ML14027A515

WCAP-17828-NP, Revision 0, Indian Point Unit 2 H* Alternate Repair Criteria for the Tubesheet Hydraulic Expansion Region (Model 44F - 4-Loop)

ML14027A515
Person / Time
Site:	Indian Point
Issue date:	01/16/2014
From:	Lamantia W, Whiteman G, Yurko N Westinghouse
To:	Office of Nuclear Reactor Regulation
Shared Package
ML14027A529	List: ML14027A515 NL-14-001, Indian Point, Unit 2 - Proposed License Amendment for Alternate Repair Criteria for Steam Generator Tube Inspection and Repair NL-14-001, Proposed License Amendment for Alternate Repair Criteria for Steam Generator Tube Inspection and Repair
References
NL-14-001 WCAP-17828-NP, Rev. 0
Download: ML14027A515 (108)

Text

ENCLOSURE 2 TO NL-14-001 WESTINGHOUSE WCAP-17828, INDIAN POINT UNIT 2 H* ALTERNATE REPAIR CRITERIA FOR THE TUBESHEET HYDRAULIC EXPANSION REGION (MODEL 44F-4-LOOP) (NON-PROPRIETARY)

Westinghouse Non-Proprietary Class 3 WCAP-17828-NP January 2014 Revision 0 Indian Point Unit 2 H*

Alternate Repair Criteria for the Tubesheet Hydraulic Expansion Region (Model 44F Loop)

Westinghouse

WESTINGHOUSE NON-PROPRIETARY CLASS 3 WCAP-17828-NP Revision 0 Indian Point Unit 2 H*

Alternate Repair Criteria for the Tubesheet Hydraulic Expansion Region (Model 44F Loop)

January 2014 William R. LaMantia*

Steam Generator Management Programs Nicholas D. Yurko*

Steam Generator Management Programs Gary W. Whiteman*

Regulatory Compliance Reviewer: Hermann 0. Lagally*, Consultant Steam Generator Management Programs Approved: William J. Bedont*. Manager Steam Generator 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

© 2014 Westinghouse Electric Company LLC All Rights Reserved WCAP-17828-NP (2).docx-010914

ii REVISION RECORD WCAP-17828-NP January 2014 Revision 0

iii TABLE OF CONTENTS L IS T O F TA B L E S ........................................................................................................................................ v L IS T O F F IG U R ES .................................................................................................................................... v ii T RO D DIN U C T IO N ........................................................................................................................  !-1 1.1 ORIGINAL NRC RAI RESOLUTION ACTION PLAN DISCUSSION ................... 1-1 1.2 ROAD MAP TO FINAL RESPONSE TO 14 NRC RAI EXCEPT RA I #5 A N D RA I # 12 ..................................................................................................... 1-2 1.2.1 Need for Alternate Leakage Factor Approach ................................................. 1-2 1.2.2 C 2 Model Contact Pressures Results ................................................................ 1-3 1.2.3 Process for Determining the Limiting H* Value ............................................. 1-3 1.3

SUMMARY

OF THE IMPACT OF INDEPENDENT REVIEW ON H* ....................... 1-5 1.4 RESPONSE TO FINAL REoUEST FOR ADDITIONAL INFORMATION ................. 1-6 1.5 RE F E REN C E S ................................................................................................................ 1-6 SQUARE CELL (C2) MODEL ANALYSIS ................................................................................ 2-1 2.1 PURPOSE OF THE C 2 ANALYSIS ................................................................................ 2-1 2.2 DEFINITION OF THE C 2 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 M ATER IA L PRO PERTIES ............................................................................................. 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 FE R EN C E S .............................................................................................................. 2-18 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 ...................................................... .......................................... 3-2 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 .................................................. 3-17 3.3.1 M ethod D iscussion ........................................................................................ 3-17 3.3.2 Development of Displacements for Square Cell ........................................... 3-17 3.3.3 A ssum ptions .................................................................................................. 3-19 3 .3 .4 In p u t ............................................................................................................... 3-19 3 .3 .5 G eom etry ....................................................................................................... 3-19 3.3.6 M esh D iscussion ............................................................................................ 3-19 3.3.7 B oundary C onditions ..................................................................................... 3-2 1 WCAP-17828-NP January 2014 Revision 0

iv TABLE OF CONTENTS (cont.)

3.3.8 C 2 FE A R esults .............................................................................................. 3-22 3.3.9 Model 44F (Indian Point Unit 2) Square Cell Model Results ....................... 3-22 3.3.10 M ean H

• C alculations ................................................................................... 3-32 3.3.11 Number of Elevations to Define Contact Pressure Profile ............................ 3-32 3.3.12 Circumferential Contact Pressure .................................................................. 3-33 3.4 CALCULATIONS OF PROBABILISTIC H* USING THE C2 MODEL .................... 3-38 3 .4 .1 A ssum ptions .................................................................................................. 3-39 3.4.2 M ethods D iscussion ....................................................................................... 3-39 3.4.3 Application to the Indian Point Unit 2 Model 44F SG .................................. 3-44 3.5 POISSON CONTRACTION EFFECT ON H* ............................................................. 3-53 3.5.1 M ethods D iscussion ....................................................................................... 3-53 3 .5 .2 In p u t ............................................................................................................... 3-54 3.5.3 Calculation of Radial D ilation ....................................................................... 3-54 3.5.4 Calculation of Contact Pressure Reduction from Poisson Effect .................. 3-55 3.6 CREVICE PRESSURE ADJUSTMENT LENGTH ...................................................... 3-64 3.7 CALCULATION OF FINAL H* ................................................................................... 3-65 3.8 RE FE RE N C E S .............................................................................................................. 3-66 4 C2 MODEL LEAKAGE INTEGRITY DISCUSSION ................................................................. 4-1 4.1 RE FERE N C E S ................................................................................................................ 4-3 5 REPORT

SUMMARY

AND CONCLUSIONS ............................................................................ 5-1 5.1 RE FEREN C E S ................................................................................................................ 5-4 WCAP- I 7828-NP January 2014 Revision 0

V LIST OF TABLES Table 2-1 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 Com parison of C 2 and Thick Shell Results .................................................................... 2-18 Table 3-1 Input Boundary Conditions for Model 44F (Indian Point Unit 2 ) .................................. 3-6 Table 3-2 M odulus of Elasticity for M aterials ................................................................................. 3-7 Table 3-3 Coefficient of Thermal Expansion for Materials ............................................................. 3-7 Table 3-4 Interpolated Ratios of Equivalent Material Properties for Analysis of Perforated Plate for the M odel 44F .................................................................................. 3-7 Table 3-5 Equivalent Properties for Tubesheet for Model 44F SG (Indian Point Unit 2) ............... 3-8 Table 3-6 Model 44F Indian Point Unit 2 Inputs and Results, 2.655 inch Radius ......................... 3-23 Table 3-7 Model 44F Indian Point Unit 2 Inputs and Results, 7.219 inch Radius ......................... 3-24 Table 3-8 Model 44F Indian Point Unit 2 Inputs and Results, 18.171 inch Radius ....................... 3-25 Table 3-9 Model 44F Indian Point Unit 2 Inputs and Results, 28.21 inch Radius ......................... 3-26 Table 3-10 Model 44F Indian Point Unit 2 Inputs and Results, 34.598 inch Radius ....................... 3-27 Table 3-11 Model 44F Indian Point Unit 2 Inputs and Results., 48.288 inch Radius ....................... 3-28 Table 3-12 H

• Input Sum m ary (Reference 3-1) ............................................................................. 3-34 Table 3-13 Summary of H* Mean Values before Poisson Correction (A ll dim ensions in inches) ............................................................................................. 3-34 Table 3-14 Summary of H* Mean Values after Poisson Correction (A ll dim ensions in inches) ............................................................................................. 3-34 Table 3-15 Typical M onte Carlo Result O utput ............................................................................... 3-45 Table 3-16 Positive Variations about the Mean TS CTE used for FEA (U nits of 10-6 in/in/I F) ................................................................................................... 3-45 Table 3-17 Negative Variations about the Mean Tube CTE used for FEA (U nits of 10-6 ini ini0 F) ................................................................................................... 3-46 Table 3-18 Required Probabilistic Estim ate for H * ......................................................................... 3-46 Table 3-19 Monte Carlo Data Used in Comparative Probabilistic Analysis .................................... 3-47 WCAP- 17828-NP January 2014 Revision 0

vi LIST OF TABLES (cont.)

Table 3-20 Typical Variation of CTEs Over a Range of Rank Order Statistics ............................... 3-48 Table 3-21 Variation of H* for Adjacent Rank Order Variables (Ref. Model F C 2 Results) ............ 3-49 Table 3-22 Indian Point U nit 2 H

• R esults ...................................................................................... 3-49 Table 3-23 Calculation of Radial Dilation Due to Poisson Effects .................................................. 3-57 Table 3-24 Calculation of Elastic C onstants .................................................................................... 3-57 Table 3-25 Calculation of Reduction in Contact Pressure from Poisson Effects ............................. 3-57 Table 3-26 Baseline and Adjusted Mean H* Calculation for Model 44F (Ind ian Point U nit 2) ...................................................................................................... 3-58 Table 3-27 Distance for Poisson Effect to Attenuate ....................................................................... 3-58 Table 3-28 Adjusted Mean H* Including Poisson Attenuation for Model 44F (Indian Point U nit 2) ...................................................................................................... 3-59 Table 3-29 Com parison of M ean H

• Values .................................................................................... 3-59 Table 3-30 Baseline and Adjusted Probabilistic H* Calculation for Model 44F ............................. 3-60 Table 3-31 Baseline and Adjusted Probabilistic H* Calculation for Model 44F 4 Loop ................. 3-61 Table 3-32 Distance for Poisson Effect to Attenuate Probabilistic H* Values ................................. 3-61 Table 3-33 H* Calculation Including Poisson Attenuation Model 44F (Indian Point Unit 2) ......... 3-62 Table 3-34 H* Calculation Including Poisson Attenuation Model 44F (Indian Point Unit 2) ......... 3-63 Table 3-35 Model 44F SG Probabilistic H* Values (inches) ........................................................... 3-63 Table 3-36 Summary of Model 44F Probabilistic Estimates ........................................................... 3-65 Table 5-1 Results of Probabilistic Comparison Study for the Indian Point Unit 2 SGs ................... 5-3 WCAP-1 7828-NP January 2014 Revision 0

vii LIST OF FIGURES Figure 2-1 Current Licensing Basis Tubesheet Bore Displacements ................................................ 2-2 Figure 2-2 C2 Model Tubesheet Bore Displacements ........................................................................ 2-2 Figure 2-3 Typical Low er SG Com plex M odel ................................................................................. 2-4 Figure 2-4 Square Cell M odel "Core Sam ple" ................................................................................. 2-4 Figure 2-5 Square C ell M odel ........................................................................................................... 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 C ollar A ssem bly ....................................................................................... 2-13 Figure 2-11 Constant Tubesheet Bore Dilation Model ...................................................................... 2-13 Figure 3-1 Typical Representation of Severed Divider Plate Condition ........................................... 3-9 Figure 3-2 Typical Solid Model for Intact Divider Plate ................................................................... 3-9 Figure 3-3 Model 44F (Indian Point Unit 2) Mesh, View Down Z-Axis ........................................ 3-10 Figure 3-4 Model 44F (Indian Point Unit 2) Mesh, View Down Y-Axis ........................................ 3-10 Figure 3-5 Model 44F (Indian Point Unit 2) Mesh, View Down X-Axis ........................................ 3-1 1 Figure 3-6 Model 44F (Indian Point Unit 2) Results of NOP Thermal Analysis ............................ 3-11 Figure 3-7 Model 44F (Indian Point Unit 2) Results of Thermal-Structural Analysis, Y -D eform ation ............................................................................................................... 3-12 Figure 3-8 Model 44F (Indian Point Unit 2) Results of Thermal-Structural Analysis, X -D eform ation on H ot Leg Face ................................................................................... 3-13 Figure 3-9 Model 44F (Indian Point Unit 2) Results of Thermal-Structural Analysis, Z-D eform ation on H ot Leg ............................................................................................ 3-14 Figure 3-10 Model 44F (Indian Point Unit 2) Results of SLB Thermal Analysis ............................. 3-15 Figure 3-11 Model 44F (Indian Point Unit 2) Results of SLB Thermal-Structural Analysis, X -D eform ation on H ot Leg Face ................................................................................... 3-16 Figure 3-12 Model 44F (Indian Point Unit 2) Results of SLB Thermal-Structural Analysis, Z-D eform ation on H ot Leg ............................................................................................ 3-16 Figure 3-13 Sub-Model for Computational Analysis ........................................................................ 3-17 Figure 3-14 R epresentative Solid M odel ........................................................................................... 3-20 Figure 3-15 Representative Dimensions for All Models ................................................................... 3-20 WCAP-17828-NP January 2014 Revision 0

viii LIST OF FIGURES (cont.)

Figure 3-16 Implemented Model Mesh, View Down Z-Axis ............................................................ 3-21 Figure 3-17 Boundary Conditions for A ll M odels ............................................................................. 3-22 Figure 3-18 Model 44F Contact Pressure Results, 2.655 inch Radius .............................................. 3-29 Figure 3-19 Model 44F Contact Pressure Results, 7.219 inch Radius .............................................. 3-29 Figure 3-20 Model 44F Contact Pressure Results, 18.171 inch Radius ............................................ 3-30 Figure 3-21 Model 44F Contact Pressure Results, 28.21 inch Radius .............................................. 3-30 Figure 3-22 Model 44F Contact Pressure Results, 34.598 inch Radius ............................................ 3-31 Figure 3-23 Model 44F Contact Pressure Results, 48.288 inch Radius ............................................ 3-31 Figure 3-24 Model 44F: Circumferential Contact Pressure at the Critical Radius ............................ 3-35 Figure 3-25 Model 44F: Circumferential Contact Pressure at the Minimum Radius ........................ 3-36 Figure 3-26 Model 44F: Circumferential Contact Pressure at the Maximum Radius ....................... 3-37 Figure 3-27 Typical Result for Plotting the Combined Tube and Tubesheet CTE Values vs.

H* from the Licensing Basis Analysis (Ref. Model D5 NOP) ...................................... 3-50 Figure 3-28 Typical Result of Combined Tube and Tubesheet CTE Values vs. Monte Carlo Rank Order from the Licensing Basis Analysis (Ref. Model D5 SLB) ......................... 3-50 Figure 3-29 H* Curves from Response Surface (Ref. Model F) - without Poisson Contraction Effect and Crevice Pressure Adjustm ent ........................................................................ 3-51 Figure 3-30 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) ................................ 3-51 Figure 3-31 Model 44F NOP Combined CTET and CTETS vs. Monte Carlo Rank Order ................. 3-52 Figure 3-32 Indian Point Unit 2 Model 44F NOP Combined CTET and CTETS vs. H* Value .......... 3-52 Figure 3-33 Model 44F H* Summary Showing Linear Fit Results (with Poisson Contraction Effect and without Crevice Pressure Adjustment) ......................................................... 3-53 Figure 3-34 Effect of Poisson Contraction on Contact Pressure; Model 44F .................................... 3-64 Figure 3-35 Model 44F Crevice Pressure Adjustment Curve ............................................................ 3-65 WCAP- 17828-NP January 2014 Revision 0

i-1 1 INTRODUCTION The purpose of H* (H-star) is to replace the tube end weld with the hydraulic expansion joint as the primary pressure boundary in the steam generator (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.

H* has been licensed by the United States Nuclear Regulatory Commission (USNRC) for permanent application at a number of operating plants since March 2012, including plants with Model F, Model D5, Model 51F and Model 44F SGs. Reference 1-1 documents the approval of H* for a plant with Model 44F SGs. Applicability of H* for Model 44F SGs is currently limited to 3-loop plants. Indian Point Unit 2 is a 4-loop plant that was not included in the determination of the bounding Model 44F SG plant; therefore, it was necessary to repeat the analysis specifically for Indian Point Unit 2. The methods employed in the Indian Point Unit 2-specific analyses are the same as those employed for the prior technical justification of H*. There are no deviations to the previously approved methodologies. All prior technical issues (Reference 1-2) and NRC requests for information have been addressed and are included in this report.

The current licensing basis for H* for the Model 44F is principally WCAP-17091-P, Reference 1-3, and prior documents included by reference in Reference 1-4. The same documents apply equally to the technical justification of H* for Indian Point Unit 2.

The following sections are included for consistency with prior reports, although some of the information has been obviated by NRC approvals of permanent H* licenses for other plants.

1.1 ORIGINAL NRC RAI RESOLUTION ACTION PLAN DISCUSSION Reference 1-2 documents NRC questions regarding the original H* calculation approach. Westinghouse interpreted the thrust of the NRC questions as follows:

The original 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" (SF) model 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 was subtracted from the contact pressure generated due to tube-to-tubesheet differential thermal and pressure expansions.

Because the transient conditions for one of the types of the affected steam generators (Model D5) required application of this model for conditions outside of the applicability of the reference model, a second model, the "Square-Cell" (C) model, 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.

Both models are based on conservative analysis and assumptions; however, Westinghouse believes that the C2 model more accurately represents the physical structure. Originally, the principal purpose of the WCAP- I17828-NP January 2014 Revision 0

1-2 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 C2. are entirely different approaches; thus it was not expected that the results from both models would provide identical 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 l-1 must be clearly, if not directly, addressed. 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.

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 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, as requested by RAI Question #5, is provided by this report.

RAI Question #12 did not require a final response for the Model 44F SG.

1.2.1 Need for Alternate Leakage Factor Approach The Darcy formulation was used in Reference 1-3 to develop the ratio of leak rates between postulated accident induced conditions (steam line break (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 (gt). In Reference 1-3, 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 C 2 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.

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 Reference 1-3 to show that no correlation exists between loss coefficient and contact pressure. However, because the data exhibit WCAP- 17828-NP January 2014 Revision 0

1-3 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 SG is the steam line break (SLB) condition. The Model 44F SGs do not have a feedline break transient condition in their licensing basis.

The contact pressure in the Model 44F SGs during SLB meets or exceeds the contact pressure during NOP. The criterion for contact pressure (PcsLB:PCNoP > 1) is met in application of the C 2 model as well as the SF model.

1.2.2 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 C 2 model are not always greater than the SF model results. Using the C 2 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. The H* analysis documented in this report is based on application of the C2 model, the same process that was applied for the analyses of the plants that have received licenses for permanent application of H*.

1.2.3 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 C 2 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 Reference 1-3, the principal variables affecting the probabilistic value of H* are the coefficients of thermal expansion of the tube and tubesheet materials. For the Indian Point Unit 2 steam generators, the specific values of these variables that define probabilistic analysis of H* based on the C 2 model are determined from a variability surface similar to that which is described in Figure 8-5 of Reference 1-3. Application of these values in the C 2 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 WCAP- 17828-NP January 2014 Revision 0

1-4 adjustment for crevice pressure distribution is discussed in Reference 1-3 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 Reference 1-3). 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 Reference 1-3 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 C2 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 C2 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 C2 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 Reference 1-3 and in Section 3.6 of this report. The crevice pressure adjustment is applied after the adjustment for Poisson contraction because the Poisson contraction is an adjustment for a loading condition that is independent of the crevice pressure correction.

WCAP- 17828-NP January 2014 Revision 0

1-5 As a result of the issues discussed above, the action plan shifted from demonstrating the conservatism of application of the thick-shell equation approach to the following:

1. Using the more accurate C 2 model to confirn that the contact pressures at accident conditions exceed those at nonnal operating conditions, and to demonstrate that the criterion for contact pressure (PcSLB:PcNoP>I) for each of the model SGs in the H* fleet is met at all tubesheet bundle radii.

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.

Previously, two reports were provided for the population of H* candidate plants and have been provided to the NRC for licensing review:

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

WCAP- I7345-P, Rev. 2, a combined report for the 3-loop Model 44F and 51 F plants. This report addresses the C 2 model results for the 3-loop Model 44F and 51 F SGs and provides a final response to RAI Question Numbers 5 and 12. The remainder of the NRC RAIls have been answered in previous submittals as discussed in Section 1.2 above.

This report, WCAP-17828-P, is required because Indian Point Unit 2 is a 4-loop plant with Model 44F steam generators and the plant operating conditions are not enveloped by the limiting 3-loop plants with Model 44 F steam generators, Turkey Point Units 3 and 4.

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 penranent 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 I 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 RESPONSE TO FINAL REOUEST FOR ADDITIONAL INFORMATION Subsequent to the submittal of WCAP-17330-P, Rev. I and WCAP-17345-P, Rev. 2 to the NRC via License Amendment Requests (LARs), an additional RAI was received from the NRC. The response to this RAI was provided via Reference 1-11. Although this response is specific for the Model 5 1F SG, communication was received that the response provided in Reference 1-lI was sufficient for the Model 44F SG under consideration except for the questions dealing with plant-specific issues such as Technical Specifications, etc.

1.5 REFERENCES

1-1. USNRC Letter dated November 5, 2012, "Turkey Point Nuclear Generating Station Unit Nos. 3 and 4-Issuance of Amendments regarding Permanent Alternate Repair Criteria for Steam Generator Tubes (TAC NOS. ME8515 and ME8516)."

1-2. USNRC Letter, "Vogtle Electric Generating Plant, Units I and 2 - Transmittal of Unresolved Issues Regarding Permanent Alternate Repair Criteria for Steam Generators (TAC Nos. ME 1339 and ME1340)," 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. LTR-SGMP-13-49, Rev. 1, "Indian Point Unit 2: Transmittal of H* Technical Justification Documents," August 2013.

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 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/DCE/DDP/TCX," November 2003.

1-11. LTR-SGMMP-12-29 P-Attachment, Rev. 1, "Response to USNRC Request for Additional Information Regarding the Catawba License Amendment Request for Permanent Application of the Alternate Repair Criterion H*," January 24, 2012.

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2-1 2 SQUARE CELL (C ) 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 C 2 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 to the Model 44F 4-loop plant steam generator.

2.1 PURPOSE OF THE C2 ANALYSIS Figure 1-1 in 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 Referefice 2-1, which is 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 C 2 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- 17828-NP January 2014 Revision 0

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)

- '4

- '4

/ '4 I

I I

I I

4.

'4

'4 -

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 C2 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.e inches. The outer nominal tube radius is [ ]a,,,, inch. The inner nominal tube radius is

]a.... 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 ANSYS1 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.

1. ANSYS is a registered trademark of ANSYS, Inc., or its subsidiaries in the United States or other countries.

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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-17828-NP January 2014 Revision 0

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-17828-NP January 2014 Revision 0

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- I7828-NP January 2014 Revision 0

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 WCAP- 17828-NP January 2014 Revision 0

2-8 of 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-17828-NP January 2014 Revision 0

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 (I 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 due to 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 [ ]a'.. 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 the 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 3-2 and Table 3-3.

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2-10 The Poisson's Ratio used for the tube material is 0.282. 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 ANSI'S 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., gi = [ ]c.e).

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 [ ]a.... contact elements along the tube-to-tube bore interface.3 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

2. 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.

3. The final meshing scheme used in the C 2 results described in this report for the calculation of H* has approximately [ ]'cecontact 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 3-16.

The C2 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 stiffness 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 1013 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 1010 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- 17828-NP January 2014 Revision 0

2-12 initial offset of +OEOO 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 the 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.... 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 C 2 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., azz = 0 psi). The assembled model geometry appears in Figure 2-10.

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2-13 TSCollar \

Tube -A 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:

2 a TUBE (t - tRF)

(Equation 2-1)

Where OD is the outer diameter of the tube, ,TUBE 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 Specified TS ID Dilation Figure 2-11 Constant Tubesheet Bore Dilation Model January 2014 WCAP- 7828-NP WCAP-117828-NP January 2014 Revision 0

2-14 In Figure 2-11, pi 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., p, = P3). There are no other applied pressures on the system so p, = p4 = 0 psi.

The differential free radial expansion of the tube at normal operating conditions (NOP. t = [ ]a.c,e F) and steam line break conditions (SLB, t = [ ]a.... "F), calculated using Equation 2-1 and the material properties defined in Table 3-2 and Table 3-3. The NOP operating temperature of [ ]a.¢c, oF 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:

ARTUBE Er'TBEb 2 - a2 L 0 p b2 )+ (I + V )b- (p, - P, (Equation 2-2)

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, ETUBEis the Young's modulus of the tube at the given operating condition and VTLBE 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:

AR= E0 e cb2 2

[- V7rsXP3b2 - P 4 C2)+ (l+ v")b 2 c 2 (P3 - P4 (Equation 2-3)

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, Ezs 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 ]r= - [ARTUBE ]r=h (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 = E b (1

[7- S 2 b2) 2Vs)(P + ,")b2 C- (P2 -

E7 s cý -b2 ( b 2)b -

b - 1 -b + (1 +E'ba)(-r2 (- P2) (Equation 2-5)

Re-arranging to solve for p2 gives the final result.

p0 :A*Eb ), /

(c1-_b (bb)+,l+,,)e'-]+ b I0 -v,,,(b2)+(l + vTUBEa (Equation 2-6)

E, ( - bETURAC2 -b 2)

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 C2 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 C2 approach with the contact law as described is a very close approximation of the thick WCAP-17828-NP January 2014 Revision 0

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 uTUBE T tREF AR Condition in in/in- 0 F OF OF in a,c,e NOP 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 1- in t in I

0.3810 0.3811 i1  !

0.3813 0.3815 L 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 cc (SLB) in/in-0 F Poisson's Ratio WCAP-17828-NP January 2014 Revision 0

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

Nominal TS Properties Variable Description Value Units c OR in b IR in E (NOP) psi E (SLB) psi a (NOP) in/in-0 F a (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 KTable 2-6 Calculated Tubesheet Inner Diameter Dilation Thermal Expansion of TS ID (in.) ]j....e APCREv Expansion Tubesheet Elevation (in.) Combined Expansion (in.)

a,c,e BTS Neutral Axis (NA)

TTS WCAP-17828-NP January 2014 Revision 0

2-18 Table 2-7 Comparison of C2 and Thick Shell Results Contact Pressure Results TTS NA BTS ac,e Max (psi) _

Min (psi)

Average (psi)

Thick Shell

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 PublishingCo..

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 2007.

2-4. STD-MC-06-1 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 2007.

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

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3-1 3 STRUCTURAL CALCULATIONS FOR H*

Section 2 of this report provided a description of the C2 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 SG.

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 to the Indian Point Unit 2 4-loop SG compared to 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 for each tubesheet radius for Indian Point Unit 2 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 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. Section 3.6 discusses the inclusion of the crevice pressure adjustment to the 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 ([ ]ace inches for the Indian Point Unit 2 Model 44F SG 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 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 C2 model and the thick shell model.

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 WCAP-17828-NP January 2014 Revision 0

3-2 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 thick shell model for H*. Application of the C 2 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 C 2 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 tile 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.

The 3-D FEA model mesh was also modified for other reasons not directly related to application of the C 2 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 Reference 3-1. The plants are analyzed for low T,,g normal operating conditions (NOP) and steam line break (SLB), which have been determined to be limiting conditions in Reference 3-1. 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.

3.2.2 Assumptions The assumptions below, with the exception of the thermal temperature profile through the tubesheet, are copied from Reference 3-1. For each analysis condition, a combined thermal-structural analysis was WCAP-17828-NP January 2014 Revision 0

3-3 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 Reference 3-1 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* is 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 is 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 Reactor Coolant System (RCS).

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 channelhead penetrations, such as the manways, tends to decrease displacements in the tubesheet. Decreasing tubesheet displacements will produce shorter H*

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3-4 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).

Reference 3-1 shows 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, 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 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 American Society of Mechanical Engineers (ASME) Code, and pressure and temperature conditions from the PCWG parameters and transients.

The input boundary conditions for Indian Point Unit 2 are shown in Table 3-1. These are the same values included in Reference 3-2. The modulus of elasticity and coefficients of thermal expansion are provided in Table 3-2 and Table 3-3. 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 Reference 3-1.

3.2.4 Geometry The structural model geometry analyzed for the Model 44F is essentially identical to that considered in the baseline analyses in Reference 3-I. 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, showing the truncated divider plate, and Figure 3-2, showing the model with the intact divider plate.

In Reference 3-1, 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 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 Reference 3-1 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 WCAP-17828-NP January 2014 Revision 0

3-5 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 Model 44F are essentially the same as the meshes documented in Reference 3-1. Additional constraints were added to the current mesh to accommodate the vertical partition through the tubesheet.

The mesh used is shown in Figure 3-3, Figure 3-4, and Figure 3-5 for the principal axes.

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 Reference 3-1. The same equivalent properties used in Reference 3-1 were used in the current analysis. Information from those references is included here for completeness.

Interpolated ratios of equivalent properties are in Table 3-4, 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 3-2 to obtain the temperature-dependent equivalent properties. The equivalent properties for the tubesheet are in Table 3-5 for the Model 44F SG.

3.2.7 Boundary Conditions Table 3-1 summarizes the specific boundary conditions and how they are applied to the 3-D FEA model consistent with the prior analyses (Reference 3-1). Two different analyses were performed with the 3-D FEA model of the lower SG tubesheet complex to support application of the C2 model:

I. Thermal Analysis: The absolute operating temperature conditions were applied to the SG, as opposed to a difference in temperature with a reference temperature of 707F. The result from this analysis is purely a temperature profile through the tubesheet.

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 thick shell model. For the Indian Point Unit 2 analyses a combined thermal-structural analysis was performed.

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3-6 The applied loads and temperatures are shown in Table 3-1. The analysis was applied only to the limiting conditions required 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 3.3.10 for the limiting operating conditions for the Model 44F SG).

3.2.8 Tubesheet Complex 3-D FEA Analysis Results The results of the thermal analysis for Indian Point Unit 2 for nonnal operating conditions are shown in Figure 3-6. Figure 3-7 through Figure 3-9 show the results of the thermal-structural analysis for Indian Point Unit 2 for 100% power. Figure 3-10 shows the results of the SLB thermal analysis for Indian Point Unit 2.

Figure 3-11 and Figure 3-12 show the X- and Z-deformations for SLB for Indian Point Unit 2. The results of the current 3-D FEA are taken from Reference 3-6.

Table 3-1 Input Boundary Conditions for Model 44F (Indian Point Unit 2)

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

SG Outlet Pressure (psia)

Secondary Pressure (psia)

Hot Leg Temperature (0 F)

SG Outlet Temperature ('F)

Steam Temperature ("F)

Feedwater Temperature (fF)

Mean Shell Radius rm (inches)

Shell Thickness t (inches)

Calculated Values a~c,e Secondary Fluid Temperature ('F)

Vessel End Cap Pressure (psia)

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3-7 Table 3-2 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 3-3 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 3-4 Interpolated Ratios of Equivalent Material Properties for Analysis of Perforated Plate for the Model 44F a,c,e Gy*/Gy Ey*/Ey Ep*/Ep Gp*/Gp Poisson's Ratio WCAP-1 7828-NP January 2014 Revision 0

3-8 Table 3-5 Equivalent Properties for Tubesheet for Model 44F SG (Indian Point Unit 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 January 2014 17828-NP WCAP- 17828-NP January 2014 Revision 0

3-9 a~c~e Figure 3-1 Typical Representation of Severed Divider Plate Condition a,c.e Figure 3-2 Typical Solid Model for Intact Divider Plate WCAP- 17828-NP January 2014 Revision 0

3-10 a.ce Figure 3-3 Model 44F (Indian Point Unit 2) Mesh, View Down Z-Axis ac.e Figure 3-4 Model 44F (Indian Point Unit 2) Mesh, View Down Y-Axis WCAP- 17828-NP January 2014 Revision 0

3-11 a,c,e Figure 3-5 Model 44F (Indian Point Unit 2) Mesh, View Down X-Axis a,c.e Figure 3-6 Model 44F (Indian Point Unit 2) Results of NOP Thermal Analysis WCAP-17828-NP January 2014 Revision 0

3-12 ac~e Figure 3-7 Model 44F (Indian Point Unit 2) Results of Thermal-Structural Analysis, Y-Deformation January 2014 WCAP-1 7828-NP WCAP-17828-NP January 2014 Revision 0

3-13 axc,e Figure 3-8 Model 44F (Indian Point Unit 2) Results of Thermal-Structural Analysis, X-Deformation on Hot Leg Face WCAP-17828-NP January 2014 Revision 0

3-14 a~c.e Figure 3-9 Model 44F (Indian Point Unit 2) Results of Thermal-Structural Analysis, Z-Deformation on Hot Leg WCAP-17828-NP January 2014 Revision 0

3-15 axc.e Figure 3-10 Model 44F (Indian Point Unit 2) Results of SLB Thermal Analysis WCAP-17828-NP January 2014 Revision 0

3-16 axcxe Figure 3-11 Model 44F (Indian Point Unit 2) Results of SLB Thermal-Structural Analysis, X-Deformation on Hot Leg Face a,c~e Figure 3-12 Model 44F (Indian Point Unit 2) Results of SLB Thermal-Structural Analysis, Z-Deformation on Hot Leg WCAP-17828-NP January 2014 Revision 0

3-17 3.3 CALCULATION OF MEAN H* FROM C2 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 Model 44F SG tubesheet and corresponding tube in increments throughout the entire tubesheet thickness of 21.81 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 elevations, for the Model 44F SG at which the contact pressure is calculated. For each operating condition, a thernal-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 Z-direction (both in the same plane). For calculation of the displacements in the X-direction, the WCAP- 17828-NP January 2014 Revision 0

3-18 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):

a*U xj U X.\.+1- U .... 11 ax 2Ax (Equation 3- 1)

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

aU,., - Uxj+2 + 4U,.,,+ - 3U.,

ax 2Ax aU., + U.,'_2 - 4Ux,1_ + 3Ux, ax 2Ax (Equation 3-2)

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:

Ax'q,,recell = 0.5

• P

• E_

(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:

U._j U j+2 - U..

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 Zz-direction; therefore, the strain in the Z-direction necessarily vanishes there. Since the displacement is zero on that face, the equation can be simplified:

DU:., U..,+2 Dz 2P (Equation 3-5)

Calculation of the applied displacements from the strain is identical:

A-squarecell 0. 5~P~ * (Equation 3-6)

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3-19 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...

(Reference 3-1), and a pinball radius of [ ]a.ce inches, which is half the value of the surface roughness tolerance from Reference 3-13. The analysis also uses a normal stiffness factor of [ ]as.,

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 Indian Point Unit 2 Model 44F SG, material properties from tile 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 Model 44F are taken from Reference 3-1.

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 Reference 3-1 and 3-19.

3.3.5 Geometry Figure 3-14 shows a representation of the solid model used. The model was created in ANSYS WorkbenchTM' 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 tile 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 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.

ANSYS Workbench MT - ANSYS and ANSYS Workbench are registered trademarks or trademarks of ANSYS, Inc., or its subsidiaries in the United States or other countries.

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3-20 ac.e Figure 3-14 Representative Solid Model a.c,e Figure 3-15 Representative Dimensions for All Models WCAP-17828-NP January 2014 Revision 0

3-21 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 inside diameter (ID) and the crevice pressure on the tube outside diameter (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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3-22 a.c.e Figure 3-17 Boundary Conditions for All Models 3.3.8 C2 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 "Pcon Theta" represents the contact pressure between the tube and tubesheet.

3.3.9 Model 44F (Indian Point Unit 2) 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 C2 model and the thick shell equation model used in Reference 3-1. The results based on the C2 model calculations for the Model 44F are provided in Table 3-6 through Table 3-11. 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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3-23 The tabular results in Table 3-6 through Table 3-11 are shown graphically in Figure 3-18 through Figure 3-23. These figures show the contact pressure trends of the nonnal 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.

Table 3-6 Model 44F Indian Point Unit 2 Inputs and Results, 2.655 inch Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi axc,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 I

16.368 NA 10.905 5.442 3.523 2.000 ITS 0.000 WCAP- 17828-NP January 2014 Revision 0

3-24 Table 3-7 Model 44F Indian Point Unit 2 Inputs and Results, 7.219 inch Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi ace 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.ce BTS 21.810 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 1TrS 0.000 WCAP- 17828-NP January 2014 Revision 0

3-25 Table 3-8 Model 44F Indian Point Unit 2 Inputs and Results, 18.171 inch Radius NOP TS Elevation AX AZ AP Temperature PCON Theta in in in psi OF psi a4,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 TS I 0.000 WCAP-17828-NP January 2014 Revision 0

3-26 Table 3-9 Model 44F Indian Point Unit 2 Inputs and Results, 28.21 inch 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 UTS 0.000 WCAP-17828-NP January 2014 Revision 0

3-27 Table 3-10 Model 44F Indian Point Unit 2 Inputs and Results, 34.598 inch 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-17828-NP January 2014 Revision 0

3-28 Table 3-11 Model 44F Indian Point Unit 2 Inputs and Results, 48.288 inch 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 axc,e BTS 21.810 19.810 18.287 16.368 NA 10.905 5.442 3.523 2.000 TTS 0.000 WCAP-17828-NP January 2014 Revision 0

3-29 ac,e Figure 3-18 Model 44F Contact Pressure Results, 2.655 inch Radius a.c.e Figure 3-19 Model 44F Contact Pressure Results, 7.219 inch Radius WCAP-17828-NP January 2014 Revision 0

3-30 a.c.e 7

Figure 3-20 Model 44F Contact Pressure Results, 18.171 inch Radius a.c~e Figure 3-21 Model 44F Contact Pressure Results, 28.21 inch Radius WCAP-17828-NP January 2014 Revision 0

3-31 a~c.e Figure 3-22 Model 44F Contact Pressure Results, 34.598 inch Radius a,c.e Figure 3-23 Model 44F Contact Pressure Results, 48.288 inch Radius WCAP-17828-NP January 2014 Revision 0

3-32 3.3.10 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 Reference 3-1L Equation 1-3.

Equation 1-3 from Reference 3-1 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 pull out load. The pull out load is calculated in Reference 3-20 by the same methods utilized in Reference 3-I.

Table 3-13 summarizes the mean H* values for the Indian Point Unit 2 Model 44F 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 (critical) radius on the tubesheet at which the probabilistic values of H* are calculated. Table 3-14 summarizes the results of the mean H* calculations after correction for Poisson contraction. The critical radius for the Model 44F 4-Loop is determined to be [ ]... inches.

The limiting tubesheet radius, for the case of the mean material condition with the addition of the Poisson correction, is determined to be the same as in the current licensing basis for the Indian Point Unit 2 Model 44F 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 NOPLOWTAVG. and main steam line break, SLB, consistent with the current licensing bases. From Reference 3-1, it is concluded that the limiting condition for the Indian Point Unit 2 SGs is NOR 3.3.11 Number of Elevations to Define Contact Pressure Profile 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*. There is positive contact pressure for the entire thickness of the tubesheet at the critical radius for the Indian Point Unit 2 Model 44F SGs (See Figure 3-20). It is concluded that the number of elevations utilized for contact pressure calculations accurately represent the contact pressure profile.

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3-33 3.3.12 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 3-24 through 3-26 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 C 2 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.

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 Indian Point Unit 2 SGs.

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3-34 Table 3-12 H* Input Summary (Reference 3-1)

NOP SLB SG Model/Tube OD") End Cap Load (Ib) End Cap Load (lb) a,c,e Notes:

44F/ 1lac.e

]1 I. Maximum tubesheet bore diameter.

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

Table 3-13 Summary of H* Mean Values before Poisson Correction (All dimensions in inches)

SG Model Radius NOP H* a,c~e SLB H*

44F 2.655 (I) 7.219 18.171 28.21 34.598 48.288 Note:

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

Table 3-14 Summary of H* Mean Values after Poisson Correction (All dimensions in inches)

SG Model Radius NOP H* a,ce SLB H*

44F 2.655 (I) 7.219 18.171 28.21 34.598 48.288 Note:

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

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3-35 a,c,e Figure 3-24 Model 44F: Circumferential Contact Pressure at the Critical Radius WCAP-17828-NP January 2014 Revision 0

3-36 a,c,e Figure 3-25 Model 44F: Circumferential Contact Pressure at the Minimum Radius WCAP-17828-NP January 2014 Revision 0

3-37 a,c,e Figure 3-26 Model 44F: Circumferential Contact Pressure at the Maximum Radius January 2014 WCAP- I 7828-NP WCAP-17828-NP January 2014 Revision 0

3-38 3.4 CALCULATIONS OF PROBABILISTIC H* USING THE C2 MODEL Development of the probabilistic value of H* for the thick shell model is documented in References 3-1 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 (Reference 3-17). 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 C 2 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 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 C 2 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 Reference 3-1 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 C 2 model are somewhat different than those predicted by the thick shell model. The difference between the models reflects, in part, 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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3-39 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 detennine the sensitivity of H* to variations of the significant variable (tube and tubesheet CTEs) over a large domain using the C 2 model. Therefore, a similar structural response variability surface, as documented in Figure 8-5 in Reference 3-1, is used as the basis for determining the combinations of these variables that lead to the high probability values of H* for Indian Point Unit 2. The revised H* response surface (Reference 3-17) is necessary for the Indian Point Unit 2 SGs because the normal plant operating conditions are not bounded by the limiting plant in the H* fleet for the Model 44F SGs. 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 tile tubesheet material) are taken from References 3-1 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 confidence values of H*, because the specific input values of the variables are saved along with the values of H* (Reference 3-18). 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 mnFlTS, and tile variation in the tube CTE about its mean value in terms of HUT where in and n are the multipliers (positive or negative) on standard deviations added to the mean value of the respective CTEs (see Table 3-15).

For the range of multipliers in and n on the tubesheet and tube CTE standard deviations, respectively, shown on Table 3-15, the absolute values for the CTEs used in the analysis are shown on Table 3-16 for the tubesheet material and on Table 3-17 for the tube material. The result of using the material properties in Table 3-16 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 3-17 are used as input to the square cell analysis.

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3-40 "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 3-15). This approach was originally documented in Reference 3-li. 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 3-27 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 3-27 are taken from the analysis of the Model D5 SG.) 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 using 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 3-28 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 C 2 model. For example, if a specific rank order H* estimate is desired, say the 9500h, 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 C-2 analysis were selected based on the required rank order statistics that met the probabilistic goals for H*. For example, the 9 5th percentile H* estimate at the 50'h 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 negative (decreasing) variation on the tubesheet, but an exceedingly large (greater than -4y) 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*.

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3-41 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 3-29). 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 3-30 shows the typical variation in H* over a range of CTE combinations ("alpha") for the bounding rank orders in the Model 44F NOP response surface from Reference 3-1.

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 F SG (See Table 3-20). 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 3-21 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 C 2 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 a2 = np(1 - p) (Equation 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 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.

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3-42 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 3-18. 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.x 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 C2 model.

The specific rank order points selected for each of the limiting plants in the H* fleet are listed in Table 3-19.

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 Reference 3-1 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.

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 3-29 shows the results based on the NOP condition analysis for the Model F SG (without Poisson Contraction effect). It is observed that in the rank order range of interest, the results are well 2 approximated by a straight line. It is further observed that the value of H* is increased based on the C model compared to the thick shell model. As noted previously, this difference is the result of application WCAP-17828-NP January 2014 Revision 0

3-43 of the more accurate C 2 model in conjunction with modified displacement results from the updated 3-D FEA model of the tubesheet region (see Section 3.1 ).

That the H* values calculated using the new inputs to the square cell model correspond closely to the rank order statistic from the thick shell model 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 3-20 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 3-21, 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 C 2 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 C 2 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 C 2 output. The specific trend that the comparison between the C 2 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 thick shell model analysis include the effect of the tubesheet thermal distribution offset, and a 0.30 inch distance is added to address the potential uncertainty in the location of the bottom of the expansion transition (BET) at the top of the tubesheet (TTS), the impact of Poisson contraction effect, 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 Reference 3-1 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.

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 C2 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 3-15 showed by independent approach that the breakline approach is reasonable and correct.

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3-44 3.4.3 Application to the Indian Point Unit 2 Model 44F SG The same general approach to the probabilistic analysis for H* is applied for all models of SGs that are candidates for H*. For the Model 44F Indian Point Unit 2 SGs, there are no exceptions that are required to this process. Because the limiting condition for a 4-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 tile probabilistic analysis using the C2 model for the Model 44F SG are:

The limiting operating condition for H*. The limiting operating condition for the Model 44F 4-loop SGs was determined to be the NOP condition.

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

Based on the Monte Carlo (MC) sampling results, the definition of the break line for the Model 44F SGs (Figure 3-31) in the upper 10% of the rank order is characteristically the same as that shown in Figure 3-28.

Figure 3-32 shows the same data as Figure 3-31 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 3-31 are the points selected for the Model 44F SGs as shown on Table 3-19.

Figure 3-33 is a plot of H* versus the selected rank order values.

3.4.3.1 Model 44F (Indian Point Unit 2) Results The H* values (without the crevice pressure adjustment and with Poisson Contraction effect) from the contact pressure distributions developed using the C2 model at the limiting TS radius are shown in Table 3-22 together with the rank order of the input values as discussed above. Also shown for comparison is the raw H* value from the reference analysis of Reference 3-1. The H* estimates based on the C2 model results are about four to five inches greater than those from the thick shell model. The results shown in Table 3-22 are represented graphically in Figure 3-33 for both tile reference analysis and for application of the C 2 model.

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 3-33 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:

H*RO = ]a,.e

where, RO = the desired Rank Order statistic between 9042 and 9895.

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3-45 Table 3-15 Typical Monte Carlo Result Output Rank # HSTAR nCFT roMTS Alpha axc,e 9000

-I 9001 9002 9003 9004 9995 9996 9997 9998 9999 10000 Note:

I. f7'T is the multiplier on a for the tube; is the multiplier on a for the tubesheet.

ainets Table 3-16 Positive Variations about the Mean TS CTE used for FEA (Units of 10-6 in/in/IF)

Temp. *F Mean 0.60 0.76 0.82 1.03 1.26 1.88 1.43 2.28 2.63 70 6.50 6.56 6.58 6.59 6.61 6.63 6.70 6.65 6.74 6.78 200 6.67 6.73 6.75 6.76 6.78 6.81 6.87 6.83 6.92 6.95 300 6.87 6.94 6.95 6.96 6.98 7.01 7.08 7.03 7.12 7.16 400 7.07 7.14 7.16 7.16 7.19 7.21 7.29 7.23 7.33 7.37 500 7.25 7.32 7.34 7.35 7.37 7.40 7.47 7.42 7.52 7.56 600 7.42 7.49 7.51 7.52 7.54 7.57 7.65 7.59 7.69 7.74 700 7.59 7.66 7.68 7.69 7.72 7.74 7.82 7.77 7.87 7.91 WCAP-1 7828-NP January 2014 Revision 0

3-46 Table 3-17 Negative Variations about the Mean Tube CTE used for FEA (Units of 10-6 in/in/ 0 F)

Temp. *F Mean 3.12 3.19 3.26 3.28 3.32 3.34 3.35 3.67 3.70 3.77 4.33 3.81 3.66 3.75 212 7.22 6.70 6.68 6.67 6.67 6.66 6.66 6.66 6.60 6.60 6.59 6.49 6.58 6.60 6.59 300 7.40 6.86 6.85 6.84 6.83 6.83 6.82 6.82 6.77 6.76 6.75 6.65 6.74 6.77 6.75 420 7.60 7.05 7.04 7.02 7.02 7.01 7.01 7.01 6.95 6.94 6.93 6.83 6.93 6.95 6.94 500 7.70 7.14 7.13 7.12 7.11 7.10 7.10 7.10 7.04 7.04 7.02 6.92 7.02 7.04 7.03 600 7.82 7.25 7.24 7.23 7.22 7.22 7.21 7.21 7.15 7.15 7.13 7.03 7.13 7.15 7.14 628 7.85 7.28 7.27 7.25 7.25 7.24 7.24 7.24 7.18 7.17 7.16 7.06 7.15 7.18 7.17 Table 3-18 Required Probabilistic Estimate for H*

Whole Bundle Estimate Whole Plant Estimate Model SG 95/50 95/95 95/50 95/95 a3.c,e F N/A 3 N/A 3 D5 9500 9536 3 3 44F N/A N/A 3-Loop 44F N/A 3 N/A' 3

2-LoopN/

44F NA 44F N/A 3 N/A 3 4-Loop 51F N/A3 N/A 3

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.

3. Whole bundle does not apply because NOP is the limiting condition for H*

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3-47 Table 3-19 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 SG Condition Statistic"M deviations) deviations) Alpha Basis a,c,e F NOP D5 SLB 44F NOP 3-Loop 44F SLB(2-2-Loop 44F NOP 4-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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3-48 Table 3-20 Typical Variation of CTEs Over a Range of Rank Order Statistics H*(Thick Shell Rank Model Results) 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 January 2014 WCAP-1 7828-NP WCAP-17828-NP January 2014 Revision 0

3-49 Table 3-21 Variation of H* for Adjacent Rank Order Variables (Ref. Model F C 2 Results)

Variation Input MC T CTE TS CTE C 2 H*

1. n/ ma in. a~c,e 9889 F 9890 9891 Table 3-22 Indian Point Unit 2 H* Results (Without Pc.... Adjustment and With Poisson Contraction Effect)

H* Results from Thick Shell Model H* Result from (Reference 3-1) Square Cell Analysis MC Rank in 10,000 Simulations Model 44F (in.) a,c,e 9042 9623 9895 WCAP- 17828-NP January 2014 Revision 0

3-50 a,c,e Figure 3-27 Typical Result for Plotting the Combined Tube and Tubesheet CTE Values vs. H*

7x from the Licensing Basis Analysis (Ref. Model D5 NOP) a~c.e Figure 3-28 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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3-51 ace Figure 3-29 H* Curves from Response Surface (Ref. Model F) - without Poisson Contraction Effect and Crevice Pressure Adjustment a.c,e Figure 3-30 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 a,c,e 7

Figure 3-31 Model 44F NOP Combined CTET and CTETS vs. Monte Carlo Rank Order axce Figure 3-32 Indian Point Unit 2 Model 44F NOP Combined CTET and CTETS vs. H* Value WCAP-17828-NP January 2014 Revision 0

3-53 a,c.e Figure 3-33 Model 44F H* Summary Showing Linear Fit Results (with Poisson Contraction Effect and without Crevice Pressure Adjustment) 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 (Reference 3-20). 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 Reference 3-1. 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).

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3-54 3.5.2 Input The input for this analysis consists of steam generator dimensions for the Indian Point Unit 2 Model 44F SGs, material properties from the ASME Code, and pressure and temperature conditions for the applicable operating condition (100% Power) as defined in References 3-2 and 3-6.

The end cap load for the Model 44F SGs for NOP is [ ]a.. psi, see Table 3-12. This includes a factor of safety of 3.0 on the NOP pressure differential. The modulus of elasticity is taken from Table 3-2.

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.e F for NOP conditions.

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= [r [I -_2v)(p,1'__p,,r.2)+( V) 2 , -P PP (Equation 3-8)

E,(1'-,  ; [ r2

where, P = End cap load (pounds)

I/ = Poisson's ratio r = Radial coordinate (inches)

I'll = Outer radius of tube (inches)

., = Inner radius of tube (inches) p, = Pressure on inside of tube (psi) po = Pressure on outside of tube (psi)

E, = Elastic Modulus of tube (psi) 71 = 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 ARe,,,,,,,p - -E r2_

2 (Equation 3-9)

EzT r:7 r-This equation is used to calculate radial dilations due to the Poisson contraction alone (Table 3-23). As can be seen, there is a small radial contraction (approximately [ ]ja.. micro-inches) due to Poisson effects.

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3-55 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 (Reference 3-1): a,c,e (Equation 3-10) where.

P, = Internal primary side pressure, psi Pre,, = Crevice pressure, psi r, = Inside radius of tube, in r,, = Outside radius of tube, in a, = Coefficient of thermal expansion of tube, in/in/°F E, = Modulus of Elasticity of tube, psi E,, = Modulus of Elasticity of tubesheet, psi T, = Temperature of tube, 'F V = Poisson's Ratio of the material Pco,,,c, = 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.

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3-56 In Step 3, it is clear that the relationship between contact pressure and radial geometric interference

[ I should be linear, as the thick shell equations are linear elastic. Therefore, it is appropriate to calculate contact pressure reduction by simply dividing the differential radial displacement due to Poisson's ratio effects by the elastic constant in the denominator above:

(Equation 3-11)

Results of the calculation of the elastic constants are provided in Table 3-24 for the Indian Point Unit 2 SGs. Substituting the differential radial dilation from Table 3-23 into the above equation yields the contact pressure reductions shown in Table 3-25. As can be seen, there is a reduction of[ ]... psi at NOP conditions for the Model 44F 4-loop.

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 FfntaLPac'dY (Equation 3-12)

Where .t is the coefficient of friction, [ ]a-,, as discussed in References 3-1 and 3-20. Calculations for the increased H* are shown on Table 3-26 for the Indian Point Unit 2. The typical adjustment to the contact pressure profile is shown in Figure 3-34. As can be seen, the contact pressure curve is shifted down by the appropriate amount. Baseline numbers are included on Table 3-26 for comparison. The increase in H* due to Poisson effects amounts to approximately [ ]a.... inches for the Model 44F (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 3-27.

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.

Calculations are tabulated in Table 3-28 for the Indian Point Unit 2 Model 44F. A summary of the final H* values after adjusting for Poisson contraction and attenuation are in Table 3-29. As can be seen, the difference is [ ]"".. inches for the Model 44F 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 Tables 3-30 through 3-34. A summary of the effect of Poisson's contraction on the probabilistic values of H* is in Table 3-35. As can be seen, the effect is approximately [ ]a... inch for the probabilistic H* value for the Model 44F SG.

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3-57 Table 3-23 Calculation of Radial Dilation Due to Poisson Effects Model 44F 4-Loop Parameter NOP a,c,e Tube r, (in)

Tube r. (in)

E,,,b, (Msi)

End Cap Load (Ibs)

AR (micro-inch, 10-6 in)

Table 3-24 Calculation of Elastic Constants Model 44F 4-Loop Parameter NOP SLB ac.e Tube ri (in)

Tube r0 (in)

Collar Ro (in)

Tube E (Msi)

Tubesheet E (Msi)

V Elastic Constant (in3/Ib)

Table 3-25 Calculation of Reduction in Contact Pressure from Poisson Effects Model 44F 4-Loop Parameter NOP ace AR due to v (pin) 1 Elastic Constant (in3/Ib)

Pcon Reduction (psi)

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3-58 Table 3-26 Baseline and Adjusted Mean H* Calculation for Model 44F (Indian Point Unit 2)

NOP, I I"'.in. Radius End Cap Load = I I""' pounds Accumulated Accumulated Pull Pull Out Load Out Load Elevation from Distance Pcon (psi) (pounds) Pcon (psi) (pounds)

Bottom of from TTS Tubesheet (in) (in) Baseline (Unadjusted Mean H*) H*Adjusted for Poisson Effect a,c,e 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) t Table 3-27 Distance for Poisson Effect to Attenuate SG Model Model 44F 4-Loop Distance for Poisson Effect to Attenuate (inches) [ ]x'¢e WCAP-17828-NP January 2014 Revision 0

3-59 rable 3-28 Adjusted Mean H* Including Poisson Attenuation for Model 44F (Indian Point Unit 2)

NOP 100% Power, ( Ia.. in. Radius End Cap Load = [ a... pounds Elevation from Bottom of Distance from Accumulated Pull Out Tubesheet (in) TTS (in) Peon (psi) Load (pounds) ace 0.000 21.810 2.000 19.810 3.523 18.287 5.442 16.368 10.905 10.905 14.871 6.560 16.368 5.442 18.287 3.523 19.810 2.000 21.810 0.000 H* (inches) L Table 3-29 Comparison of Mean H* Values Parameter Model 44F 4-Loop (in.) ace H* Unmodified H* + Poisson H* + Poisson + Attenuation I~~

Final Difference L WCAP- 17828-NP January 2014 Revision 0

3-60 Table 3-30 Baseline and Adjusted Probabilistic H* Calculation for Model 44F (Monte Carlo Rank 9732*)

NOP, I I""' in. Radius End Cap Load = I ]'... pounds Elevation Baseline Shifted due to Poisson from Bottom Distance from of Tubesheet TTS Pco, Accumulated Pull Pco, Accumulated Pull (in) (in) (psi) Out Load (pounds) (psi) Out Load (pounds) a,c,e 0.000 21.810 --

2.000 19.810 3.523 18.287 5.442 16.368 10.905 10.905 16.368 5.442 18.287 3.532 19.810 2.000 21.810 0.000 H* (inches)

• 9732 is the single bundle equivalent to the 9000 whole plant analysis WCAP-17828-NP January 2014 Revision 0

3-61 Table 3-31 Baseline and Adjusted Probabilistic H* Calculation for Model 44F 4-Loop (Monte Carlo Rank 9886)

NOP, I I .. in. Radius End Cap Load = I 1ac. pounds Elevation Baseline Shifted due to Poisson 4-from Bottom Distance from of Tubesheet TTS Peon Accumulated Pull Peon Accumulated Pull (in) (in) (psi) Out Load (pounds) (psi) Out Load (pounds) 4- +-- 4 4- +

0.000 21.810 2.000 19.810 3.523 18.287 5.442 16.368 10.905 10.905 16.368 5.442 18.287 3.532 19.810 2.000 21.810 0.000 H* (inches)

Table 3-32 Distance for Poisson Effect to Attenuate Probabilistic H* Values (inches)

Model SG Model 44F MC Rank 9732 [ ]a...e MC Rank 9886 1]a.c.e WCAP-17828-NP January 2014 Revision 0

3-62 Table 3-33 H* Calculation Including Poisson Attenuation Model 44F (Indian Point Unit 2)

(With Attenuation, MC Rank 9732)

NOP, I I."" in. Radius End Cap Load = 1..... pounds Elevation Above Distance from TTS Pcon Bottom of TS (in) (in) (psi) Accumulated Pull Out Load (pounds) a,c,e 0.000 21.810 2.000 19.810 3.523 18.287 5.442 16.368 7.723 14.087 10.905 10.905 16.368 5.442 18.287 3.523 19.810 2.000 21.810 0.000 H* (inches) 17.154 from TTS WCAP-17828-NP January 2014 Revision 0

3-63 Table 3-34 H* Calculation Including Poisson Attenuation Model 44F (Indian Point Unit 2)

(With Attenuation, MC Rank 9886)

NOP, I I"ce in. Radius End Cap Load = I I .. pounds Elevation Above Distance from TTS Pcon Accumulated Pull Out Bottom of TS (in) (in) (psi) Load (pounds) a~c~e 0.000 21.810 2.000 19.810 3.523 18.287 5.442 16.368 6.932 14.878 10.905 10.905 16.368 5.442 18.287 .3523 19.810 2.000 21.810 0.000 H* (inches) 17.778 from TITS Table 3-35 Model 44F SG Probabilistic H* Values (inches)

Model 44F Parameter Mean Rank Order 9732 Rank Order 9886 ace H* Unmodified H* + Poisson H* + Poisson +

Attenuation Final Difference WCAP- 17828-NP January 2014 Revision 0

3-64 a.c.e 71 Figure 3-34 Effect of Poisson Contraction on Contact Pressure; Model 44F 3.6 CREVICE PRESSURE ADJUSTMENT LENGTH As discussed in Reference 3-1, 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 tile 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 ) contains the crevice pressure correction curves. The curves are reproduced below as Figure 3-35 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*.

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3-65 a,c,e Figure 3-35 Model 44F Crevice Pressure Adjustment Curve 3.7 CALCULATION OF FINAL H*

After the probabilistic values of H* are determined as discussed in Section 3.4, and tile 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 3-35, are shown in Table 3-36 for the Indian Point Unit 2 Model 44F SGs (Reference 3-8).

Table 3-36 Summary of Model 44F Probabilistic Estimates Attenuated MC Rank in Poisson 10K H* - C2 Offset Pcrev Final Description Simulations (in.) (in.) (in.) a,c, (in.)

Whole Plant, 95/50 9883 18.83 Whole Plant, 95/95 9886 18.85 January 2014 WCAP-1 7828-NP WCAP-17828-NP January 2014 Revision 0

3-66

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. Entergy Nuclear Northeast Letter No. IP-DE- 13-007, "Applicable Operating Conditions to be Used for the Indian Point Unit 2 H* Analysis," July 2013.

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. 3, "3-D Finite Element Analyses of Limiting Plants for H* with Thermal Profile," December 2013.

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. 3, "Square Cell Finite Element Analyses for Models D5, F, 44F and 51 F Plants for H*," December 2013.

3-9. Not used.

3-10. ASME B&PV Code, 2007 Edition, No Addenda, Section I1, Part D, Subpart 2: Physical Properties Tables, Table PRD.

3-11. 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.

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

Rosso, R., McGraw-Hill, © 1997.

3-13. Westinghouse Drawing 1105.05, Rev. 3, "Tube Plate Drilling."

3-14. Advanced Mechanics ofMaterials, 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 2011.

3-16. LTR-SGDA-1 1-87, "High-Confidence Variances for Tube and Tubesheet CTE for H*,"

May 2011.

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3-67 3-17. CN-SGMP-09-20, Revision 1, "Tube and Tubesheet Surface Sampling Verification for H-Star,"

December 2013.

3-18. CN-SGMP-09-19, Revision 1, "Probabilistic Programs for H-STAR Considering Tubesheet Regions," December, 2013.

3-19 CN-SGMP-10-19, Revision 2, "Probabilistic Comparison of the Square Cell Analysis of the Model F/Model D5/Model 44F 3-Loop and 4-Loop/ Model 51F 3-Loop in Support of H*,"

December 2013.

3-20 CN-SGMP-13-22, "The Effect of Radial Poisson Contraction on H*," December 2013.

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4-1 4 C MODEL LEAKAGE INTEGRITY DISCUSSION It is necessary to consider only the SLB transient in the development of the accident induced to normal operating leakage factors because, as noted in Reference 4-1, the licensing basis for plants with Model 44F steam generators does not include considerations of the feedwater line break (FLB) transient.

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

0- =Ap (Equation 4-1)

where, Q = the flow rate of the fluid through the porous medium Ap = the driving potential (primary-to-secondary pressure difference)

Pt = the fluid dynamic viscosity K = the loss coefficient for flow through the porous medium I = the length of the porous medium The Darcy formulation (Equation 4-1) is used to develop the ratio of leak rates between postulated accident-induced conditions and normal operating conditions (NOP). Expressed as a ratio between two operating conditions, the Darcy flow equation ratio can be separated into four "subfactors" as follows:

LDBA-- p NOP KNOP l'OP (Equation 4-2)

QNOP APNOP /DBA KDBA 'DBA As described below, it has been determined that none of the four subfactors identified in Equation 4-2 are impacted; therefore, the SLB leakage factor established in References 4-1 and 4- 2 continues to apply. A review of each of the subfactor ratios in the Darcy Equation follows:

The driving head (Ap) at both NOP and SLB conditions for Indian Point Unit 2 are unchanged from the values used in References 4-1 and 4-2. The limiting steam line break pressure differential used to calculate the driving heads subfactor for Indian Point Unit 2, taken from Reference 4-1, is 2642 psid and the normal operating pressure differential is 1509 psid (Reference 4-3). This results in a driving head subfactor of 1.75.

The viscosity subfactor (ItNoP/ISLB) remains the same as that included in References 4-1 and 4-2 for the postulated SLB condition for Indian Point Unit 2. A SLB event is a cooldown event and the postulated SLB event does not result in a temperature increase above the normal operating conditions. Therefore, the viscosity subfactor can conservatively be considered to be 1.0.

The SLB leakage factor assumes 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 and 4-2 to show that no WCAP-17828-NP January 2014 Revision 0

4-2 correlation between loss coefficient and contact pressure exists for conditions that simulate the Model D5 SG conditions. Because of uncertainty in the data, a requirement was applied to tile 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> I) in order to assume that the loss coefficient subfactor is equal to 1.0. (This requirement is included in the existing licensing basis for all plants in the H* fleet.)

For the Indian Point Unit 2 Model 44F steam generators, the results of the square cell analysis show that the contact pressure during steam line break conditions at various tubesheet elevations between 0 and 21.81 inches (Model 44F) at all radii in the tube bundle either meets or exceeds the contact pressure above the H* distance from the top of the tubesheet during normal operating conditions, thereby meeting the intent of the criterion (PCsLB:PCNop>I).

For all tube bundle radii, SLB contact pressure exceeds NOP contact pressure at all tubesheet elevations except as follows. At tube bundle radius 2.655 inches, for the first approximately 3 inches from the top of the tubesheet, the average contact pressure during SLB conditions is calculated to be slightly less than the contact pressure during normal operating conditions (less than 200 psi maximum contact pressure difference). It is Westinghouse's engineering judgment that these contact pressure results are essentially the same within the accuracy of the analysis.

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 Reference 4-1, the "effective crevice length" is defined as the length of positive contact between the tube and the tubesheet (above H*). Again, for the 4-loop Model 44F SG, the effective crevice length during a postulated SLB event meets or exceeds the effective length of crevice for normal operating conditions for the Indian Point Unit 2 Model 44F steam generators at all tube bundle radii (Reference 4- 6).

Therefore, the effective length ratio subfactor for (INOP/IDBA) is determined to be 1.0.

As shown by Equation 4-2, the final leakage factor is a product of the four subfactors. Therefore, the SLB leakage factor is calculated to be 1.75 for the Indian Point Unit 2 steam generators (Reference 4-7).

Application of the leak rate factor is as follows:

For the condition monitoring (CM) assessment, the component of leakage from a prior cycle below the H* distance would be multiplied by the leak rate factor (1.75) and added to leakage from any other source and compared to the allowable accident induced leakage limit.

For the operational assessment (OA), the difference in leakage between the allowable leakage limit and the accident leakage limit from all sources other than the tubesheet expansion region (below the H* distance) will be divided by the leak rate factor (1.75) and compared to the observed operational leakage. If necessary, an administrative limit for operational leakage can be established to ensure that the allowable accident leakage limit is not exceeded.

As discussed in Reference 4-1, the design specification curves for the locked rotor and control rod ejection events apply for the leakage factors for these transients. The same leakage factors (<1.0) for a postulated locked rotor and control rod ejection event included in References 4-1 and 4-2 apply (0.84 for WCAP- 17828-NP January 2014 Revision 0

4-3 a postulated locked rotor event and 0.39 for a postulated control rod ejection event) for the Indian Point Unit 2 steam generators. As discussed in Section 9.5 of Reference 4-I, because of the short duration of the elevated pressure differential across the tubesheet for these transients, the leakage factors are less than 1.0 and are not used.

Based on the above, it is concluded that the leakage factors identified in Reference 4-2 for Indian Point Unit 2 apply when considering the C 2 model results.

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. 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.

4-3. Entergy Nuclear Northeast Letter No. IP-DE-13-007., "Applicable Operating Conditions to be Used for the Indian Point Unit 2 H* Analysis," July 2013.

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/DCE/DDP/TCX.," November 2003.

4-6. CN-SGMP-10-3, Rev. 3, "Square Cell Finite Element Analyses for Model D5, F, 44F and 51F Plants for H*," December 2013.

4-7. LTR-RC-13-54, Rev. 1. "Indian Point Unit 2 H* Leak Rate Factors." December 2013.

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5-1 5 REPORT

SUMMARY

AND CONCLUSIONS Prior to granting licenses for permanent application of H* to a number of utilities in 2012, the NRC had identified one open technical issue in regard to adequacy of the technical justification of H*. This issue was addressed in prior reports for the various plants and models of SG. The prior report for the Model 44F SGs (Reference 5-2) did not include the detenriination of the H* inspection depth for the Indian Point Unit 2 SGs. The Indian Point Unit 2 SGs are Model 44F SGs but the plant is a 4-loop plant that was not previously included in the determination of the bounding Model 44F plant. The purpose of this report is to provide the same final resolution of the NRC technical issue regarding tubesheet bore eccentricity on the H* criterion contained in Reference 5-2, but specifically applicable to the Indian Point Unit 2 SGs. The methods used are identical to those used for all other plants that have received licenses for permanent application of H*. There are no deviations to the previously approved methodologies.

There are two principal requirements for H*:

1. Assure that tubes 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 tile tube-to-tubesheet crevice is no greater than that assumed in the final safety analysis report (FSAR) for the most limiting accident.

Concerning Item 1L 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 Indian Point Unit 2 Model 44F SG, the value of H* inspection depth required to meet the structural integrity goals of the plant increases by approximately 4 inches when using the square cell model versus using thick shell equation to calculate the H* length . A direct comparison between the thick shell model probabilistic H* value and the square cell analysis probabilistic H* values for the Model 44F steam generators is shown in Table 5-1. The H* value which provides tube pull out capability that meets the structural integrity acceptance criteria identified in Section 4.1 of Reference 5-1 is 18.83 inches for Indian Point Unit 2.

The impact of the square cell model results on the prior thick shell model leak rate factors provided in Reference 5-3 for the Model 44F was evaluated. It was determined that the square cell model results do not affect the thick shell model basis leakage rate factors. The driving heads (Ap) at NOP and SLB conditions are known and remain unchanged from the thick-shell equation approach, and the temperatures and pressures remain the same to define the fluid viscosity ([t). Therefore, the pressure and viscosity subfactors in tile Darcy formulation for leakage 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 inches (Model 44F) at all radii in the tube bundle 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 WCAP-17828-NP January 2014 Revision 0

5-2 operating conditions for the Model 44F. Therefore, the effective length ratio subfactor for (INoP/IDRA) can be assumed to be 1.0 during a postulated steam line break event for the Indian Point Unit 2 steam generators.

Concerning all other design basis accidents that model accident condition leakage, as discussed in Reference 5-1, 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 included in the prior technical basis (Reference 5-3) continue to apply.

Based on the above, with the use of the leakage factors included in the prior technical basis (References 5-3), 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.

The prior satisfactory resolution of the NRC technical issue regarding tubesheet bore eccentricity was completed in the Reference 5-2 report. Together with documents provided under separate cover, (e.g.,

Reference 5-4) this report completes the response to the RAI provided in Reference 5-5 for Indian Point Unit 2. Application of the C 2 model has provided independent confirmation that the structural criteria are met. Probabilistic H* values were calculated based on application of the C 2 model and substantially confirm the values determined using the thick shell model. The differences between the H* results based on the C 2 model and those from the prior application of the thick shell model are explained. The leakage factors contained in Reference 5-3 and as defined in this report for Indian Point Unit 2 SGs are shown to be conservative and acceptable for implementation of H*.

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5-3 Table 5-1 Results of Probabilistic Comparison Study for the Indian Point Unit 2 SGs Thick Shell Calculations Square Cell Calculations Previously References 3-19 and 3-20 Implemented H*(') Whole Plant 95/95 Plant Limiting Whole Plant Tech. Spec. 95/50 95/95 Operating Thick Shell Model SG Model/ Limiting Plant Condition Methodology in. in. in. in.

Model 44F/ Indian Point NOP WCAP- 1709 1-P 14.92 N/A")l 18.83 18.85 Unit 2 Note:

I. An implemented H* result is not available for Indian Point Unit 2 because this plant was not included in the original H* fleet of plants.

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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-17345-P, Rev. 2, "H*: Resolution of NRC Technical Issue Regarding Tubesheet Bore Eccentricity (3-Loop Model 44F/Model 51 F)," June 2011.

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 I and 2 - Transmittal of Unresolved Issues Regarding Permanent Alternate Repair Criteria for Steam Generators (TAC Nos. ME 1339 and ME 1340)," November 23, 2009.

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