7 27.4 500 27.0 29.0 27.3 27.0 600 26.4 28.7 26.7 26.4 700 25.3 28.2 25.5 25.3 Table 3-4 Coefficient of Thermal Expansion for Materials SA-216 Grade Temperature SA-508 Class 2A Alloy 600 WCC SA-533 Grade A Class 2 (OF) (pin/in) (pin/in) (pin/in) (pin/in) 70 6.50 6.90 5.53 7.06 200 6.67 7.20 5.89 7.25 300 6.87 7.40 6.26 7.43 400 7.07 7.57 6.61 7.58 500 7.25 7.70 6.91 7.70 600 7.42 7.82 7.17 7.83 700 7.59 7.94 7.41 7.94 Table 3-5 Interpolated Ratios of Equivalent Material Properties for Analysis of Perforated Plate Property Model 44F Model 51F() a,c,e Gy*/Gy Ey*/Ey Ep*/Ep Gp*/Gp Poisson's Ratio Notes:

1. These values differ from the values shown in Reference 3-2; however, they are the actual values used in the analysis documented in Reference 3-2.

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3-9 Table 3-6 Equivalent Properties for Tubesheet for Model 44F SG (Turkey Point Units 3 & 4)

Out-of-Plane In-Plane Temperature (IF) E (Msi) G (Msi) E (Msi) G (Msi) a,c,e 70 F 200 300 400 500 600 700 Table 3-7 Equivalent Properties for Tubesheet for Model 51F SG (Surry Units 1 & 2)

Out-of-Plane In-Plane Temperature (IF) E (Msi) G (Msi) E (Msi) G (Msi) a,c,e 70 200 300 400 500 600 700 WCAP-17345-NP June 2011 Revision 2

3-10 a,c,e 17-Figure 3-1 Typical Representation of Severed Divider Plate Condition; Model 51F (Surry Unit 1 Configuration Shown) a,c,e 7

Figure 3-2 Typical Solid Model for Intact Divider Plate; Model 44F (Turkey Point Units 3 & 4 Configuration Shown)

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3-11 a,c,e Figure 3-3 Model 51F (Surry Unit 1) Mesh, View Down Z-Axis a,c,e Figure 3-4 Model 51F (Surry Unit 1) Mesh, View Down Y-Axis WCAP- 17345-NP June 2011 Revision 2

3-12 a,c,e Figure 3-5 Model 51F (Surry Unit 1) Mesh, View Down X-Axis a c,e Figure 3-6 Model 51F (Surry Unit 1) Results of NOP Thermal Analysis WCAP-17345-NP June 2011 Revision 2

3-13 a.c.e Figure 3-7 Model 51F (Surry Unit 1) Results of Thermal-Structural Analysis, Y Deformation a,c,e Figure 3-8 Model 51F (Surry Unit 1) Results of Thermal-Structural Analysis, X Deformation on Hot Leg Face WCAP-17345-NP June 2011 Revision 2

3-14 a,c,e Figure 3-9 Model 51F (Surry Unit 1) Results of Thermal-Structural Analysis, Z Deformation on Hot Leg a,c,e Figure 3-10 Model 51F (Surry Unit 1) Results of SLB Thermal Analysis WCAP-17345-NP June 2011 Revision 2

3-15 a,c,e Figure 3-11 Model 51F (Surry Unit 1) Results of SLB Thermal-Structural Analysis, X Deformation on Hot Leg Face a.c.e Figure 3-12 Model 51F (Surry Unit 1) Results of SLB Thermal-Structural Analysis, Z Deformation on Hot Leg WCAP-17345-NP June 2011 Revision 2

3-16 3.3 CALCULATION OF MEAN H* FROM C MODEL 3.3.1 Method Discussion The structural analysis for the tube-to-tubesheet contact pressures is based on a 2-D finite element model.

The 2-D finite element model is a pseudo sub-model of the SG tubesheet and corresponding tube in increments throughout the entire tubesheet thickness of approximately 21 inches. This model is then quartered to simplify the computations as seen in Figure 3-13.

Each tubesheet radius of each SG model is computed and graphed separately. At each tubesheet radius, there are nine and twelve elevations, respectively, for the Model 44F and 5 IF SGs at which the contact pressure is calculated. (An exception is for the Model 5 IF SLB condition for which only nine elevations are calculated.) For each operating condition, a thermal and thermal-structural analysis was performed with the 3-D FEA model (see Sections 3.1 and 3.2) to determine the tubesheet displacements used as input to the square cell model to calculate the contact pressures of the tubes with regards to the tubesheet.

All of the analyses were static and linear elastic.

a,c,e Figure 3-13 Sub-Model for Computational Analysis 3.3.2 Development of Displacements for Square Cell The displacements to apply to the square cell model are calculated from the displacements on the 3-D model using a finite difference technique to approximate the strain. The applied displacements simulate the strain across one-half of one pitch of the steam generator from all of the loads applied to the 3-D FEA model. There are two displacements to consider, those in the X-direction and those in the June2011 WCAP- 7345-NP WCAP-117345-NP June 2011 Revision 2

3-17 Z-direction (both in the same plane). For calculation of the displacements in the X-direction, the X-displacements on the hot leg face of the perforated section of the tubesheet are utilized. After being exported from ANSYS, they are processed using a finite difference method to calculate the strain, which is the derivative of displacement. This utilizes the central difference formula of second order (Reference 3-5, pp 83-85):

au, -_

ax 2Ax (Equation 3-1)

At the edges of the perforated region, of necessity, the forward and backward differences of second order are used:

aUx, Uxi+2 + 4Ux,i+1 - 3Ux,i g ai ,x, Ox 2Ax aUxi + UxJi2 - 4Uxi_I1 + 3Uxi EA 23x (Equation 3-2)

(x The displacement to apply to the square cell model is the strain times the length of the model, which is one-half of a pitch:

AXsquareceII = 0.5

• P

• ex (Equation 3-3)

The calculation of the z-displacements uses the z-displacements from the 3-D FEA model which are two pitches back from the hot leg face. A similar central difference formula is used to calculate the derivative:

a Uzi UJ,*+ 2 - Uzi az 2Az (Equation 3-4)

This equation is slightly modified to calculate the strain in the z-direction one pitch back from the cut face of the 3-D model. This is necessary because the cut face has a symmetry condition in the z-direction; therefore, the strain in the z-direction necessarily vanishes there. Since the displacement is zero on that face, the equation can be simplified:

aUz,i Uz~+

az 2P (Equation 3-5)

Calculation of the applied displacements from the strain is identical:

Asquarecell = 0.5

• P

• e, (Equation 3-6)

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3-18 3.3.3 Assumptions The axial thermal profile for the tubesheet is discussed in Section 3.2. In the thermal analysis, the secondary side of the tubesheet was assumed to be at a temperature equal to the average of the steam temperature and the feedwater temperature.

For the connections between the tube and tubesheet, this model uses a friction coefficient of [ ]a.c,c (References 3-1 and 3-2), and a pinball radius of [ ]a,¢, inches; which is half the value of the surface roughness tolerance from Reference 3-13. The analysis also uses a normal stiffness factor of

]a,c,*, which determines how quickly the model will converge depending on the degree of bending deformation, which was based on several trials that defined this value for acceptable convergence of the model.

The square cell model does not use the Goodier model, and does not assume the tubesheet collar is a continuous structure. The applied loading on the tubesheet bends the tube within the tubesheet because the tube is a continuous structure. This bending is caused by temperature change as well as the pressure differential across the tubesheet and increases contact pressure. Neglecting tubesheet bending is conservative because the increased contact pressure between the tube and the tubesheet would reduce the H* distance.

3.3.4 Input The input for this analysis consists of steam generator dimensions for the limiting Model 44F and Model 51 F plants, material properties from the ASME Code, and pressure and temperature conditions from the PCWG parameters and transients. The dimensions, the material properties, and the PCWG parameters used for the 44F and 51F models are taken from References 3-1, 3-2, and 3-17, respectively. It is important to note that the H* distance identified in Reference 3-17 has been superseded. Also, it remains Westinghouse's conclusion that plant operation of H.B. Robinson Unit 2 with the current number of tubes plugged in each SG is acceptable and is bounded by the operating parameters identified in Reference 3-17.

Because the analysis is a static, linear, and elastic methodology, the material properties used as inputs are the elastic moduli and coefficients of thermal expansion. The tubesheet is SA-508 Class 2A and the tube is Alloy 600 Thermally Treated (TT). The modulus of elasticity and coefficients of thermal expansion are taken from References 3-1 and 3-2.

3.3.5 Geometry Figure 3-14 shows a representation of the solid model used. The model was created in ANSYS Workbench Design Modeler. The associated representative dimensions for all models are shown in Figure 3-15.

3.3.6 Mesh Discussion The mesh used in the analysis combines the tube and tubesheet in one model and creates one mesh for both pieces. This grid of nodes allows for easy post-processing and interpolation of deformations on the WCAP-17345-NP June 2011 Revision 2

3-19 face. The density in this region is judged to be adequate from experience and comparison to prior models.

The actual mesh for all models analyzed is shown in Figure 3-16.

a,c,e Figure 3-14 Representative Solid Model a,c,e Figure 3-15 Representative Dimensions for All Models WCAP- 17345-NP June 2011 Revision 2

3-20 a,c,e Figure 3-16 Implemented Model Mesh, View Down Z-Axis 3.3.7 Boundary Conditions The applied boundary conditions consisted of pressure loads, thermal loads, and constraints. The pressure loads consist of the internal fluid pressure and the crevice pressure, which is represented as the pressure difference on the inside surface of the tube. The thermal loads were applied as fixed temperature boundary conditions on the bodies for the thermal analysis. Three constraints are applied:

1. The upper edge of the model was constrained in the X-direction.

2. The lower edge of the model was constrained in the Y-direction.

3. The pressure differential on the tube was determined as the difference between the primary pressure on the tube ID and the crevice pressure on the tube OD.

The typical application of these boundary conditions is shown in Figure 3-17.

All of the applied loads and temperatures are described in Section 3.2.

(Note: For analytical convenience, the coordinate system for this model is X-Y, which is equivalent to the X-Z SG coordinates as noted in Section 2.)

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3-21 a,c,e Figure 3-17 Boundary Conditions for All Models 3.3.8 C 2 FEA Results Inputs and contact pressure plots of the finite element analysis (FEA) results for each individual model, radius and elevation are included in this section. The thermal analysis results are steady-state with fixed boundary conditions (Reference 3-8).

Within each table, the explanations of the categories are as follows: TS Elevation stands for tubesheet elevation, AX and AZ represent the displacement in the respective direction of the square cell model, AP represents the difference between the reference pressure and the crevice pressure which was empirically determined, the temperature of the tubesheet, and "Pco Theta" represents the contact pressure between the tube and tubesheet.

3.3.9 Model 44F (Turkey Point Units 3 & 4) Square Cell Model Results Contact pressure axial profiles were calculated at the same six radii considered in Reference 3-1 to provide directly comparable results between the C 2 model and the thick shell equation model used in Reference 3-1. The results based on the C 2 model calculations for the Model 44F are provided in Table 3-8 through Table 3-13. Tables are provided for the NOP and SLB conditions in this section. In these tables, the zero reference is the top of the tubesheet.

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3-22 The tabular results in Table 3-8 through Table 3-13 are shown graphically in Figure 3-18 through Figure 3-23. These figures show the contact pressure trends of the normal operating condition compared to the steam line break conditions at various elevations between 0.0 and 21.81 inches, where 0.0 represents the top of the tubesheet and 21.81 represents the bottom of the tubesheet.

3.3.10 Model 51F (Surry Units 1 & 2) Square Cell Model Results Contact pressure axial profiles were calculated at the same six radii considered in Reference 3-2 to provide directly comparable results between the C 2 model and the thick shell equation model used in Reference 3-2. The results based on the C 2 model calculations for the Model 5 IF SGs are provided in Table 3-14 through Table 3-19. Tables are provided for the NOP and SLB conditions.

The tabular results in Table 3-14 through Table 3-19 are shown graphically in Figure 3-24 through Figure 3-29. These figures show the contact pressure trends of the normal operating condition compared to the steam line break conditions at various elevations between 0.0 and 21.03 inches, where 0.0 represents the top of the tubesheet and 21.03 represents the bottom of the tubesheet.

The selection of zero reference in the tables and figures is the same as for the Model 44F discussed in Section 3.3.9.

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3-23 Table 3-8 Model 44F Turkey Points Units 3 & 4 Inputs and Results, 2.655 in. Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.810 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 SLB TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a.c.e BTS 21.810 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 WCAP-1 7345-NP June 2011 Revision 2

3-24 Table 3-9 Model 44F Turkey Point Units 3 & 4 Inputs and Results, 7.219 in. Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.810 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 SLB TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.810 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 WCAP- 17345-NP June 2011 Revision 2

3-25 Table 3-10 Model 44F Turkey Point Units 3 & 4 Inputs and Results, 18.171 in. Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.810 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 SLB TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.810 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 WCAP-17345-NP June 2011 Revision 2

3-26 Table 3-11 Model 44F Turkey Point Units 3 &4 Inputs and Results, 28.21 in. Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.810 F 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 SLB TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.810 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 WCAP- 17345-NP June 2011 Revision 2

3-27 Table 3-12 Model 44F Turkey Point Units 3 & 4 Inputs and Results, 34.598 in. Radius NOP TS Elevation AX AZ AP Temperature PCON Theta a,c,e in in in psi OF psi BTS 21.810 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 SLB TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.810 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 WCAP-17345-NP June 2011 Revision 2

3-28 Table 3-13 Model 44F Turkey Points Units 3 & 4 Inputs and Results, 48.288 in. Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.810 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 SLB TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.810 19.810 18.287 7

16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 WCAP-17345-NP June 2011 Revision 2

3-29 Table 3-14 Model 51F Surry Units 1 & 2 Inputs and Results, 4.016 in. Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.030 19.030 17.030 16.030 15.030 12.773 NA 10.515 8.030 4.129 2.000 1.000 TTS 0.000 SLB TS Elevation AX AZ AP Temperature PCON Theta a,c,e in in in psi °F psi BTS 21.030 19.030 17.030 15.030 NA 10.515 4.129 2.000 1.000 TTS 0.000 WCAP-17345-NP June 2011 Revision 2

3-30 Table 3-15 Model 51F Surry Units I & 2 Inputs and Results, 11.772 in. Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi ae BTS 21.030 19.030 17.030 16.030 15.030 12.773 NA 10.515 8.030 4.129 2.000 1.000 TTS 0.000 SLB TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi BTS 21.030 19.030 17.030 15.030 NA 10.515 4.129 2.000 1.000 TTS 0.000 WCAP- 17345-NP June 2011 Revision 2

3-31 Table 3-16 Model 51F Surry Units 1 & 2 Inputs and Results, 20.498 in. Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.030 19.030 17.030 16.030 15.030 12.773 NA 10.515 8.030 4.129 2.000 1.000 TTS 0.000 SLB TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.030 19.030 17.030 15.030 NA 10.515 4.129 2.000 1.000 TTS 0.000 June2011 WCAP-1 7345-NP WCAP-17345-NP June 2011 Revision 2

3-32 Table 3-17 Model 51F Surry Units 1 & 2 Inputs and Results, 30.193 in. Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.030 19.030 17.030 16.030 15.030 12.773 NA 10.515 8.030 ac 4.129 2.000 1.000 TTS 0.000 SLB TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.030 19.030 17.030 15.030 NA 10.515 4.129 2.000 1.000 TTS 0.000 WCAP- 17345-NP June 2011 Revision 2

i3-33 Table 3-18 Model 51F Surry Units 1 & 2 Inputs and Results, 48.613 in. Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.030 19.030 17.030 16.030 15.030 12.773 NA 10.515 8.030 4.129 2.000 1.000 TTS 0.000 SLB TS Elevation AX AZ AP Temperature PCON Theta a,c,e in in in psi OF psi BTS 21.030 19.030 17.030 15.030 NA 10.515 4.129 2.000 1.000 TTS 0.000 WCAP-17345-NP June 2011 Revision 2

3-34 Table 3-19 Model 51F Surry Units 1 & 2 Inputs and Results, 58.308 in. Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.030 19.030 17.030 16.030 15.030 12.773 NA 10.515 8.030 4.129 2.000 1.000 TTS 0.000 SLB TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a,c,e BTS 21.030 19.030 17.030 15.030 NA 10.515 4.129 2.000 1.000 TTS 0.000 WCAP- 17345-NP June 2011 Revision 2

3-35 a,c,e Figure 3-18 Model 44F Contact Pressure Results, 2.655 in. Radius a,c,e Figure 3-19 Model 44F Contact Pressure Results, 7.219 in. Radius WCAP-17345-NP June 2011 Revision 2

3-36 a,c,e Figure 3-20 Model 44F Contact Pressure Results, 18.171 in. Radius a,c,e Figure 3-21 Model 44F Contact Pressure Results, 28.21 in. Radius WCAP- 17345-NP June 2011 Revision 2

3-37 a,c,e Figure 3-22 Model 44F Contact Pressure Results, 34.598 in. Radius a,c,e Figure 3-23 Model 44F Contact Pressure Results, 48.288 in. Radius June 2011 WCAP-1 7345-NP WCAP-17345-NP June 2011 Revision 2

3-38 a,c,e Figure 3-24 Model 51F Contact Pressure Results, 4.016 in. Radius a,c,e Figure 3-25 Model 51F Contact Pressure Results, 11.772 in. Radius WCAP-17345-NP June 2011 Revision 2

3-39 a,c,e Figure 3-26 Model 51F Contact Pressure Results, 20.498 in. Radius a,c,e Figure 3-27 Model 51F Contact Pressure Results, 30.193 in. Radius WCAP-17345-NP June 2011 Revision 2

3-40 a,c,e Figure 3-28 Model 51F Contact Pressure Results, 48.613 in. Radius a,c,e Figure 3-29 Model 51F Contact Pressure Results, 58.308 in. Radius WCAP- 17345-NP June 2011 Revision 2

3-41 3.3.11 Mean H* Calculations Based on the calculated contact pressures for each radius, it is then possible to calculate a mean H* for each radius. The equation used is the same as in References 3-1 and 3-2, Equation 1-3. Table 3-20 contains the end cap loads used to determine the.H*'s along with the contact pressures.

Equation 1-3 from References 3-1 and 3-2 is used to generate the cumulative pull out load throughout the thickness of the tubesheet at each elevation. These accumulated pull out loads are determined by integrating the axial contact pressure profile using the trapezoidal rule. The mean H* value is determined by interpolating the cumulative pull out resistance curve to determine the point where the pull out resisting load equals the predetermined pull out loads for each model (References 3-1 and 3-2).

Table 3-21 summarizes the mean H* values for the Model 44F and Model 51F SGs for the NOP and SLB conditions, as appropriate, prior to the correction for Poisson contraction of the tubes. Poisson contraction must be considered in determining the mean H* to define the critical radius because it is a physically real property of the material.

The process for calculating Poisson contraction is described in Section 3.5. While principally required to establish the final value of the probabilistic H*, it is possible for the Poisson contraction correction to affect the definition of the limiting radius on the tubesheet at which the probabilistic values of H* are calculated. Table 3-22 summarizes the results of the mean H* calculations after correction for Poisson contraction. The critical radius for the Model 44F is determined to be [ ]a"c"e inches and that for the Model 51 F, [ ]a,c,, inches. The limiting tubesheet radius, for the case of the mean material condition with the addition of the Poisson correction, was determined to be the same as in the current licensing basis for the Model 44F and 5IF SGs.

The limiting operating condition for H* is the operating condition that produces the most conservative (i.e., longest) predicted mean H* depth. The operating conditions considered were normal operating condition at low temperature (average conditions), NOP or NOPLOW TAVcG and main steam line break, SLB, consistent with the current licensing bases for the limiting Model 44F plant (Turkey Point Units 3 & 4) and the limiting Model 5IF plant (Surry Units 1 & 2). From References 3-1 and 3-2, it is concluded that the limiting condition for both the Model 44F and 51 F SGs is NOP.

3.3.12 Axial Location of Departure from Zero Contact Pressure The H* distance is determined by integration of the axial contact pressure distribution from the top of the tubesheet through the thickness of the tubesheet to establish the distance required to equilibrate the applied pull out forces. Historically, nine axial locations have been considered through the thickness of the tubesheet to define the contact pressures. These points are assumed to be linearly connected to facilitate the integration for H*. Application of the C2 model resulted in a distance of zero contact pressure at the top of the tubesheet and a relatively long span between the last zero contact pressure point and the first non-zero contact pressure point for the Model 5 1F SGs. If the distance between the first non-zero contact pressure point and the last zero-contact pressure point is large, different assumptions can be made regarding the slope of the first non-zero segment of the contact pressure profile, leading to uncertainty regarding the value of the H* distance. To address this issue, the number of axial points for calculating contact pressure for the Model 51 F SGs was increased to provide better definition of the profile near the zero contact pressure point. For the Model 5 IF, the number of axial points was increased WCAP- 17345-NP June 2011 Revision 2

3-42 from nine to twelve for NOP conditions only. The number of axial points was maintained at 9 for the Model 5IF SLB analysis and the Model 44F NOP and SLB analysis. The axial distance between the last zero contact pressure point and the first non-zero contact pressure point is approximately [ ]a,c,e inches at the critical radius for the Model 44F, [ ]ace inches (Figure 3-26). At the critical radius for the Model 5 IF, [ ]a,c,, inches (Figure 3-20), the axial separation between the last zero contact pressure point and the first non-zero contact pressure point is approximately [ ]a,c,, inches. Between these points, respectively, the contact pressure is very low; thus, even if a steeper slope of the contact pressure profile were assumed, the effect on H* would be negligible. Therefore, it is concluded that the number of elevations utilized for contact pressure calculations accurately represent the contact pressure profile and assumptions of different slopes to the zero contact pressure point will have an insignificant impact on the calculated value of H*.

3.3.13 Circumferential Contact Pressure The contact pressure reported for each tubesheet elevation is the circumferential average of the contact pressure along the tube and tubesheet contact surface (i.e., the outer surface of the tube and the inner surface of the tubesheet tube bore). The average contact pressure along the contact surface is defined as taking the sum of the nodal normal stress in the radial direction and dividing by the number of nodes along the contact surface. Figures 3-30 through 3-35 show examples of the circumferential contact pressure at the contact surface used in defining the average contact pressure in the H* analysis for the critical radius, the minimum radius and the maximum radius. The figures show the contact pressures at each node on the interface between the tube and the tubesheet based on the C2 model results. The typical variation in amplitude for the circumferential distribution of contact pressure is on the order of 500 psi.

The reported non-zero average contact pressure at an elevation accounts for the variation in contact pressure as a function of circumferential position. Therefore, the variation in contact pressure around the circumference of a tube is not great enough to generate a leakage channel. For the Model 44F, at the critical radius [ ]a,c*, inches, the first non-zero contact pressure point is defined at approximately

]a,,,, inches below the top of the tubesheet (see Figure 3-20, NOP condition).

For the Model 5 IF, at the critical radius, [ ]a,cc inches, the first non-zero contact pressure point is defined at approximately [ ]ac'c inches (see Figure 3-26, NOP condition). From Figure 3-33 it is seen that the predicted contact pressures at less than [ ] inches below the top of the tubesheet appear to oscillate around zero. However, the net average contact pressure is slightly greater than zero (see Table 3-11). The variations about the mean contact pressures are artifacts of the model and its convergence criteria.

The results of the symmetric square cell model show that positive contact pressure exists circumferentially around the tube for a significant portion of the SG tube bore elevations for the Model 44F and Model 5 IF SGs.

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3-43 Table 3-20 H* Input Summary (References 3-1 and 3-2)

NOP SLB SG Model/Tube OD1 ) End Cap Load (lb) End Cap Load (lb) a,c,e 44F/[ ]ac.e 5 1 F /[ ]Ja . . .

Notes:

1. Maximum tubesheet bore diameter.

2. End cap loads based on 3AP for H* structural analysis.

Table 3-21 Summary of H* Mean Values before Poisson Correction (All dimensions in inches)

SG Model Radius NOP H* SLB H*

44F 2.655 (l) 7.219 18.171 28.21 34.598 48.288 4.016 (2) 51F 11.772 20.498 30.193 48.613 58.308 Notes:

1. The limiting condition for the Model 44F SG is NOP based on Reference 3-1.

2. The limiting condition for the Model 51F SG is NOP based on Reference 3-2.

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3-44 Table 3-22 Summary of H* Mean Values after Poisson Correction (All dimensions in inches)

SG Model Radius NOP H* SLB H*

~ace 44F 2.655 ()

7.219 18.171 28.21 34.598 48.288 4.016 (2) 51F 11.772 20.498 30.193 48.613 58.308 Notes:

1. The limiting condition for the Model 44F SG is NOP based on Reference 3-1.

2. The limiting condition for the Model 51F SG is NOP based on Reference 3-2.

WCAP- 17345-NP June 2011 Revision 2

3-45 a,c,e Figure 3-30 Model 44F: Circumferential Contact Pressure at the Critical Radius WCAP- 17345-NP June 2011 Revision 2

3-46 a,c,e Figure 3-31 Model 44F: Circumferential Contact Pressure at the Minimum Radius WCAP- 17345-NP June 2011 Revision 2

3-47 a,c,e Figure 3-32 Model 44F: Circumferential Contact Pressure at the Maximum Radius WCAP- 17345-NP June 2011 Revision 2

3-48 a,c,e Figure 3-33 Model 51F: Circumferential Contact Pressure at the Critical Radius WCAP-17345-NP June 2011 Revision 2

3-49 a,c,e Figure 3-34 Model 51F: Circumferential Contact Pressure at the Minimum Radius WCAP- 17345-NP June 2011 Revision 2

3-50 a,c,e Figure 3-35 Model 51F: Circumferential Contact Pressure at the Maximum Radius WCAP-17345-NP June 2011 Revision 2

3-51 3.4 CALCULATIONS OF PROBABILISTIC H* USING THE C' MODEL Development of the probabilistic value of H* for the current licensing basis, is documented in References 3-1, 3-2 and 3-11 based on application of the thick shell equations. The variability surface was developed for the key variables that influence H*, the tube and tubesheet coefficients of thermal expansion (CTE) in those analyses. This surface was randomly sampled using a Monte Carlo approach, and from this, the probabilistic values of H* were determined. Development of the variability surface was straightforward because the application of the thick shell equations enabled rapid solutions for H* over a large number of input parameter variations.

Application of the square cell (C2) model to develop the variability surface poses a significant challenge because calculation of the H* values requires an extremely large number of calculations with both the 3-D FEA tubesheet model and the square cell model. Therefore, a simplified approach was employed that utilizes the prior variability results from the thick shell model to reduce the number of additional analyses required with the C2 model. This approach is justified because both the thick shell model and the square cell model represent identically the same structure. The same structure with the same material properties must respond to variations in input parameters in the same manner, regardless of which analytical model is used to represent it. The detailed responses from separate models are expected to be different but the general trend of the response must be the same.

In References 3-1, 3-2 and 3-11, it was determined that the limiting values of H* occur when the variation of the tubesheet CTE is greater than its mean value in conjunction with variation of the tube CTE less than its mean. This relationship must hold true for maximum values of H* regardless of which analytical model is applied. Therefore, it is possible to define a reduced data set for application of the C2 model using the results of the thick shell model as a guide. Further, the specific combinations of the tube and tubesheet CTEs that lead to the required probabilistic values of H* should be essentially the same regardless of which analytical model is employed.

The Monte Carlo simulation process by which the distribution of H* is computed for a given CTE response surface is described in Reference 3-11 for application of the thick shell model. The analyses described in this section address the relative behavior of the square cell and thick shell models in the local region of CTE space (tube-CTE and tubesheet-CTE) that leads to the 95th percentile value of H*.

The C2 model is a structural model which replaces the thick shell equation approach of References 3-1 and 3-2 used to determine the contact pressure distribution between the tube and the tubesheet that are used to calculate H*. The results of using the C2 analysis confirm the prior results using the thick shell model; that is, that mean and probabilistic values for H* are defined within the span of the tubesheet. As expected, the H* values predicted using the C2 model are somewhat different than those predicted by the thick shell model. The difference between the models reflects, in part, the difference in the models and also the changes to the 3-D FEA model discussed in Section 3.2 and Section 3.3 which resulted in updated tubesheet displacements and contact pressures. The C2 model is described in Section 3.3 of this report.

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3-52 3.4.1 Assumptions The assumptions made for the structural analyses of the tubes and tubesheet also apply to the analysis of the probabilistic value of H*. Sections 3.1 through 3.3 of this report provide a description of those assumptions.

3.4.2 Methods Discussion 3.4.2.1 General Methodology It is not practicable to determine the sensitivity of H* to variations of the significant variable (tube and tubesheet CTEs) over a large domain using the C 2 model. Therefore, the structural response variability surface, as documented in the current licensing basis, i.e., Figure 8-5 in References 3-1 and 3-2, is used as the basis for determining the combinations of these variables that lead to the high probability values of H*. It has been determined that the high probability values of H* always occur when the tube CTE varies negatively from its mean and the tubesheet CTE varies positively from its mean. As noted above, this conclusion is independent of the model used to represent the same physical structure. Consequently, the gross response of the structure to variations in the significant input parameters will be the same. For example, it must be true that the maximum probabilistic value of H* will occur when the tubesheet CTE varies from its mean in a positive manner and when the tube CTE varies from its mean in a negative manner. The mean values of CTEs for the tube and the tubesheet and their respective standard deviations 2.33 % for the tube material CTE and 1.6% for the tubesheet material) are taken from References 3-1, 3-2, and 3-16.

The results of Monte Carlo sampling from the response surface defines the specific combination of the significant variables that lead to the high probability values of H*, because the specific input values of the variables are saved along with the values of H*. The results for the upper 10% tail of the H* distribution (e.g., rank order 9000 to rank order 10,000 in 10,000 simulations) from the licensing basis analysis were output as a 4 column by 1000 row matrix. The values in the matrix are the rank order statistic (i.e., 9001 to 10000), the H* value at the given rank order, the variation in the tubesheet CTE about its mean value in terms of mOTs, and the variation in the tube CTE about its mean value in terms of naT where m and n are the multipliers (positive or negative) on standard deviations added to the mean value of the respective CTEs (see Table 3-23).

For the range of multipliers m and n on the tubesheet and tube CTE standard deviations, respectively, shown on Table 3-23, the absolute values for the CTEs used in the analysis are shown on Table 3-24 for the tubesheet material and on Table 3-25 for the tube material. The result of using the material properties in Table 3-24 in the finite element analysis of the lower SG complex is the tubesheet displacement as a function of elevation. This result, along with the variation in the tube properties described in Table 3-25 are used as input to the square cell analysis.

"Break Line" Approach The individual CTEs that result in the desired probabilistic values of H* can be combined into a single variable, which is the square root of the sum of the squares of the individual CTE values for the tube and tubesheet (shown as the last column in Table 3-23). This approach was originally documented in WCAP- 17345-NP June 2011 Revision 2

3-53 Reference 3-11. The typical range of values for the combined variable for H* rank orders between 9,000 and 10,000 is between three and six for all steam generators.

Figure 3-36 shows the typical relationship between the combined significant variables and the H* values above the 9 0 th percentile from the licensing basis analysis for a SG candidate for H*. (The results in Figure 3-36 are taken from the analysis of the Model D5 SG.1) The figure illustrates that the rank order points of interest all fall above a very well defined line. The lower bound of the data is termed the "break line." The break line is the maximum value of H* for a constant value of "alpha," the combined significant variables affecting H*. Therefore, the break line contains the limiting H*. The "break line" can be fit uging the data points that define the lower bound of the data; however, experience has shown that the fit is essentially linear. In this application, the linear fit was used.

Because the value of the combined significant variables are taken directly from the rank ordered results from the original analysis, the break line can also be defined in terms of the rank order instead of H*

values. Figure 3-37 shows the break line defined by the rank order of the points selected.

The break line is used to determine specific combinations of the tube and tubesheet CTE to be used in a series of structural analysis cases using both the 3-D FEA model and the C2 model. For example, if a specific rank order H* estimate is desired, say the 9 5 0 0 th, the matrix of data from the upper 10% of the Monte Carlo Analysis based on the thick shell variability analysis is entered and the specific values of CTE for the tube and the tubesheet are selected that correspond to the desired rank order.

The values of tube and tubesheet CTE used in the C2 analysis were selected based on the required rank order statistics that met the probabilistic goals for H*. For example, the 9 5 th percentile H* estimate at the 50"' percentile confidence interval, corresponds to a rank order statistic of 9500 out of 10000 trials. The selected values typically fall on the break line, but, in the case where a specific rank order is required to meet a higher probabilistic estimate and confidence value (i.e., 95/95), the exact CTE properties at the required (or bounding) rank order were selected except as discussed below.

When used in the C2 analysis, the specific values of tubesheet CTE are always greater than the mean and the specific values of tube CTE are always less than the mean. Because of the nature of Monte Carlo process, and because, for each 10,000 simulation set, only one tubesheet is assumed, it is possible for the upper 10% of the rank ordered simulations to include CTE combinations in which the tubesheet CTE varies negatively but is compensated for by a very large negative tube CTE variation. For example, suppose that at a given required rank order, the combination of tube and tubesheet CTE resulted in a

1. Although based on the same data, Figure 3-36 is characteristically the same but different in detail than Figure 3-32 in Rev. 0 of this report. Both figures are correct but they represent different steps in the calculation process. Because only one tubesheet is represented in the Monte Carlo sampling from the uncertainty surface, half of the 10,000 samples reflect negative variations of the tubesheet CTE. When the tube and tubesheet variables are combined to form the "alpha" term, the sign of the negative TS CTE variation is lost, and the "alpha" value is fictitious for those cases. While only a few percent of these combinations of CTE's are among the top 10% of the rank ordered statistic, those cases do result in upward scatter in Figure 3-32 in Revision 0 of this report; however, they must be included to properly represent the top 10% of the rank ordered Monte Carlo results. Figure 3-36 in this report shows the same data but without the points that have negative values of tubesheet CTE variation. These points were removed because there is no sensitivity data for negative TS variations in H* values among the top 10% of 10,000 Monte Carlo simulations.

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3-54 negative (decreasing) variation on the tubesheet, but an exceedingly large (greater than -4a) variation on the tube CTE. Such a combination of material properties at that rank order was rejected as being practically unrealistic in favor of a rank order close to (greater than) the required rank order value with a positive tubesheet CTE variation and a smaller negative tube CTE variation. It is shown below that this choice does not result in significant variations in H*.

The opposite case, in which a positive tube CTE value may be selected that is compensated for by a very large positive tubesheet CTE, does not occur because, given the large number of tubes that are sampled, the probability of this case occurring is exceptionally small. While theoretically possible, cases like this have not been experienced in the probabilistic analysis of H*.

The rank orders and CTE values used in the C2 H* analysis are always selected so that they bound the rank order required to meet the stated probabilistic goals for H* (e.g., 95/50 or 95/95) and so that the actual rank order value can be interpolated from the analysis results if necessary (Figure 3-3 8). In order to accommodate that goal, it is sometimes necessary to use CTE values that do not fall directly on the break line. Use of the tube and tubesheet CTE data that varies from the break line is not a concern because the variation in H* for the licensing basis response surface (using the thick shell equations) about a given point at a specified rank order is less than 2% of the value of H*, on the order of 0.10 inch or less.

Figure 3-39 and Figure 3-40 show the typical variation in H* over a range of CTE combinations ("alpha")

for the bounding rank orders in the Model 44F NOP and Model 51 F NOP response surfaces from Reference 3-1 and Reference 3-2.

The expected variation from a linear fit over the required range of rank order values is less than 0.10 inch regardless of CTE value in the Model 44F SG. The expected variation from a linear fit over the required range of rank order values is less than 0.10 inch regardless of CTE value in the Model 51F SG. A similar analysis using the C2 model has shown that the same level of small variation (on the order of 0.05 inch or less) occurs with different combinations of CTEs at about the same rank order. Table 3-29 shows the H*

results using C2 data from the Model F NOP analysis results at approximately the 95th percentile probability and 95th percentile confidence rank order. Therefore, it is concluded that a range of CTE combinations in a narrow band of order statistics will produce no significant changes in the resulting value of H* for both the thick shell and C2 models and that the use of the input variables associated with specific order statistics based on the thick shell model will produce consistent results when applied in the C2 model.

Higher Confidence Limits The order statistic for higher confidence intervals (e.g., 95%) is calculated using a method described in Reference 3-12. This method involves calculating the run-to-run variance in Monte Carlo order statistics and calculating a bounding order statistic to ensure a higher confidence. The run-to-run variance is

=?1p=I -(Equation p* 3-7)

Where n is the number of trials and p is the desired probability level. For 10,000 trials and a probability of 95%, the run-to-run standard deviation is 22. For a confidence of 95%, the appropriate adjustment factor of 1.645 is multiplied by this value, giving an adjustment of 36. Therefore, the appropriate order statistic for 95/95 is 9536 (9500+36). In order to ensure that the final result is attained at 95% confidence, other WCAP-17345-NP June 2011 Revision 2

3-55 sources of uncertainty must be bounded at 95% confidence. In this analysis, the other sources of uncertainty are the tube and tubesheet CTE standard deviations. Work documented in Reference 3-16 has shown that the values for the tube and tubesheet standard deviation for CTE conservatively bound 95% confidence values. Therefore, a high-confidence value can be obtained by simply moving to a higher order statistic by the method described above.

Whole Plant Analysis The rank orders from 10,000 simulations required to meet the probabilistic H* values for each of the limiting plants in the H* fleet are listed in Table 3-26. The difference in the required order statistic for the whole bundle H* estimates and the whole plant H* estimates is based on the population of the tubes in the plant. The number of tubes in a plant depends on the SG model and the number of SGs in a plant. For simplicity, the entire design population of tubes, including currently plugged tubes, is considered.

The difference between a whole bundle value of 9,500 (95/50) and a whole plant value is defined by the 9500th H* value for the combined results of 10,000 simulations of each SG in the plant. For example, consider a 4-loop plant: Performing the 10,000 trial Monte Carlo simulation four times to represent four different generators yields four different sets of rank ordered vectors in terms of H*, TS CTE variation and T CTE variation. All four vectors will be similar, but yield slightly different H* values at the same rank order. A fifth vector is then produced whose ith element consists of the maximum H* among the ith elements of the four beginning vectors. This vector is then sorted, and the rank order statistic for 95/50 is the 9,500th value of H* for the whole plant. This value of H* is then searched for in an ordered input vector to determine approximately what rank order statistic for a single steam generator corresponds to the 9,500th rank order H* for an entire plant.

To apply the method discussed herein, it is necessary to identify the whole bundle rank order of the H*

value that is the same as the 95% H* value for the whole plant. For example, the value of the 95% H* for the four SGs in a Model F plant is equivalent to the [ ]a"c" H* value for a single Model F bundle.

Other plants have different SG populations than those using the Model F SG; therefore, the equivalent rank order for the different model SG will also be different. The difference between the whole bundle H*

value and the whole plant H* value comes from using the tube and tubesheet CTE values associated with the H* value for the whole plant 95% in the calculations using the C 2 model.

The specific rank order points selected for each of the limiting plants in the H* fleet are listed in Table 3-27.

The selected values of the tubesheet CTE are used in a 3-D finite element analysis of the lower SG complex. The structural model, analysis method, assumptions and inputs to the lower SG complex analysis are the same to those described in References 3-1 and 3-2 but modified as discussed in Section 3.2 of this report. The resulting tubesheet displacements calculated from the model using the increased tubesheet CTE, with the matching decreased tube CTE properties, become inputs to the square cell model, which calculates the contact pressures for the specific combination of tube and tubesheet CTE applied. The resulting contact pressures are then used to calculate the value of H* for that combination of tube and tubesheet CTE. This process is repeated for each of the selected data points along the break line.

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3-56 The H* values for the same values of rank order statistic in the licensing basis and the square cell analysis are directly compared by plotting the resulting H* values as a function of the rank order statistic.

Figure 3-38 shows the results based on the NOP condition analysis for the Model F SG It is observed that in the rank order range of interest, the results are well approximated by a straight line. It is further observed that the value of H* is increased based on the C2 model compared to the thick shell model. As noted previously, this difference is the result of application of the more accurate C2 model in conjunction with modified displacement results from the updated 3-D FEA model of the tubesheet region (see Section 3.1).

Figure 3-38 can be used to interpolate the H* value of the rank order statistic based on the required rank order given in Table 3-26 for each of the models of SG. For the current application, C2 model analyses were performed for the specific CTE inputs associated with the desired rank order statistic.

That the H* values calculated using the new inputs to the square cell model correspond closely to the rank order statistic from the licensing basis was verified by considering points on the break line adjacent to the selected points. Adjacent points often exhibit significant difference in the CTE values for the tube and tubesheet compared to a selected point. This is shown on Table 3-28 which shows the variations among the CTEs for a typical range of rank order results selected at random from among the results of the Monte Carlo analyses performed for the current licensing basis. More specifically, when a narrow range of rank 2 order results is considered, as shown on Table 3-29, consideration of adjacent point input values to the C model yielded essentially the same results. The H* results for any given rank order may vary slightly from one point to the next but the absolute difference in the predicted H* value is less than 0.10 inch. This confirms that the process of defining input values for the C2 model from the Monte Carlo results based on the thick shell model is a valid approach and that the probabilistic H* results based on the C2 model are in close agreement with the rank order statistics based on the thick shell model. This is an important result because it shows that the general trends and conclusions from the prior thick shell model analysis apply to the C2 output. The specific trend that the comparison between the C2 result and the thick shell result shows is that in the probabilistic region of interest the response surface can be approximated by a linear slope.

Final H* Calculation Process The H* results from the licensing basis analysis include the effect of the tubesheet thermal distribution offset, and a 0.30 inch distance is added to address potential uncertainty in the location of the bottom of the expansion transition (BET) at the top of the tubesheet (TTS) but do not include the adjustment for crevice pressure or any benefit from the installation process (e.g., residual contact pressure).

Section 6.4.5, Section 6.4.8, and Section 8.1.1 in References 3-1 and 3-2 discuss the effects of crevice pressure and the reasons for adjusting the final tube length in the H* calculation process. The crevice pressure adjustment is discussed in Section 3.6. The final H* value for the desired rank order statistic is the H* value obtained from the interpolation of the bounding H* values plus the crevice pressure adjustment as discussed in Section 3.6.

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3-57 3.4.2.2 Independent Validation of Method To further confirm that the approach discussed above, that is, to use the significant variable combinations for desired rank order statistic from the thick shell model analysis as input to the C 2 analysis, an independent analysis was performed which confirmed the C 2 model approach used. Reference 3-15 documents an approach based on differential thermal expansion; i.e., the combination of tube and tubesheet CTE that yield high confidence H* values. Reference M-15 showed by independent approach that the breakline approach is reasonable and correct.

3.4.3 Application to Bounding Model 44F SG (Turkey Point Units 3 & 4)

The general approach to the probabilistic analysis for H* is applied for all models of SGs that are candidates for H*. For the Model 44F (Turkey Point Units 3 & 4) SGs, there are no exceptions that are required to this process. Because the limiting condition for a 3-Loop plant with Model 44F SG is NOP, it is necessary to perform the analysis for the whole plant complement of tubes because all loops are subject to the NOP conditions.

The necessary inputs for the probabilistic analysis using the C 2 model for the Model 44F SG are:

The limiting operating condition for H*. The limiting operating condition for the Model 44F 3-loop SGs was determined to be the NOP condition.

• The limiting radius for H* for the Model 44F SGs, which is [ ] inches.

Based on the Monte Carlo (MC) sampling results, the definition of the breakline for the Model 44F SGs (Figure 3-44) in the upper 10% of the rank order is characteristically the same as that shown in Figure 3-37. Figure 3-45 shows the same data as Figure 3-44 but plotted as H* against the combined tube and tubesheet CTE values in the range of interest for the probabilistic H*. The three points shown as open symbols on Figure 3-44 are the points selected for the Model 44F SGs as shown on Table 3-27.

Figure 3-46 is a plot of H* versus the selected rank order values.

3.4.3.1 Model 44F (Turkey Point Units 3 & 4) Results The H* values (without the crevice pressure adjustment) from the contact pressure distributions developed using the C 2 model at the limiting TS radius are shown in Table 3-30 together with the rank order of the input values as discussed above. Also shown is for comparison is the raw H* value from the reference analysis of Reference 3-1. The H* estimates based on the C 2 model results are about two to three inches greater than those from the current licensing basis. The results shown in Table 3-27 are represented graphically in Figure 3-46 for both the reference analysis and for application of the C 2 model.

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3-58 Although the values of H* at the required rank orders of interest were calculated directly with the C2 model using the CTE inputs corresponding to those rank orders, Figure 3-46 provides an example of how the break line concept can be applied for other rank orders of interest. The linear fit used to interpolate the value of H* at the desired rank order statistic for the Model 44F is given by:

[ ]a,c,c H*RO =

where, RO = the desired Rank Order statistic between 9158 and 9760.

3.4.4 Application to Bounding Model 51F SGs (Surry Unit 1)

The general approach to the probabilistic analysis for H* is applied for all models of SGs that are candidates for H*. There are no exceptions that are required to this process. Because the limiting condition for a 3-loop plant with Model 44F SG is NOP, it is necessary to perform the analysis for the whole plant complement of tubes because all loops are subject to the NOP conditions:

1. The limiting operating condition for H*. The limiting operating condition for the Model 5 IF 3-Loop SGs was determined to be the NOP condition.

2. The limiting radius for H* for the Model 51F SGs, which is [ ]ace inches.

The necessary inputs for the probabilistic analysis using the C 2 model for the Model 5 IF SGs are:

The limiting operating condition for H*. The limiting operating condition for the Model 51 F SGs was determined to be the NOP condition.

The limiting radius for H* for the Model 5 IF SGs. The limiting radius for Surry Unit 1 is I ]a,c,, inches. All other structural models and inputs are the same as discussed in Reference 3-2 including the range of significant material properties, CTEs for the tubesheet and tube material.

Based on the MC sampling results, the definition of the break line (Figure 3-41) in the upper 10% of the rank order is characteristically the same as that shown in Figure 3-37. Figure 3-42 shows the same data as Figure 3-44 but plotted as H* against the Monte Carlo rank order in the range of interest for the probabilistic H*. The three points shown as open symbols on Figure 3-43 are the points selected for the Model 51F SGs as shown on Table 3-30.

3.4.4.1 Model 51F (Surry Unit 1) Results The H* values (without the crevice pressure adjustment) from the contact pressure distributions developed usingthe C 2 model at the limiting TS radius are shown in Table 3-30 together with the rank order of the input values as discussed above. The results shown in Table 3-30 are represented graphically in Figure 3-43. The results from the C 2 model are approximately 2 inches less than the results from the Reference 3-2 analysis, but are characteristically the same.

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3-59 Although the values of H* at the required rank orders of interest were calculated directly with the C2 model using the CTE inputs corresponding to those rank orders, Figure 3-46 provides a second example of how the break line concept can be applied for other rank orders of interest. The linear fit used to interpolate the value of H* at the ddsired rank order statistic for the Model 5 IF is given by:

H*RO = [ ]a,ce

where, RO = the desired Rank Order statistic between 9025 and 9901.

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3-60 Table 3-23 Typical Monte Carlo Result Output Rank # HSTAR nFOT() maTs(1) Alpha 9000 9001 9002 9003 9004 9995 9996 9997 9998 9999 10000 Note:

1. nGT is the multiplier on a for the tube; maYs is the multiplier on c for the tubesheet.

Table 3-24 Positive Variations About the Mean TS CTE Used for FEA (Units of 10-6 in/in/0 F)

Multiplier on Standard Deviation Temp. OF 70 200 300 400 500 600 700 WCAP- 17345-NP June 2011 Revision 2

3-61 Table 3-25 Negative Variations About the Mean Tube CTE Used for FEA (Units of 10-6 in/in/0 F)

Multiplier on Standard Deviation a, Cce Temp. IF Mean 212 7.22 300 7.40 420 7.60 500 7.70 600 7.82 628 7.85 Table 3-26 Required Probabilistic Estimate for H*

Whole Bundle Estimate Whole Plant Estimate Model SG 95/50 95/95 95/50 95/95 a,cc,e F 9500 9536 D5 9500 953.6 44F 9500 9536 44F 9500 9536 2-Loop 51F 9500 9536 Notes:

1. Whole plant does not apply because SLB is the limiting condition for H*.

2. Values are the whole bundle rank orders based on whole plant rank order equivalent H* to recover the corresponding values of tube and tubesheet CTE.

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3-62 Table 3-27 Monte Carlo Data Used in Comparative Probabilistic Analysis Tubesheet Tube CTE H* from Limiting CTE Variation Variation Current Model Operating Rank Order standard (standard Licensing 1

SG Condition Statistic0 ) deviations) deviations) Alpha Basis a,c,e F NOP D5 SLB 44F NOP 3-Loop 44F SLB(2) 2-Loop 51F NOP Notes:

1. Based on 10,000 simulations.

2. Point Beach specific H* values did not exist in the previous licensing basis.

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3-63 Table 3-28 Typical Variation of CTEs Over a Range of Rank Order Statistics (Ref. Model F C2 Results)

Rank H* Tube CTE Tubesheet CTE "Alpha" a,c,e 9880 9881 9882 9883 9884 9885 9886 9887 9888 9889 9890 9891 9892 9893 9894 9895 9896 9897 9898 9899 9900 Table 3-29 Variation of H* for Adjacent Rank Order Variables (Ref. Model F C2 Results)

Variation Input MC T CTE TS CTE C, H*

1. nc ma in.

a,c,e 9889 9890 9891 WCAP-17345-NP June 2011 Revision 2

3-64 Table 3-30 Model 44F and Model 51F H* Results (Without P.... Adjustment)

H* Results from Current Licensing Basis H* Result from (References 3-1, 3-2) Square Cell Analysis MC Rank in 10,000 Simulations Model 44F (in.) a,c,e 9158 9697 9760 Model 51F (in.) a,c,e 9025 9673 9901 WCAP-17345-NP June 2011 Revision 2

3-65 a,c,e Figure 3-36 Typical Result for Plotting the Combined Tube and Tubesheet CTE Values vs. H*

from the Licensing Basis Analysis (Ref. Model D5 NOP) a,c,e Figure 3-37 Typical Result of Combined Tube and Tubesheet CTE Values vs. Monte Carlo Rank Order from the Licensing Basis Analysis (Ref. Model D5 SLB)

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i 3-66 a,c,e Figure 3-38 H* Curves from Response Surface (Ref. Model F) ac Figure 3-39 Variation in H* from a Linear Fit of H* Results in a Range of Order Statistics Required to Meet Probabilistic H* Goals (Ref. Model 44F NOP)

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3-67 a,c,e Figure 3-40 Variation in H* from a Linear Fit of H* Results in a Range of Order Statistics Required to Meet Probabilistic H* Goals (Ref. Model 51F NOP) a,c,e Figure 3-41 Model 51F NOP Combined CTET and CTETS vs. Monte Carlo Rank Order WCAP-17345-NP June 2011 Revision 2

3-68 a,c,e Figure 3-42 Model 51F NOP Combined CTET and CTETS vs. H* Value a,c,e Figure 3-43 Model 51F H* Summary Showing Linear Fit Results WCAP-17345-NP June 2011 Revision 2

3-69 a,c,e L

Figure 3-44 Model 44F NOP Combined CTET and CTETS vs. Monte Carlo Rank Order a,c,e Figure 3-45 Model 44F NOP Combined CTET and CTETS vs. H* Value WCAP- 17345-NP June 2011 Revision 2

3-70 a,c,e Figure 3-46 Model 44F H* Summary Showing Linear Fit Results June2011 WCAP- 17345-NP WCAP-17345-NP June 2011 Revision 2

3-71 3.5 POISSON CONTRACTION EFFECT ON H*

An evaluation was performed to determine the effect of Poisson contraction of the tube on H* due to end cap loading. The pressure differential across the tube wall creates an effective end cap load, generating a positive axial stress state in the tube. This will cause a radial contraction of the tube via Poisson's ratio, which will necessarily reduce the contact pressure between the tube and tubesheet, hence increasing H*.

The purpose of this section of the report is to address the impact of Poisson contraction on the values calculated for H* using the C 2 model.

3.5.1 Methods Discussion The method used to evaluate the effect of Poisson's ratio on H* is a simplified approach using approximations to determine the reduction in contact pressure. A classical thick shell formula is used to calculate the change in radius due to Poisson's ratio effects from an applied end cap load. This change in radius is directly converted to a contact pressure utilizing the thick shell equations in References 3-1 and 3-2. This contact pressure is then subtracted from the calculated contact pressure curve and the final H* distance is calculated. All calculations for Poisson's contraction are based on an end cap load without a factor of safety, as it is unrealistic to apply a factor of safety to a physical effect such as Poisson's contraction. The end cap load used to generate H*, however, continues to include the appropriate safety factor (3.0 for 100% power, 1.4 for SLB).

3.5.2 Input The input for this analysis consists of steam generator dimensions for the Model 44F and Model 5 IF SGs, material properties from the ASME Code, and pressure and temperature conditions for the applicable operating condition (100% Power) as defined in Reference 3-6.

The end cap load for the Model 44F SGs for NOP is [ ]ace psi. This includes a factor of safety of 3.0 on the NOP pressure differential. The end cap load for the Model 5IF SGs is [ ]a.c.. psi. This includes a factor of safety of 3.0 on the NOP pressure differential. The modulus of elasticity is the taken from Table 3-3. Poisson's ratio for Alloy 600 is 0.31 as taken from the ASME Code, Reference 3-10.

Material properties were taken at temperatures consistent with those used in the FEA discussed in Section 3.1. Material properties are taken at [ ]a,c,C 'F for NOP conditions for both the Model 44F and 5IF SGs.

3.5.3 Calculation of Radial Dilation From Reference 3-14 (Page 396), the radial dilation of a pressurized thick-wall cylinder is given by:

AR== EtI (r02

, r _ri2 [(1 2vXpir -Pro2)+(l+v) r2ro2(P r Po) (Euton32 (Equation 38)

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3-72

where, P = End cap load (pounds) v = Poisson's ratio r = Radial coordinate (inches) ro = Outer radius of tube (inches) ri = Inner radius of tube (inches) pi = Pressure on inside of tube (psi) po = Pressure on outside of tube (psi)

E, = Elastic Modulus of tube (psi)

Tr = pi (3.14159...)

AR = Change in radial coordinate due to loadings (inches)

Since the figure of interest is the radial contact at the outside radius due to the applied end cap load, the difference is:

- rovP re,,cap (Equation 3-9)

This equation is used to calculate radial dilations due to the Poisson contraction alone (Table 3-31). As can be seen, there is a small radial contraction (approximately [ ]ac~e micro-inches) due to Poisson effects.

3.5.4 Calculation of Contact Pressure Reduction from Poisson Effect The contact pressure change due to Poisson effects can be estimated by using the thick shell equations from Reference 3-1. The thick shell formula is (page 6-91 of Reference 3-1): a,c,e (Equation 3-10)

where, Pj = Internal primary side pressure, psi Perey = Crevice pressure, psi ri = Inside radius of tube, in ro = Outside radius of tube, in a, = Coefficient of thermal expansion of tube, in/in/!F Et = Modulus of Elasticity of tube, psi E,, = Modulus of Elasticity of tubesheet, psi WCAP-17345-NP June 2011 Revision 2

3-73 T, = Temperature of tube, 'F v = Poisson's Ratio of the material

= Contact Pressure D = Outside radius of cylinder which provides the same radial stiffness as the tubesheet As can be seen, the thick shell equation for contact pressure is simply a sum of radial displacements divided by an effective elastic constant. This makes intuitive sense because the physical interpretation of the thick shell equations is as follows:

1. Apply internal pressure, crevice pressure, and thermal loads to a free tube which has a nominal outside diameter equivalent to the collar bore ID. Calculate the resultant radial dilation.

2. Calculate the bore displacement of a free collar from crevice pressure and the applied dilation from the 3-D FEA model.

3. If the answers to one and two above possess a geometric interference (the resultant tube radius is larger than the bore), then there exists positive contact pressure. The positive contact pressure can be calculated as that pressure which, when applied to both the tube OD and the collar ID, eliminates the geometric interference, producing line-on-line contact.

In Step 3, it is clear that the relationship between contact pressure and radial geometric interference should be linear, as the thick shell equations are linear elastic. Therefore, it is appropriate to calculate

[(Equation contact pressure reduction by simply dividing the differential radial displacement due to Poisson's ratio effects by the elastic constant in the denominator above: a,c,e 3-li)

Results of the calculation of the elastic constants are provided in Table 3-32 for the Model 44F and Model 5 IF SGs. Substituting the differential radial dilation from Table 3-31 into the above equation yields the contact pressure reductions shown in Table 3-33. As can be seen, there is a reduction of

[I ]c,e psi at NOP conditions for the Model 44F and [ ]a,,,e psi at NOP conditions for the Model 5 IF.

The effect of Poisson contraction on H* was calculated for the critical radius because this radius determines the value of H*. In order to calculate the change in H* values due to the decreased contact pressure, the contact pressure curves from Section 3.3 must be reduced by the incremental contact pressures discussed above. The resulting contact pressure curve then must be integrated again to determine the adjusted H*. The reference square cell analysis (Section 3.3) explains the methodology for calculating H*. The formula for pull out load is F O=lTd°P,°,tacdy (Equation 3-12)

Where [t is the coefficient of friction, [ ]a,cc, as discussed in References 3-1 and 3-2.

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3-74 Calculations for the increased H* are shown on Table 3-34 and Table 3-35 for the Model 44F and Model 5 IF, respectively. The typical adjustment to the contact pressure profile is shown in Figure 3-47.

As can be seen, the contact pressure curve is shifted down by the appropriate amount. Baseline numbers are included on Table 3-34 and Table 3-35 for comparison. The increase in H* due to Poisson effects amounts to approximately [ ]a,,,, inches for the Model 44F and approximately [ ]a.c.. inch for the Model 5 IF (both values considered before attenuation). These contraction values assume Poisson contraction occurs along the entire length. A more realistic calculation will account for the Poisson effect attenuating after an accumulated pull out resistance equal to the end cap load is attained. This correction is obtained by interpolation using the same methodology as for H*, but with an end cap load that does not have a factor of safety. The interpolated attenuation distance is provided in Table 3-36.

Because the axial stress in the tube goes to zero at the attenuation point, the next step in the process is to calculate new H* values with contact pressures that are reduced only inside the attenuation distance. This involves interpolating the predicted contact pressure curves from Section 3.3 and shifting only the portion of it above the attenuation point. Calculations are-tabulated in Table 3-37 and Table 3-38 for the Model 44F and Model 5 IF, respectively. A summary of the final H* values after adjusting for Poisson contraction and attenuation are in Table 3-39. As can be seen, the difference is [ ]a.....inches for the Model 44F and [ ]a,c,c inch for the Model 51F for the mean value of H*.

The final figure of merit is the effect that Poisson contraction has on the probabilistic H* values.

Calculations for the probabilistic values are in Table 3-40 through Table 3-48.

A summary of the effect of Poisson's contraction on the probabilistic values of H* is in Table 3-49.

As can be seen, the effect is approximately [ ]ac, inch for the probabilistic H* value for the Model 44F SG and approximately [ ]a,c,e inch for the Model 5 IF SG.

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3-75 Table 3-31 Calculation of Radial Dilation Due to Poisson Effects Model 44F Model 51F Parameter NOP NOP a,c,e Tube ri (in)

Tube ro (in)

Etwbe (Msi)

End Cap Load (lbs)

AR (micro-inch, 10-6 in)

Table 3-32 Calculation of Elastic Constants Model 44F Model 51F Parameter NOP SLB NOP SLB a,c,e Tube ri (in)

Tube ro (in)

Collar R. (in)

Tube E (Msi)

Tubesheet E (Msi) v Elastic Constant (in 3/lb)

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3-76 Table 3-33 Calculation of Reduction in Contact Pressure from Poisson Effects Model 44F Model 51F Parameter NOP NOP a,c,e AR due to v (gtin)

Elastic Constant (in3/lb)

Pon Reduction (psi)

Table 3-34 Baseline and Adjusted Mean H* Calculation for Model 44F (Turkey Point Units 3 & 4)

(Without Attenuation)

NOP, [ ]a.....in. Radius End Cap Load = I " pounds Accumulated Accumulated Elevation Pull Out Load Pull Out Load from Bottom Distance PCon (psi) (pounds) Pcon (psi) (pounds) of Tubesheet from TTS a,c,e (in) (in) Baseline (Unadjusted Mean H*) H*Adjusted for Poisson Effect 0 21.81 2 19.81 3.523 18.287 5.442 16.368 10.905 10.905 16.368 5.442 18.287 3.523 19.81 2 21.81 0 H* (inches)

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3-77 Table 3-35 Baseline and Adjusted Mean H* Calculation for Model 51F (Surry Units 1 & 2)

(Without Attenuation)

NOP, [ ]".... in. Radius End Cap Load = [ Ia,,,, pounds Accumulated Pull Accumulated Elevation Out Load Pull Out Load from Bottom Distance Peon (psi) (pounds) Peo. (psi) (pounds) of Tubesheet from TTS (in) (in) Baseline (Unadjusted Mean H*) H*Adjusted for Poisson Effect a,c,e 0 21.03 2 19.03 4 17.03 5 16.03 6 15.03 8.25 12.77 10.52 10.52 13 8.03 16.90 4.13 19.03 2 20.03 1 21.03 0 H* (inches)

Table 3-36 Distance for Poisson Effect to Attenuate SG Model 44F 51F Distance for Poisson Effect to Attenuate (inches) [ ].ace ]a.c.e WCAP- 17345-NP June 2011 Revision 2

3-78 Table 3-37 Adjusted Mean H* Including Poisson Attenuation for Model 44F (Turkey Point Units 3 & 4)

NOP 100% Power, [ ]".....in. Radius End Cap Load = [ ]'.....pounds Elevation from Bottom of Distance from Accumulated Pull Out Tubesheet (in) TTS (in) Pco. (psi) Load (pounds) a,c,e 0 21.810 I 2 19.810 3.523 18.287 5.442 16.368 10.905 10.905 15.250 6.560 16.368 5.442 18.287 3.523 19.810 2.000 21.810 0.000 H* (inches)

A N WCAP- 17345-NP June 2011 Revision 2

3-79 Fable 3-38 Adjusted Mean H* Including Poisson Attenuation for Model 51F (Surly Units 1 & 2)

NOP, I Iac'ein. Radius End Cap Load = I " pounds Elevation from Bottom of Distance from Accumulated Pull Out Tubesheet (in) TTS (in) P... (psi) Load (pounds) a,c,e 0 21.03 2 19.03 4 17.03 5 16.03 6 15.03 8.25 12.77 10.52 10.52 12.68 8.34 13 8.03 16.90 4.13 19.03 2 20.03 1 21.03 0 H* (inches)

Table 3-39 Comparison of Mean H* Values Parameter Model 44F (in.) Model 51F (in.) a,c,e H* Unmodified H* + Poisson H* + Poisson + Attenuation Final Difference WCAP- 17345-NP June 2011 Revision 2

3-80 rable 3-40 Baseline and Adjusted Probabilistic H* Calculation for Model 44F (Monte Carlo Rank 9158)

NOP, [ ]a.....in. Radius End Cap Load = [ ]a.....pounds Elevation Baseline Shifted due to Poisson from Bottom Distance from of Tubesheet TTS Peon Accumulated Pull Peon Accumulated Pull (in) (in) (psi) Out Load (pounds) (psi) Out Load (pounds) a,c,e 0 21.81 2 19.81 3.523 18.287 5.442 16.368 8 13.81 10.905 10.905 12 9.81 14 7.81 16.368 5.442 18.287 3.523 19.81 2 21.81 0 H* (inches)

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3-81 Table 3-41 Baseline and Adjusted Probabilistic H* Calculation for Model 51F (Monte Carlo Rank 9025)

NOP, [ ]a.....in. Radius End Cap Load = [ ]',','.pounds Elevation Baseline Shifted due to Poisson from Bottom Distance from of Tubesheet TTS Pcon Accumulated Pull Peon Accumulated Pull (in) (in) (psi) Out Load (pounds) (psi) Out Load (pounds) a,c,e 0 21.03 2 19.03 4 17.03 6 15.03 8 13.03 10.52 10.52 12 9.03 14 7.03 16.90 4.13 19.03 2 20.03 1 21.03 0 H* (inches)

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3-82 Table 3-42 Baseline and Adjusted Probabilistic H* Calculation for Model 44F (Monte Carlo Rank 9760)

NOP, [ Ja.....in. Radius End Cap Load = [ ]a"c"e pounds Elevation Baseline Shifted due to Poisson from Bottom Distance from of Tubesheet TTS Pcon Accumulated Pull Pcon Accumulated Pull (in) (in) (psi) Out Load (pounds) (psi) Out Load (pounds) a~ce 0 21.81 2 19.81 3.523 18.287 5.442 16.368 8 13.81 10.905 10.905 12 9.81 14 7.81 16.368 5.442 18.287 3.523 19.81 2 21.81 0 H* (inches)

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3-83 Table 3-43 Baseline and Adjusted Probabilistic H* Calculation for Model 51F (Monte Carlo Rank 9901)

NOP, I ]ac'e in. Radius End Cap Load = [ c,e pounds Elevation Baseline Shifted due to Poisson from Bottom Distance from of Tubesheet TTS PCoU Accumulated Pull Pcn Accumulated Pull (in) (in) (psi) Out Load (pounds) (psi) Out Load (pounds) a,c,e 0 21.03 2 19.03 4 17.03 6 15.03 8 13.03 10.515 10.515 12 9.03 14 7.03 16.901 4.129 19.03 2 20.03 1 21.03 0 H* (inches)

Table 3-44 Distance for Poisson Effect to Attenuate Probabilistic H* Values (inches)

Model SG Model 44F Model 51F MC Rank 9025 N/A [ ]a...e MC Rank 9901 N/A [ ]a..ce MC Rank 9158 [ ].... N/A MC Rank 9760 [ ]a,c,e N/A WCAP-17345-NP June 2011 Revision 2

3-84 Table 3-45 H* Calculation Including Poisson Attenuation Model 44F (Turkey Point Units 3 & 4)

(With Attenuation, MC Rank 9158)

NOP, [ ]".... in. Radius End Cap Load = [ ]',, 'pounds Elevation Above Distance from TTS Peon Bottom of TS (in) (in) (psi) Accumulated Pull Out Load (pounds) a,c,e 0.00 21.810 2.00 19.810 3.52 18.287 5.44 16.368 8.00 13.810 8.61 13.200 10.91 10.905 12.00 9.810 14.00 7.810 16.37 5.442 18.29 3.523 19.81 2.000 21.81 0.000 H* (inches)

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3-85 Table 3-46 H* Calculation Including Poisson Attenuation Model 44F (Turkey Point Units 3 & 4)

(With Attenuation, MC Rank 9760)

NOP, I ]a.... in. Radius End Cap Load [ ]a.....pounds Elevation Above Distance from TTS Peon Accumulated Pull Out Bottom of TS (in) (in) (psi) Load (pounds) a,c,e 0.00 21.810 2.00 19.810 3.52 18.287 5.44 16.368 7.86 13.951 8.00 13.810 10.91 10.905 12.00 9.810 14.00 7.810 16.37 5.442 18.29 3.523 19.81 2.000 21.81 0.000 H* (inches)

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3-86 Table 3-47 H* Calculation Including Poisson Attenuation Model 51F (Surry Units 1 & 2)

(With Attenuation, MC Rank 9025)

NOP, [ ].a..e in. Radius End Cap Load = [ ]..... pounds Elevation Above Distance from TTS Peon Bottom of TS (in) (in) (psi) Accumulated Pull Out Load (pounds) a,c,e 0 21.03 -I 2 19.03 4 17.03 6 15.03 7.42 13.60 8 13.03' 10.52 10.52 12 9.03 14 7.03 16.90 4.13 19.03 2 20.03 1 21.03 0 H* (inches)

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3-87 Table 3-48 H* Calculation Including Poisson Attenuation Model 51F (Surry Units 1 & 2)

(With Attenuation, MC Rank 9901)

NOP, [ ]".... in. Radius End Cap Load =[ ]a..e pounds Elevation Above Distance from TTS Peon Accumulated Pull Out Bottom of TS (in) (in) (psi) Load (pounds) a,c,e 0 21.03 2 19.03 4 17.03 6 15.03 6.57 14.46 8 13.03 10.52 10.52 12 9.03 14 7.03 16.90 4.13 19.03 2 20.03 1 21.03 0 H* (inches)

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0 3-88 Table 3-49 Comparison of Model 44F and Model 51F SG Probabilistic H* Values (inches)

Model 44F Model 51F Rank Order Rank Order Rank Order Rank Order Parameter Mean 9158 9760 Mean 9025 9901 a,c,e H*

Unmodified H* + Poisson H* + Poisson

+ Attenuation Final Difference a,c,e Figure 3-47 Effect of Poisson Contraction on Contact Pressure; Model 44F June 2011 17345-NP WCAP- 17345-NP June 2011 Revision 2

3-89 3.6 CREVICE PRESSURE ADJUSTMENT LENGTH As discussed in References 3-1 and 3-2, the solution for H* is iterative to address the axial distribution of crevice pressure. Initially, it is assumed that a crack exists at the bottom of the tubesheet and that the crevice pressure axial distribution applies over the entire thickness of the tubesheet. The H* value predicted based on this assumption is less than the full depth of the tubesheet. Because the effective crevice length is no longer the full depth of the tubesheet, the axial distribution of crevice pressure is applied over the initial prediction of H* and a new value of H* is calculated.

The Model 44F (Reference 3-1) and Model 5 IF analyses (Reference 3-2) contain the crevice pressure correction curves. The curves are reproduced below as Figure 3-48 and Figure 3-49 for convenience.

When the probabilistic value of H*, corrected for Poisson contraction is available, the curve is entered with that value of "initial prediction" and the necessary length adjustment is read. The adjustment is added to the "initial prediction" as defined above to develop the final value of H*.

June 2011 WCAP-l 7345-NP WCAP- 17345-NP June 2011 Revision 2

3-90

-,C,e Figure 3-48 Model 44F Crevice Pressure Adjustment Curve ac e Figure 3-49 Model 51F Crevice Pressure Adjustment Curve WCAP-17345-NP June 2011 Revision 2

3-91 3.7 . CALCULATION OF FINAL H*

After the probabilistic values of H* are determined as discussed in Section 3.4, and the correction is made for Poisson contraction of the tube to define the initial estimate of the probabilistic H* discussed in Section 3.5, the adjustment for crevice pressure distribution as discussed in Section 3.6 is made. The final probabilistic values of H*, with the corresponding crevice pressure length adjustments taken from Figure 3-48 and Figure 3-49, are shown in Table 3-50 and Table 3-51 for the Model 44F and Model 5IF SGs, respectively.

Table 3-50 Summary of Model 44F Probabilistic Estimates Attenuated MC Rank in Poisson 2

10K H* - C Offset Pcrev Final Description Simulations (in.) (in.) (in.) a,c,c (in.)

Whole Bundle, 95/50 9500 17.77 Whole Bundle, 95/95 9536 17.82 Whole Plant, 95/50(l) 9760 18.09 Whole Plant, 95/95 9774 18.11 Note:

1. 95/50 Rank Order value determined from linear interpolation.

Table 3-51 Summary of Model 51F Probabilistic Estimates MC Rank in Attenuated 10K H* - C' Poisson Offset Pcrev Final Description Simulations (in.) (in.) (in.) a.c.e (in.)

Whole Bundle,. 95/50 9500 17.63 Whole Bundle, 95/95 9536 17.64 Whole Plant, 95/50(1) 9818 17.88 Whole Plant, 95/95 9834 17.89 Note:

1. 95/50 Rank Order value determined from linear interpolation.

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3-92

3.8 REFERENCES

3-1. WCAP-17091-P, Rev. 0, "H*: Alternate Repair Criteria for the Tubesheet Expansion Region in Steam Generators with Hydraulically Expanded Tubes (Model 44F)," June 2009.

3-2. WCAP-17092-P, Rev. 0, "H*: Alternate Repair Criteria for the Tubesheet Expansion Region in Steam Generators with Hydraulically Expanded Tubes (Model 5 IF)," June 2009.

3-3. WTD-SM-75-072, "Temperature Distributions for Calculation of Secondary Skin Stress in D2-D3 Tubesheet Analysis," August 1975.

3-4. Report 1014982, "Divider Plate Cracking in Steam Generators: Results of Phase I: Analysis of Primary Water Stress Corrosion Cracking and Mechanical Fatigue in the Alloy 600 Stub Runner to Divider Plate Weld Material," EPRI, Palo Alto, CA; 2007.

3-5. Jaluria, Yogesh, "Computer Methods for Engineering," Taylor and Francis, 1996.

3-6. CN-SGMP- 10-15, Rev. 1, "3-D Finite Element Analyses of Limiting Plants for H* with Thermal Profile," November 2010.

3-7. WNET-150, Volume 3, "Model E2, Steam Generator Stress Report, Primary Chamber Components Interactions Analysis," December 1978.

3-8. CN-SGMP-10-3, Rev. 1, "Square Cell Finite Element Analyses for Models D5, F, 44F and 51F Plants for H*," November 2010.

3-9. Not used.

3-10. ASME B&PV Code, 2007 Edition, No Addenda,Section II, Part D, Subpart 2: Physical Properties Tables, Table PRD.

3-11. LTR-SGMP-09-100 P-Attachment, Rev. 1, "Responses to NRC Request for Additional Information on H*; Model F and Model D5 Steam Generators," September 2010.

3-12. Statistics, ProbabilityandReliabilityfor Civil and EnvironmentalEngineers, Kottegoda, N.T.,

Rosso, R., McGraw-Hill, © 1997.

3-13. Westinghouse Drawing 1105J05, Rev. 3, "Tube Plate Drilling."

3-14. Advanced Mechanics of Materials,Boresi, Arthur P and Schmidt, Richard J, Sixth Edition, John Wiley and Sons Publishing.

3-15. LTR-SGMP-1 1-40, "Calculation of Required Parameters for Extreme H* Values," May 6, 2011.

3-16. LTR-SGDA-11-87, "High-Confidence Variances for Tube and Tubesheet CTE for H*,"

May 5, 2011.

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3-93 3-17. LTR-SGMP-09-147, "An Assessment of the Impact of Measurement Uncertainty Recapture Uprate Conditions on the H.B. Robinson Unit 2 H* Calculation," October 23, 2009.

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4-1 4 C2 MODEL LEAKAGE INTEGRITY DISCUSSION As noted in References 4-1 and 4-2, the licensing basis for the plants with Model 44F and Model 51F steam generators does not include considerations of the feedwater line break (FLB) transient; therefore it is necessary to consider only the SLB transient in the development of the accident induced to normal operating leakage factors.

The model for leakage applied in References 4-1, 4-2, and 4-3 is the Darcy formulation for flow through a porous medium. The Darcy equation is:

Ap 12bXKl (Equation 4-1)

where, Ap = the driving potential (primary-to-secondary pressure difference) t = the fluid dynamic viscosity K = the loss coefficient for flow through the porous medium L = the length of the porous medium The Darcy formulation (Equation 4-1) is used in References 4-1, 4-2, and 4-3 to develop the ratio of leak rates between postulated accident induced conditions and normal operating conditions (NOP). The resulting Darcy flow equation ratio can be separated into four "subfactors" as follows:

QoA_ n~ /-oK oIo, QDBA - XADBA PA/OP KNOP A/OP (Equation 4-2)

QNOl ApNoP /-DBAKDBAX DBA The purpose of this section of the report is to address the impact of the new square cell model results on the existing licensing basis leak rate factors provided in Reference 4-3 for the Model 44F and Model 5 IF steam generators in 3-loop plants. It was determined that application of the square cell model results does not affect any of the four subfactors identified in Equation 4-2 above; therefore, the leakage factors established in the current licensing basis are unchanged.

The driving head (Ap) at both NOP and SLB conditions are known and remain unchanged from the current licensing basis. Also, the temperatures and pressures, which define the fluid viscosity (i'), remain the same. Therefore, the pressure and viscosity subfactors in Equation 4-2 above remain unchanged.

As discussed in Section 9.1.1 of References 4-1 and 4-2, the current licensing basis leakage factors assume a loss coefficient subfactor of 1.0. The available data for hydraulically expanded tubes in tubesheet simulants (References 4-4 and 4-5), both at room temperature and at elevated temperature, are utilized in References 4-1 through 4-3 to show that no correlation between loss coefficient and contact pressure exists for conditions that simulate the Model D5 SG conditions. However, because the data exhibit considerable scatter, confidence in this data analysis is low. Engineering judgment could suggest that loss coefficient might be related to the absolute contact pressure between the tubes and the tubesheet.

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4-2 Hence, a requirement was applied to the H* leakage analysis by the regulatory authorities that it is necessary to show that the contact pressure at accident induced conditions exceeds the contact pressure at normal operating conditions (PCFLB/SLB:PCNoP> 1) in order to assume that the loss coefficient subfactor is equal to 1.0.

For both the Model 44F and 51F steam generators in 3-loop plants, the results of the square cell analysis show that the contact pressure during steam line break conditions at various elevations between 0 and 21.81 (Model 44F)/21.03 (Model 51F) inches at all radii in the tube bundle always meets or exceeds the contact pressure above the H* distance from the top of the tubesheet during normal operating conditions as shown on Figure 3-18 through Figure 3-23 for the Model 44F steam generator and Figure 3-24 through Figure 3-29 for the Model 5 IF steam generator, thereby meeting the intent of the criterion (PCSLB:PCNop>I). It is noted that these figures do not include the effect of Poisson contraction, however it has been confirmed that this criterion is still met when the effects of Poisson contraction are considered. Therefore, it is concluded that it is acceptable to apply a loss coefficient subfactor, KNOP/KDBA of 1.0.

Addressing the effective crevice length subfactor, as discussed in References 4-1 and 4-2, recall that "effective crevice length" is defined as the length of positive contact between the tube and the tubesheet (above H*). Again, based on a review of Figure 3-18 through Figure 3-23 for the Model 44F steam generator and Figure 3-24 through Figure 3-29 for the Model 5 iF steam generator, the effective crevice length during a postulated SLB event meets or exceeds the effective length of crevice for normal operating conditions for the Model 44F/5 IF steam generators in 3-loop plants. Therefore, the effective length ratio subfactor for (1NOp/1DBA) can be assumed to be 1.0 during a postulated steam line break event for the Model 44F and Model 5 IF steam generators.

As discussed in References 4-1 and 4-2, the design specification curves for the locked rotor and control rod ejection events apply for the leakage factors for these transients. These transients are of very short duration, for which the H* leakage calculations employ a time integrated leakage approach. The same leakage factors (<1.0) for a postulated locked rotor and control rod ejection event for the Model 44F and 51F SGs in the H* fleet included in Reference 4-3 continue to apply.

Based on the above, it is concluded that the current licensing basis leakage factors identified in Reference 4-3 continue to apply when considering the C 2 model results.

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4-3

4.1 REFERENCES

4-1. WCAP-17091-P, Rev. 0, "H*: Alternate Repair Criteria for the Tubesheet Expansion Region in Steam Generators with Hydraulically Expanded Tubes (Model 44F)," June 2009.

4-2. WCAP-17092-P, Rev. 0, "H*: Alternate Repair Criteria for the Tubesheet Expansion Region in Steam Generators with Hydraulically Expanded Tubes (Model 5 IF)," June 2009.

4-3. LTR-SGMP 100 P-Attachment, Rev. 1, "Responses to NRC Request for Additional Information on H*; Model F and Model D5 Steam Generators," September 2010.

4-4. CN-SGDA-03-119, Rev. 1, "Calculation of Loss Coefficient for Model D5 Steam Generators,"

Westinghouse Electric Company LLC, June 2004.

4-5. STD-MCE-03-49, "Determination of the Model D5 Tube-to-Tubesheet Leakage Resistance for H-Star Program for CBE/CDE/DDP/TCX," November 4, 2003.

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5-1 5 REPORT

SUMMARY

AND CONCLUSIONS The purpose of this report is to provide final resolution of the NRC technical issue regarding tubesheet

-bore eccentricity on the H* criterion. As a result, the NRC staff asked 14 questions related to this issue.

As stated in Section 1.0 of this report, the content of this report primarily focuses on resolving NRC Request for Additional Information (RAI) #5 and #12. A roadmap was provided in Section 1.0 to previous documents issued by Westinghouse in response to the remainder of the 14 RAI.

There are two principal requirements for H*:

1. Assure that tube(s) do not pull out of the tubesheet under the most limiting loadings during normal or accident conditions.

2. Assure that primary-to-secondary coolant leakage through the tube-to-tubesheet crevice is no greater than that assumed in the final safety analysis report (FSAR) for the most limiting accident.

Concerning Item 1, the Westinghouse action plan to resolve the NRC staff tube pull out concerns relating to tube bore eccentricity involved the development of a more accurate analysis model for calculating tube joint contact pressure. As discussed in Section 3 of this report, the square cell (C2) model analysis is an independent method of modeling the contact pressure distribution between the tube and the tubesheet throughout the tubesheet thickness.

For the Model 44F SG in 3-loop plants, the value of H* inspection depth required to meet the structural integrity goals of the plant increased by 3.02 inches. The value for the H* inspection depth for the Model 5IF SGs increased by 2.31 inches. The differences between the two models are the results of different tubesheet thicknesses, tubesheet displacements and contact pressure distributions. A direct comparison between the licensing basis probabilistic H* values and the square cell analysis probabilistic H* values for the Model 44F and Model 5IF steam generators is shown in Table 5-1. The H* values in Table 5-1 provide tube pull out capability that meet or exceed the structural integrity acceptance criteria identified in Section 4.1 of References 5-1 and 5-2.

The impact of the new square cell model results on the existing licensing basis leak rate factors provided in Reference 5-3 for the Model 44F and Model 5 IF steam generators in 3-loop plants was evaluated. It has been determined that the square cell model results do not affect the current licensing basis leakage rate factors. The driving heads (Ap) at NOP and SLB conditions are known and remain unchanged from the current licensing basis as well as the temperatures and pressures remain the same to define the fluid viscosity (g). Therefore, the pressure and viscosity subfactors remain unchanged.

The results of the square cell analysis show that the contact pressure during steam line break conditions at various elevations between 0 and 21.81 (Model 44F)/21.03 (Model 5 IF) inches at all radii in the tube bundle always meets or exceeds the contact pressure above the H* distance from the top of the tubesheet during normal operating conditions. Therefore, it is concluded that it is acceptable to apply a loss coefficient subfactor, KNOP/KDBA of 1.0. Also, the effective crevice length during a postulated SLB event meets or exceeds the effective length of crevice for normal operating conditions for the Model 44F/5 1F steam generators in 3-loop plants. Therefore, the effective length ratio subfactor for (1NOP/IDBA) can be assumed to be 1.0 during a postulated steam line break event for the Model 44F/5 IF steam generators.

WCAP- 17345-NP June 2011 Revision 2

5-2 Concerning all other design basis accidents that model accident condition leakage, as discussed in References 5-1 and 5-2, the design specification curves for the locked rotor and control rod ejection events apply for the leakage factors for these transients. These transients are of very short duration and the H* leakage calculations employ a time integrated leakage approach. The same leakage factors for a postulated locked rotor and control rod ejection event for the Model 44F and 5 1F SGs included in the.

current licensing basis (References 5-3 and 5-7) continue to apply.

Based on the above, with the use the leakage factors included in the current licensing basis (References 5-3 and 5-7), it is concluded that primary-to-secondary leakage through the tube-to-tubesheet crevice is bounded by the values assumed in the final safety analysis report (FSAR) for the most limiting accident.

Satisfactory resolution of the NRC technical issue regarding tubesheet bore eccentricity is complete.

Together with documents provided under separate cover, (e.g., Reference 5-4) this document completes the response to the RAI provided in Reference 5-5. Application of the C2 model has provided independent confirmation that the structural criteria are met. Probabilistic H* values were re-calculated based on application of the C2 model and substantially confirm the values contained in the current licensing basis.

The differences between the H* results based on the C2 model and those from the prior application of the thick shell model are explained. The leakage factors contained in the current licensing basis for the Model 44F and Model 51F SGs are shown to be conservative and acceptable for implementation of H*.

June2011 WCAP-1 7345-NP WCAP-17345-NP June 2011 Revision 2

5-3 Table 5-1 Results of Probabilistic Comparison Study for the Limiting Plants for Models 44F and 51F Thick Shell Calculations Square Cell Calculations (Reference 5-6) Implemented H*(') Whole Bundle Whole Plant 95/50 95/95 Whole Whole Plant SG Model/ Limiting Bundle Plant Tech. Spec. 95/50 95/95 95/50 95/95 Limiting Operating Current Licensing Plant Condition Basis in. in. in. in. in. in. in.

Model 44F/

Turkey Point NOP WCAP-17091-P 13.31 15.09 17.28 17.77 17.82 18.09 18.11 Units 3 & 4 Model 51F/

Surry NOP WCAP-17092-P 13.14 15.58 16.70 17.63 17.64 17.88 17.89 Units 1 & 2 Note:

1. Values taken from utilities' 2009 license amendment requests.

WCAP- 17345-NP June 2011 Revision 2

5-4

5.1 REFERENCES

5-1. WCAP-17091-P, Rev. 0, "H*: Alternate Repair Criteria for the Tubesheet Expansion Region in Steam Generators with Hydraulically expanded Tubes (Model 44F)", June 2009.

5-2. WCAP-17092-P, Rev. 0, "H*: Alternate Repair Criteria for the Tubesheet Expansion Region in Steam Generators with Hydraulically expanded Tubes (Model 5 IF)," June 2009.

5-3. LTR-SGMP-09-100 P-Attachment, Rev. 1, "Responses to NRC Request for Additional Information H*; Model F and Model D5 Steam Generators," September 2010.

5-4. LTR-SGMP-10-33 P-Attachment, "H*: Response to NRC Questions Regarding Tubesheet Bore Eccentricity," September 2010.

5-5. USNRC Letter, "Vogtle Electric Generating Plant, Units 1 and 2 - Transmittal of Unresolved Issues Regarding Permanent Alternate Repair Criteria for Steam Generators (TAC Nos. ME 1339 and ME 1340)," November 23, 2009.

5-6. LTR-SGMP-09-104 P-Attachment, Rev. 1, "White Paper on Probabilistic Assessment of H*,"

August 13, 2009.

5-7. LTR-SGMP-09-147, "An Assessment of the Impact of Measurement Uncertainty Recapture Uprate Conditions on the H.B. Robinson Unit 2 H* Calculations," October 23, 2009.

WCAP- 17345-NP June 2011 Revision 2

Serial No.11-403 Docket Nos. 50-280/281 ATTACHMENT 6 WESTINGHOUSE ELECTRIC COMPANY LLC LETTER CAW-11-3187, "APPLICATION FOR WITHHOLDING PROPRIETARY INFORMATION FROM PUBLIC DISCLOSURE," JUNE 20, 2011 VIRGINIA ELECTRIC AND POWER COMPANY (DOMINION)

SURRY POWER STATION UNITS 1 AND 2

(Westinghouse Nudear Services Westinghouse Electric Company 1000 Westinghouse Drive Cranberry Township, PA 16066 USA U.S. Nuclear Regulatory Commission Direct tel: (412) 374-4643 Document Control Desk Direct fax: (724) 720-0754 11555 Rockville Pike e-mail: greshaja@westinghouse.com Rockville, MD 20852 Proj letter: VRA- 11-32 CAW-1 1-3187 June 20, 2011 APPLICATION FOR WITHHOLDING PROPRIETARY INFORMATION FROM PUBLIC DISCLOSURE

Subject:

WCAP-17345-P, Revision 2, "H*: Resolution of NRC Technical Issue Regarding Tubesheet Bore Eccentricity (3-Loop Model 44F/Model 5 IF)" (Proprietary)

The proprietary information for which withholding is being requested in the above-referenced report is further identified in Affidavit CAW- 11-3187 signed by the owner of the proprietary information, Westinghouse Electric Company LLC. The affidavit, which accompanies this letter, sets forth the basis on which the information may be withheld from public disclosure by the Commission and addresses with specificity the considerations listed in paragraph (b)(4) of 10 CFR Section 2.390 of the Commission's regulations.

Accordingly, this letter authorizes the utilization of the accompanying affidavit by Virginia Electric and Power-Company.

Correspondence with respect to the proprietary aspects of the application for withholding or the Westinghouse affidavit should reference this letter, CAW-1 1-3187, and should be addressed to J. A. Gresham, Manager, Regulatory Compliance, Westinghouse Electric Company LLC, Suite 428, 1000 Westinghouse Drive, Cranberry Township, PA 16066.

Very truly yours, A. Gresham, Manager Regulatory Compliance Enclosures

CAW-1 1-3187 AFFIDAVIT COMMONWEALTH OF PENNSYLVANIA:

ss COUNTY OF BUTLER:

Before me, the undersigned authority, personally appeared J. A. Gresham, who, being by me duly sworn according to law, deposes and says that he is authorized to execute this Affidavit on behalf of Westinghouse Electric Company LLC (Westinghouse), and that the averments of fact set forth in this Affidavit are true and correct to the best of his knowledge, information, and belief:

J. A. Gresham, Manager Regulatory Compliance Sworn to and subscribed before me this 20th day of June 2011 Notary Public COMMONWEALTH OF PENNSYLVANIA Notmial 5eat Cynthila Olesfc,, Nota1y Pubick Manor Boro, Westmoretand County My Conmsslon Exptres ,u1y 16, 2014 Momber, Pennilsvalfa Assodadon of"Notarfes

2 CAW-I 1-3187 (1) 1am Manager, Regulatory Compliance, in Nuclear Services, Westinghouse Electric Company LLC (Westinghouse), and as such, I have been specifically delegated the function of reviewing the proprietary information sought to be withheld from public disclosure in connection with nuclear power plant licensing and rule making proceedings, and am authorized to apply for its withholding on behalf of Westinghouse.

(2) I am making this Affidavit in conformance with the provisions of 10 CFR Section 2.390 of the Commission's regulations and in conjunction with the Westinghouse Application for Withholding Proprietary Information from Public Disclosure accompanying this Affidavit.

(3) 1 have personal knowledge of the criteria and procedures utilized by Westinghouse in designating information as a trade secret, privileged or as confidential commercial or financial information.

(4) Pursuant to the provisions of paragraph (b)(4) of Section 2.390 of the Commission's regulations, the following.is furnished for consideration by the Commission in determining whether the information sought to be withheld from public disclosure should be withheld.

(i) The information sought to be withheld from public disclosure is owned and has been held in confidence by Westinghouse.

(ii) The information is of a type customarily held in confidence by Westinghouse and not customarily disclosed to the public. Westinghouse has a rational basis for determining the types of information customarily held in confidence by it and, in that connection, utilizes a system to determine when and whether to hold certain types of information in confidence. The application of that system and the substance of that system constitutes Westinghouse policy and provides the rational basis required.

Under that system, information is held in confidence if it falls in one or more of several types, the release of which might result in the loss of an existing or potential competitive advantage, as follows:

(a) The information reveals the distinguishing aspects of a process (or component, structure, tool, method, etc.) where prevention of its use by any of

3 CAW-1 1-3187 Westinghouse's competitors without license from Westinghouse constitutes a competitive economic advantage over other companies.

(b) It consists of supporting data, including test data, relative to a process (or component, structure, tool, method, etc.), the application of which data secures a competitive economic advantage, e.g., by optimization or improved marketability.

(c) Its use by a competitor would reduce his expenditure of resources or improve his competitive position in the design, manufacture, shipment, installation, assurance of quality, or licensing a similar product.

(d) It reveals cost or price information, production capacities, budget levels, or commercial strategies of Westinghouse, its customers or suppliers.

(e) It reveals aspects of past, present, or future Westinghouse or customer funded development plans and programs of potential commercial value to Westinghouse.

(f) It contains patentable ideas, for which patent protection may be desirable.

There are sound policy reasons behind the Westinghouse system which include. the following:

(a) The use of such information by Westinghouse gives Westinghouse a competitive advantage over-its competitors. It is, therefore, withheld from disclosure to protect the Westinghouse competitive position.

(b) It is information that is marketable in many ways. The extent to which such information is available to competitors diminishes the Westinghouse ability to sell products and services involving the use of the information.

(c) Use by our competitor would put Westinghouse at a competitive disadvantage by reducing his expenditure of resources at our expense.

4 CAW-11-3187 (d) Each component of proprietary information pertinent to a particular competitive advantage is potentially as valuable as the total competitive advantage. If competitors acquire components of proprietary information, any one component may be the key to the entire puzzle, thereby depriving Westinghouse of a competitive advantage.

(e) Unrestricted disclosure would jeopardize the position of prominence of Westinghouse in the world market, and thereby give a market advantage to the competition of those countries.

(f) The Westinghouse capacity to invest corporate assets in research and development depends upon the success in obtaining and maintaining a competitive advantage.

(iii) The information is being transmitted to the Commission in confidence and, under the provisions of 10 CFR Section 2.390; it is to be received in confidence by the

• Commission.

(iv) The information sought to be protected is not available in public sources or available information has not been previously employed in the same original manner or method to the best of our knowledge and belief.

(v) The proprietary information sought to be withheld in this submittal is that which is appropriately marked in WCAP-1 7345-P, Revision 2, "H*: Resolution of NRC Technical Issue Regarding Tubesheet Bore Eccentricity (3-Loop Model 44F/Model 5 IF)" I (Proprietary), dated June 2011, for submittal to the Commission, being transmitted by Virginia Electric and Power Company Letter and Application for Withholding Proprietary Information from Public Disclosure, to the Document Control Desk. The proprietary information as submitted by Westinghouse for Surry Power Station, Units I and 2, is that associated with the technical justification of the H* Alternate Repair Criteria for hydraulically expanded steam generator tubes and may be used only for that purpose.

5 CAW-1 1-3187 This information is part of that which will enable Westinghouse to:

(a) License the H* Alternate Repair Criteria.

Further this information has substantial commercial value as follows:

(a) Westinghouse plans to sell the use of the information to its customers for the purpose of licensing the H* Alternate Repair Criteria.

(b) Westinghouse can sell support and defense of the H* criteria.

(c) The information requested to be withheld reveals the distinguishing aspects of a methodology which was developed by Westinghouse.

Public disclosure of this proprietary information is likely to cause substantial harm to the competitive position of Westinghouse because it would enhance the ability of competitors to provide similar technical justification and licensing defense services for commercial power reactors without commensurate expenses. Also, public disclosure of the information would enable others to use the information to meet NRC requirements for licensing documentation without purchasing the right to use the information.

The development of the technology described in part by the information is the result of applying the results of many years of experience in an intensive Westinghouse effort and the expenditure of a considerable sum of money, In order for competitors of Westinghouse to duplicate this information, similar technical programs would have to be performed and a significant manpower effort, having the requisite talent and experience, would have to be expended.

Further the deponent sayeth not.

PROPRIETARY INPFORMATION NOTICE Transmitted herewith are proprietary and/or non-proprietary versions of documents furnished to the NRC in connection with requests for generic and/or plant-specific review and approval.

In order to conform to the requirements of 10 CFR 2.390 of the Commission's regulations concerning the protection of proprietary information so submitted to the NRC, the information which is proprietary in the proprietary versions is contained within brackets, and where the proprietary information has been deleted in the non-proprietary versions, only the brackets remain (the information that was contained within the brackets in the proprietary versions having been deleted). The justification for claiming the information so designated as proprietary is indicated in both versions by means of lower case letters (a) through (f) located as a superscript immediately following the brackets enclosing each item of information being identified as proprietary or in the margin opposite such information. These lower case letters refer to the types of information Westinghouse customarily holds in confidence identified in Sections (4)(ii)(a) through (4)(ii)(f) of the affidavit accompanying this transmittal pursuant to 10 CFR 2.390(b)(1).

COPYRIGHT NOTICE The reports transmitted herewith each bear a Westinghouse copyright notice. The NRC is permitted to make the number of copies of the information contained in these reports which are necessary for its internal use in connection with generic and plant-specific reviews and approvals as well as the issuance, denial, amendment, transfer, renewal, modification, suspension, revocation, or violation of a license, permit, order, or regulation subject to the requirements of 10 CFR 2.390 regarding restrictions on public disclosure to the extent such information has been identified as proprietary by Westinghouse, copyright protection notwithstanding. With respect to the non-proprietary versions of these reports, the NRC is permitted to make the number of copies beyond those necessary for its internal use which are necessary in order to have one copy available for public viewing in the appropriate docket files in the public document room in Washington, DC and in local public document rooms as may be required by NRC regulations if the number of copies submitted is insufficient for this purpose. Copies made by the NRC must include the copyright notice in all instances and the proprietary notice if the original was identified as proprietary.