RA-20-0247, Supplement to Proposed Alternative for RPV Nozzle-to-Vessel Weld and Inner Radii Examination Requirements in Accordance with 10 CFR 50.55a(z)(1)
| ML20212L731 | |
| Person / Time | |
|---|---|
| Site: | Brunswick  |
| Issue date: | 07/30/2020 |
| From: | Krakuszeski J Duke Energy Progress |
| To: | Document Control Desk, Office of Nuclear Reactor Regulation |
| References | |
| RA-20-0247 | |
| Download: ML20212L731 (47) | |
Text
John A. Krakuszeski Vice President Brunswick Nuclear Plant 8470 River Rd SE Southport, NC 28461 o: 910.832.3698 July 30, 2020 10 CFR 50.55a Serial: RA-20-0247 U.S. Nuclear Regulatory Commission ATTN: Document Control Desk Washington, DC 20555-0001 Brunswick Steam Electric Plant, Unit Nos. 1 and 2 Renewed Facility Operating License Nos. DPR-71 and DPR-62 Docket Nos. 50-325 and 50-324
Subject:
Supplement to Proposed Alternative for RPV Nozzle-to-Vessel Weld and Inner Radii Examination Requirements in Accordance with 10 CFR 50.55a(z)(1)
References:
- 1. Letter from John A. Krakuszeski (Duke Energy) to U.S. Nuclear Regulatory Commission Document Control Desk, "Proposed Alternative for RPV Nozzle-to-Vessel Weld and Inner Radii Examination Requirements in Accordance with 10 CFR 50.55a(z)(1)," dated June 23, 2020, ADAMS Accession Number ML20181A004
- 2. NRR E-mail Capture - Brunswick Units 1 and 2 - Supplemental Information Needed for Acceptance of Requested Licensing Action Re: Request for Alternative for RPV Nozzle-to-vessel weld and inner radii Examination Requirements, dated July 29, 2020 (EPID L-2020-LLR-0091), ADAMS Accession Number ML20211M246.
Ladies and Gentlemen:
On June 23, 2020 (i.e., Reference 1), Duke Energy Progress, LLC (Duke Energy), requested an In-service Inspection (ISI) alternative for the Brunswick Steam Electric Plant (BSEP), Units 1 and 2. The proposed alternative will allow reduced requirements for reactor pressure vessel nozzle-to-vessel weld and inner radius examinations.
On July 29, 2020 (i.e., Reference 2), by electronic mail, the NRC requested information regarding the probabilistic fracture mechanics (PFM) evaluation summarized in Enclosure 4 of the June 23, 2020, submittal. In response to this request, Enclosure 1 contains the Stress Analysis and Probabilistic Fracture Mechanics Evaluation for Brunswick Recirculation Outlet (N1) Nozzles.
RA-20-0247 Page 2 of 2 This document contains no new regulatory commitments. Please refer any questions regarding this submittal to Mr. Art Zaremba, Director - Nuclear Fleet Licensing, at (980) 373-2062.
Sincerely, John A. Krakuszeski Site Vice President Brunswick Steam Electric Plant
Enclosure:
- 1. Stress Analysis and Probabilistic Fracture Mechanics Evaluation for Brunswick Recirculation Outlet (N 1) Nozzles cc:
Ms. Laura Dudes, Regional Administrator, Region II Mr. Andrew Hon, Project Manager Mr. Gale Smith, NRC Senior Resident Inspector Chair - North Carolina Utilities Commission Mr. W. Lee Cox, Ill Section Chief, Radiation Protection Section, NC DHHS
RA-20-0247 Enclosure 1 Enclosure 1 Stress Analysis and Probabilistic Fracture Mechanics Evaluation for Brunswick Recirculation Outlet (N1) Nozzles
File No.: 1901228.301P Project No.: 1901228 Quality Program Type: Nuclear Commercial CALCULATION PACKAGE PROJECT NAME:
Brunswick Code Case N702 Analysis CONTRACT NO.:
03021365 00042 CLIENT: PLANT:
Duke Energy Brunswick Steam Electric Plant, Units 1 and 2 CALCULATION TITLE:
Stress Analysis and Probabilistic Fracture Mechanics Evaluation for Brunswick Recirculation Outlet (N1)
Nozzles Project Manager Preparer(s) &
Document Affected Revision Description Approval Checker(s)
Revision Pages Signature & Date Signatures & Date 0 1 - 41 A A-3 Initial Issue Garivalde Dominguez Kevin Wong 04/10/20 04/10/20 Kevin Wong 04/10/20 1 Section 3.3.1, Revised bounding Figure 1, transient and reran Figure 3, analysis Figure 4, Garivalde Dominguez Figure 8, 05/11/20 Table 7, Kevin Wong Table 8, 05/11/20 Appendix A Kevin Wong 05/11/20
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Table of Contents
1.0 INTRODUCTION
......................................................................................................... 6 2.0 METHODOLOGY ........................................................................................................ 6 3.0 STRESS ANALYSIS ................................................................................................... 6 3.1 Assumptions for Stress Analysis ..................................................................... 7 3.2 Design Inputs for Stress Analysis .................................................................... 7 3.2.1 Geometry ......................................................................................................... 7 3.2.2 Material Properties .......................................................................................... 7 3.3 Loads............................................................................................................... 8 3.3.1 Thermal Transient ........................................................................................... 8 3.3.2 Internal Pressure ............................................................................................. 8 3.4 Heat Transfer Coefficients ............................................................................... 9 3.4.1 Internal Heat Transfer Coefficients, Forced Convection.................................. 9 3.4.2 Internal Heat Transfer Coefficients, Natural Convection ............................... 11 3.5 Finite Element Model ..................................................................................... 12 4.0 PROBABLISTIC FRACTURE MECHANICS EVALUATION ..................................... 13 4.1 Assumptions for Probabilistic Fracture Mechanics ........................................ 14 4.2 Design Inputs for Probabilistic Fracture Mechanics ...................................... 14 4.2.1 Deterministic Parameters .............................................................................. 14 4.2.2 Random Variables ......................................................................................... 15 5.0 RESULTS AND CONCLUSIONS .............................................................................. 17
6.0 REFERENCES
.......................................................................................................... 18 SUPPORTING FILES ....................................................................................A-1 File No.: 1901228.301P Page 3 of 41 Revision: 1 F0306-01R4
List of Tables Table 1: Properties for SA-182, 18Cr-8Ni (ASME 2007-2008a Code Edition) ..................... 20 Table 2: Properties for SA-336, Class F9 Type 304, 9Cr-1Mo (ASME 2007-2008a Code Edition) ...................................................................... 21 Table 3: Properties for SA-508, Class II, 3 1/2Ni-1 3/4Cr-1/2Mo-V (ASME 2007-2008a Code Edition) ...................................................................... 22 Table 4: Properties for SA-533, Class I Grade B, Mn-1/2Mo-1/2Ni (ASME 2007-2008a Code Edition) ...................................................................... 23 Table 5: Recirculation Outlet Nozzle Thermal Transients .................................................... 24 Table 6: Properties of Liquid Water...................................................................................... 24 Table 7: Transient: Improper Start of Cold Recirculation Loop [6b] ...................................... 25 Table 8: Recirculation Nozzle Path Polynomial Stress Coefficients ..................................... 26 Table 9: Deterministic Parameter Summary ........................................................................ 27 Table 10: Probability of Detection (PoD) Distribution [11] ..................................................... 27 Table 11: Random Variables Parameter Summary .............................................................. 28 Table 12: Probability of Failure for Period of Extended Operation ....................................... 29 File No.: 1901228.301P Page 4 of 41 Revision: 1 F0306-01R4
List of Figures Figure 1: Solidworks 3D Model ............................................................................................ 30 Figure 2: Material Specification ............................................................................................ 31 Figure 3: Improper Start of Cold Recirculation Loop, Sections 17-18 [6.b] .......................... 32 Figure 4: FEM Thermal Loads and Boundary Conditions .................................................... 33 Figure 5: FEM Static Loads and Boundary Conditions ........................................................ 34 Figure 6: Recirculation Nozzle-to-RPV Shell Finite Element Model...................................... 35 Figure 7: Unit Pressure Analysis Maximum Stress Intensity Location .................................. 36 Figure 8: Thermal Transient Analysis Maximum Stress Intensity Location ........................... 37 Figure 9: Stress Extraction Path Orientations in the N1 Nozzle ........................................... 38 Figure 10: Unit Pressure Stress Distributions ...................................................................... 39 Figure 11: Through-wall Stress Distributions, Thermal Transient (Improper Start of Cold Recirc. Loop).................................................................. 40 Figure 12: Weld Residual Stress Distribution for Paths 3 and 4 .......................................... 41 File No.: 1901228.301P Page 5 of 41 Revision: 1 F0306-01R4
1.0 INTRODUCTION
Duke Energy intends to extend the applicability of Code Case N-702 [1] for the Brunswick Steam Electric Plant, Units 1 and 2 (BSEP) through the end of the period of extended operation (PEO). The Code Case allows reduction of in-service inspection from 100% to 25% of all nozzle blend radii and nozzle-to-shell welds every 10 years, including one nozzle from each system and pipe size, except for feedwater (FW) and control rod drive (CRD) return nozzles.
Technical documents BWRVIP-108 [2, 3] and BWRVIP-241 [4] provide the basis for the code case, but only consider 40 year plant operation. To extend the applicability of Code Case N-702, a probabilistic fracture mechanics (PFM) evaluation, consistent with the methods of BWRVIP-108 and BWRVIP-241, is performed to ensure that the probability of failure (PoF) remains acceptable.
The plant specific PFM evaluation is for the BSEP Recirculation Outlet Nozzles (N1) to extend applicability to 60 years for PEO. In BWRVIP-241, the N1 nozzles are identified as the bounding nozzles when fluence is not considered [4]. The evaluation consists of two parts: Finite Element Model (FEM) Stress Analysis and PFM Analysis.
2.0 METHODOLOGY This evaluation considers the nozzle-to-shell weld and nozzle blend radius on the BSEP N1 nozzles per References [3] and [4] and confirms that the nozzle still meets the acceptable failure probability considering the bounding fluence at the end of the PEO. The probability of failure expressed in this calculation is equivalent to the through-wall cracking frequency.
The acceptance criterion limits the difference in probability of failure per year due to the low temperature over pressure (LTOP) event to be no more than 5x10-6 when changing from full (100%) in-service inspection to 25% inspection for the PEO. In this analysis, the case of 25% inspection for 60 years is used. If the resulting probability of failure (PoF) per year due to a postulated LTOP event (including 1x10-3 probability of LTOP event occurrence per year [3, pg. 5-13]) is less than the allowable PoF of 5x10-6 per year from NUREG-1806 [21], then the inspection reduction based on Code Case N-702 can be extended to 60 years.
Stress analysis is performed on a finite element model of the BSEP Recirculation Outlet Nozzle.
Stresses are extracted for stress paths at the nozzle blend radius and the nozzle-to-shell weld and used in the probabilistic fracture mechanics evaluation, which is consistent with the methodology in BWRVIP-05 [9].
3.0 STRESS ANALYSIS Finite element analysis is employed using a 3-D finite element model (FEM) of the recirculation outlet nozzle. The model geometry is discussed in detailed in this section. A bounding thermal transient analysis is performed based on system thermal cycling that occurs at the recirculation outlet nozzle.
Concurrent with the thermal transients, pressure is also considered. For the internal pressure, unit load analyses are scaled appropriately based on the magnitude of the pressure. The results due to internal pressure is combined with stresses from corresponding thermal transients. All necessary stress tensor such as in circumferential and axial direction are used in the subsequent probabilistic fracture mechanics (PFM) evaluation.
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3.1 Assumptions for Stress Analysis The following items detail the assumptions used for the stress analysis:
- 1. The values of density and Poissons ratio are assumed to be temperature independent for the limited range of temperatures used in this evaluation. The change in density over the range of temperatures applicable to this analysis is negligible and Poissons ratio is temperature independent.
- 2. The heat transfer coefficient at the blending region between the recirculation nozzle and the reactor pressure vessel is conservatively assumed to be the same as that of the recirculation piping.
- 3. A stress-free temperature of 70 °F is assumed for this stress analysis.
3.2 Design Inputs for Stress Analysis A 3-dimentional quarter FEM of the recirculation outlet nozzle is developed using the program ANSYS Workbench [11]. Solid elements are used for the structural and thermal analysis within the program.
The model includes the safe end, the nozzle forging, the cladding, and any relevant portions of the attached RPV wall and recirculation piping. Further details of the model boundary conditions and the application of loads to the model will be described in the subsequent subsections.
3.2.1 Geometry The finite element model is to be constructed using the dimensions from Reference [5] to create a 3-dimensional model using Solidworks [12], as shown in Figure 1 Circled dimensions are as-modeled to aid in the model development:
The safe end/pipe dimensions modeled (ID of 13.0625 and OD of 14.1725) do not match the safe end or pipe dimensions. However, the pipe end is just a load application and boundary condition point for the model, so the exact dimensions modeled have a negligible impact on the stresses used in the evaluation (nozzle-to-shell and inner radius).
The length of modeled pipe/safe end (5.4375) and RPV shell length (115.6875) are arbitrary and have no impact on the stress results.
The dimensions associated with the nozzle-to-shell weld, i.e., the distance between the nozzle centerline to the weld centerline (30.8) and the width of the weld (.7938), are modeled to aid in meshing. Since the weld and RPV are modeled as the same material, the dimensional difference is negligible.
Reference [5.c] lists the OD of the RPV as 115.875. Reference [5.f] lists the RPV OD as 115.75. The value of 115.875 was modeled. The difference in the dimensions is negligible.
3.2.2 Material Properties Per Reference [5.c], the material types for the nozzle forging, safe end and nozzle-to-vessel weld are SA-508 Class-II, SA-336 Class F9, and SA-533 Class I, Grade B, respectively. The vessel material is SA-533 Class I, Grade B [3], the cladding material is SA-336 Class F9 [13], and the safe-end weld attachment material is Alloy 182 [3]. The ASME 2007 Code with 2008 Addenda [14] is used in this calculation. The material properties are listed in Table 1 through Table 4. The material specifications per nozzle and vessel shell component are illustrated in Figure 2.
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3.3 Loads The temperature and pressure used in the analysis is based on the thermal cycle drawings [6.a, 6.b]
with modification based on the specific plant power uprate program [7].
3.3.1 Thermal Transient Table 5 lists the transients for BSEP Units 1 and 2 for RPV recirculation nozzle. The design basis thermal cycle diagram (TCD) [6.a, Region B] is used as the basis for the transients for the evaluation of the nozzle. The following transients are considered in the analysis:
Start-up/Shutdown [6.a, Region B, 3-4, 21-24], consist of temperature difference of 451°F and a rate of change of 100°F/hr.
Loss of Feedwater Heater Pump [6.a, Region B, 11-12], consist of maximum temperature difference of 251°F and a rate of change of 100°F/hr.
Improper Start of Cold Recirculation Loop [6.b, Region B, 17-18], consist of maximum temperature difference of 392°F and a step-down and step-up temperature change.
All other transients are considered negligible in comparison to the transients above since they have small temperature difference and rate of change.
Between the given transients, Transient Improper Start of Cold Recirculation Loop is used as the bounding thermal transient load for the stress analysis since it has the most severe rate of temperature change (step) and a considerable large temperature difference. Thus, all 491 cycles from all the transients in Table 5, which are scaled up to 737 cycles for 60 years, will be applied to the bounding transient.
Figure 3 illustrates the temperature and flow rate for the bounding Improper Start of Cold Recirculation Loop transient. At the beginning and end of the transient, the recirculation outlet nozzle experiences the Region B temperature, per the Recirculation Outlet Nozzle Thermal Diagram [6.b, Note 1], which is 522 °F, per the RPV Thermal Cycle Diagram [6.b] and does not changed with EPU [7, Section 4.4.1, Items b and d]. The 100% and 50% rated flows are increased to 47,800 gpm and 23,900 gpm, respectively, for EPU [7, Section 4.4.2, Item a]. The intermediate temperatures and reverse flow of 5500 gpm during the transient are specified in the Recirculation Outlet Nozzle Thermal Diagram [6.b]
and do not change with EPU.
The thermal loads and thermal boundary conditions are illustrated in Figure 4.
3.3.2 Internal Pressure A 1000 psi unit pressure stress analysis is implemented to a separate FEM. In addition, pressure end-cap loads to account to axial stress effect both on the nozzle and vessel shell side. The end-cap load due to internal pressure are as follows:
(3-1)
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where Ri is the inner radius of the vessel or attached piping and Ro is the outer radius of the vessel or attached piping. These cap loads are applied to exert tension on the model.
For the internal pressure, the static loads and boundary conditions are illustrated in Figure 5.
3.4 Heat Transfer Coefficients 3.4.1 Internal Heat Transfer Coefficients, Forced Convection Holman [15, Eq. 6-4, pp. 226-227] gives the following equation for turbulent flow heating in tubes:
. . (3-2) 0.023
- where, Nu = Nusselt number = hD/k Re = Reynolds number = VD/
Pr = Prandtl number, non-dimensional h = heat transfer coefficient, Btu/hr-ft2-F D = inside diameter, ft k = thermal conductivity, Btu/hr-ft-F V = velocity, ft/sec = Q/(D2/4)
Q = volumetric flow rate, ft3/sec
= kinematic viscosity, ft2/sec In the above equation, the exponent may be conservatively applied as n = 0.4 when the Prandtl number is greater than 1, and n = 0.3 for all other cases, per Equation 6-4 of Reference [15]. This logic assures that the maximum possible heat transfer coefficients are applied to the analysis in all scenarios. This is conservative, as maximum heat transfer coefficients take advantage of the temperature differentials in the component (and therefore the thermal stresses). Per Table 6, the lowest Prandtl number is 0.87.
Therefore, for fully developed turbulent flow in a pipe, the difference when applying the two coefficients is less than 2%. Thus, the n = 0.4 coefficient may be used in all cases, since ample conservatism is applied in other areas of the analysis.
Solving for heat transfer coefficient and substituting V = Q/(D2/4) yields:
h = 0.023 (k/D) (VD/)0.8 Pr0.4 h = 0.023 (k/D) [4QD/(D2)]0.8 Pr0.4 h = 0.023 (k/D) [4Q/(D)]0.8 Pr0.4 0.023 4/ .
1/ .
. (3-3a)
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It is convenient to express D in inches and Q in gallons per minute (gpm). In the equation, Q/(D) is dimensionless, and k/D must yield h units. Therefore, conversion factors from gpm to ft3/sec for Q and inches to feet for D must be included:
4 0.00228ft 12 inch , gpm (3-3b) 0.023 . .
sec gpm ft , inch 0.018472 . .
(3-3c)
The temperature dependent factor, 1, is defined as:
0.018472 (3-4)
Thus: .
(3-5)
The above equation is valid for Reynolds number, Re, greater than 2300 [15, p. 172]; Re is given by:
4 0.00228ft 12 inch (3-6) sec gpm ft (3-7)
- where, 0.03404 (3-8)
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3.4.2 Internal Heat Transfer Coefficients, Natural Convection For transients where no flow rate or heat transfer coefficient is given, the flow rate is assumed to be zero, and heat transfer coefficients are determined based on natural circulation. Radiative heat transfer is deemed insignificant. For natural circulation in enclosed vertical or horizontal cylinders, Holman [15, Eq.
7-56, p. 289] gives the following formula:
0.55 . (3-9) where Grf = Grashof number, dimensionless = g T D3/2
= temperature coefficient of volume expansion (fluid), 1/F g = acceleration due to gravity = 32.174 ft/sec2 T = temperature difference between the fluid and wall, F
= kinematic viscosity, ft2/sec D = inside diameter, ft Other symbols are the same as previously defined. The subscript f indicates that the properties are evaluated at the film temperature, which is the average of the free-stream fluid temperature and the wall temperature [15, p. 273]. Separating constants and physical properties as before, the equation becomes:
h = 0.55 (k/D) (g T D3 Prf/2)1/4 h = 0.55 k [g T D3 Prf/(D4 2)]1/4 h = 0.55 k [g T Prf/(D 2)]1/4
/
/
0.55 / (3-10)
The portion inside the curly brackets is defined as B and is temperature dependent.
All outside surfaces are assumed to be perfectly insulated. This conservatism is reasonable as it is assumed that there is no heat loss to the environment. Table 6 lists the properties of liquid water [16, Appendix 35.A], which are used to calculate heat transfer coefficients.
Parameters 1 and B are evaluated at each temperature in Table 6, and then interpolated to the temperatures in Table 7. Heat transfer coefficients are calculated as h = 1 (Q)0.8/D1.8 (for transients with flow) or B (T/D)1/4 (for transients without flow) as appropriate for each time point in Table 6. For transients without flow, T is taken as 451°F (551°F -100°F = 451°F [6.a]), obtained from the bounding transient, which is the largest temperature difference (Start-up) during the natural circulation flow (see Section 3.3.1).
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3.5 Finite Element Model The FEM was constructed using the dimensions shown in Figure 1, per References [5.c], to create a 3-D model using the Solidworks [12] (see Figure 1). Materials used in the FEM are outlined in Section 3.2.2, with properties taken from Reference [3, 13, 14]. The type of material for each component modeled is shown in Figure 2. The Solidworks model is then converted to a Parasolid (.x_t) file that is compatible to the ANSYS 3-D Model.
Figure 6b illustrates the defined mesh for the recirculation outlet nozzle. The static and thermal analyses are performed in a separate ANSYS Workbench analysis systems. The FEM consists of 8-node linear, SOLID185, structural elements.
The critical stress paths are selected for two locations on the recirculation outlet nozzle. Two paths (P1 and P2) are chosen at the blend radius which have the maximum stress intensities due to pressure load (Figure 7). Two additional paths (P3 and P4) are selected at the nozzle-to-vessel shell welds which have the maximum stress intensities due to thermal transient load (Figure 8).
Detailed nodal location of paths (see Figure 9) are as follows:
Path 1, P1 = (nozzle-to-vessel shell blend radius) from node 15718 to node 286, Path 2, P2 = (nozzle-to-vessel shell blend radius) from node 15748 to node 5412, Path 3, P3 = (nozzle-to-vessel shell weld) from node 13578 to node 9725, Path 4, P4 = (nozzle-to-vessel shell weld) from node 13457 to node 12915.
ANSYS macro, Genstress.mac, is used to extract the circumferential stress (RSYS=5, nozzle orientation) of each path. The output consists of third order polynomial stress coefficients and is used in the PFM analysis. Table 8 summarizes the extracted coefficients for each path.
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4.0 PROBABLISTIC FRACTURE MECHANICS EVALUATION The probabilistic evaluation is performed for the case of 25% inspection for the extended operating period with 25% inspection for the initial 40 years of operation.
For the nozzle blend radius region, a nozzle blend radius crack model from Reference [20] is used in the probabilistic fracture mechanics evaluation. For this location and crack model, the applicable stress is the stress perpendicular to a path defined 90 degrees from the tangent drawn at the blend radius.
For the nozzle-to-shell weld, either a circumferential or an axial crack, depending on weld orientation, can initiate due to either component fabrication (i.e. considering only welding process) or stress corrosion cracking. The probability of failure for a circumferential crack is less than an axial crack, due to the difference in the stress (hoop versus axial) and the influence on the crack model. However, this probabilistic fracture mechanics evaluation for the nozzle and vessel shell weld considers both circumferential and axial cracks (depending on weld orientation).
An axial elliptical crack model with a crack aspect ratio of a/l = 0.5 is used in the evaluation for the nozzle-to-shell weld. The inspection probability of detection (PoD) curve from BWRVIP-05 [9, Table 10]
is utilized with a ten-year inspection interval. The calculation of stress intensity factor is at the deepest point of the crack.
The approach used for this evaluation is consistent with the methodology presented in BWRVIP-05 [9].
A Monte Carlo simulation is performed using a variant of the VIPER program [10]. The Monte Carlo method can be used to solve probabilistic problems using deterministic computation. A mean value, standard deviation, and distribution curve as defined in the random variables summary (Table 11) defines a set of possible inputs and their probabilities of occurring. Using this domain of possible inputs, a set of inputs are generated for use in determining whether the nozzle will fail using conventional deterministic fracture mechanics methodology. This is repeated 2 million times. The number of simulations in which the nozzle is determined to fail divided by the number of simulations run gives the probability of failure.
The VIPER program was developed as part of the BWRVIP-05P effort for Boiling Water Reactor (BWR) reactor pressure vessel (RPV) shell weld inspection recommendations. The software was modified into a separate version, identified as VIPERNOZ, for use in this evaluation. The detailed description of the methodology incorporated in the VIPER/VIPERNOZ program is documented in References [9] and [3].
The modified software for this project is identified as VIPERNOZ to distinguish from the original VIPER software, and is verified on a project specific basis [8] to ensure the modifications made to the VIPER software are fully quality assured.
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4.1 Assumptions for Probabilistic Fracture Mechanics The following assumptions used in the evaluation are based on previous BWRVIP development projects. Details of each assumption are provided.
- 1. Flaws are assumed to be aligned parallel with the weld direction as justified in BWRVIP-05P [9].
- 2. One stress corrosion crack initiation and 0.1 fabrication flaws is assumed per nozzle blend radius as justified in BWRVIP-108 [3] and BWRVIP-108 SER [2].
- 3. One stress corrosion crack initiation and 1.0 fabrication flaw is assumed per nozzle/shell weld as justified in BWRVIP-108 [3].
- 4. The NRC Pressure Vessel Research Users Facility (PVRUF) flaw size distribution is assumed to apply as justified in EPRI Report W-EPRI-180-302 [17].
- 5. The weld residual stress distribution at the nozzle/shell weld is assumed to be a cosine distribution through the wall thickness with 8 ksi mean amplitude and 5 ksi standard deviation as justified in BWRVIP-108 [3].
- 6. Upper shelf fracture toughness is set to 200 ksiin with a standard deviation of 0 ksiin for un-irradiated material consistent with BWRVIP-108 [2].
- 7. Standard deviation of the mean KIC is set to 15 percent of the mean value of the KIC as justified in BWRVIP-108 SER [2].
4.2 Design Inputs for Probabilistic Fracture Mechanics Section 4.2.1 presents the inputs modeled deterministically as constants, and Section 4.2.2 describes the probabilistic inputs considered to be random variables.
4.2.1 Deterministic Parameters Table 9 summarizes the BSEP RPV dimensions from the nozzle drawings [5] and normal operating conditions from the thermal cycle diagrams [6a]. The LTOP event pressure and temperature are specified in the BWRVIP-05P Safety Evaluation [22].
More detailed input parameters used for inservice inspection (ISI) interval, fatigue cycles, and stress distributions are described in the following sections.
4.2.1.1 In-Service Inspection In this analysis, 25% inspection is used for all 60 years. The probability of detection (PoD) distribution function associated with inspection is shown in Table 10 [11].
4.2.1.2 Fatigue Cycles Table 5 lists the six-recirculation outlet nozzle thermal transients [6.b] and 40-year cycles from the Thermal Cycle Diagram [6.a]. Cycles for sixty years of PEO are scaled from the calculated cycles per ten years.
Improper Start of Cold Recirculation Loop (Reference Numbers 17-18) is considered the bounding transient with the greatest temperature change a short period of time [6b]. As such, all fatigue cycles are conservatively applied to one bounding transient.
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4.2.1.3 Stresses From Section 3, stresses due to internal pressure and thermal transients were determined in the stress analysis. Coefficients of linearized stress paths are obtained for the PFM analysis (see Figure 10 and Figure 11).
4.2.1.1 Weld Residual Stresses Weld residual stresses (WRS) are assumed present in the nozzle-to-shell welds for Paths 3 and 4. The WRS distribution at the nozzle/shell weld is assumed to be a cosine distribution through the wall thickness with 8 ksi mean amplitude and 5 ksi standard deviation (see Figure 12). No WRS is present in the nozzle blend radius region for Paths 1 and 2.
4.2.2 Random Variables Random variables used in the N-702 evaluation are summarized in Table 11. More detailed input parameters used for SCC Initiation, SCC Growth and fatigue crack growth are described in the following sections.
4.2.2.1 Material Chemistry Table 11 presents the weld chemistries (%Cu and %Ni) along with the standard deviation and distributions for the nozzle forging and the nozzle-to-vessel welds, which are from BWRVIP-108 [3] and the BWRVIP-108 Safety Evaluation [2].
4.2.2.2 Fluence For both units, the only RPV nozzles that experience fluence greater than 1.00E+17 n/cm2 for PEO are the N16A and N16B nozzles [23, Section 5.0 p9, Table 7 & 8]. As such, a bounded fluence of 1.00E+17 n/cm2 is used for the evaluation of the Recirculation Outlet Nozzles.
4.2.2.3 Stress Corrosion Cracking Initiation The cladding stress corrosion cracking (SCC) initiation model in the VIPERNOZ program is a power law relationship. Since there is no cladding specific SCC initiation data, the cast stainless steel SCC data in a BWR environment is used as specified in BWRVIP-05 [9, Section 8.2.2.2], and used in BWRVIP-108
[3] and BWRVIP-241 [4]. This model has the form; 84.2 10 (4-1) where: T = time, hours
= applied stress, ksi File No.: 1901228.301P Page 15 of 41 Revision: 1 F0306-01R4
The residual plot shows that a lognormal distribution produces the best fit for the data. The lognormal residual plot with the linear fit of the data is shown below:
0.9248 0.0003 (4-2) where: = (x - ) /
= data mean
= data standard deviation x = ln (Tactual/Tpredicted) 4.2.2.4 Stress Corrosion Cracking Growth The SCC growth model in VIPERNOZ program is a power law relationship from NUREG/CR-6923 [18].
The relationship used is:
(4-3) 6.82 10 where: da/dt = stress corrosion crack growth rate, in/hr K = sustained crack tip stress intensity factor, ksiin The residual plot shows that a Weibull distribution produces the best fit for the data. The Weibull residual plot with the linear fit of the data is shown below:
0.9085 0.3389 (4-4) where: Y = ln (ln (1/ (1-F) ))
F = cumulative distribution from 0 to 1 x = ln ((da/dt) actual / (da/dt) predicted) 4.2.2.5 Fatigue Crack Growth The fatigue crack growth data for SA-533 Grade B Class I and SA-508 Class II (carbon-molybdenum steels) in a reactor water environments are reported in Reference [19] for weld metal testing at an R-ratio (algebraic ratio of Kmin/Kmax, R) of 0.2 and 0.7. To produce a fatigue crack growth law and distribution for the VIPERNOZ software, the data for R= 0.7 was fitted into the form of Paris Law. The R= 0.7 fatigue crack growth law was chosen for conservatism. The curve fit results of the mean fatigue crack growth law is presented with the Paris law shown as follows:
. (4-5) 3.817 10 where a = crack depth, in n = cycles K = Kmax - Kmin, ksi-in0.5 A comparison to the ASME Section XI fatigue crack growth law in a reactor water environment is documented in Reference [11] and it shows a reasonable comparison where the Section XI law is more conservative on growth rate at high K.
File No.: 1901228.301P Page 16 of 41 Revision: 1 F0306-01R4 T
Using the rank ordered residual plot, it is shown that a Weibull distribution is representative for the data.
The Weibull residual plot with the linear curve fit of the data is shown below:
4.1500 0.3712 (4-6) where y = ln(ln(1/(1-F))
x = ln((da/dn)actual/(da/dn)mean)
F = cumulative probability distribution 5.0 RESULTS AND CONCLUSIONS Table 12 presents the results of the probabilistic fracture mechanics evaluation for normal operation and LTOP events.
For normal operation for paths at the nozzle blend radius and the nozzle-to-shell weld, no failures occurred in any path for 1 million simulations for 60 years with 25% inspection. The probability of failure (PoF) for normal operation is calculated to be less than 1 failure / 1 million simulations / 60 years = 1.67 x 10-8 per year. The calculated PoF for normal operation is less than the allowable PoF of 5x10-6 per year and meets the acceptance criterion from NUREG-1806 [21].
For LTOP events for paths at the nozzle blend radius and the nozzle-to-shell weld, no failures occurred in any path for 1 million simulations for 60 years with 25% inspection. The conditional probability of failure (conditional PoF) for LTOP events is calculated to be less than 1 failure / 1 million simulations /
60 years = 1.67 x 10-8 per year. Accounting for an LTOP event occurrence of 1 x 10-3 per year [3, pg 5-13], the PoF for LTOP events is less than 1.67 x 10-11 per year. The calculated PoF for LTOP events is less than the allowable PoF of 5x10-6 per year and meets the acceptance criterion from NUREG-1806
[21].
Thus, after consideration of the additional thermal cycles and fluence for the period of extended operation, the Recirculation Outlet Nozzles (N1) are qualified for reduced inspection using ASME Code Case N-702 through the end of the period of extended operation.
File No.: 1901228.301P Page 17 of 41 Revision: 1 F0306-01R4
6.0 REFERENCES
- 1. Code Case N-702, Alternative Requirements for Boiling Water Reactor (BWR) Nozzle Inner Radius and Nozzle-to-Shell Welds,Section XI, Division 1, February 20, 2004.
- 2. Safety Evaluation of Proprietary EPRI Report, BWR Vessel and Internal Project, Technical Basis for the Reduction of Inspection Requirements for the Boiling Water Reactor Nozzle-to-Vessel Shell Welds and Nozzle Inner Radius (BWRVIP-108), December 19, 2007, SI File No. BWRVIP.108P.
PROPRIETARY.
- 3. BWRVIP Report, BWR Vessel and Internals Project Technical Basis for the Reduction of Inspection Requirements for Boiling Water Reactor Nozzle-to-Vessel Shell Welds and Nozzle Blend Radii, -
(BWRVIP-108), Electric Power Research Institute TR-1003557, October 2002. EPRI PROPRIETARY.
- 4. BWRVIP-241: BWR Vessel Internal Project, Probabilistic Fracture Mechanics Evaluation for the Boiling Water Reactor Nozzle-to-Vessel Shell Welds and Nozzle Blend Radii, EPRI, Palo Alto, CA.
1021005. EPRI PROPRIETARY.
- a. Duke Energy Drawing No. 0-FP-5002, Special Forgings Nozzles N1A & N1B.
- b. Duke Energy Drawing No. 0-FP-5003, Special Forgings Nozzles N2A thru N2K.
- c. Duke Energy Drawing No. 0-FP-5049, 36 x 28 Nozzle N1 A/B Assembly.
- d. Duke Energy Drawing No. 0-FP-5050, Units 1 & 2, General Electric Special Stub Forgings for 12 Diameter Recirculation Inlet Nozzles.
- e. Duke Energy Drawing No. 0-FP-05489, Units 1 & 2 General Electric Reactor Vessel Thermal Sleeve.
- f. Chicago Bridge and Iron Company, 68-247-1/2, Drawing 13, Revision 7, Shell Plate Assembly #1, Half Ring.
- 6. Thermal Cycle Diagrams, SI File No. 1901228.211.
- a. Duke Energy Drawing No. 0-FP-05044, Reactor Thermal Cycles.
- b. Duke Energy Drawing No. 0-FP-05036, Sheet 1, Revision 1, Nozzle Thermal Cycles (Recirculation Outlet).
- 7. GE Nuclear Energy Document: 25A5062, Revision 2, Reactor Vessel Power Uprate, Certified Design Specification, Brunswick 1 and 2, Product Summary Section 7, SI File No. 1901228.213
- 8. SI Calculation 1901228.302, Revision 0, Verification of Software VIPERNOZ Version 1.1.
- 9. BWRVIP Report, BWR Reactor Pressure Vessel Shell Weld Inspection Recommendations (BWRVIP-05P), Electric Power Research Institute TR-105697, September 1995. EPRI PROPRIETARY.
- 10. VIPER, Vessel Inspection Program Evaluation for Reliability, Version 1.2 (1/5/98), Structural Integrity Associates.
- 11. ANSYS Workbench (UP20170403) (March 31, 2017), Release 18.1, SAS IP, Inc.
- 12. Solidworks 2018 x64 Edition, SP02, Professional, Solidworks Corp, Dassault Systemes.
File No.: 1901228.301P Page 18 of 41 Revision: 1 F0306-01R4
- 13. File No. 06-21-11-1033, Reactor Recirculation Outlet Nozzle N1 A/B, N4-AD Nozzle, SI File No.
CPL-53Q-223
- 14. ASME Boiler and Pressure Vessel Code 2007 Edition with 2008 Addenda, Section II-Part D, Properties (Customary).
- 15. Holman, J.P., Heat Transfer, Fifth Edition, McGraw-Hill, 1981.
- 16. Lindeburg, M. R., Mechanical Engineering Reference Manual, 12th Ed, Professional Publications, Inc. 2006.
- 17. EPRI Report No. W-EPRI-180-302, Evaluation of effect of inspection on the probability of failure for BWR Nozzle-to-Shell-Welds and Nozzle Blend Radii Region, Revision 0.
- 18. NUREG/CR-6923, Appendix B.8, Expert Panel Report on Proactive Materials Degradation Assessment, Published February 2007.
- 19. Bamford, W. H., Application of corrosion fatigue crack growth rate data to integrity analyses of nuclear reactor vessels, Journal of Engineering Materials and Technology, Vol. 101, 1979, SI File No. 1300341.213.
- 20. Delvin, S. A., Riccardella, P. C., Fracture mechanics analysis of JAERI model pressure vessel test, ASME PVP Conference, Paper 78-PVP-91, 1978.
- 21. Technical Basis for Revision of Pressurized Thermal Shock (PTS) Screening Limit in the PTS Rule (10 CFR 50.61), NUREG-1806, Vol. 1, August 2007.
- 22. USNRC Report, Final Safety Evaluation of the BWR Vessel Internals Project BWRVIP-05 Report, TAC No. M93925, Division of Engineering Office of Nuclear Reactor Regulation, Nuclear Regulatory Commission, July 28, 1998.
- 23. Duke Energy Document No. 0B11-0062, Revision 004, Pressure and Temperature Limits Report for 54 Effective Full-Power Years, SI File No. 1901228.209.
- 24. EPRI Letter 2012-138, BWRVIP Support of ASME Code Case N-702 Inservice Inspection Relief, August 31, 2012, SI File No. 1300341.213.
File No.: 1901228.301P Page 19 of 41 Revision: 1 F0306-01R4
Table 1: Properties for SA-182, 18Cr-8Ni (ASME 2007-2008a Code Edition)
Youngs Mean Thermal Thermal Thermal Specific Temperature Modulus Expansion Conductivity Diffusivity Heat (F) (ft2/hr) (3)
(x106 psi) (1) (x10-6 in/in/F) (2) (Btu/hr-ft-F) (3) (Btu/lb-F) (4) 70 28.30 8.5 8.6 0.151 0.118 100 28.12 8.6 8.7 0.152 0.118 150 27.81 8.8 9.0 0.154 0.121 200 27.50 8.9 9.3 0.156 0.123 250 27.25 9.1 9.6 0.158 0.126 300 27.00 9.2 9.8 0.16 0.127 350 26.70 9.4 10.1 0.162 0.129 400 26.40 9.5 10.4 0.165 0.130 450 26.15 9.6 10.6 0.167 0.131 500 25.90 9.7 10.9 0.169 0.133 550 25.60 9.8 11.1 0.172 0.133 600 25.30 9.8 11.3 0.174 0.134 Notes:
(1) Table TM-1 of Reference [14], Youngs Modulus at 100°F, 150°F, 250°F, 350°F, 450°F, 550°F are linearly interpolated.
(2) Mean coefficient of thermal expansion, Table TE-1 of Reference [14], The mean coefficient of thermal expansion at 70°F is equivalent to the instantaneous coefficient of thermal expansion at 70°F.
(3) Table TCD-1 of Reference [14].
(4) Calculated per TableI-TCD-1 of Reference [14], using a constant material density (), as Specific Heat = TC / (TD * ).
(5) Density () = 0.280 lbm/in3, and Poissons ratio () = 0.3 [14, Table NF-2], both assumed to be temperature independent.
File No.: 1901228.301P Page 20 of 41 Revision: 1 F0306-01R4
Table 2: Properties for SA-336, Class F9 Type 304, 9Cr-1Mo (ASME 2007-2008a Code Edition)
Youngs Mean Thermal Thermal Thermal Specific Temperature Modulus Expansion Conductivity Diffusivity Heat (F) (ft2/hr) (3)
(x106 psi) (1) (x10-6 in/in/F) (2) (Btu/hr-ft-F) (3) (Btu/lb-F) (4) 70 31.00 5.8 12.8 0.256 0.103 100 30.84 5.9 13.1 0.257 0.105 150 30.57 5.9 13.6 0.258 0.109 200 30.30 6.0 14.0 0.260 0.111 250 30.00 6.1 14.4 0.261 0.114 300 29.70 6.2 14.7 0.262 0.116 350 29.45 6.2 15.0 0.262 0.118 400 29.20 6.3 15.2 0.260 0.121 450 28.90 6.3 15.4 0.254 0.125 500 28.60 6.4 15.6 0.250 0.129 550 28.35 6.5 15.8 0.245 0.133 600 28.10 6.5 15.9 0.239 0.137 Notes:
(1) Table TM-1 of Reference [14], Youngs Modulus at 100°F, 150°F, 250°F, 350°F, 450°F, 550°F are linearly interpolated.
(2) Mean coefficient of thermal expansion, Table TE-1 of Reference [14], The mean coefficient of thermal expansion at 70°F is equivalent to the instantaneous coefficient of thermal expansion at 70°F.
(3) Table TCD-1 of Reference [14].
(4) Calculated per TableI-TCD-1 of Reference [14], using a constant material density (), as Specific Heat = TC / (TD * ).
(5) Density () = 0.280 lbm/in3, and Poissons ratio () = 0.3 [14, Table NF-2], both assumed to be temperature independent.
File No.: 1901228.301P Page 21 of 41 Revision: 1 F0306-01R4
Table 3: Properties for SA-508, Class II, 3 1/2Ni-1 3/4Cr-1/2Mo-V (ASME 2007-2008a Code Edition)
Youngs Mean Thermal Thermal Thermal Temperature Specific Heat Modulus Expansion Conductivity Diffusivity (F) (ft2/hr) (3) (Btu/lb-F) (4)
(x106 psi) (1) (x10-6 in/in/F) (2) (Btu/hr-ft-F) (3) 70 27.80 6.4 23.7 0.459 0.107 100 27.64 6.5 23.6 0.451 0.108 150 27.37 6.6 23.5 0.437 0.111 200 27.10 6.7 23.5 0.424 0.115 250 26.90 6.8 23.4 0.412 0.117 300 26.70 6.9 23.4 0.401 0.121 350 26.45 7.0 23.3 0.390 0.123 400 26.20 7.1 23.1 0.379 0.126 450 25.95 7.2 23.0 0.368 0.129 500 25.70 7.3 22.7 0.357 0.131 550 25.40 7.3 22.5 0.347 0.134 600 25.10 7.4 22.2 0.336 0.137 Notes:
(1) Table TM-1 of Reference [14], Youngs Modulus at 100°F, 150°F, 250°F, 350°F, 450°F, 550°F are linearly interpolated.
(2) Mean coefficient of thermal expansion, Table TE-1 of Reference [14], The mean coefficient of thermal expansion at 70°F is equivalent to the instantaneous coefficient of thermal expansion at 70°F.
(3) Table TCD-1 of Reference [14].
(4) Calculated per TableI-TCD-1 of Reference [14], using a constant material density (), as Specific Heat = TC / (TD * ).
(5) Density () = 0.280 lbm/in3, and Poissons ratio () = 0.3 [14, Table NF-2], both assumed to be temperature independent.
File No.: 1901228.301P Page 22 of 41 Revision: 1 F0306-01R4
Table 4: Properties for SA-533, Class I Grade B, Mn-1/2Mo-1/2Ni (ASME 2007-2008a Code Edition)
Youngs Mean Thermal Thermal Thermal Temperature Specific Heat Modulus Expansion Conductivity Diffusivity (F) (ft2/hr) (3) (Btu/lb-F) (4)
(x106 psi) (1) (x10-6 in/in/F) (2) (Btu/hr-ft-F) (3) 70 29.00 7.0 23.7 0.459 0.107 100 28.88 7.1 23.6 0.451 0.108 150 28.69 7.2 23.5 0.437 0.111 200 28.50 7.3 23.5 0.424 0.115 250 28.25 7.3 23.4 0.412 0.117 300 28.00 7.4 23.4 0.401 0.121 350 27.80 7.5 23.3 0.390 0.123 400 27.60 7.6 23.1 0.379 0.126 450 27.30 7.6 23.0 0.368 0.129 500 27.00 7.7 22.7 0.357 0.131 550 26.65 7.8 22.5 0.347 0.134 600 26.30 7.8 22.2 0.336 0.137 Notes:
(1) Table TM-1 of Reference [14], Youngs Modulus at 100°F, 150°F, 250°F, 350°F, 450°F, 550°F are linearly interpolated.
(2) Mean coefficient of thermal expansion, Table TE-1 of Reference [14], The mean coefficient of thermal expansion at 70°F is equivalent to the instantaneous coefficient of thermal expansion at 70°F.
(3) Table TCD-1 of Reference [14].
(4) Calculated per TableI-TCD-1 of Reference [14], using a constant material density (), as Specific Heat = TC / (TD * ).
(5) Density () = 0.280 lbm/in3, and Poissons ratio () = 0.3 [14, Table NF-2], both assumed to be temperature independent.
File No.: 1901228.301P Page 23 of 41 Revision: 1 F0306-01R4
Table 5: Recirculation Outlet Nozzle Thermal Transients Source: Thermal Cycle Diagrams (TCD) [6]
Reference 40-Year Cycles Transient Numbers Cycles per year Startup 3-4 120 3 Turbine Roll & Increased to Rated Power 4-5 120 3 Loss of Feedwater Pumps, Isolation Valves Close 11-12 10 0.25 Improper Start of Cold Recirc Loop 17-18 5 0.125 Reduction to 0% Power 19-20 118 2.95 Shutdown (after Vessel Flooding) 23-24 118 2.95 All Transients Total: 491 12.275 Table 6: Properties of Liquid Water
, lbm/ft- k, Btu/hr-T, °F sec , ft2/sec ft-°F Pr , 1/F 32 1.20E-3 1.93E-5 0.319 13.7 -0.37E-4 40 1.04E-3 1.67E-5 0.325 11.6 0.20E-4 50 0.88E-3 1.40E-5 0.332 9.55 0.49E-4 60 0.76E-3 1.22E-5 0.340 8.03 0.85E-4 70 0.658E-3 1.06E-5 0.347 6.82 1.2E-4 80 0.578E-3 0.93E-5 0.353 5.89 1.5E-4 90 0.514E-3 0.825E-5 0.359 5.13 1.8E-4 100 0.458E-3 0.74E-5 0.364 4.52 2.0E-4 150 0.292E-3 0.477E-5 0.384 2.74 3.1E-4 200 0.205E-3 0.341E-5 0.394 1.88 4.0E-4 250 0.158E-3 0.269E-5 0.396 1.45 4.8E-4 300 0.126E-3 0.220E-5 0.395 1.18 6.0E-4 350 0.105E-3 0.189E-5 0.391 1.02 6.9E-4 400 0.091E-3 0.170E-5 0.381 0.927 8.0E-4 450 0.080E-3 0.155E-5 0.367 0.876 9.0E-4 500 0.071E-3 0.145E-5 0.349 0.87 10.0E-4 550 0.064E-3 0.139E-5 0.325 0.93 11.0E-4 600 0.058E-3 0.137E-5 0.292 1.09 12.0E-4 File No.: 1901228.301P Page 24 of 41 Revision: 1 F0306-01R4
Table 7: Transient: Improper Start of Cold Recirculation Loop [6b]
h, nozzle h,vessel h, pipe h,vessel Time, sec T, °F Q, gpm Btu/hr-ft²-°F Btu/hr-ft²-°F Btu/ses-in²-°F Btu/sec-in²-°F 0 522 47800 4551 96 0.00878 0.02660 30 522 47800 4551 96 0.00878 0.02660 30.1 522 0 242 141 0.00047 0.03929 40 522 0 242 141 0.00047 0.03929 40.1 130 0 166 97 0.00032 0.02691 62 130 -5500 504 97 0.00097 0.02691 66 130 -5500 504 97 0.00097 0.02691 66.1 522 -5500 807 141 0.00156 0.03929 76 522 -5500 807 141 0.00156 0.03929 76.1 522 23900 2614 55 0.00504 0.01528 81 522 23900 2614 55 0.00504 0.01528 81.1 522 47800 4551 96 0.00878 0.02660 111 522 47800 4551 96 0.00878 0.02660 File No.: 1901228.301P Page 25 of 41 Revision: 1 F0306-01R4
Table 8: Recirculation Nozzle Path Polynomial Stress Coefficients Unit Pressure C0 C1 C2 C3 P1 51.705 -7.824 0.726 -0.032 P2 5.645 1.121 -0.152 0.011 P3 5.670 2.124 -0.060 0.010 P4 31.755 -3.989 0.564 -0.050 Maximum Thermal Transient C0 C1 C2 C3 P1 47.791 -30.663 4.884 -0.232 P2 51.940 -33.235 5.489 -0.274 P3 79.789 -96.639 30.034 -2.762 P4 82.632 -102.425 32.399 -3.044 Minimum Thermal Transient C0 C1 C2 C3 P1 13.785 -5.842 0.724 -0.029 P2 15.490 -5.495 0.614 -0.024 P3 35.566 -23.895 3.197 -0.074 P4 28.863 -18.790 1.931 0.033 Weld Residual C0 C1 C2 C3 P3 10.356 11.280 2.019 -0.008 P4 10.356 11.280 2.019 -0.008 Note: Refer to Figure 9 for the path locations of P1, P2, P3 and P4.
File No.: 1901228.301P Page 26 of 41 Revision: 1 F0306-01R4
Table 9: Deterministic Parameter Summary Parameter Value Ref.
Dimensions RPV Thickness (excludes cladding) 5.6875 inches [5]
RPV Radius (to vessel surface) 115.8750 inches [5]
Clad Thickness 0.1875 inches [5]
Operating Conditions (EPU)
Normal Operating Temperature (Region B) 551 °F [7]
Normal Operating Pressure (Region B) 1035 psig [7]
LTOP Event Temperature 100 °F [22]
LTOP Event Pressure 1200 psig [22]
Table 10: Probability of Detection (PoD) Distribution [11]
Flaw Size, in. Cumulative PoD 0.00 0.20 0.05 0.32 0.10 0.46 0.15 0.61 0.20 0.75 0.25 0.85 0.30 0.91 0.35 0.95 0.40 0.96 0.45 0.97 0.50 0.98 0.55 0.99 0.60 1.00 File No.: 1901228.301P Page 27 of 41 Revision: 1 F0306-01R4
Table 11: Random Variables Parameter Summary Random Parameter Mean Std Dev Distribution Ref.
Flaw density, nozzle/shell 1 per weld Mean Poisson [3,3,3]
weld (fabrication)
Flaw density, nozzle and nozzle/shell weld (SCC 1 per weld Mean Poisson [3,3,3]
initiation)
Flaw density, nozzle blend 0.1 per nozzle Mean Poisson [2,2,3]
radius (fabrication)
Flaw size (fabrication) n/a n/a PVRUF [3]
Flaw size (stress corrosion) Clad thickness n/a Constant [3,3]
8 Weld residual stress, inside surface 5 Normal [3,3,3]
through-wall (ksi) cosine distribution Clad residual stress (ksi)* 32 5 Normal [3,3,3]
% Cu 0.26 0.045 Normal [3,3,3]
% Ni 1.2 0.0165 Normal [3,3,3]
to shell Initial RTndt weld -20 13 Normal [3,3,3]
(F)
% Cu 0.09189 0.04407 Normal [2,2,3]
N1 nozzle % Ni 0.78 0.068 Normal [2,2,3]
forging Initial RTndt 24.13 26.48 Normal [2,2,3]
(F)
Fast neutron fluence 1.00e17 0.2 (20%) n/a [23,3]
(n/cm2)
KIC upper shelf (ksiin) 200 0 Normal [2,24,3]
Residual SCC initiation time (hr) = 84.2x1018()-10.5 y=0.9248x- Lognormal [2,3,3]
0.0003 K dependent Residual da/dt = 6.82x10-12(K)4 y=0.9085x- Weibull [18,3,3]
K >50 ksiin 0.3389 SCCG (in/hr)
K independent da/dt = 2.8x10-6, n/a n/a [18]
K <50 ksiin SCC threshold (ksiin) 10 2 Normal [2,3,3]
Residual Fatigue crack growth (FCG) da/dn=3.82 y=4.155x- Weibull [3, 3, 3]
(in/cycle) x10-9(dK)2.927 0.3712 FCG threshold (ksiin) 0 0 Normal [3, 3, 3]
- Note: The mean clad stress used already includes the effects of post-weld heat treatment.
File No.: 1901228.301P Page 28 of 41 Revision: 1 F0306-01R4
Table 12: Probability of Failure for Period of Extended Operation Probability of Failure (PoF) 25% inspection for 60-years of PEO Allowable PoF per Location Path (25% inspection for initial 40 years) year from PoF per year due to PoF per year due to NUREG-1806 [21]
Normal Operation (1) LTOP Event (1) (2)
Path 1 < 1.67 x 10-8 < 1.67 x 10-11 Nozzle Blend Radius Path 2 < 1.67 x 10-8 < 1.67 x 10-11 5.0 x 10-6 Path 3 < 1.67 x 10-8 < 1.67 x 10-11 Nozzle-to-Shell Weld Path 4 < 1.67 x 10-8 < 1.67 x 10-11 Notes:
(1) For all paths, no failures occurred in 1 million simulations with 25% inspection for 60 years.
(2) The LTOP PoF accounts for a 1x 10-3 probability of LTOP event occurrence per year
[3, pg 5-13].
File No.: 1901228.301P Page 29 of 41 Revision: 1 F0306-01R4
Figure 1: Solidworks 3D Model Note: Model dimensions are from Reference [5]. Circled dimensions are as-modeled to aid in the model development, as discussed in Section 3.2.1.
File No.: 1901228.301P Page 30 of 41 Revision: 1 F0306-01R4
Figure 2: Material Specification File No.: 1901228.301P Page 31 of 41 Revision: 1 F0306-01R4
Flow Rate Temperature 60000 600 50000 500 Flow Rate, gpm Temperature, °F 40000 400 30000 300 20000 200 10000 0 100
-10000 0 0 10 20 30 40 50 60 70 80 90 100 110 time, sec Figure 3: Improper Start of Cold Recirculation Loop, Sections 17-18 [6.b]
File No.: 1901228.301P Page 32 of 41 Revision: 1 F0306-01R4
Figure 4: FEM Thermal Loads and Boundary Conditions File No.: 1901228.301P Page 33 of 41 Revision: 1 F0306-01R4
Figure 5: FEM Static Loads and Boundary Conditions File No.: 1901228.301P Page 34 of 41 Revision: 1 F0306-01R4
(7a)
(7b)
Figure 6: Recirculation Nozzle-to-RPV Shell Finite Element Model File No.: 1901228.301P Page 35 of 41 Revision: 1 F0306-01R4
Figure 7: Unit Pressure Analysis Maximum Stress Intensity Location File No.: 1901228.301P Page 36 of 41 Revision: 1 F0306-01R4
Figure 8: Thermal Transient Analysis Maximum Stress Intensity Location File No.: 1901228.301P Page 37 of 41 Revision: 1 F0306-01R4
P2 P4 P1 P3 Figure 9: Stress Extraction Path Orientations in the N1 Nozzle File No.: 1901228.301P Page 38 of 41 Revision: 1 F0306-01R4
60 Path 1 Path 2 50 Crack Driving Stress (ksi)
Path 3 Path 4 40 30 20 10 0
0.0 2.0 4.0 6.0 8.0 10.0 12.0 Path length (in)
Figure 10: Unit Pressure Stress Distributions File No.: 1901228.301P Page 39 of 41 Revision: 1 F0306-01R4
Figure 11: Through-wall Stress Distributions, Thermal Transient (Improper Start of Cold Recirc. Loop)
File No.: 1901228.301P Page 40 of 41 Revision: 1 F0306-01R4
15.0 y = -0.0081x3 + 2.019x2 - 11.28x + 10.356 10.0 Weld Residua Stress (ksi) 5.0 0.0 0.0 2.0 4.0 6.0
-5.0
-10.0 weld thickness (inch)
Figure 12: Weld Residual Stress Distribution for Paths 3 and 4 File No.: 1901228.301P Page 41 of 41 Revision: 1 F0306-01R4
SUPPORTING FILES File No.: 1901228.301P Page A-1 of A-3 Revision: 1 F0306-01R4
Stress Analysis Supporting Files Filename Description Spreadsheet calculation of the nozzle and vessel BSEP_RecircNoz_Transient R1.xlxs shell heat transfer coefficient.
Solidworks nozzle-to-vessel component, Part Files
$ = safe-end
$.SLDPRT = safe-end weld
= nozzle-to-vessel
= cladding Nozzle-to-Vessel.SLDASM Model Assembly Solidworks File Nozzle-to-Vessel.x_t Model Assembly Parasolid File 1901228 Recir Nozzle R1.wbpj FEM ANSYS Workbench Project File 1901228 Recir Nozzle R1_file FEM ANSYS Workbench Project Folder Input File generated from Ansys Workbench
- _Workbench_Main.inp # = Press (Unit Pressure run)
= TTransient (Thermal Transient run)
Output File generated from Ansys Workbench
- _Workbench_Main.out # = Press (Unit Pressure run)
= TTransient (Thermal Transient run)
Macro that generate polynomial coefficients of GenStress.mac stress for all paths.
GETPATH.TXT Text File that defines stress paths Results File generated from Ansys Workbench
- .rst # = Press (Unit Pressure run)
= TTransient (Thermal Transient run)
Stress coefficients outputs
- = Press (Unit Pressure run)
- COE_%.CSV
= TTransient (Thermal Transient run)
% = P1, P2, P3, P4 BSEP_RecircNoz_StressCoeff R1.xlsx Path Polynomial Distribution Summary File No.: 1901228.301P Page A-2 of A-3 Revision: 1 F0306-01R4
Probabilistic Fracture Mechanics Supporting Files File Name Description Path1.INP VIPERNOZ input and output files for Path 1 at nozzle blend radius.
Path1.OUT Path2.INP VIPERNOZ input and output files for Path 2 at nozzle blend radius.
Path2.OUT Path3.INP VIPERNOZ input and output files for Path 3 at nozzle-to-shell-weld.
Path3.OUT Path4.INP VIPERNOZ input and output files for Path 4 at nozzle-to-shell-weld.
Path4.OUT VIPERNOZ1p1.EXE VIPERNOZ executable program ISPCTPOD.EXE VIPERNOZ probability of detection curve input file FLWDSTRB.EXE VIPERNOZ flaw size distribution curve input file File No.: 1901228.301P Page A-3 of A-3 Revision: 1 F0306-01R4