ML15322A091
Text
V Structural Integrity Associates, Inc.Y File No.: 1001527.303 Project No.: 1001527CALCULATION PACKAGE Quality Program:
[] Nuclear [] Commercial PROJECT NAME:Plant Hatch Unit l&2 P-T Curve Evaluation CONTRACT NO.:P0: SNG10018845, Rev. 0 CONTRACT:
19862, Rev. 0CALCULATION TITLE:Feedwater, Water Level Instrument, and Core DP Nozzle Fracture Mechanics Evaluation for Hatch Unit 1dLIu UIII L r I~uI Lullli '.uL w JVW1Up1L~11 Document Affected Project Manager Preparer(s)
&Revision Pages Revision Description Approval Checker(s)
Signature
& Date Signatures
& Date01 -30 Initial Issue Responsible Eni~ineer D. V. Sommerville D. V. Sommerville 12/30/2011 12/30/2011 Responsible Verifiers M. Qin*12/30/2011 T. J. Griesbach 12/30/2011 Page 1 of 30F0306-01R1
$jmSbiwbra kIturity Associates, Inc.=Table of Contents1.0 OBJECTIVE
...................................................................................
42.0 METHODOLOGY.............................................................................
42.1 Unit and Nozzle Specific Methodology Overview
...............................
62.1.1 Fee dwater Nozzle .....................................................................
62.1.2 Water Level Instrument Nozzle ......................................................
72.1.3 Core Differential Pressure Nozzle...................................................
82.2 2-D FEM Correction Factor ........................................................
82.3 Boundary Integral Equation
/ Influence Function Methodology
...............
102.4 WRC Bulletin 175 Methodology
..............
..................................
112.5 ASME XI, G-22 14.3 Methodology for Radial Thermal Gradients
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123.0 DESIGN INPUTS...................................
- .......................................
124.0 ASSUMPTIONS............................................................................
135.0 CALCULATIONS
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- ....................................................
145.1 Hatch Uniti1........................................................................
145.1.1 Feedwater Nozzle ....................................................................
145.1.2 Water Level Instrument Nozzle......
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155.1.3 Core Differential Pressure Nozzle .................................................
155.2 Hatch Unit 2........:................................................................
165.2.1 Feedwater Nozzle ....................................................................
165.2.2 Water Level Instrument Nozzle.............................................
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175.3 Justification for Linear Scaling of Thermal Stress Intensity Factor Solutions 176.0 SUMMARY OF RESULTS...............................................................
1
87.0 REFERENCES
.............................................................................
18File No.: 1001527.303 Page 2 of 30Revision:
$jsbcrm~raI tor~ly Associates, Inc.=List of TablesTable 1 : Hatch Unit 1 FW Nozzle Blend Radius Path Stress Distributions
...................
22Table 2: Hatch Unit 2 FW Nozzle Blend Radius Path Stress Distributions...................
23Table 3: Hatch Unit 1 Core DP Nozzle 1000 psi Internal Pressure Load CasePath Stress Distribution................................................................
24Table 4: Hatch Unit 1 FW Nozzle K1p and KIT using the BIB/IF Methodology...............
25Table 5: Hatch Unit 2 FW Nozzle K1p and KIT using the BIB/IF Methodology................
25Table 6: Hatch Unit 1 Core DP Nozzle K1p using the BIB/IF Methodology...................
25Table 7: Hatch Unit 1 FW Nozzle K1p using the WRC Bulletin 175 Methodology...........
25Table 8: Hatch Unit 1 Core DP Nozzle K1p using the WRC Bulletin 175 Methodology.....25 Table 9: Hatch Unit 2 FW Nozzle K1p using the WRC Bulletin 175 Methodology...........
26Table 1.0: Summary of Nozzle K1t Results Using the BIB/IF andG-221 14.3 Methodologies.................................
i.............................
26Table 11 : Maximum Stress Intensity Factor for WLI Nozzle Considering Thermal Load Cases......................................................
- .............
26Table 12: Summary of Nozzle Stress Intensity Factors .........................................
27List of FiguresFigure 1. Typical Nozzle Corner Crack Stress Extraction Path Orientation...................
28Figure 2. WRC Bulletin 175, Figure A5-i, Bstimates of Stress Intensity Factorsfor Flaws at a Nozzle Corner ..................................................
........28Figure 3. Hatch Unit 1 FW Nozzle Blend Radius Path Stress Distributions...................
29Figure 4. Hatch Unit 2 FW Nozzle Blend Radius Path Stress Distributions...................
29Figure 5. Hatch Unit 1 Core DP Nozzle 1000 psi Internal Pressure Load CasePath Stress Distribution................................................................
30Figure 6. Plant C WLI Nozzle KIT for Three Thermal Transients
..............................
30File No.: 1001527.303 Page 3 of 30Revision:
1.0 OBJECTIVE
The objective of this calculation is to calculate the Mode I stress intensity
- factors, KI, for the Edwin I.Hatch Unit 1 and Unit 2 Feedwater (FW) nozzles and Water Level Instrument (WLI) nozzles, and theUnit 1 Core Differential Pressure (DP) nozzle, necessary for creation of the Pressure-Temperature (P-T)limit curves for the pressure test (Curve A), core not critical (Curve B) and core critical (Curve C)conditions for the Hatch Unit 1 and Unit 2 reactor pressure vessels (RPV). Both internal pressure andthermal transient load cases are considered.
2.0 METHODOLOGY
Consistent with the Structural Integrity Associates, Inc. (SI) Boiling Water Reactor (BWR) P-T CurveLicensing Topical Report (LTR) [1], the FW nozzle is normally taken as the limiting component in thenon-beltline region of the RPV. This assumption is made because:1. The geometric discontinuity caused by the nozzle penetration in the RPV shell causes a stressconcentration which results in larger pressure induced stresses than would be calculated in theshell regions of the RPV,2. The FW nozzle experiences more severe thermal transients than most of the other nozzlesbecause of the feedwater injection temperature which causes larger thermal stresses than areexperienced in the shell regions of the RPV,3. Although some other nozzles can experience thermal transients which would cause thermalstresses larger than those calculated for the shell regions of the RPV and some nozzles are largerdiameter than the FW nozzle, which could result in a slightly larger KIp, the combined stressesfrom the applied thermal and pressure loads are considered to bound all other non-beltline discontinuities.
The Hatch Unit 1 and Unit 2 Adjusted Reference Temperature calculations
[2] identify the WLI nozzleas contained within the beltline region of both the Unit 1 and Unit 2 RPV. Consequently, the effects ofthese nozzles must be considered in the beltline P-T curve development.
These nozzles will cause astress intensification in the beltline shells. Further, since the beltline region experiences a reduction intoughness caused by neutron irradiation, it is not obvious whether the FW nozzle will bound the WLINozzle throughout the life of Hatch Unit 1 and Unit 2. Consequently, the effects of the WLI Nozzle onthe beltline P-T curves must be specifically considered.
The SI P-T Curve LTR [1] addresses the bottom head penetrations by conservatively applying a stressconcentration factor (SCF) of 3.0 for a hole in a flat plate to the pressure induced membrane stress in thebottom head shell and using the thermal stress intensity factor solution given in ASME XI, Non-mandatory Appendix G, Paragraph G-22 14.3 [8]; discussed below. Review of the Hatch Unit 1 generalassembly drawing [30] shows that the Core DP nozzle exists in the thinnest section of the bottom head.Based on prior experience from a similar bottom head design, application of the conservative SCF=3.0methodology to the Core DP nozzle penetration will result in a bottom head P-T curve which controlsthe entire RPV. Consequently, a detailed evaluation of the Core DP nozzle is performed to removeexcess conservatism.
File No.: 1001527.303 Page 4 of 30Revision:
0F0306-01R1 Consistent with 10OCFR50 Appendix G [3] the RPV P-T curves are applicable for normal operation andall anticipated operating occurrences.
Consequently, all Level A and Level B (Normal and Upset)operating events defined on the RPV, FW nozzle, WLI nozzle, and Core DP nozzle thermal cyclediagrams (TCD) [4, 5, 6] are considered in selecting bounding thermal and pressure conditions forpreparing P-T curves.The SI P-T Curve LTR [1 ] identifies acceptable methodologies for calculating applied pressure andthermal stress intensity factors for postulated nozzle corner flaws. These methodologies include:Pressure Load Case:1. Welding Research Council Bulletin 175 [7]2. Boundary Integral Equation
/ Influence Function (BIE/IF)
[1]*Thermal Transient Load Case:1. BIB/IF [1]2. ASME XI, Non-mandatory Appendix G, Paragraph G-2214.3
[8]The WRC Bulletin 175 [7] methodology for calculating a KI for an internal pressure load case isconvenient to apply since no nozzle specific finite element analysis (FEA) is necessary.
The only inputsrequired are the nozzle and vessel geometry and the hoop stress calculated for the vessel shell, remotefrom discontinuities.
The BIB/IF methodology is applicable to any load case provided that a third order polynomial curve fitto the applicable stress distribution is available.
The appropriate path for a postulated nozzle cornercrack has a path origin located at the peak stress location in the blend radius for the pressure load caseand it is oriented parallel to a 45° line through the nozzle, as shown in Figure 1. This methodology requires detailed stress distributions through the nozzle blend radius which are typically obtained from aplant specific FEA.The flat plate thermal stress intensity factor solution given in the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel (B&PV) Code Section XI, Non-mandatory Appendix G,Paragraph G-22 14.3 [8] is considered to be a conservative, simplified methodology for obtaining the KITat the nozzle corner path resulting from a heat-up/cool-down transient of constant rate (i.e. 100 °F/hr),when the wall thickness is taken asthe path length along the 450 path identified in Figure 1. Thisapproach is considered to be conservative because:1. Geometric discontinuities do not intensify thermal stresses in a manner similar to stresses frommechanical loading; thus, fracture mechanics solutions which inherently consider the nozzlegeometry are not necessarily
- required,
- 2. Thermal stresses increase as section thickness increases because the differential thermal strainincreases with thickness.
Consequently, the practice of taking a wall thickness determined by thepath length of the 450 path results in a thicker wall.File No.: 1001527.303 Page 5 of 30Revision:
Integrit Associates, Inc:SI has prepared a complementary P-T Curve LTR [9] which provides simplified methods for calculating the K~p and KIT for the BWR WLI nozzles.
This method is convenient since the necessary stressintensity factors can be calculated using simple geometry and material properties data without the needfor a plant specific FEA.The methods identified above are used in this calculation to calculate stress intensity factors for theHatch Unit 1 and Unit 2 FW nozzles and WLI nozzles, and the Unit 1 Core DP nozzle. The sectionsbelow identify the general methodology applied for each nozzle at each unit.2.1 Unit and Nozzle Specific Methodology OverviewThe specific methodologies used to calculate the Kjp and KIT for the FW nozzle, the WLI nozzle, and theCore DP nozzle are discussed separately below.2.1.1 Feedwater NozzleVarious FW nozzle fracture mechanics analyses have previously been performed for Hatch Unit 1 [10]and Unit 2 [11] to satisfy the requirements of NUREG-0619
[ 12] regarding FW nozzle rapid thermalcycling caused by leakage past the thermal sleeve seals. The load cases necessary for development ofP-T curves and those required to address NUREG-06 19 are similar.
Consequently, the previousevaluations performed for Hatch Units 1 and 2 will be utilized, as appropriate, for the present evaluation.
The following methodology is used:Internal Pressure Load Case1. Pressure stress distributions reported in References
[10, 11] for Hatch Unit 1 and Unit 2 are takenfor the 1000 psig internal pressure load case.2. Recognizing that the Reference
[10, 11] evaluations were performed using a 2-D axi-symmetric finite element model (FEM) and that it is known that the stress intensification caused by thenozzle geometry is under predicted in a 2-D axi-symmetric representation of the nozzle, acorrection factor must be applied to the stresses obtained from the 2-D axi-symmetric FEM. Theinternal pressure load case stresses, in the nozzle blend radius region, are corrected using themethodology presented in Reference
[13]. Plant specific dimensions are used to calculate thecorrection factor.3. The BIE/IF methodology presented in the SI P-T Curve LTR [1] is used to calculate K~p byfitting a third order polynomial equation to the path stress distribution for each plant specificpressure load case. The resulting K1p can be linearly scaled to determine the K1p for various RPVinternal pressures.
- 4. 'The methodology given in WRC Bulletin 175 [7] is used to obtain an independent confirmation of the K1p calculated for each unit. The resulting K1p can be linearly scaled to determine the K~pfor various RPV internal pressures.
File No.: 1001527.303 Page 6 of 30Revision:
0F0306-01RI iuru hItud Associates, Inc."Thermal Transient Load Case1. Thermal shock load case path stress distributions reported in References
[10, 11] for Hatch Unit1 and Unit 2 are taken. The FW nozzle thermal shock is the most severe Level A/B thermaltransient for the FW nozzle; thus, the load case considered in References
[10, 11] is appropriate for P-T curve calculations.
When path stress distributions at multiple times are presented inReferences
[10, 11 ] the bounding distribution is selected for the current evaluation.
- 2. The BIE/IF methodology presented in the SI P-T Curve LTR [1] is used to calculate KIT byfitting a third order polynomial equation to the path stress distribution for each plant specificthermal shock load case. The resulting KIT can be linearly scaled to determine the KIT forvarious shock amplitudes.
- 3. A KIT for a uniform 100 °F/hr and 200 "F/hr heat-up/cool-down transient is calculated using theequation given for a radial thermal gradient in ASME XI, Appendix G, Paragraph G-22 14.3 [8]4. Results from various plant specific evaluations are presented to support the use of G-22 14.3 [8]for calculating KIT for 100 "F/hr and 200 0F/hr heat-up/cool-down transients.
2.1.2 Water Level Instrument NozzleSimplified methods for calculating the K~p and KIT for the WLI nozzles in General Electric designedBWRs are given in Reference
[9], which is a companion LTR to the P-T curve LTR [1]. The K~p andKIT terms are calculated using Equations (8-1) and (8-2) of Reference
[9], which are repeated below, forconvenience, as Eq. (1) and Eq. (2):K1Pesue .94~ ~1000Q psig internal pressure (1)KIRa,np =
++/-t,)]- 20.715, 100 °F/hr cooldown transient (2)Where: R is the inside radius of the pressure vessel, intv is the wall thickness of the pressure vessel, intn is the thickness of the WLI nozzle insert near the postulated cracklocation, inoa is the coefficient of thermal expansion at the highest temperature inthe transient, in/in/°FThe units of Ki in Eq. (1) and Eq. (2) are ksi-in°5.File No.: 1001527.303 Page 7 of 30Revision:
0F0306-01R1 jS b-c orl Aitii~ ssociates, In.=2.1.3 Core Differential Pressure NozzleThe following methodology is used:Internal Pressure Load Case:1. The methodology given in WRC Bulletin 175 [7] is used to calculate the K1p. The resulting K1pcan be linearly scaled to determine the K~p for various RPV internal pressures.
- 2. Since a 2-D axi-symmetric finite element analysis of a Core DP nozzle for a plant with a similardesign has previously been performed for development of P-T curves [28], and since thedimensions of the Core DP nozzle modeled [29], in the vicinity of the bottom head penetration, are identical to Hatch Unit 1 [30], the results of the previous Core DP nozzle evaluation may beused to obtain an independent benchmark of the K1p obtained using the WRC Bulletin 175 [7]methodology.
- 3. A path stress distribution, in the vicinity of the Core DP nozzle, caused by a 1000 psig internalpressure load case, is taken from Reference
[28]. The location and orientation of the path areconsistent with that used for nozzle evaluations.
- 4. The BIE/IF methodology presented in the SI P-T Curve LTR [1] is used to calculate K1p byfitting a third order polynomial equation to the path stress distribution for the plant specificpressure load case.Thermal Transient Load Case:1. Similar to the methodology given in the P-T Curve LTR [1], a KIT for a uniform 100 °F/hr and200 0F/hr heat-up/cool-down transient is calculated using the equation given for a radial thermalgradient in ASME XI, Appendix G, Paragraph G-22 14.3 [8]2. Results from various plant specific evaluations are presented to support the use of G-2214.3
[8]for calculating KIT- for 100 0F/hr and 200 °F/hr heat-up/cool-down transients.
2.2 2-D FEM Correction FactorWhen a cylindrical nozzle intersection with a cylindrical pressure vessel is modeled using a 2-D axi-symmetric simplification, the geometry is approximated as a nozzle intersection with a spherical shell.This simplification results in a non-conservative treatment of the geometric discontinuity at the blendradius region as well as a resulting reduction in the far field membrane stress in the shell caused by theapproximation of the pressure vessel as a sphere rather than a cylinder.
Consequently, stress resultsobtained from a 2-D axi-symmetric FEM, for mechanical loads such as pressure, must be corrected before they can be used in subsequent analyses.
Sommerville and Walter [13] describe a methodology for correcting stress distributions obtained from the nozzle blend radius region of 2-D axi-symmetric models. The correction factor is given in Reference
[13] as:File No.: 1001527.303 Page 8 of 30Revision:
~jSbircraI laturif Associatus, Inc:SCF3DHoCF = 2. 3DHo (3)SCF2D)_HoopWhere: SCF3DHoop is the stress concentration factor (SCF) defined with respect to thethe hoop stress direction, for the 3D geometry.
SCF2DHoop is the stress concentration factor for the 2D geometry.
The expected SCF for the 3-D geometry can be estimated using the following equation for a circularhole in a pressurized cylinder
[14]:For 0132,K(, (/) = 2.5899 +0.8002.13+/-+4.0112.132
_-1.8235-/83
+ 0.3751 ./34 (4a)~j.( 2)f2 " (4b)Where: Kt(I3) is the SCF defined with respect to the far field hoop stress, PR/t.v is the Poisson's ratio of the material, assumed equal to 0.3.r is the radius of the nozzle bore, inR is the inside radius of the pressure vessel, intv is the wall thickness of the pressure vessel, inKt(t3) is used for the SCF3D)_Hoop term in Eq. (3). The SCF2DHoop can be calculated from the results of the2-D axi-symmetric FEM by calculating the SCF using the following equation:
2 ., O'totl,max (5)SCF2-H°°P = P. RWhere: P is the RPV internal pressure for the pressure load case, psiO'total,max is the largest total hoop stress in the blend radius region, psiInserting Eq. (5) and Eq. (4a, 4b) into Eq. (3) gives the correction factor which can be used to uniformly scale the pressure load case path stress distribution from the 2-D axi-symmetric FEM. This path stressdistribution can then be fit with the equation for a 3rd order polynomial and used with the BIE/IFsolution described in Reference
[1], and discussed below, to obtain Kjp.File No.: 1001527.303 Page 9 of 30Revision:
0F0306-01R1 mIhtugril Associates, Inc.=2.3 Boundary Integral Equation
/ Influence Function Methodology The following discussion is excerpted from the SI P-T curve LTR [1]. Note that the equation andreference numbers in the excerpt below refer to Reference
[1]:The stress intensity factors for the feedwater nozzle may be calculated using theresults of a detailed finite element model of the nozzle. In some cases, such resultsmay already be available from the governing design basis stress report for thefee dwater nozzle. The details of the finite element process are not included here,"rather, the extraction of the. appropriate finite element results and their use indeveloping P-T limit curves is discussed.
For a path through the limiting nozzle inner blend radius corner, as shown inFigure 2-7, the thermal and pressure hoop stress distributions should be extracted from the finite element model. Each of the stress distributions should befit with athird-order polynomial that reasonably fits the calculated stresses in the region ofinterest.
The thermal stress intensity factor, K1t, is computed based on either of the nozzlecorner solutions shown in Figure 2 -8 for a postulated 1/4t (based on the sectionthickness) axial defect, as follows."
K1, = [ 0.723 C0, + 0.55 1 ~1)C1, + 0.462~Z C2, + 0.408 j J C3,] (2.5.3-3 a)K1, V~[O.06C~
+0.53 C1 + .44~ i~j C, +/-.39~jj ~ 3~j(2.5.3-3b) where: Kit the thermal stress intensity factor for the limitingnormal/upset transient (psi inc)a = 1/4tpostulatedflaw depth (inches)t = thickness of the cross-section through the limitingnozzle inner blend radius corner, as Shown inFigure 2- 7.Co,, C1,., C2,, C3, thermal stress polynomial coefficients based on fitsto finite element analysis.
File No.: 1001527.303 Page 10 of 30Revision:
$bSl wc~ Ilte! grit Associates, Inc.=Equation 2.5.3-3 a is based upon a Boundary Integral Equation
/ Influence Function(BIE/IF) solution developed for a quarter crack in an infinite quarter space.Equation 2.5. 3-3b is the average of the BIE/IF solutions developed for a quartercrack in an infinite quarter space and a semicircular crack in an infinite half space.These equations have been investigated by the NRC and Oak Ridge NationalLaboratory and shown to be acceptable for use in calculating the applied stressintensity factor for a corner cracked nozzle [16]. Although both solutions givenabove are evaluated in Reference
[16], it is acknowledged by the original authorsof these formulations, in the basis work used to develop the approach
[171, that thetwvo formulations differ very little and in fact provide KI values which differ only byapproximately 5%. This can be seen by review of the coefficients used in eachequation above. Consequently, either Equation 2.5.3-3 a or 2.5.3-3b may be usedfor any nozzle configuration in a BWR.The BIE/IF solution introduced above is applicable to any load case and any BWRnozzle; thus, it is applied both to the internal pressure and thermal transient loadsconsidered for P-T curve development.
2.4 WRC Bulletin 175 Methodology An alternative solution for determining the applied pressure stress intensity factor, Kip, is to use themethod given in Appendix 5 of WRC Bulletin
.175 [7], where:K1~ zFar~.P l~ (6Where: K1p is the applied pressure stress intensity factor, psi icP is the operating
- pressure, psia is the 1/4t postulated flaw depth, inchesR is the vessel inner radius, inchesis the thickness of the vessel shell, inchesF(a/r,) is the shape factor given in Figure 2, where rn ri + 0.29rc,ri is the actual inner radius of nozzle, inchesrc is the nozzle blend radius, inchesA functional form of F(a/rn) is given in Reference
[15, Pg. 11.1-17]
as:= .42 .0 .46 (7)Where, Eq. (7) is applicable for 0.,07 < a/rn< 0.9.File No.: 1001527.303 Page 11 of 30Revision:
$jtSinwwrul I~l~itedt Associates, Inc.*2.5 ASME XI, G-2214.3 Methodology for Radial Thermal Gradients ASME XI, Non-mandatory Appendix G, Paragraph G-22 14.3 [8] gives the following, simplified methodfor calculating KIT for a radial thermal gradient:
Kt =-0.953.10-3**CR. tv25 (8)Where: CR is the cooldown rate, 0F/hr.tv is the thickness of the vessel shell, inchesParagraph G-22 14.3 [8] states that Eq. (8) will yield conservative results if used for cool-down ratesgreater than 100 °F/hr.This methodology is used to calculate the KIT in the nozzle blend radius region by using the path lengthalong the 450 path shown in Figure 1 as the shell thickness, tv.3.0 DESIGN INPUTSThe following design inputs are used for this evaluation:
- Previous NUREG-0619 evaluations:
References
[10, 11]* Core DP Nozzle evaluation:
Reference
[28]* Thermal transient definitions for Level A/B: References
[4, 5, 6]* WLI Nozzle dimensions and material:
Reference
[16]Hatch Unit 1 :Nozzle insert material:
- Inconel, SB- 166RPV inside radius: 110.375 inchesNozzle insert thickness:
0.28 1 inchesVessel shell thickness:
5.375 inchesNote." Some drawings show a shell thickness of 5.875 inches;"
- however, theminimum dimension given in the general arrangement drawing is used for thisevaluation.
Hatch Unit 2:Nozzle insert material:
- Inconel, SB- 166RPV inside radius: 110.375 inchesNozzle insert thickness:
0.66 1 inchesVessel shell thickness:
5.375 inchesFile No.: 1001527.303 Page 12 of 30Revision:
$j~biicfriru Iutugdty Associates, Inc.e* FW Nozzle dimensions:
Hatch Unit 1:Nozzle bore diameter:
Nozzle blend radius:RPV inside radius:Vessel shell thickness:
Hatch Unit 2:Nozzle bore diameter:
Nozzle blend radius:RPV inside radius:Vessel shell thickness:
- Core DP Nozzle dimensions:
Hatch Unit 1:Vessel shell thickness:
Bottom head radius:Nozzle inside radius:* Material Properties:
Hatch Unit 1 and Unit 2 WLI Nozzle Insert:Coefficient of thermal expansion:
Poisson's ratio:Reference
[ 17]6.7 inches2.5 inches110.375 inches5.375 inches6.5 inches5.0 inches110.375 inches5.375 inchesReference
[30]3.188 inches110.5 inches1.250 inches, see assumption 3.Reference
[ 18]7.7x106 in/ir/°F at 550 0F0.3 (assumed)
4.0 ASSUMPTIONS
The following assumptions are used in this calculation and supported by data presented below:1. The thermal stress intensity factor, KIT, for a 200 °F/hr thermal transient can be conservatively calculated using Eq. (8) above for vessel shells and forged vessel nozzles, where the shellthickness in the equation is taken as the vessel shell thickness when evaluating the shell, and thenozzle blend radius path length when evaluating forged nozzles.
Adequacy of this assumption isdemonstrated in Section 5.3 below.2. The thermal stress intensity factor, KIT, for a 200 °F/hr thermal transient can be conservatively calculated using Eq. (2) above for a WLI nozzle by scaling the KIT obtained from Eq. (2) by 2.Similarly higher heat-up/cool-down rates can be addressed by appropriate scaling factors.Adequacy of this assumption is demonstrated in Section 5.3 below.File No.: 1001527.303 Revision:
0Page 13 of 30F0306-01RI
$b~ml inc.=3. The stress concentration effect of the Core DP penetration in the bottom head is conservatively addressed by treating the penetration as a nozzle in which the radius considered in the WRCBulletin 175 pressure stress intensity methodology is taken as the radius of the hole in the shellrather than the ID of the Core DP penetration.
This assumption is validated in Section 5.1.3below by comparing the KIP obtained using this approach with the KIP obtained using theBIB/IF methodology.
5.0 CALCULATIONS
The calculations for the FW nozzles, WLI nozzles, and Core DP nozzle are presented for each unit,separately, below.5.1 Hatch Unit 1The calculations for the FW, WLI, and Core DP nozzles are presented in separate sections.
5.1.1 Feedwater NozzleTable 1 presents a tabulation of the path stress distribution taken from the Unit 1 plant specific FWnozzle FEM, in the blend radius region of the nozzle. Both the 1000 psig internal pressure and 450 0Fthermal shock load case path stress distributions are taken from Reference
[i10a]. The thermal transient load case path stress distribution is fit with a 3rd order polynomial equation.
In the previous evaluation
[10a], the pressure load case path stress distribution was corrected using a different methodology thanutilized for the present calculation; therefore, this correction factor is removed before the correction factor calculated using the methodology described in Section 2.2 is applied.
The corrected pressure pathstress distribution is fit with a 3rd order polynomial equation.
The Hath Unit 1 FW nozzle correction factor is calculated below:r = 6.7 in FW nozzle bore radiusR = 110.38 in RPV radius adjacent to FW nozzletv= 5.38 in RPV shell thickness adjacent to FW nozzle3=- 0.177 -Eq. (4)Kt 2.85 -SCF for hole in cylinder, Eq. (4)SCF20= 2.38 -SCF from 2-D axi-symmetric FEA, Eq. (5)CF = 2.39 -Correction factor, Eq. (3)Figure 3 is a plot of the pressure and thermal shock path stress distribution in the Hatch Unit 1 FWnozzle blend radius region with the polynomial curve fit equations and correlation coefficients shown.Table 4 summarizes the polynomial coefficients for each load case and presents the Kip and KIT for theHatch Unit 1 FW nozzle.Table 7 presents the K1p calculated using the WRC Bulletin 175 methodology
[7].File No.: 1001527.303 Page 14 of 30Revision:
$b~o~grl Associates, Inc.=Recognizing that the BIB/IF methodology has been shown to provide conservative estimates of the stressintensity factors for both pressure and thermal load cases [19, 20] and that both the WRC Bulletin 175[7] and BIE/IF [1] methodologies are accepted methods for calculating the KI from the pressure loadcase, the lower KI is used for this evaluation.
Reference
[10Ob] identifies that the extended power uprate conditions result in an increase in the RPVdome pressure of 50 psig (1000 psig to 1050 psig) and an increase in the FW fluid temperature of 6 °F(450 °F to 456 'F). The increase in dome pressure is accommodated by linear scaling during preparation of the P-T curves in a subsequent calculation.
The increase in the FW fluid temperature is a change ofless than 1.5%. The work documented in References
[19, 20] shows that the BIB/IF methodology issignificantly conservative (on the order of 30-50% when compared to the RMS K1 calculated from a 3-Dfinite element fracture mechanics evaluation) for the 1/4 thickness flaws required for P-T curves;consequently, the KIT calculated for the 450 °F shock is not further increased in this evaluation toaccount for the small increase in FW temperature.
5.1.2 Water Level Instrument NozzleUsing Eq. (1) and (2) and considering Hatch Unit 1 WLI nozzle dimensions and material properties, theK1p and KIT are calculated below:tv= 5.38 in RPV shell thickness adjacent to WLI nozzleR = 110.38 in RPV radius adjacent to WLI nozzletn= 0.28 1 in WLI nozzle thickness cx 7.70E-06 in/in/OF Thermal expansion coefficient for nozzle material,
- Inconel, 550 'FK = 71.6 ksi-in0.5 1000 psi pressure stress intensity factor, Eq. (1)KIT = 17.4 ksi-in0.5 100 'F/hr cool-down transient stress intensity factor, Eq. (2)KIT= 34.8ksi-n 05 200 'F/hr cool-down transient stress intensity factor, Eq. (2) scaled by aKXT = 34.8ksi'n°'S factor of 25.1.3 Core Difjferential Pressure NozzleThe K1p calculated using the WRC Bulletin 175 methodology
[7] is shown in Table 8.The pressure path stress distribution is extracted from Reference
[28]. The stress distribution istabulated in Table 3 and plotted in Figure 5. Because of the orientation of the path and the configuration of the nozzle, which contains a tube which penetrates the RPV, the path stress distribution exhibits alower stress at the path origin than slightly inboard along the path. Consequently, the 3rd orderpolynomial equation is fit to the stress distribution, after omitting the first point along the curve. Thecurve fit and equation are shown in Figure 5. The resulting polynomial coefficients and K1p obtainedusing the BIB/IF methodology are listed in Table 6.File No.: 1001527.303 Page 15 of 30Revision:
$j~bvg~aunIlatgrily ssoca~tes, Inc.'The K~p calculated using the BIE/IF methodology
[1] benchmarks well against the K1p calculated usingthe WRC Bulletin 175 methodology
[7]. Recognizing that the BIE/IF methodology has been shown toprovide conservative estimates of the stress intensity factors for both pressure and thermal load cases[ 19, 20] and that both the WRC Bulletin 175 [7] and BIE/IF [1 ] methodologies are accepted methods forcalculating the K1 from the pressure load case, the lower KI is used for this evaluation.
The KIT term is calculated using Eq. (8) and is presented in Table 12 for heat-up/cool-down rates of 1000F/hr and 200 0F/hr. Section 5.3 provides justification for using the ASME XI, Non-mandatory Appendix G, Paragraph G-2214.3
[8] methodology for heat-up/cool-down rates greater than 100 0F/hr.5.2 Hatch Unit 2The calculations for the FW and WLJ nozzles are presented in separate sections.
5.2.1 Feedwater NozzleTable 2 presents a tabulation of the path stress distribution taken from the Unit 2 plant specific FWnozzle FEM, in the blend radius region of the nozzle. Both the internal pressure and thermal shock loadcase path stress distributions are taken from Reference
[11 la]. The thermal transient load case path stressdistribution is fit with a 3r order polynomial equation.
In the previous evaluation
[1 la], the pressureload case path stress distribution was corrected using a different methodology than utilized for thepresent calculation; therefore, this correction factor is removed before the correction factor calculated using the methodology described inSectioh 2.2 is applied.
The corrected pressure path stressdistribution is fit with a 3rd order polynomial equation.
The Hath Unit 2 FW nozzle correction factor is calculated below:r = 6.5 in FW nozzle bore radiusR = 110.38 in RPV radius adjacent to FW nozzlet-- 5.38 in R!PV shell thickness adjacent to FW nozzle13= 0.172 -Eq. (4)Kt 2.84 -SCF for hole in cylinder, Eq. (4)SCF2D = 2.05 -SCF from 2-D axi-symmetric FEA, Eq. (5)CF = 2.77 -Correction factor, Eq. (3)Figure 4 is a plot of the pressure and thermal shock path stress distribution in the Hatch Unit 2 FWnozzle blend radius region with the polynomial curve fit equations and correlation coefficients shown.Table 5 summarizes the polynomial coefficients for each load case and presents the K1p and KIT for theHatch Unit 2 FW nozzle.Table 9 presents the K1p calculated using the WRC BUlletin 175 [7] methodology.
File No.: 1001527.303 Page 16 of 30Revision:
hi/t egd/ty Associateus, Inc."Recognizing that the BIE/IF methodology has been shown to provide conservative estimates of the stressintensity factors [19, 20] and that both the WRC Bulletin 175 [7] and BIE/IF [1] methodologies areaccepted methods for calculating the KI from the pressure load case, the lower K1 is used for thisevaluation.
Reference
[1 lc] identifies that the extended power uprate conditions result in an increase in the RPVdome pressure of 50 psig (1000 psig to 1050 psig) and an increase in the FW fluid temperature of 6 0F(delta T from 450 0F to 456 0F). The increase in dome pressure is accommodated by linear scalingduring preparation of the P-T curves in a subsequent calculation.
The increase in the FW fluidtemperature is a change of less than 1.5%. The work documented in References
[19, 20] shows that theBIE/IF methodology is significantly conservative (on the order of 3 0-50% when compared to the RMSK1 calculated from a 3-D finite element fracture mechanics evaluation) for the 1/4 thickness flawsrequired for P-T curves; consequently, the KIT calculated for the 450 0F shock is not further increased inthis evaluation to account for the small increase in FW temperature.
5.2.2 Water Level Instfrument NozzleUsing Eq. (1) and (2) and considering Hatch Unit 2 WLI nozzle dimensions and material properties, theK~p and KIT are calculated below:tv= 5.38 in RPV shell thickness adjacent to W/LI nozzleR = 110.38 in RPV radius 'adjacent to WLI nozzletn= 0.66 1 in WLI nozzle thickness ct= 7.70E-06 in/in/°F Thermal expansion coefficient for nozzle material,
- Inconel, 550 0FKw= 80.0 ksi-in°'s 1000 psi pressure stress intensity factor, Eq. (1)KI1 = 19.9 ksi-in°'s 100 °F/hr cooldown transient stress intensity factor, Eq. (2)200 °F/hr cooldown transient stress intensity factor, Eq. (2) scaled by a factorKIT = 39.9 ksi-in°'s of 2.05.3 Justification for Linear Scaling of Thermal Stress Intensity Factor Solutions Data is presented in this section which supports the Assumptions 1 and 2 identified in Section 4.0.Table 10 summarizes the KIT calculated for four nozzles from three separate BWRs. Both a 100 0F/hrand a 300 0F/hr cool-down rate were evaluated.
Both the BIE/IF methodology
[1] and the methodology given in ASME XI, Non-mandatory Appendix G, Paragraph G-22 14.3 [8] were used to calculate KIT.The results confirm that the simplified method given in Paragraph G-22 14.3 [8] may be used to obtain aKIT. Further, as suggested in WRC 175 [7] and G-2214.3
[8] use of this methodology is expected to beincreasingly conservative for cool-down rates larger than 100 0F/hr. This trend is seen in the two KITresults Obtained for Plant .C at 100 0F/hr and 300 0F/hr, where it is shown that the KIT calculated usingthe flat plate solution exceeds that calculated using the BIB/IF methodology by a ratio of 2.34 for a 1000F/hr ramp rate and 2.71 for ai 300 0F/hr ramp rate. Since the flat plate solution given in the ASME Code[8] is obtained from a quasi-steady state temperature distribution through the wall thickness it isanticipated that the solution becomes increasingly conservative for faster ramp rates since there isFile No.: 1001527.303 Page 17 of 30Revision:
$SbwouraI hIterf Associates, Inc."insufficient time for a quasi-steady state temperature distribution to develop through-wall since thevessel cools from approximately 550 0F to 100 °F; for faster ramp rates the temperature ramp endsbefore a quasi-steady state thermal distribution can develop.Table 11 presents the KIT calculated using the BIE/IF methodology and using the simplified methodology given in the WLI Nozzle LTR [9] which was developed for a 100 0F/hr cool-down transient.
Considering that the stress analysis and fracture mechanics methodologies are both linearelastic methods, the results should be scalable.
It is recognized that at faster ramp rates the vessel willnot be able to develop the quasi-steady state temperature distribution possible for slower ramp rates;therefore, the methodology given in Reference
[9] is expected to yield conservative results for ramprates faster than 100 °F/hr. The results in Table 11 and Figure 6 show a trend consistent withexpectations.
Consequently, the methodology given in Reference
[9] for the 100 °F/hr ramp rate may beused to obtain a conservative KIT value for higher ramp rates.6.0 SUMMARY OF RESULTSTable 12 summarizes the KI values calculated for the FW, WLI, and Core DP nozzles at Hatch Unit 1and Unit 2 for the internal pressure load case, a 450 0F thermal shock, a 100 °F/hr, and a 200 °F/hr cool-down transient.
These values will be used in subsequent calculations to prepare P-T curves for bothHatch Units.
7.0 REFERENCES
- 1. Sommerville, D.V., "Pressure-Temperature Limits Report Methodology for Boiling WaterReactors,"
SIR-05-044, Rev. 1, June 2011.2. Adjusted Reference Temperature Calculations:
SICalculation No. 1001527.301, Rev. 0.b. Sommerville, D.V., "Hatch Unit 1 RPV Material Summary and ART Calculation,"
SICalculation No. 1001527.302, Rev. 0.3. Title 10 Code of Federal Regulations Part 50, Appendix G, "Fracture Toughness Requirements."
- 4. Reactor Pressure Vessel Thermal Cycle Diagrams:
- a. SNOC Dwg. S 15025, GE Dwg. 729E762, "Reactor Thermal Cycles,"
SI File No. GPCO-31 Q-209.b. SNOC Dwg. S-41615, GE Dwg. 761E246, Sht. 1, "Reactor Vessel Thermal Cycles (Including Black Start),"
SI File No. 1001527.211.
- c. SNOC Dwg. S-416 16, GE Dwg. 761E246, Sht. 2, "Reactor Vessel Thermal Cycles (Including Black Start),"
SI File No. 1001527.211.
File No.: 1001527.303 Page 18 of 30Revision:
hItugdl Associates, Inc."5. Feedwater Nozzle Thermal Cycle Diagrams:
SI File No. 1001527.211.
- b. SNOC Dwg. $26421, GE Dwg. 158B8369, Sht. 4, Rev. 2, "Nozzle Thermal Cycles -Including Black Start (Feedwater
-Normal & Upset Conditions),"
SI File No. 1001527.211.
- c. SNOC Dwg. S26422, GE Dwg. 158B8369, Sht. 5, Rev. 2, "Nozzle Thermal Cycles -Including Black Start (Feedwater-Emergency
& Fault Conditions),"
SI File No. 1001527.211.
- 6. Water Level Instrument Nozzle Thermal Cycle Diagrams:
- a. GE Dwg. 135B9990, Sht. 7, Rev. 0, "Nozzle Thermal Cycles (Instrumentation
& Core Diff.Press & Liquid Control),"
SI File No. 1001527.211.
- b. SNOC Dwg. S26426, GE Dwg. 1 58B 8369, Sht. 9, Rev. 2, "Nozzle Thermal Cycles -Including Black Start (Instrumentation
& Core Diff. Press & Liquid C," SI File No. 1001527.211.
- 7. PVRC Recommendations on Toughness Requirements for Ferritic Materials, WRC Bulletin 175,August 1972.8. American Society of Mechanical Engineers, Boiler and Pressure Vessel Code,Section XI, Rules forInservice Inspection of Nuclear Power Plant Components, Non-mandatory Appendix G, "Fracture Toughness Criteria for Protection Against Failure,"
2001 Ed. through 2003 Addenda.9. Sommerville, D. V., "Linear Elastic Fracture Mechanics Evaluation of General Electric BoilingWater Reactor Water Level Instrument Nozzles for Pressure-Temperature Curve Evaluations,"
SIReport 0900876.401, Rev. 0, June 2011.10. Hatch Unit 1 NUREG-0619 Evaluations:
- a. Liffengren, D. J., et al., "Edwin I. Hatch Nuclear Power Station, Unit 1 Feedwater NozzleFracture Mechanics Analysis to Show Compliance with N UREG-06 19," NEDE-30238, DRF-137-0010, August 1983, General Electric Company.
SI File No. 1001527.210.
GEProprietary Information.
- b. Bothne, D., "Power Uprate Evaluation Report for Edwin I. Hatch Unit 1, Feedwater NozzleNUREG-06 19 Fracture Mechanics Analysis for Extended Power Uprate Conditions,"
GE-NE-B13-01869-065-01, July 1997, General Electric Company.
SI File No. 1001527.210.
GEProprietary Information.
File No.: 1001527.303 Page 19 of 30Revision:
it Associates, 11. Hatch Unit 2 NUREG-0619 Evaluations:
- a. Liffengren, D. J., et al., "Edwin I. Hatch Nuclear Power Station, Unit 2 Feedwater NozzleFracture Mechanics Analysis to Show Compliance with NUREG-0619,"
NEDC-30256, DRF-137-0010, August 1983, General Electric Company.
SI File No. 1001527.210.
GEProprietary Information.
- b. Stevens, G. L., "Updated Feedwater Nozzle Fracture Mechanics Analysis for Edwin I. HatchNuclear Power Station Unit 2," GE-NE-523-95-0991, Rev. 0, DRF B 13-01524, September 1991, General Electric Company.
SI File No. 1001527.210.
- c. Bothne, D., "Power Uprate Evaluation Report for Edwin I. Hatch Unit 2, Feedwater NozzleNUREG-0619 Fracture Mechanics Analysis for Extended Power Uprate Conditions,"
GE-NE-B13-01869-065-02, July 1997, General Electric Company.
SI File No. 1001527.210.
GEProprietary Information.
- 12. BWR Feedwater Nozzle and Control Rod Drive Return Line Nozzle Cracking, NUREG-06 19,November 1980, Nuclear Regulatory Commission.
- 13. Sommerville, D., Walter, M., "An Investigation into the Effects of Modeling Cylindrical Nozzle toCylindrical Vessel Intersections Using 2D Axisymmetric Finite Element models and a ProposedMethod for Correcting the Results,"
ASME PVP201 1-57001, Proceedings of the 2011 ASMEPressure Vessel and Piping Division Conference.
- 14. Pilkey, W.D., Pilkey, D.F., Peterson's Stress Concentration
- Factors, 3rd. Ed., John Wiley & Sons,2008.15. Zahoor, A., "Ductile Fracture Handbook,"
EPRI Report NP-6301, Volume 3. January 1991.16. Water Level Instrument Nozzle Drawings:
- a. SNOC Sketch 1-BE-i, Rev. 0, "Nil, N12, and N16 Instrumentation Nozzle Detail,"
SI FileNo. 1001527.208.
- b. SNOC Sketch 2-BE-2, Rev. 1, "2N12 and 2N16 Instrumentation Nozzle Detail,"
SI File No.1001527.209.
- 17. Feedwater Nozzle Drawings:
- a. SNOC Dwg. SX18921, "Reactor Vessel Feedwater Nozzle As Built," SI File No.100 1527.208b. SNOC Sketch 2-BF-4, Rev. 1, "2N4 Nozzle Assembly (Feedwater),"
SI File No. GPCO-31Q-208.18. American Society of Mechanical Engineers, Boiler and Pressure Vessel Code,Section II, Part D,Materials, 2001 Ed. through 2003 Addenda.19. Yin, S., Bass, B. R., Stevens, G. L., Stress and Fracture Mechanics Analyses of Boiling WaterReactor and Pressurized Water Reactor Pressure Vessel Nozzles, ORNL/TM--2010/246, December2010.File No.: 1001527.303 Page 20 of 30Revision:
0F0306-O01R1 rai lte gril Associates, Inc;"20. Sommerville, D.V., Qin, M., Houston, E., "An Investigation of the Adequacy of a Simplified Boundary Integral Equation
/ Influence Function Equation Linear Elastic Fracture Mechanics Solution for Nozzle Corner Cracking,"
ASME PVP201 1-57742, Proceedings of the 2011 ASMEPressure Vessel and Piping Division Conference.
- 21. SI Calculation Package 1100445.302, Rev. 0.22. SI Calculation Package 1100445.303, Rev. 0.23. SI Calculation Package NPPD-13Q-302, Rev. 1.24. SI Calculation Package 1000847.302, Rev. 0.25. SI Calculation Package 1000847.303, Rev. 2.26. SI Calculation Package 1100151.302, Rev. 0.27. S1 Calculation Package 1100151.303, Rev. 0.28. SI Calculation Package 1100445.304, Rev. 0.29. Combustion Engineering Drawing 232-242, Nozzle Details, SI File No. 1100445.204.
- 30. Core DP Nozzle Drawings:
- a. SNOC Dwg. S-15227A, Combustion Engineering Drawing 234-244-5, Nozzle Details for218" I.D. BWR, SI File No. 1001527.208.
- b. SNOC Sketch 1-BE-2, Rev. 1, "N10 Standby Liquid Control & Core Differential PressureNozzle Detail,"
SI File No. 100 1527.208.
- c. SNOC Dwg. S15523, Combustion Engineering Drawing 234-270, Rev. 3, "General.
Arrangement Elevation for 218" ID BWR," SI File No. 100 1527.208.
File No.: 1001527.303 Revision:
0Page 21 of3O0F0306-01R1
$Sbwcbuu hlgl Assadate
.°Table 1: Hatch Unit 1 FW Nozzle Blend Radius Path Stress Distributions.
1000 psig Internal Pressure Load CaseThermal Load Case450 "F shockPathDistance,
°h) Oh(2' 3o, Gb,in. pipsi psi psi0.000 f.l }.1 24461 58463 Di Di0.075 ]} 24052 57486 II }I0.225 1 /] 23283 55649 i }J-0.400 ft }1 22437 53626 1}0.600 It Di 21527 51452 U1 Di0.850 U /] 20466 48916 [ }.i.1.150 }1 19262 46037 Di }11.500 J} 18081 43215 ft }11.960 1.1 }1 16848 40268 Ii 1.2.476 ft }1 15206 36344 Di Di3.052 I.I ]J 13724 32802 Ui Di3.628 II }i 12372 29571 Di4.204 II 11110 26554 IL Di4.779 Di }) 9898 23657 lit Di5.355 Di Di 8692 20774 sD5.93 1 Di Di 7439 17780 ft }6.507 Di 1) 6073 14515 UJ Di6.811 Di }i 5384 12868 ft DiNotes:1. From Reference [10a], with CF=1.6557.
- 2. From Reference
[l0a], with CF=1.6557 removed.3. From Reference [10a], with CF as given in PVP201 1-5700 1 [13].File No.: 1001527.30, Revision: 03Page 22 of 30This page contains GEH PROPRIETARY INFORMATION which has been redactedF0306-01IRI mnssa t whlt A~ s A,.Table 2: Hatch Unit 2 FW Nozzle Blend Radius Path Stress Distributions. 1000 psig Internal Pressure Load CaseThermal Load Case450 OF shockPathin. pipsi psi psi0.000 U1 } 21010 58242 L1 }IL.0.075 LI }) 20651 57247 Li IL0.225 LI }i 19970 55359 H I0.400 I( }L 19213 53261 fL IL0.600 Li II 18403 51015 Li IL0.850 Li /) 17440 48345 LI II.1.150 IL 16452 45607 Li IL1.500 LI IL 15206 42153 Li IL1.954 Li IL 14233 39455 Li IL2.693 LI IL 11909 33013 Li }L3.284 LI II 10634 29479 {L Li3.874 Zl H9468 26245 IL4.465 Li II 8365 23188 {L }L5.056 Li I}. 7289 20206 LI IL5.647 LiII} 6194 17170 Li IL6.247 Li IL 5029 13941 Li IL6.838 LI II! 3718 10307 Li IL7.127 Li IL 3040 8427 LI ILNotes:1. From Reference
- 2. From Reference
- 3. From Reference
[1 la], with CF=1.5987. [1 la], with CF=1.5987 removed.[1 la], with CF as given in PVP201 1-5700 1 [13].File No.: 1001527.303 Revision: 0Page 23 of 30This page contains GEH PROPRIETARY INFORMATION Iwhich has been redactedF0306-01RI $b~jSlcrral hIt Writ Associates, Inc.=Table 3: Hatch Unit 1 Core DP Nozzle 1000 psi Internal Pressure Load Case Path StressDistribution [281.Path Distance, ah,in. psi0.000 261860.225 316100.450 305250.675 284490.901 263771.126 235181.351 222721.576 211891.801 202222.026 193512.251 185592.476 178312.702 171562.927 165223.152 159163.377 153273.602 147463.827 141694.052 135944.277 128384.503 12045File No.: 1001527.303 Revision: 0Page 24 of 30F0306-01R1 8 q trailafugri Associates, mnc:Table 4: Hatch Unit 1 FW Nozzle K1p and KIT using the BIE/IF Methodology. Pressure JThermalA0 58242 51488Al -11913 -15980'A2 1484.2 2002.4A3 -105.18 -127.21K1 81.1 65.3 ksi-in°'5Table 5: Hatch Unit 2 FW Nozzle K1p and KIT using the BIE/IF Methodology. Pressure II ThermalA0 58136 48077Al -12560 -28076A2 1522.5 4948.5A3 -103.53 -598.8K1 81.3 46.8' ksi-in°'5Table 6: Hatch Unit 1 Core DP Nozzle Kwp using the BIE/IF Methodology. PressureA0 35123Al -12874A2 3144.7A3 ,316.07KI 38.9 ksi-inO.S Table 7: Hatch Unit 1 FW Nozzle K1p using the WRC Bulletin 175 Methodology. F(a/rn) 1.61 -PR1/t(7ta)05 47.49 ksi-in°'5KI 76.6 ksi-in°'s Table 8: Hatch Unit 1 Core DP Nozzle K~p using the WRC Bulletin 175 Methodology. F(a/rn) j0.99 -PRi/t(ira)° 5 32.58 ksi-in°'5K______ I 32.3 ksi-in°'s File No.: 1001527.303 Page 25 of 30Revision: 0F0306-01R1
Assaciatus, Irnc=Table 9: Hatch Unit 2 FW Nozzle K~p using the WRC Bulletin 175 Methodology. F(a/r,) 1.62 -PRi/t~ta) 05 48.58 ksi-in°5K~p78.9 ksi-in0'5Table 10: Summary of Nozzle KIT Results Using the BIE/IF and G-22114.3 Methodologies. NozzleKIKT Plant ID Tp()Path Length, (BIE/IF Solution), (Flat Plate Soln.), Ratio Reference Te2 in ksi-in°'5 ksi-in°'5Plant A (3) FW 7.60 11.1 15.2 1.37 [21], [22], [23]Plant B FW 7.73 7.0 15.8 2.26 [24],[25] Plant B RI 9.29 9.4 25.1 2.67 [25]Plant C (1) FW 8.66 23.3 63.1 2.71 [26]Plant C FW 8.66 9.0 21.0 2.34 [27]1.2.3.300 *F/hr cooldown transient. FW is Feedwater nozzle, RI is Recirculation Inlet nozzle.Path length taken as 205 *RPV shell thickness to estimate the 45 degree path length.Table 11: Maximum Stress Intensity Factor for WLI Nozzle Considering Thermal Load Cases."ksi'in°0S Ratio of Simplified Method to.*Load Case BIEiIF Simplified. ... ..BIE/IF Methiod1271 MethodShutdown with 100 °F/hr 39.2 37.1 0.95Shutdown with 300 0F/hr 60.5 111.3 1.84Turbine By-Pass & SRV Blow-down 55.11. Where Reference [27] gives tv=5.98 inches, tn=0.795 inches, xc=9.75E-6 in~in/°FFile No.: 1001527.303 Revision: 0Page 26 of 30F0306-01RI $jj'sinww l Interity Associates, Inc.Table 12: Summary of Nozzle Stress Intensity Factors.Pressure (1,3)(1000 psig)Thermal (1,4)(450 TF shock)Thermal (1,5)(100 °F/hr)(200 °F/hr)...Nozzle j Unit 1 Unit 2 Unit 1 Unit 2 J Unit 1 Unit 2 Unit o1 Unit 2FW J 76.6 78.9 65.3 46.8 j 11.5 12.9 j 23.1 25.8WLI j 71.6 80.0 n/a n/a 17.4 19.9 34.8 39.9Core DP 32.3 n/a n/a n/a 1.73 n/a 3.46 n/a1. KI in units of ksi-in°5.2. 200 °F/hr results are scaled from 100 °F/hr assuming response is linear.3. Pressure load case results are obtained using WRC 175 methodology [7].4. Thermal shock results are obtained using BIE/IF methodology [1].5. Thermal ramp results are obtained using ASMIE XI, Non-mandatory Appendix G, Paragraph G-2214.4 methodology [81.File No.: 1001527.303 Revision: 0Page 27 of 30F0306-01RI 'jjuwtowau lategrify Associates, Inc."Nozzle BlendRadius Path NNozzle CornerCrack LocationFigure 1. Typical Nozzle Corner Crack Stress Extraction Path Orientation. 2A"o t(3.1 0.2 0.), 0.4 0.5' (3,0 0.1RA1IO OF-CRACIK SIZE T'O MDI,, OR NO)ZZ'L[ RAOiUS lilyn0,5 0.9Figure 2. 'WRC Bulletin 175, Figure A5-i, Estimates of Stress Intensity Factors for Flaws at aNozzle Corner [71.File No.: 1001527.303 Revision: 0Page 28 of 30F0306-01R1 Figure 3. Hatch Unit 1 FW Nozzle Blend Radius Path Stress Distributions [10b].Figure 4. Hatch Unit 2 FW Nozzle Blend Radius Path Stress Distributions [lla].File No.: 1001527.302 Revision: 03Page 29 of 30SThis page contains GEH PROPRIETARY INFORMATION which has been redactedF0306-01R 1 350000 -Ivy= -316.07x3 + 3144.7x2 -12874x + 3512325 0 ....... I ... ..R = 0.9964 ...* .1 50 0 ...... ....... .. ..... .0 0.5 1 1.5 2 2.5 3 3.5 4 4.5Nozzle Path Distance, in,,,,OOO00 psig PressureNote: The first data point in the series is excluded for the curve fit.Figure 5. Hatch Unit 1 Core DP Nozzle 1000 psi Internal Pressure Load Case Path StressDistribution. 70................................... ........ ... .... .. ........um Krr= 6 6.5 M Pa'rnm (t0.5 60 ~~~~~MaximumKIA= 60.6 MPa im (15_5.1 ksh ............. 5040,#2o-10--.-Shutdown at 55.56 degree C/hr-e-Shutdown at 166.67 degree C/;nro Turbne By-Pa. & SRVM Biowdown6000 8000 10000 12000 14000 16000 18000 20000Thne (sec)02000 4000Figure 6. Plant C WLI Nozzle KIT for Three Thermal Transients 1271.File No.: 1001527.303 Revision: 0Page 30 of 30F0306-0I1R V Structural Integrity Associates, Inc.Y File No.: 1001527.303 Project No.: 1001527CALCULATION PACKAGE Quality Program: [] Nuclear [] Commercial PROJECT NAME:Plant Hatch Unit l&2 P-T Curve Evaluation CONTRACT NO.:P0: SNG10018845, Rev. 0 CONTRACT: 19862, Rev. 0CALCULATION TITLE:Feedwater, Water Level Instrument, and Core DP Nozzle Fracture Mechanics Evaluation for Hatch Unit 1dLIu UIII L r I~uI Lullli '.uL w JVW1Up1L~11 Document Affected Project Manager Preparer(s) &Revision Pages Revision Description Approval Checker(s) Signature & Date Signatures & Date01 -30 Initial Issue Responsible Eni~ineer D. V. Sommerville D. V. Sommerville 12/30/2011 12/30/2011 Responsible Verifiers M. Qin*12/30/2011 T. J. Griesbach 12/30/2011 Page 1 of 30F0306-01R1 $jmSbiwbra kIturity Associates, Inc.=Table of Contents1.0 OBJECTIVE ................................................................................... 42.0 METHODOLOGY............................................................................. 42.1 Unit and Nozzle Specific Methodology Overview ............................... 62.1.1 Fee dwater Nozzle ..................................................................... 62.1.2 Water Level Instrument Nozzle ...................................................... 72.1.3 Core Differential Pressure Nozzle................................................... 82.2 2-D FEM Correction Factor ........................................................ 82.3 Boundary Integral Equation / Influence Function Methodology ............... 102.4 WRC Bulletin 175 Methodology .............. .................................. 112.5 ASME XI, G-22 14.3 Methodology for Radial Thermal Gradients ............ 123.0 DESIGN INPUTS...................................
- .......................................
124.0 ASSUMPTIONS............................................................................ 135.0 CALCULATIONS .....................
- ....................................................
145.1 Hatch Uniti1........................................................................ 145.1.1 Feedwater Nozzle .................................................................... 145.1.2 Water Level Instrument Nozzle...... .................................. 155.1.3 Core Differential Pressure Nozzle ................................................. 155.2 Hatch Unit 2........:................................................................ 165.2.1 Feedwater Nozzle .................................................................... 165.2.2 Water Level Instrument Nozzle............................................. ......... 175.3 Justification for Linear Scaling of Thermal Stress Intensity Factor Solutions 176.0 SUMMARY OF RESULTS............................................................... 1
87.0 REFERENCES
............................................................................. 18File No.: 1001527.303 Page 2 of 30Revision: 0F0306-01RI $jsbcrm~raI tor~ly Associates, Inc.=List of TablesTable 1 : Hatch Unit 1 FW Nozzle Blend Radius Path Stress Distributions ................... 22Table 2: Hatch Unit 2 FW Nozzle Blend Radius Path Stress Distributions................... 23Table 3: Hatch Unit 1 Core DP Nozzle 1000 psi Internal Pressure Load CasePath Stress Distribution................................................................ 24Table 4: Hatch Unit 1 FW Nozzle K1p and KIT using the BIB/IF Methodology............... 25Table 5: Hatch Unit 2 FW Nozzle K1p and KIT using the BIB/IF Methodology................ 25Table 6: Hatch Unit 1 Core DP Nozzle K1p using the BIB/IF Methodology................... 25Table 7: Hatch Unit 1 FW Nozzle K1p using the WRC Bulletin 175 Methodology........... 25Table 8: Hatch Unit 1 Core DP Nozzle K1p using the WRC Bulletin 175 Methodology.....25 Table 9: Hatch Unit 2 FW Nozzle K1p using the WRC Bulletin 175 Methodology........... 26Table 1.0: Summary of Nozzle K1t Results Using the BIB/IF andG-221 14.3 Methodologies................................. i............................. 26Table 11 : Maximum Stress Intensity Factor for WLI Nozzle Considering Thermal Load Cases......................................................
- .............
26Table 12: Summary of Nozzle Stress Intensity Factors ......................................... 27List of FiguresFigure 1. Typical Nozzle Corner Crack Stress Extraction Path Orientation................... 28Figure 2. WRC Bulletin 175, Figure A5-i, Bstimates of Stress Intensity Factorsfor Flaws at a Nozzle Corner .................................................. ........28Figure 3. Hatch Unit 1 FW Nozzle Blend Radius Path Stress Distributions................... 29Figure 4. Hatch Unit 2 FW Nozzle Blend Radius Path Stress Distributions................... 29Figure 5. Hatch Unit 1 Core DP Nozzle 1000 psi Internal Pressure Load CasePath Stress Distribution................................................................ 30Figure 6. Plant C WLI Nozzle KIT for Three Thermal Transients .............................. 30File No.: 1001527.303 Page 3 of 30Revision: 0F0306-01RI
1.0 OBJECTIVE
The objective of this calculation is to calculate the Mode I stress intensity
- factors, KI, for the Edwin I.Hatch Unit 1 and Unit 2 Feedwater (FW) nozzles and Water Level Instrument (WLI) nozzles, and theUnit 1 Core Differential Pressure (DP) nozzle, necessary for creation of the Pressure-Temperature (P-T)limit curves for the pressure test (Curve A), core not critical (Curve B) and core critical (Curve C)conditions for the Hatch Unit 1 and Unit 2 reactor pressure vessels (RPV). Both internal pressure andthermal transient load cases are considered.
2.0 METHODOLOGY
Consistent with the Structural Integrity Associates, Inc. (SI) Boiling Water Reactor (BWR) P-T CurveLicensing Topical Report (LTR) [1], the FW nozzle is normally taken as the limiting component in thenon-beltline region of the RPV. This assumption is made because:1. The geometric discontinuity caused by the nozzle penetration in the RPV shell causes a stressconcentration which results in larger pressure induced stresses than would be calculated in theshell regions of the RPV,2. The FW nozzle experiences more severe thermal transients than most of the other nozzlesbecause of the feedwater injection temperature which causes larger thermal stresses than areexperienced in the shell regions of the RPV,3. Although some other nozzles can experience thermal transients which would cause thermalstresses larger than those calculated for the shell regions of the RPV and some nozzles are largerdiameter than the FW nozzle, which could result in a slightly larger KIp, the combined stressesfrom the applied thermal and pressure loads are considered to bound all other non-beltline discontinuities. The Hatch Unit 1 and Unit 2 Adjusted Reference Temperature calculations [2] identify the WLI nozzleas contained within the beltline region of both the Unit 1 and Unit 2 RPV. Consequently, the effects ofthese nozzles must be considered in the beltline P-T curve development. These nozzles will cause astress intensification in the beltline shells. Further, since the beltline region experiences a reduction intoughness caused by neutron irradiation, it is not obvious whether the FW nozzle will bound the WLINozzle throughout the life of Hatch Unit 1 and Unit 2. Consequently, the effects of the WLI Nozzle onthe beltline P-T curves must be specifically considered. The SI P-T Curve LTR [1] addresses the bottom head penetrations by conservatively applying a stressconcentration factor (SCF) of 3.0 for a hole in a flat plate to the pressure induced membrane stress in thebottom head shell and using the thermal stress intensity factor solution given in ASME XI, Non-mandatory Appendix G, Paragraph G-22 14.3 [8]; discussed below. Review of the Hatch Unit 1 generalassembly drawing [30] shows that the Core DP nozzle exists in the thinnest section of the bottom head.Based on prior experience from a similar bottom head design, application of the conservative SCF=3.0methodology to the Core DP nozzle penetration will result in a bottom head P-T curve which controlsthe entire RPV. Consequently, a detailed evaluation of the Core DP nozzle is performed to removeexcess conservatism. File No.: 1001527.303 Page 4 of 30Revision: 0F0306-01R1 Consistent with 10OCFR50 Appendix G [3] the RPV P-T curves are applicable for normal operation andall anticipated operating occurrences. Consequently, all Level A and Level B (Normal and Upset)operating events defined on the RPV, FW nozzle, WLI nozzle, and Core DP nozzle thermal cyclediagrams (TCD) [4, 5, 6] are considered in selecting bounding thermal and pressure conditions forpreparing P-T curves.The SI P-T Curve LTR [1 ] identifies acceptable methodologies for calculating applied pressure andthermal stress intensity factors for postulated nozzle corner flaws. These methodologies include:Pressure Load Case:1. Welding Research Council Bulletin 175 [7]2. Boundary Integral Equation / Influence Function (BIE/IF) [1]*Thermal Transient Load Case:1. BIB/IF [1]2. ASME XI, Non-mandatory Appendix G, Paragraph G-2214.3 [8]The WRC Bulletin 175 [7] methodology for calculating a KI for an internal pressure load case isconvenient to apply since no nozzle specific finite element analysis (FEA) is necessary. The only inputsrequired are the nozzle and vessel geometry and the hoop stress calculated for the vessel shell, remotefrom discontinuities. The BIB/IF methodology is applicable to any load case provided that a third order polynomial curve fitto the applicable stress distribution is available. The appropriate path for a postulated nozzle cornercrack has a path origin located at the peak stress location in the blend radius for the pressure load caseand it is oriented parallel to a 45° line through the nozzle, as shown in Figure 1. This methodology requires detailed stress distributions through the nozzle blend radius which are typically obtained from aplant specific FEA.The flat plate thermal stress intensity factor solution given in the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel (B&PV) Code Section XI, Non-mandatory Appendix G,Paragraph G-22 14.3 [8] is considered to be a conservative, simplified methodology for obtaining the KITat the nozzle corner path resulting from a heat-up/cool-down transient of constant rate (i.e. 100 °F/hr),when the wall thickness is taken asthe path length along the 450 path identified in Figure 1. Thisapproach is considered to be conservative because:1. Geometric discontinuities do not intensify thermal stresses in a manner similar to stresses frommechanical loading; thus, fracture mechanics solutions which inherently consider the nozzlegeometry are not necessarily
- required,
- 2. Thermal stresses increase as section thickness increases because the differential thermal strainincreases with thickness.
Consequently, the practice of taking a wall thickness determined by thepath length of the 450 path results in a thicker wall.File No.: 1001527.303 Page 5 of 30Revision: 0F0306-01IRI
Integrit Associates, Inc:SI has prepared a complementary P-T Curve LTR [9] which provides simplified methods for calculating the K~p and KIT for the BWR WLI nozzles. This method is convenient since the necessary stressintensity factors can be calculated using simple geometry and material properties data without the needfor a plant specific FEA.The methods identified above are used in this calculation to calculate stress intensity factors for theHatch Unit 1 and Unit 2 FW nozzles and WLI nozzles, and the Unit 1 Core DP nozzle. The sectionsbelow identify the general methodology applied for each nozzle at each unit.2.1 Unit and Nozzle Specific Methodology OverviewThe specific methodologies used to calculate the Kjp and KIT for the FW nozzle, the WLI nozzle, and theCore DP nozzle are discussed separately below.2.1.1 Feedwater NozzleVarious FW nozzle fracture mechanics analyses have previously been performed for Hatch Unit 1 [10]and Unit 2 [11] to satisfy the requirements of NUREG-0619 [ 12] regarding FW nozzle rapid thermalcycling caused by leakage past the thermal sleeve seals. The load cases necessary for development ofP-T curves and those required to address NUREG-06 19 are similar. Consequently, the previousevaluations performed for Hatch Units 1 and 2 will be utilized, as appropriate, for the present evaluation. The following methodology is used:Internal Pressure Load Case1. Pressure stress distributions reported in References [10, 11] for Hatch Unit 1 and Unit 2 are takenfor the 1000 psig internal pressure load case.2. Recognizing that the Reference [10, 11] evaluations were performed using a 2-D axi-symmetric finite element model (FEM) and that it is known that the stress intensification caused by thenozzle geometry is under predicted in a 2-D axi-symmetric representation of the nozzle, acorrection factor must be applied to the stresses obtained from the 2-D axi-symmetric FEM. Theinternal pressure load case stresses, in the nozzle blend radius region, are corrected using themethodology presented in Reference [13]. Plant specific dimensions are used to calculate thecorrection factor.3. The BIE/IF methodology presented in the SI P-T Curve LTR [1] is used to calculate K~p byfitting a third order polynomial equation to the path stress distribution for each plant specificpressure load case. The resulting K1p can be linearly scaled to determine the K1p for various RPVinternal pressures.
- 4. 'The methodology given in WRC Bulletin 175 [7] is used to obtain an independent confirmation of the K1p calculated for each unit. The resulting K1p can be linearly scaled to determine the K~pfor various RPV internal pressures.
File No.: 1001527.303 Page 6 of 30Revision: 0F0306-01RI iuru hItud Associates, Inc."Thermal Transient Load Case1. Thermal shock load case path stress distributions reported in References [10, 11] for Hatch Unit1 and Unit 2 are taken. The FW nozzle thermal shock is the most severe Level A/B thermaltransient for the FW nozzle; thus, the load case considered in References [10, 11] is appropriate for P-T curve calculations. When path stress distributions at multiple times are presented inReferences [10, 11 ] the bounding distribution is selected for the current evaluation.
- 2. The BIE/IF methodology presented in the SI P-T Curve LTR [1] is used to calculate KIT byfitting a third order polynomial equation to the path stress distribution for each plant specificthermal shock load case. The resulting KIT can be linearly scaled to determine the KIT forvarious shock amplitudes.
- 3. A KIT for a uniform 100 °F/hr and 200 "F/hr heat-up/cool-down transient is calculated using theequation given for a radial thermal gradient in ASME XI, Appendix G, Paragraph G-22 14.3 [8]4. Results from various plant specific evaluations are presented to support the use of G-22 14.3 [8]for calculating KIT for 100 "F/hr and 200 0F/hr heat-up/cool-down transients.
2.1.2 Water Level Instrument NozzleSimplified methods for calculating the K~p and KIT for the WLI nozzles in General Electric designedBWRs are given in Reference [9], which is a companion LTR to the P-T curve LTR [1]. The K~p andKIT terms are calculated using Equations (8-1) and (8-2) of Reference [9], which are repeated below, forconvenience, as Eq. (1) and Eq. (2):K1Pesue .94~ ~1000Q psig internal pressure (1)KIRa,np = ++/-t,)]- 20.715, 100 °F/hr cooldown transient (2)Where: R is the inside radius of the pressure vessel, intv is the wall thickness of the pressure vessel, intn is the thickness of the WLI nozzle insert near the postulated cracklocation, inoa is the coefficient of thermal expansion at the highest temperature inthe transient, in/in/°FThe units of Ki in Eq. (1) and Eq. (2) are ksi-in°5.File No.: 1001527.303 Page 7 of 30Revision: 0F0306-01R1 jS b-c orl Aitii~ ssociates, In.=2.1.3 Core Differential Pressure NozzleThe following methodology is used:Internal Pressure Load Case:1. The methodology given in WRC Bulletin 175 [7] is used to calculate the K1p. The resulting K1pcan be linearly scaled to determine the K~p for various RPV internal pressures.
- 2. Since a 2-D axi-symmetric finite element analysis of a Core DP nozzle for a plant with a similardesign has previously been performed for development of P-T curves [28], and since thedimensions of the Core DP nozzle modeled [29], in the vicinity of the bottom head penetration, are identical to Hatch Unit 1 [30], the results of the previous Core DP nozzle evaluation may beused to obtain an independent benchmark of the K1p obtained using the WRC Bulletin 175 [7]methodology.
- 3. A path stress distribution, in the vicinity of the Core DP nozzle, caused by a 1000 psig internalpressure load case, is taken from Reference
[28]. The location and orientation of the path areconsistent with that used for nozzle evaluations.
- 4. The BIE/IF methodology presented in the SI P-T Curve LTR [1] is used to calculate K1p byfitting a third order polynomial equation to the path stress distribution for the plant specificpressure load case.Thermal Transient Load Case:1. Similar to the methodology given in the P-T Curve LTR [1], a KIT for a uniform 100 °F/hr and200 0F/hr heat-up/cool-down transient is calculated using the equation given for a radial thermalgradient in ASME XI, Appendix G, Paragraph G-22 14.3 [8]2. Results from various plant specific evaluations are presented to support the use of G-2214.3
[8]for calculating KIT- for 100 0F/hr and 200 °F/hr heat-up/cool-down transients. 2.2 2-D FEM Correction FactorWhen a cylindrical nozzle intersection with a cylindrical pressure vessel is modeled using a 2-D axi-symmetric simplification, the geometry is approximated as a nozzle intersection with a spherical shell.This simplification results in a non-conservative treatment of the geometric discontinuity at the blendradius region as well as a resulting reduction in the far field membrane stress in the shell caused by theapproximation of the pressure vessel as a sphere rather than a cylinder. Consequently, stress resultsobtained from a 2-D axi-symmetric FEM, for mechanical loads such as pressure, must be corrected before they can be used in subsequent analyses. Sommerville and Walter [13] describe a methodology for correcting stress distributions obtained from the nozzle blend radius region of 2-D axi-symmetric models. The correction factor is given in Reference [13] as:File No.: 1001527.303 Page 8 of 30Revision: 0F0306-01RI ~jSbircraI laturif Associatus, Inc:SCF3DHoCF = 2. 3DHo (3)SCF2D)_HoopWhere: SCF3DHoop is the stress concentration factor (SCF) defined with respect to thethe hoop stress direction, for the 3D geometry. SCF2DHoop is the stress concentration factor for the 2D geometry. The expected SCF for the 3-D geometry can be estimated using the following equation for a circularhole in a pressurized cylinder [14]:For 0132,K(, (/) = 2.5899 +0.8002.13+/-+4.0112.132 _-1.8235-/83 + 0.3751 ./34 (4a)~j.( 2)f2 " (4b)Where: Kt(I3) is the SCF defined with respect to the far field hoop stress, PR/t.v is the Poisson's ratio of the material, assumed equal to 0.3.r is the radius of the nozzle bore, inR is the inside radius of the pressure vessel, intv is the wall thickness of the pressure vessel, inKt(t3) is used for the SCF3D)_Hoop term in Eq. (3). The SCF2DHoop can be calculated from the results of the2-D axi-symmetric FEM by calculating the SCF using the following equation: 2 ., O'totl,max (5)SCF2-H°°P = P. RWhere: P is the RPV internal pressure for the pressure load case, psiO'total,max is the largest total hoop stress in the blend radius region, psiInserting Eq. (5) and Eq. (4a, 4b) into Eq. (3) gives the correction factor which can be used to uniformly scale the pressure load case path stress distribution from the 2-D axi-symmetric FEM. This path stressdistribution can then be fit with the equation for a 3rd order polynomial and used with the BIE/IFsolution described in Reference [1], and discussed below, to obtain Kjp.File No.: 1001527.303 Page 9 of 30Revision: 0F0306-01R1 mIhtugril Associates, Inc.=2.3 Boundary Integral Equation / Influence Function Methodology The following discussion is excerpted from the SI P-T curve LTR [1]. Note that the equation andreference numbers in the excerpt below refer to Reference [1]:The stress intensity factors for the feedwater nozzle may be calculated using theresults of a detailed finite element model of the nozzle. In some cases, such resultsmay already be available from the governing design basis stress report for thefee dwater nozzle. The details of the finite element process are not included here,"rather, the extraction of the. appropriate finite element results and their use indeveloping P-T limit curves is discussed. For a path through the limiting nozzle inner blend radius corner, as shown inFigure 2-7, the thermal and pressure hoop stress distributions should be extracted from the finite element model. Each of the stress distributions should befit with athird-order polynomial that reasonably fits the calculated stresses in the region ofinterest. The thermal stress intensity factor, K1t, is computed based on either of the nozzlecorner solutions shown in Figure 2 -8 for a postulated 1/4t (based on the sectionthickness) axial defect, as follows." K1, = [ 0.723 C0, + 0.55 1 ~1)C1, + 0.462~Z C2, + 0.408 j J C3,] (2.5.3-3 a)K1, V~[O.06C~ +0.53 C1 + .44~ i~j C, +/-.39~jj ~ 3~j(2.5.3-3b) where: Kit the thermal stress intensity factor for the limitingnormal/upset transient (psi inc)a = 1/4tpostulatedflaw depth (inches)t = thickness of the cross-section through the limitingnozzle inner blend radius corner, as Shown inFigure 2- 7.Co,, C1,., C2,, C3, thermal stress polynomial coefficients based on fitsto finite element analysis. File No.: 1001527.303 Page 10 of 30Revision: 0F0306-01R1 $bSl wc~ Ilte! grit Associates, Inc.=Equation 2.5.3-3 a is based upon a Boundary Integral Equation / Influence Function(BIE/IF) solution developed for a quarter crack in an infinite quarter space.Equation 2.5. 3-3b is the average of the BIE/IF solutions developed for a quartercrack in an infinite quarter space and a semicircular crack in an infinite half space.These equations have been investigated by the NRC and Oak Ridge NationalLaboratory and shown to be acceptable for use in calculating the applied stressintensity factor for a corner cracked nozzle [16]. Although both solutions givenabove are evaluated in Reference [16], it is acknowledged by the original authorsof these formulations, in the basis work used to develop the approach [171, that thetwvo formulations differ very little and in fact provide KI values which differ only byapproximately 5%. This can be seen by review of the coefficients used in eachequation above. Consequently, either Equation 2.5.3-3 a or 2.5.3-3b may be usedfor any nozzle configuration in a BWR.The BIE/IF solution introduced above is applicable to any load case and any BWRnozzle; thus, it is applied both to the internal pressure and thermal transient loadsconsidered for P-T curve development. 2.4 WRC Bulletin 175 Methodology An alternative solution for determining the applied pressure stress intensity factor, Kip, is to use themethod given in Appendix 5 of WRC Bulletin .175 [7], where:K1~ zFar~.P l~ (6Where: K1p is the applied pressure stress intensity factor, psi icP is the operating
- pressure, psia is the 1/4t postulated flaw depth, inchesR is the vessel inner radius, inchesis the thickness of the vessel shell, inchesF(a/r,) is the shape factor given in Figure 2, where rn ri + 0.29rc,ri is the actual inner radius of nozzle, inchesrc is the nozzle blend radius, inchesA functional form of F(a/rn) is given in Reference
[15, Pg. 11.1-17] as:= .42 .0 .46 (7)Where, Eq. (7) is applicable for 0.,07 < a/rn< 0.9.File No.: 1001527.303 Page 11 of 30Revision: 0F0306-0lRl $jtSinwwrul I~l~itedt Associates, Inc.*2.5 ASME XI, G-2214.3 Methodology for Radial Thermal Gradients ASME XI, Non-mandatory Appendix G, Paragraph G-22 14.3 [8] gives the following, simplified methodfor calculating KIT for a radial thermal gradient: Kt =-0.953.10-3**CR. tv25 (8)Where: CR is the cooldown rate, 0F/hr.tv is the thickness of the vessel shell, inchesParagraph G-22 14.3 [8] states that Eq. (8) will yield conservative results if used for cool-down ratesgreater than 100 °F/hr.This methodology is used to calculate the KIT in the nozzle blend radius region by using the path lengthalong the 450 path shown in Figure 1 as the shell thickness, tv.3.0 DESIGN INPUTSThe following design inputs are used for this evaluation:
- Previous NUREG-0619 evaluations:
References [10, 11]* Core DP Nozzle evaluation: Reference [28]* Thermal transient definitions for Level A/B: References [4, 5, 6]* WLI Nozzle dimensions and material: Reference [16]Hatch Unit 1 :Nozzle insert material:
- Inconel, SB- 166RPV inside radius: 110.375 inchesNozzle insert thickness:
0.28 1 inchesVessel shell thickness: 5.375 inchesNote." Some drawings show a shell thickness of 5.875 inches;"
- however, theminimum dimension given in the general arrangement drawing is used for thisevaluation.
Hatch Unit 2:Nozzle insert material:
- Inconel, SB- 166RPV inside radius: 110.375 inchesNozzle insert thickness:
0.66 1 inchesVessel shell thickness: 5.375 inchesFile No.: 1001527.303 Page 12 of 30Revision: 0F0306-01IRI $j~biicfriru Iutugdty Associates, Inc.e* FW Nozzle dimensions: Hatch Unit 1:Nozzle bore diameter: Nozzle blend radius:RPV inside radius:Vessel shell thickness: Hatch Unit 2:Nozzle bore diameter: Nozzle blend radius:RPV inside radius:Vessel shell thickness:
- Core DP Nozzle dimensions:
Hatch Unit 1:Vessel shell thickness: Bottom head radius:Nozzle inside radius:* Material Properties: Hatch Unit 1 and Unit 2 WLI Nozzle Insert:Coefficient of thermal expansion: Poisson's ratio:Reference [ 17]6.7 inches2.5 inches110.375 inches5.375 inches6.5 inches5.0 inches110.375 inches5.375 inchesReference [30]3.188 inches110.5 inches1.250 inches, see assumption 3.Reference [ 18]7.7x106 in/ir/°F at 550 0F0.3 (assumed)
4.0 ASSUMPTIONS
The following assumptions are used in this calculation and supported by data presented below:1. The thermal stress intensity factor, KIT, for a 200 °F/hr thermal transient can be conservatively calculated using Eq. (8) above for vessel shells and forged vessel nozzles, where the shellthickness in the equation is taken as the vessel shell thickness when evaluating the shell, and thenozzle blend radius path length when evaluating forged nozzles. Adequacy of this assumption isdemonstrated in Section 5.3 below.2. The thermal stress intensity factor, KIT, for a 200 °F/hr thermal transient can be conservatively calculated using Eq. (2) above for a WLI nozzle by scaling the KIT obtained from Eq. (2) by 2.Similarly higher heat-up/cool-down rates can be addressed by appropriate scaling factors.Adequacy of this assumption is demonstrated in Section 5.3 below.File No.: 1001527.303 Revision: 0Page 13 of 30F0306-01RI $b~ml inc.=3. The stress concentration effect of the Core DP penetration in the bottom head is conservatively addressed by treating the penetration as a nozzle in which the radius considered in the WRCBulletin 175 pressure stress intensity methodology is taken as the radius of the hole in the shellrather than the ID of the Core DP penetration. This assumption is validated in Section 5.1.3below by comparing the KIP obtained using this approach with the KIP obtained using theBIB/IF methodology.
5.0 CALCULATIONS
The calculations for the FW nozzles, WLI nozzles, and Core DP nozzle are presented for each unit,separately, below.5.1 Hatch Unit 1The calculations for the FW, WLI, and Core DP nozzles are presented in separate sections. 5.1.1 Feedwater NozzleTable 1 presents a tabulation of the path stress distribution taken from the Unit 1 plant specific FWnozzle FEM, in the blend radius region of the nozzle. Both the 1000 psig internal pressure and 450 0Fthermal shock load case path stress distributions are taken from Reference [i10a]. The thermal transient load case path stress distribution is fit with a 3rd order polynomial equation. In the previous evaluation [10a], the pressure load case path stress distribution was corrected using a different methodology thanutilized for the present calculation; therefore, this correction factor is removed before the correction factor calculated using the methodology described in Section 2.2 is applied. The corrected pressure pathstress distribution is fit with a 3rd order polynomial equation. The Hath Unit 1 FW nozzle correction factor is calculated below:r = 6.7 in FW nozzle bore radiusR = 110.38 in RPV radius adjacent to FW nozzletv= 5.38 in RPV shell thickness adjacent to FW nozzle3=- 0.177 -Eq. (4)Kt 2.85 -SCF for hole in cylinder, Eq. (4)SCF20= 2.38 -SCF from 2-D axi-symmetric FEA, Eq. (5)CF = 2.39 -Correction factor, Eq. (3)Figure 3 is a plot of the pressure and thermal shock path stress distribution in the Hatch Unit 1 FWnozzle blend radius region with the polynomial curve fit equations and correlation coefficients shown.Table 4 summarizes the polynomial coefficients for each load case and presents the Kip and KIT for theHatch Unit 1 FW nozzle.Table 7 presents the K1p calculated using the WRC Bulletin 175 methodology [7].File No.: 1001527.303 Page 14 of 30Revision: 0F0306-0 IRI $b~o~grl Associates, Inc.=Recognizing that the BIB/IF methodology has been shown to provide conservative estimates of the stressintensity factors for both pressure and thermal load cases [19, 20] and that both the WRC Bulletin 175[7] and BIE/IF [1] methodologies are accepted methods for calculating the KI from the pressure loadcase, the lower KI is used for this evaluation. Reference [10Ob] identifies that the extended power uprate conditions result in an increase in the RPVdome pressure of 50 psig (1000 psig to 1050 psig) and an increase in the FW fluid temperature of 6 °F(450 °F to 456 'F). The increase in dome pressure is accommodated by linear scaling during preparation of the P-T curves in a subsequent calculation. The increase in the FW fluid temperature is a change ofless than 1.5%. The work documented in References [19, 20] shows that the BIB/IF methodology issignificantly conservative (on the order of 30-50% when compared to the RMS K1 calculated from a 3-Dfinite element fracture mechanics evaluation) for the 1/4 thickness flaws required for P-T curves;consequently, the KIT calculated for the 450 °F shock is not further increased in this evaluation toaccount for the small increase in FW temperature. 5.1.2 Water Level Instrument NozzleUsing Eq. (1) and (2) and considering Hatch Unit 1 WLI nozzle dimensions and material properties, theK1p and KIT are calculated below:tv= 5.38 in RPV shell thickness adjacent to WLI nozzleR = 110.38 in RPV radius adjacent to WLI nozzletn= 0.28 1 in WLI nozzle thickness cx 7.70E-06 in/in/OF Thermal expansion coefficient for nozzle material,
- Inconel, 550 'FK = 71.6 ksi-in0.5 1000 psi pressure stress intensity factor, Eq. (1)KIT = 17.4 ksi-in0.5 100 'F/hr cool-down transient stress intensity factor, Eq. (2)KIT= 34.8ksi-n 05 200 'F/hr cool-down transient stress intensity factor, Eq. (2) scaled by aKXT = 34.8ksi'n°'S factor of 25.1.3 Core Difjferential Pressure NozzleThe K1p calculated using the WRC Bulletin 175 methodology
[7] is shown in Table 8.The pressure path stress distribution is extracted from Reference [28]. The stress distribution istabulated in Table 3 and plotted in Figure 5. Because of the orientation of the path and the configuration of the nozzle, which contains a tube which penetrates the RPV, the path stress distribution exhibits alower stress at the path origin than slightly inboard along the path. Consequently, the 3rd orderpolynomial equation is fit to the stress distribution, after omitting the first point along the curve. Thecurve fit and equation are shown in Figure 5. The resulting polynomial coefficients and K1p obtainedusing the BIB/IF methodology are listed in Table 6.File No.: 1001527.303 Page 15 of 30Revision: 0F0306-01iRI $j~bvg~aunIlatgrily ssoca~tes, Inc.'The K~p calculated using the BIE/IF methodology [1] benchmarks well against the K1p calculated usingthe WRC Bulletin 175 methodology [7]. Recognizing that the BIE/IF methodology has been shown toprovide conservative estimates of the stress intensity factors for both pressure and thermal load cases[ 19, 20] and that both the WRC Bulletin 175 [7] and BIE/IF [1 ] methodologies are accepted methods forcalculating the K1 from the pressure load case, the lower KI is used for this evaluation. The KIT term is calculated using Eq. (8) and is presented in Table 12 for heat-up/cool-down rates of 1000F/hr and 200 0F/hr. Section 5.3 provides justification for using the ASME XI, Non-mandatory Appendix G, Paragraph G-2214.3 [8] methodology for heat-up/cool-down rates greater than 100 0F/hr.5.2 Hatch Unit 2The calculations for the FW and WLJ nozzles are presented in separate sections. 5.2.1 Feedwater NozzleTable 2 presents a tabulation of the path stress distribution taken from the Unit 2 plant specific FWnozzle FEM, in the blend radius region of the nozzle. Both the internal pressure and thermal shock loadcase path stress distributions are taken from Reference [11 la]. The thermal transient load case path stressdistribution is fit with a 3r order polynomial equation. In the previous evaluation [1 la], the pressureload case path stress distribution was corrected using a different methodology than utilized for thepresent calculation; therefore, this correction factor is removed before the correction factor calculated using the methodology described inSectioh 2.2 is applied. The corrected pressure path stressdistribution is fit with a 3rd order polynomial equation. The Hath Unit 2 FW nozzle correction factor is calculated below:r = 6.5 in FW nozzle bore radiusR = 110.38 in RPV radius adjacent to FW nozzlet-- 5.38 in R!PV shell thickness adjacent to FW nozzle13= 0.172 -Eq. (4)Kt 2.84 -SCF for hole in cylinder, Eq. (4)SCF2D = 2.05 -SCF from 2-D axi-symmetric FEA, Eq. (5)CF = 2.77 -Correction factor, Eq. (3)Figure 4 is a plot of the pressure and thermal shock path stress distribution in the Hatch Unit 2 FWnozzle blend radius region with the polynomial curve fit equations and correlation coefficients shown.Table 5 summarizes the polynomial coefficients for each load case and presents the K1p and KIT for theHatch Unit 2 FW nozzle.Table 9 presents the K1p calculated using the WRC BUlletin 175 [7] methodology. File No.: 1001527.303 Page 16 of 30Revision: 0F0306-01R1
hi/t egd/ty Associateus, Inc."Recognizing that the BIE/IF methodology has been shown to provide conservative estimates of the stressintensity factors [19, 20] and that both the WRC Bulletin 175 [7] and BIE/IF [1] methodologies areaccepted methods for calculating the KI from the pressure load case, the lower K1 is used for thisevaluation. Reference [1 lc] identifies that the extended power uprate conditions result in an increase in the RPVdome pressure of 50 psig (1000 psig to 1050 psig) and an increase in the FW fluid temperature of 6 0F(delta T from 450 0F to 456 0F). The increase in dome pressure is accommodated by linear scalingduring preparation of the P-T curves in a subsequent calculation. The increase in the FW fluidtemperature is a change of less than 1.5%. The work documented in References [19, 20] shows that theBIE/IF methodology is significantly conservative (on the order of 3 0-50% when compared to the RMSK1 calculated from a 3-D finite element fracture mechanics evaluation) for the 1/4 thickness flawsrequired for P-T curves; consequently, the KIT calculated for the 450 0F shock is not further increased inthis evaluation to account for the small increase in FW temperature. 5.2.2 Water Level Instfrument NozzleUsing Eq. (1) and (2) and considering Hatch Unit 2 WLI nozzle dimensions and material properties, theK~p and KIT are calculated below:tv= 5.38 in RPV shell thickness adjacent to W/LI nozzleR = 110.38 in RPV radius 'adjacent to WLI nozzletn= 0.66 1 in WLI nozzle thickness ct= 7.70E-06 in/in/°F Thermal expansion coefficient for nozzle material,
- Inconel, 550 0FKw= 80.0 ksi-in°'s 1000 psi pressure stress intensity factor, Eq. (1)KI1 = 19.9 ksi-in°'s 100 °F/hr cooldown transient stress intensity factor, Eq. (2)200 °F/hr cooldown transient stress intensity factor, Eq. (2) scaled by a factorKIT = 39.9 ksi-in°'s of 2.05.3 Justification for Linear Scaling of Thermal Stress Intensity Factor Solutions Data is presented in this section which supports the Assumptions 1 and 2 identified in Section 4.0.Table 10 summarizes the KIT calculated for four nozzles from three separate BWRs. Both a 100 0F/hrand a 300 0F/hr cool-down rate were evaluated.
Both the BIE/IF methodology [1] and the methodology given in ASME XI, Non-mandatory Appendix G, Paragraph G-22 14.3 [8] were used to calculate KIT.The results confirm that the simplified method given in Paragraph G-22 14.3 [8] may be used to obtain aKIT. Further, as suggested in WRC 175 [7] and G-2214.3 [8] use of this methodology is expected to beincreasingly conservative for cool-down rates larger than 100 0F/hr. This trend is seen in the two KITresults Obtained for Plant .C at 100 0F/hr and 300 0F/hr, where it is shown that the KIT calculated usingthe flat plate solution exceeds that calculated using the BIB/IF methodology by a ratio of 2.34 for a 1000F/hr ramp rate and 2.71 for ai 300 0F/hr ramp rate. Since the flat plate solution given in the ASME Code[8] is obtained from a quasi-steady state temperature distribution through the wall thickness it isanticipated that the solution becomes increasingly conservative for faster ramp rates since there isFile No.: 1001527.303 Page 17 of 30Revision: 0F0306-01R1 $SbwouraI hIterf Associates, Inc."insufficient time for a quasi-steady state temperature distribution to develop through-wall since thevessel cools from approximately 550 0F to 100 °F; for faster ramp rates the temperature ramp endsbefore a quasi-steady state thermal distribution can develop.Table 11 presents the KIT calculated using the BIE/IF methodology and using the simplified methodology given in the WLI Nozzle LTR [9] which was developed for a 100 0F/hr cool-down transient. Considering that the stress analysis and fracture mechanics methodologies are both linearelastic methods, the results should be scalable. It is recognized that at faster ramp rates the vessel willnot be able to develop the quasi-steady state temperature distribution possible for slower ramp rates;therefore, the methodology given in Reference [9] is expected to yield conservative results for ramprates faster than 100 °F/hr. The results in Table 11 and Figure 6 show a trend consistent withexpectations. Consequently, the methodology given in Reference [9] for the 100 °F/hr ramp rate may beused to obtain a conservative KIT value for higher ramp rates.6.0 SUMMARY OF RESULTSTable 12 summarizes the KI values calculated for the FW, WLI, and Core DP nozzles at Hatch Unit 1and Unit 2 for the internal pressure load case, a 450 0F thermal shock, a 100 °F/hr, and a 200 °F/hr cool-down transient. These values will be used in subsequent calculations to prepare P-T curves for bothHatch Units.
7.0 REFERENCES
- 1. Sommerville, D.V., "Pressure-Temperature Limits Report Methodology for Boiling WaterReactors,"
SIR-05-044, Rev. 1, June 2011.2. Adjusted Reference Temperature Calculations:
- a. Sommerville, D.V., "Hatch Unit 1 RPV Material Summary and ART Calculation,"
SICalculation No. 1001527.301, Rev. 0.b. Sommerville, D.V., "Hatch Unit 1 RPV Material Summary and ART Calculation," SICalculation No. 1001527.302, Rev. 0.3. Title 10 Code of Federal Regulations Part 50, Appendix G, "Fracture Toughness Requirements."
- 4. Reactor Pressure Vessel Thermal Cycle Diagrams:
- a. SNOC Dwg. S 15025, GE Dwg. 729E762, "Reactor Thermal Cycles,"
SI File No. GPCO-31 Q-209.b. SNOC Dwg. S-41615, GE Dwg. 761E246, Sht. 1, "Reactor Vessel Thermal Cycles (Including Black Start)," SI File No. 1001527.211.
- c. SNOC Dwg. S-416 16, GE Dwg. 761E246, Sht. 2, "Reactor Vessel Thermal Cycles (Including Black Start),"
SI File No. 1001527.211. File No.: 1001527.303 Page 18 of 30Revision: 0F0306-01R1
hItugdl Associates, Inc."5. Feedwater Nozzle Thermal Cycle Diagrams:
- a. GE Dwg. 135B9990, "Nozzle Thermal Cycles (Feedwater),"
SI File No. 1001527.211.
- b. SNOC Dwg. $26421, GE Dwg. 158B8369, Sht. 4, Rev. 2, "Nozzle Thermal Cycles -Including Black Start (Feedwater
-Normal & Upset Conditions)," SI File No. 1001527.211.
- c. SNOC Dwg. S26422, GE Dwg. 158B8369, Sht. 5, Rev. 2, "Nozzle Thermal Cycles -Including Black Start (Feedwater-Emergency
& Fault Conditions)," SI File No. 1001527.211.
- 6. Water Level Instrument Nozzle Thermal Cycle Diagrams:
- a. GE Dwg. 135B9990, Sht. 7, Rev. 0, "Nozzle Thermal Cycles (Instrumentation
& Core Diff.Press & Liquid Control)," SI File No. 1001527.211.
- b. SNOC Dwg. S26426, GE Dwg. 1 58B 8369, Sht. 9, Rev. 2, "Nozzle Thermal Cycles -Including Black Start (Instrumentation
& Core Diff. Press & Liquid C," SI File No. 1001527.211.
- 7. PVRC Recommendations on Toughness Requirements for Ferritic Materials, WRC Bulletin 175,August 1972.8. American Society of Mechanical Engineers, Boiler and Pressure Vessel Code, Section XI, Rules forInservice Inspection of Nuclear Power Plant Components, Non-mandatory Appendix G, "Fracture Toughness Criteria for Protection Against Failure,"
2001 Ed. through 2003 Addenda.9. Sommerville, D. V., "Linear Elastic Fracture Mechanics Evaluation of General Electric BoilingWater Reactor Water Level Instrument Nozzles for Pressure-Temperature Curve Evaluations," SIReport 0900876.401, Rev. 0, June 2011.10. Hatch Unit 1 NUREG-0619 Evaluations:
- a. Liffengren, D. J., et al., "Edwin I. Hatch Nuclear Power Station, Unit 1 Feedwater NozzleFracture Mechanics Analysis to Show Compliance with N UREG-06 19," NEDE-30238, DRF-137-0010, August 1983, General Electric Company.
SI File No. 1001527.210. GEProprietary Information.
- b. Bothne, D., "Power Uprate Evaluation Report for Edwin I. Hatch Unit 1, Feedwater NozzleNUREG-06 19 Fracture Mechanics Analysis for Extended Power Uprate Conditions,"
GE-NE-B13-01869-065-01, July 1997, General Electric Company. SI File No. 1001527.210. GEProprietary Information. File No.: 1001527.303 Page 19 of 30Revision: 0F0306-O01RI
it Associates, 11. Hatch Unit 2 NUREG-0619 Evaluations:
- a. Liffengren, D. J., et al., "Edwin I. Hatch Nuclear Power Station, Unit 2 Feedwater NozzleFracture Mechanics Analysis to Show Compliance with NUREG-0619,"
NEDC-30256, DRF-137-0010, August 1983, General Electric Company. SI File No. 1001527.210. GEProprietary Information.
- b. Stevens, G. L., "Updated Feedwater Nozzle Fracture Mechanics Analysis for Edwin I. HatchNuclear Power Station Unit 2," GE-NE-523-95-0991, Rev. 0, DRF B 13-01524, September 1991, General Electric Company.
SI File No. 1001527.210.
- c. Bothne, D., "Power Uprate Evaluation Report for Edwin I. Hatch Unit 2, Feedwater NozzleNUREG-0619 Fracture Mechanics Analysis for Extended Power Uprate Conditions,"
GE-NE-B13-01869-065-02, July 1997, General Electric Company. SI File No. 1001527.210. GEProprietary Information.
- 12. BWR Feedwater Nozzle and Control Rod Drive Return Line Nozzle Cracking, NUREG-06 19,November 1980, Nuclear Regulatory Commission.
- 13. Sommerville, D., Walter, M., "An Investigation into the Effects of Modeling Cylindrical Nozzle toCylindrical Vessel Intersections Using 2D Axisymmetric Finite Element models and a ProposedMethod for Correcting the Results,"
ASME PVP201 1-57001, Proceedings of the 2011 ASMEPressure Vessel and Piping Division Conference.
- 14. Pilkey, W.D., Pilkey, D.F., Peterson's Stress Concentration
- Factors, 3rd. Ed., John Wiley & Sons,2008.15. Zahoor, A., "Ductile Fracture Handbook,"
EPRI Report NP-6301, Volume 3. January 1991.16. Water Level Instrument Nozzle Drawings:
- a. SNOC Sketch 1-BE-i, Rev. 0, "Nil, N12, and N16 Instrumentation Nozzle Detail,"
SI FileNo. 1001527.208.
- b. SNOC Sketch 2-BE-2, Rev. 1, "2N12 and 2N16 Instrumentation Nozzle Detail,"
SI File No.1001527.209.
- 17. Feedwater Nozzle Drawings:
- a. SNOC Dwg. SX18921, "Reactor Vessel Feedwater Nozzle As Built," SI File No.100 1527.208b. SNOC Sketch 2-BF-4, Rev. 1, "2N4 Nozzle Assembly (Feedwater),"
SI File No. GPCO-31Q-208.18. American Society of Mechanical Engineers, Boiler and Pressure Vessel Code, Section II, Part D,Materials, 2001 Ed. through 2003 Addenda.19. Yin, S., Bass, B. R., Stevens, G. L., Stress and Fracture Mechanics Analyses of Boiling WaterReactor and Pressurized Water Reactor Pressure Vessel Nozzles, ORNL/TM--2010/246, December2010.File No.: 1001527.303 Page 20 of 30Revision: 0F0306-O01R1 rai lte gril Associates, Inc;"20. Sommerville, D.V., Qin, M., Houston, E., "An Investigation of the Adequacy of a Simplified Boundary Integral Equation / Influence Function Equation Linear Elastic Fracture Mechanics Solution for Nozzle Corner Cracking," ASME PVP201 1-57742, Proceedings of the 2011 ASMEPressure Vessel and Piping Division Conference.
- 21. SI Calculation Package 1100445.302, Rev. 0.22. SI Calculation Package 1100445.303, Rev. 0.23. SI Calculation Package NPPD-13Q-302, Rev. 1.24. SI Calculation Package 1000847.302, Rev. 0.25. SI Calculation Package 1000847.303, Rev. 2.26. SI Calculation Package 1100151.302, Rev. 0.27. S1 Calculation Package 1100151.303, Rev. 0.28. SI Calculation Package 1100445.304, Rev. 0.29. Combustion Engineering Drawing 232-242, Nozzle Details, SI File No. 1100445.204.
- 30. Core DP Nozzle Drawings:
- a. SNOC Dwg. S-15227A, Combustion Engineering Drawing 234-244-5, Nozzle Details for218" I.D. BWR, SI File No. 1001527.208.
- b. SNOC Sketch 1-BE-2, Rev. 1, "N10 Standby Liquid Control & Core Differential PressureNozzle Detail,"
SI File No. 100 1527.208.
- c. SNOC Dwg. S15523, Combustion Engineering Drawing 234-270, Rev. 3, "General.
Arrangement Elevation for 218" ID BWR," SI File No. 100 1527.208. File No.: 1001527.303 Revision: 0Page 21 of3O0F0306-01R1 $Sbwcbuu hlgl Assadate .°Table 1: Hatch Unit 1 FW Nozzle Blend Radius Path Stress Distributions. 1000 psig Internal Pressure Load CaseThermal Load Case450 "F shockPathDistance, °h) Oh(2' 3o, Gb,in. pipsi psi psi0.000 f.l }.1 24461 58463 Di Di0.075 ]} 24052 57486 II }I0.225 1 /] 23283 55649 i }J-0.400 ft }1 22437 53626 1}0.600 It Di 21527 51452 U1 Di0.850 U /] 20466 48916 [ }.i.1.150 }1 19262 46037 Di }11.500 J} 18081 43215 ft }11.960 1.1 }1 16848 40268 Ii 1.2.476 ft }1 15206 36344 Di Di3.052 I.I ]J 13724 32802 Ui Di3.628 II }i 12372 29571 Di }}4.204 II 11110 26554 IL Di4.779 Di }) 9898 23657 lit Di5.355 Di Di 8692 20774 sD5.93 1 Di Di 7439 17780 ft }6.507 Di 1) 6073 14515 UJ Di6.811 Di }i 5384 12868 ft DiNotes:1. From Reference [10a], with CF=1.6557.
- 2. From Reference
[l0a], with CF=1.6557 removed.3. From Reference [10a], with CF as given in PVP201 1-5700 1 [13].File No.: 1001527.30, Revision: 03Page 22 of 30This page contains GEH PROPRIETARY INFORMATION which has been redactedF0306-01IRI mnssa t whlt A~ s A,.Table 2: Hatch Unit 2 FW Nozzle Blend Radius Path Stress Distributions. 1000 psig Internal Pressure Load CaseThermal Load Case450 OF shockPathin. pipsi psi psi0.000 U1 } 21010 58242 L1 }IL.0.075 LI }) 20651 57247 Li IL0.225 LI }i 19970 55359 H I0.400 I( }L 19213 53261 fL IL0.600 Li II 18403 51015 Li IL0.850 Li /) 17440 48345 LI II.1.150 IL 16452 45607 Li IL1.500 LI IL 15206 42153 Li IL1.954 Li IL 14233 39455 Li IL2.693 LI IL 11909 33013 Li }L3.284 LI II 10634 29479 {L Li3.874 Zl H9468 26245 IL4.465 Li II 8365 23188 {L }L5.056 Li I}. 7289 20206 LI IL5.647 LiII} 6194 17170 Li IL6.247 Li IL 5029 13941 Li IL6.838 LI II! 3718 10307 Li IL7.127 Li IL 3040 8427 LI ILNotes:1. From Reference
- 2. From Reference
- 3. From Reference
[1 la], with CF=1.5987. [1 la], with CF=1.5987 removed.[1 la], with CF as given in PVP201 1-5700 1 [13].File No.: 1001527.303 Revision: 0Page 23 of 30This page contains GEH PROPRIETARY INFORMATION Iwhich has been redactedF0306-01RI $b~jSlcrral hIt Writ Associates, Inc.=Table 3: Hatch Unit 1 Core DP Nozzle 1000 psi Internal Pressure Load Case Path StressDistribution [281.Path Distance, ah,in. psi0.000 261860.225 316100.450 305250.675 284490.901 263771.126 235181.351 222721.576 211891.801 202222.026 193512.251 185592.476 178312.702 171562.927 165223.152 159163.377 153273.602 147463.827 141694.052 135944.277 128384.503 12045File No.: 1001527.303 Revision: 0Page 24 of 30F0306-01R1 8 q trailafugri Associates, mnc:Table 4: Hatch Unit 1 FW Nozzle K1p and KIT using the BIE/IF Methodology. Pressure JThermalA0 58242 51488Al -11913 -15980'A2 1484.2 2002.4A3 -105.18 -127.21K1 81.1 65.3 ksi-in°'5Table 5: Hatch Unit 2 FW Nozzle K1p and KIT using the BIE/IF Methodology. Pressure II ThermalA0 58136 48077Al -12560 -28076A2 1522.5 4948.5A3 -103.53 -598.8K1 81.3 46.8' ksi-in°'5Table 6: Hatch Unit 1 Core DP Nozzle Kwp using the BIE/IF Methodology. PressureA0 35123Al -12874A2 3144.7A3 ,316.07KI 38.9 ksi-inO.S Table 7: Hatch Unit 1 FW Nozzle K1p using the WRC Bulletin 175 Methodology. F(a/rn) 1.61 -PR1/t(7ta)05 47.49 ksi-in°'5KI 76.6 ksi-in°'s Table 8: Hatch Unit 1 Core DP Nozzle K~p using the WRC Bulletin 175 Methodology. F(a/rn) j0.99 -PRi/t(ira)° 5 32.58 ksi-in°'5K______ I 32.3 ksi-in°'s File No.: 1001527.303 Page 25 of 30Revision: 0F0306-01R1
Assaciatus, Irnc=Table 9: Hatch Unit 2 FW Nozzle K~p using the WRC Bulletin 175 Methodology. F(a/r,) 1.62 -PRi/t~ta) 05 48.58 ksi-in°5K~p78.9 ksi-in0'5Table 10: Summary of Nozzle KIT Results Using the BIE/IF and G-22114.3 Methodologies. NozzleKIKT Plant ID Tp()Path Length, (BIE/IF Solution), (Flat Plate Soln.), Ratio Reference Te2 in ksi-in°'5 ksi-in°'5Plant A (3) FW 7.60 11.1 15.2 1.37 [21], [22], [23]Plant B FW 7.73 7.0 15.8 2.26 [24],[25] Plant B RI 9.29 9.4 25.1 2.67 [25]Plant C (1) FW 8.66 23.3 63.1 2.71 [26]Plant C FW 8.66 9.0 21.0 2.34 [27]1.2.3.300 *F/hr cooldown transient. FW is Feedwater nozzle, RI is Recirculation Inlet nozzle.Path length taken as 205 *RPV shell thickness to estimate the 45 degree path length.Table 11: Maximum Stress Intensity Factor for WLI Nozzle Considering Thermal Load Cases."ksi'in°0S Ratio of Simplified Method to.*Load Case BIEiIF Simplified. ... ..BIE/IF Methiod1271 MethodShutdown with 100 °F/hr 39.2 37.1 0.95Shutdown with 300 0F/hr 60.5 111.3 1.84Turbine By-Pass & SRV Blow-down 55.11. Where Reference [27] gives tv=5.98 inches, tn=0.795 inches, xc=9.75E-6 in~in/°FFile No.: 1001527.303 Revision: 0Page 26 of 30F0306-01RI $jj'sinww l Interity Associates, Inc.Table 12: Summary of Nozzle Stress Intensity Factors.Pressure (1,3)(1000 psig)Thermal (1,4)(450 TF shock)Thermal (1,5)(100 °F/hr)(200 °F/hr)...Nozzle j Unit 1 Unit 2 Unit 1 Unit 2 J Unit 1 Unit 2 Unit o1 Unit 2FW J 76.6 78.9 65.3 46.8 j 11.5 12.9 j 23.1 25.8WLI j 71.6 80.0 n/a n/a 17.4 19.9 34.8 39.9Core DP 32.3 n/a n/a n/a 1.73 n/a 3.46 n/a1. KI in units of ksi-in°5.2. 200 °F/hr results are scaled from 100 °F/hr assuming response is linear.3. Pressure load case results are obtained using WRC 175 methodology [7].4. Thermal shock results are obtained using BIE/IF methodology [1].5. Thermal ramp results are obtained using ASMIE XI, Non-mandatory Appendix G, Paragraph G-2214.4 methodology [81.File No.: 1001527.303 Revision: 0Page 27 of 30F0306-01RI 'jjuwtowau lategrify Associates, Inc."Nozzle BlendRadius Path NNozzle CornerCrack LocationFigure 1. Typical Nozzle Corner Crack Stress Extraction Path Orientation. 2A"o t(3.1 0.2 0.), 0.4 0.5' (3,0 0.1RA1IO OF-CRACIK SIZE T'O MDI,, OR NO)ZZ'L[ RAOiUS lilyn0,5 0.9Figure 2. 'WRC Bulletin 175, Figure A5-i, Estimates of Stress Intensity Factors for Flaws at aNozzle Corner [71.File No.: 1001527.303 Revision: 0Page 28 of 30F0306-01R1 Figure 3. Hatch Unit 1 FW Nozzle Blend Radius Path Stress Distributions [10b].Figure 4. Hatch Unit 2 FW Nozzle Blend Radius Path Stress Distributions [lla].File No.: 1001527.302 Revision: 03Page 29 of 30SThis page contains GEH PROPRIETARY INFORMATION which has been redactedF0306-01R 1 350000 -Ivy= -316.07x3 + 3144.7x2 -12874x + 3512325 0 ....... I ... ..R = 0.9964 ...* .1 50 0 ...... ....... .. ..... .0 0.5 1 1.5 2 2.5 3 3.5 4 4.5Nozzle Path Distance, in,,,,OOO00 psig PressureNote: The first data point in the series is excluded for the curve fit.Figure 5. Hatch Unit 1 Core DP Nozzle 1000 psi Internal Pressure Load Case Path StressDistribution. 70................................... ........ ... .... .. ........um Krr= 6 6.5 M Pa'rnm (t0.5 60 ~~~~~MaximumKIA= 60.6 MPa im (15_5.1 ksh ............. 5040,#2o-10--.-Shutdown at 55.56 degree C/hr-e-Shutdown at 166.67 degree C/;nro Turbne By-Pa. & SRVM Biowdown6000 8000 10000 12000 14000 16000 18000 20000Thne (sec)02000 4000Figure 6. Plant C WLI Nozzle KIT for Three Thermal Transients 1271.File No.: 1001527.303 Revision: 0Page 30 of 30F0306-0I1R}}