NRC/ANL INDUSTRY MEETING

Dated: November 6, 2008

H* Results Study

3D Analysis ResultsRadius Dependent Tubesheet Stiffness Results

Combined Applied LoadingAxisymmetric vs. 3D Results

Background

• Reference model for H* calculations was theAxisymmetric Linear Superpositioning (ALSP) model

- Unit loads calculated separately, then combined by linear scalingand superpositioning

-. The divider plate is not an axisymmetric component-Approach benchmarked against 3D Finite Element Analysis

(FEA) and shown to be very conservative

* Current preferred approach is the 3D FEA model- Integrated loading

- Responds to staff questions

H* Contact Pressure Theory Basis

* Based on Initial work by Goodier (1943)° Includes material effects, operational

effects, etc. that affect the tube-to-tubesheet contact pressure distributionfrom the top of the.tubesheet to theelevation of a flaw within the tubesheet.

• Goodier model is refined and bench-marked by test data.

Factors in H* Contact Pressure Solution

° Crevice Pressure Distribution- Determined using Test Data and Analysis

* Tubesheet Rotation & DisplacementDetermined using 3D and Axisymmetric FEA

° Tube & Tubesheet Bore dilation and contraction- Determined using 2D FEA

* Residual Contact Pressure- Determined using 2D FEA- Test data simulates real SG manufacturing conditions

° Variation in Material Properties- Thermal growth of Tube & Tubesheet Bore- Determined using Test Data

H* Contact Pressure Evaluation

SPi = Internal primary side pressure, Ppri psi* Po= External Pressure = Crevice pressure, PcP psiSb = Inside radius of tubeSc.= Outside radius of tubeSd-= Outside radius of equivalent tubesheet collar•at = Coefficient of thermal expansion of tube, in/in/0FSEt= Modulus of Elasticity of tube, psi* ETs =Modulus of Elasticity of tubesheet collar, psi° Tt= Temperature of tube, OF* v = Poisson's Ratio of the material

Current H* Results16.0

I-

E3

14.0-

12.0

10.0

8.0

'-ALSP Worst Case Tube Hstar w/BET

"i"3D Whole Bundle Hstar w/BET

Generic Model F ResultsCondition Specific TS InputNOP ThOl = 620 IFNOP Ppo = 2250 psi

NOP P_. = 895 psiSLB Pm = 2560 psi

SLB Pse_ = 0 psi

SLB Th.t = 450 OFDP Factor = 0.64TS Stiffness varies with TS RadiusDepth based CPROepth based RCPLimited Contact Pressure Slope BasisApplied SIPC Safety Factor

0--ýI 141-

N6.0

4.0

2.0

0.0

ALSP -, lal Linear 3uperpositioing modelE-T--a ewanee-ft pnceertainty-i .position-ef- bttem-ef

expansi n transition

0 10 20 30 40 50 60 70

TS Radius, in

* Contact pressure distributions for all operating cases compared and worstcase results at each radius used for H*.*Worst case tube H* defined using SIPC, limiting TS sector, worst conditionresult (ALSP).o Whole bundle (95/50) analysis based on 5500 tubes in Model F bundle.

Crevice Pressure Distribution• Based on test data from pressure taps with axial offset.

(LTR-CDME-07-198)• Scaled to apply test specimen data to real tubesheet

crevice.* Initially applied to penalize structural and leakage

analysis using limiting median value.* NRC RAI questioned use of limiting median value and

identified an alternate ("depth based") approach(December 2007).

- The depth based approach utilizes average of crevicepressure test valuesReferences the crevice pressure distribution to thepredicted value of H*

Crevice Pressure Distribution

• Major effects on H*/Tube Integrity:-. Defines pressure expansion of tube and TS

Defines driving potential for leakage in crevice- Determines final length of tube. required and

value of H*

* Requires iterative H* solution-Scale crevice pressure length to first

prediction of H*- Recalculate H*

Crevice Pressure Distribution1 .0 0 1 1 - no - - - - -, i i

0.80

" 0.60

1°a)U 0.20 "--O-Original NOP "--E+'Original SLB

•,"'Applied NOP -M Applied SLB

0.0

0.00 0r20 0.40 0.60 0.80 1.00

Flaw location Denth Ratin I/I Tnn nf "r0•\i," 9 specimen

Crevice pressure model applied as ratio to scaleresults to final applied tube length.

Crevice Pressure Distribution

U)4)2..0.

1,20

1.00

0.80

0.60

0.40

0.20

0.00 I-0.50 0.60 0.70 0.80 0.90 1.00

Depth Ratio1.10

" ANL and WEC crevice pressure distributions are similar.* WEC test data shows larger pressure difference near TTS." WEC test results for SLB and NOP are very different.

Tubesheet Rotation &Displacement

* Two different models and approachesused in past:-3D applied loads and displacements

-Axisymmetric Linear Superposition (ALSP)

° 3D finite element analysis preferred

* NRC RAI requested 3D model tobenchmark ALSP

3D Tubes heet Displacements

o TS displacements vary with respectand angle

to radius

S.Maximum TS displacements due to pressureloading occur perpendicular to DP

l Minimum TSloading occu

displacements due to pressurer parallel to DP

TS displacements due to thermal loads aresimilar throughout the TS

* Reduced TS displacements (compared to ALSPmodel) lead to increased •T-TS Contact Pressure

ANSYS WB Model of SG

•½ symmetry and ¼ symmetry FEA models used.*Tube perforations included as separate model layer.*Anisotropic TS material model (Ref. Slot) used for global TS displacement analysis.-Perforated local TS models used for areas of concern.

Application of Thermal Loads

*Typical NOP Temperature Distributions-Uniform Body Loads produce Greater TS Displacements

* ALSP uses Uniform Body Loads° 3D FEA model uses more realistic surface loads

Application of Pressure LoadsSLB NOP

S0.2501 j 07

" 3D boundary. con ditions vary with. SG model due to geometry differences.• 3D Applied Load Cases prove that axisymmetric loading is conservative." ALSP app roach does not, capture 3D mode shape of TS.°3D Applied Load TS Disp. << Axisymnmetric Unit Load TS Disp.

3D Tubesheet Displacements'0, Row 57, Column 80, Approx. 1770 Tubes in Sector

-5------------------------------Limit of Measurable Difference in Pullout Resistance (1 % or Greatei

-10 Percent Difference Comparison based on TTS results.-10 BTS results show a greater percent difference in TS

in. Displacement with variation in TS angle due to proximity to DPDM welds.

E - _15a) "Row 47, Column 97

5% or Greater Increase in Pullout Resistance

E h -4 -..--. . - - -

Ie SG Tubesheet Coordinate System

45 ZaDP

E H 30- X

0 -35 -

10% or Greater Increase in Pullout Resistance~: -40 -- -- ----------------------------------------------------------------- -

Row 42, Column 10

-45.0 5 10 15 20 25 30 .35 40 45

TS Sector Angle (Tan-' [ZIX]), Degrees

*Primary and Secondary Pressure loads applied simultaneously*Reference case is maximum TS Radial. Displacement at 00 (900away from DP).,H* analysis. is based on worst case TS azimuth. (900 away from DP)

• Tube & Tube Bore Effects

* Goodier analysis assumes tube andtubesheet always in contact aroundcircumference.- Elastic restoring forces cause surfaces to

follow each other through deformations.* WEC analysis decomposes contact

pressure into tube effects and tubesheeteffects with T-TS interaction coefficients tomaintain compatibility.

Tube & Tube Bore EffectsW analysis conservatively allows for tube bore toýdilate. away from tube such that-no benefit tocontact pressure is gained.

No "pinching," just major axis ovalization.- Thermal growth and pressure dilation act on major

and minor axis of tube bore.- Tube effects then compared to see if tube OD

"catches up" to tube bore deformation.

- Predicted value of dilation, -10-5 in., <<bore surfacefinish; no effect on leakage analysis

* Tube & Tube Bore dilation effects in a realtubesheet quantified in tubesheet stiffness study.

Tubesheet Bore Deformation in H*

IniiWa UndefbrmedTube Hole

Thick Shel: SkAluir fo~r.Tube Hole dlatia due to

P" SSUe. 0u D SufkaeA T: S ::::::::::::

.Non-uniformdeformations mayoccur in real TS.-*The tube followsthe tubesheet.

ATS., plus Tubesheet bowfron FEA Results

.H* analysis requiresuniform deformation.-lDecomposescontributions to tube

MIWtal Undefoi"edTube Hole

Thick Shel Solutin fbrTube~ Hale Odatian due toPressue on ID Surface

ATS.

(i

and tubesheetdeformation. ATS, plus Tubesheet bow

from FEA Results

Original Tubesheet Stiffness Study

• Original TS Collar (unit cell) wall thicknessdetermined by pressurizing single tube insquare pitch bundle.

* No other TS bore pressurized.* Minimum material properties used.* Appropriate for calculation of TS

displacements around a single hole.* Underestimates TS bore stiffness in

.bundle because it ignores restoring effectsfrom adjacent pressurized tubes.

Tubesheet Stiffness Study

° Restoring effect of adjacent pressurized tubeswas determined in a separate study.

• Objective was to improve accuracy of modelinga specific tube at a given TS -radius.

* Tubesheet stiffness coefficient (TS OD, d) cannow vary with radius based on constraint fromboundary conditions.

° Result rationalizes ALSP model response touncertainties; no significant effect on 3D FEAsolution

Tubesheet Stiffness StudyTwo Plane Stress Finite Element Models used:

- Model 1: Represents limiting region in bundle,perpendicular to DPModel 2: Represents stiffest region in bundle, parallelto DP.

Two cases considered:- All tubes pressurized.

' Three "tubes of interest" pressurized.

-Shown to bound all other conditions

Two pressure cases used on tube bore:- SLB: 2560 psi, Psat 358 psi- NOP: 2250 psi, Psat 1418 psi

Tubesheet Stiffness Study•(ATSpressure)TS -cPCREv [d2-cC2

E(A TSID)F + v

FE _Pressure )-S 2 - 2)

360Psu

* AFEA represents net difference between FEA and TS Results.• Net difference is required because real tube bore dilation is

not uniform.* If AFEA>O, FEA ATSID predicts greater tube bore dilation thanThick Shell Equations.

* If AFEA<O, FEA ATS1D predicts less tube bore dilation thanThick Shell Equations.

..Tu-besh~eet. StiffnessStudyi.Model 1:Wos Cas .TSD~iplac~Model 2. Stiffest TS Sector

Model 2 *Model I results sh..ow. greatest.displacement.

a, ... Model 1 combined load case.benchmarked against 3D TS withi.....ra~dial.di spla cemnent.... .

Y

x

Tubesheet Stiffness Study.<Model 1

* 3 tube bores of interest constant in each model.e Analysis also included expanded tubes in tubesheet bores of interest.

Tubesheet Stiffness StudyH* analysis modelassumes that tube

ovalization can onlyreduce contact

pressure.I

Typical peripheral("outside") tubesheet boredeformation for apressurized tubesheet.

Typical Result Model 1 ResultOutside Tube Hole w/Expanded Tube100% NOP Primary Pressure AppliedDisplacements Magnified 500x

Tubesheet Stiffness Study

I.5z

I-

8S

47.5I

I-

I0

I-

0 45 90 135 - 180 225

Tube Hole Angle, 0 [Degrees]

270 315 360

0 45 90 135 180 225 270 315 360

Tube Hole Angle, B0

e Mode shapes of tube bore ovalizations are "constant."o Scale of deformation changes based 0on tubesheetbore pressure.* All tubesheet bore locations show less averagedeformation than Thick Shell equations.

Tubesheet Stiffness Study

C0

UC)

C)00C)

IC)C)

C)

I-

C)

U,

C.)

I-

C

C)

U)enC)0.CCCC)C

0

C)

6E-05

*5E-05

4E-05

3E-05

2E-05

1E-05

OE+000

X

.83 1.33 1.83 2.33 2.83 3.33 3.83

Tubesheet Collar Outer Diameter, d [in]

4.33 4.83

Thick Shell tube bore ID dilation is asymptotic with respect to d.H* calculation model uses dilations not predicted to be theoretically possible in a real TS;No significant effect in most of bundle.

Tubesheet Stiffness Study

Thick Shell Avg. FEACondition Location Deflection Deflection % Diff

- in in -SLB Inside 5.72E-05 3.43E-05 -40.1SLB Middle 5.72E-05 -7.53E-08 -100.1SLB Outside 5.72E-05 -2.68E-05 -146.8NOP Inside 5.24E-05 3.77E-05 -28.0NOP Middle 5.24E-05 1.79E-06 -96.6NOP Outside 5.24E-05 1.10E-06 -97.9

FEA Results predict a net reduction in tube bore ID6ompared to Thick Shell equations.Tube bore-deflection calculation in H* model must be

)ositive and uniform, but best representation of TS boreilation indicates non-uniform deformation.

,Non-uniform deformation increases contact pressure.

Tubesheet Stiffness Study

For all tube bore locations, Net FEAresultsare less than Thick Shell results.-Actual tubesheet bore dilation is less than

uniform Thick Shell estimate.

* Thick Shell results adjusted by Net FEAdifference by scaling d.

* Final d Scaling based trends from FEAResults.

Tubesheet Stiffness Study3.50

3.00

2.50

S2.000

O1.50CL

0.50

0.00

SLB Linear Fit:y = 0.0376x + 0.8593 _

R2 =0.9949

NOP Linear Fit:y =0.0352x + 1.1463

R = 0.7646

91NOP and SLB

NOP 8 SLB -Linear (SLB) -Linear (NOP)

f . _

0 10 20 30 40 50 60 70

TS Radius, in

oMinimum d value at inside tube bore (Maximum Deformation)*Maximum d value at outside tube bore (Minimum Net Deformation)

Tubesheet Stiffness Study10 T 1

Generic Model F Results

_Axisymmetric TS Displacements

U-

F-

E07

6 55, -

________-__________S..,UliIUILIUII •I.)JCUHIIL, I iI•.JUt

NOP Thot 620 'FNOP Ppr 2250 psiNOP Psec = 895 psi

SLB PpH = 2560 psiSLB P. . 0 psiSLB Thot = 450 °F

DP Factor = 0.64TS Stiffness varies with TS RadiusDepth based CPRDepth based RCPLimited Contact Pressure Slope BasisApplied SIPC Safety Factor

0.4

•- 3 -U)

0-

-4,.-MEAN Hstar w/BET

-0-MEAN Hstar w/BET, No TS Stiff Effect

0 ____.......___.

0 10 20 30 40 50 60 70

TS Radius, in

Radius specific tubesheet stiffness modification has smalleffect on mean H* (ALSP).

Summary of TubesheetStiffness Study

• No changes to existing H* analysisapproach.

* Same contact pressure equations usedwith adjusted TS'Stiffness.

* TS Interaction coefficients and TS Collarthickness vary with TS. Radius.-Tends to increase H* at TS Radius > 30".

Residual Contact Pressure

• Residual contact pressure (RCP) isdefined as that contact pressure due tohydraulic expansion only

• Mean value of RCP is defined based onpullout tests, in progress

° Variability of RCP is defined analyticallyusing a 2D FEA model

Residual Contact Pressure Study

* H* analysis tool can accommodate anyRCP distribution.

* Test results will be used to benchmarkmodified Goodier .pullout model.

• Friction model can be applied as constantvalue or non-linearly varying.model.

* Recent literature results are considered.-Soler, Bazergui et al., Allam et al., etc.

References* Goodier, J., Schoessow, G., Transactions of the ASME,

Vol. 65, July 1943, pp. 489-496.

* Soler, A., et al., 1984, Mechanical Design of HeatExchanger and Pressure Vessel Components, ArcturusPublishers, Cherry Hill.

• Allam, M., Bazergui, A. , ASME JPVT, Vol. 124,February 2002, pp. 22-31

* Merah, N., AI-Zayer, A., Shuaib, A., Arif, A., Int. J. ofPressure Vessels and Piping, Vol. 80, 2003, pp. 879-885

Residual Contact Pressure Study5000

4500

4000

30

o 3000

"p 2500

20000

1500

1000

500

06 8

Expansion Length, in

*Goodier: Assumes constant coefficient of friction..Soler: Effective coefficient of friction that varies withexpansion length.*Both models require test data to benchmark values.

H* FEA Residual Contact Pressure SensitivityPreliminary Results

Sensitivity study considers, the following set ofparameters:

- Unexpanded Tube OD- Tubesheet Hole ID-Tube wall thickness

Tube Yield Stress- Tube Elastic Modulus-Tubesheet Elastic Modulus- Expansion Pressure

.--Level of Strain Hardening

* End result of sensitivity study will be a distribution ofresidual contact pressure due to +2a variation of eachparameter

H* FEA Residual Contact Pressure Sensitivity Analysis

• Full 3600, concentric cylinder, 2-D plane stressrepresentation of tube and tubesheet

* Surface-to-surface contact between tube OD

and tubesheet hole ID

* Pressure.load applied to tube ID

* Multi-linear isotropic strain hardening

H* FEA Residual Contact Pressure SensitivityPreliminary Results

.Mean Value .•(si) ea a -2 Gy Value (psi) +2 Gy Value (psi)-_ W_ -- (psi)

Tube OD 371 108 544

S TS ID 371 530 134

Tube Wall371 391 348Thickness

Tube Ys 371 1364 30*

Tube E 371 304 438

TS E 371 438 307ýExpansionExPansiun 371 200 542Pressure

Strain Hardening 371 711 36Curve

H* FEA Residual Contact Pressure SensitivityPreliminary Results

Y214'25 2008S .: 1 .3: 2 8±: 00

&OQUA: VOLUT1'ZO

TFA M TE

E'F A .C' TC I' -

FLI 0'50"?ý'I-:2 2, * 4 02

.022873"'

0' 372102 4152

,.f}28004:

contours forundeformed

* Finite element modelcan accommodateradial springback.

* Finite element modelconservatively appliesexpansion pressure tominimize resultingcontact pressuredistribution.

* Values for plasticstrain and deformationin the expanded tubeare similar to originalstudy results.

Typical Plastic Strainmean case plotted on

configuratio n.

H* FEA Residual Contact Pressure SensitivityPreliminary Results

Average residual contact pressureapproximately 371 psi

H* analysis cu.or zero

rrently assumes either 300 psi

• Residual contact pressure m.to variations in the tube yield

Residual contact pressure is

ost sensitivestress.

I sensitive tovariations in post-yield strain hardeningbehavior

H* Results

• ALSP and 3D TS Displacement Compared

* Simplified Statistical Method (SSM) fromGuidelines used to combine variability at95/50 confidence level as a shortcut

• Minimum H* value of 3 in. is established tomeet leakage requirements

* BET bounding value of 0.3 inch isconservatively added to minimum H* value

H* Results

* Bounding Model F Operating Conditions* 6 Parameters in H* study:

- Coefficient of Friction (t -= 0.3, 1G = 0.1)

- Residual Contact Pressure (ýtIbf/in)

- 200 ibf/in, l- = 50

- Tubesheet Young's Modulus (1 a = 0.85%)Tube Young's Modulus (11G = 0.85%)

- Tubesheet CTE (1 = 1.62%)- Tube CTE (1 = = 2.33%)- Linear RCP model assumed.

* Each parameter varied independently

ALSP Model H* Results

14I

GeneAxisyCondKlnCDu- 12

-I--I--

Eo 10I,-

(D 8

0

a) 6

4-

.E 2

0

NOPNOPSLB

_ _ __SLBSL

SLB-I• " DP F•

TS SiDepti

ric Model F Results'mmetric TS Displacementslition Specific TS InputThot = 620 IF

Ppfi = 2250 psi

Psec = 895 psi

P= 2560 psi

Psec = 0 psiThor = 450 OF

actor = 0.64tiffness varies with TS Radiush based CPRh based RCPed Contact Pressure Slope Basis

ed SIPC Safety FactorN Depti

LimitAppli

--*--SSM Hstarw/BET

-I--MEAN Hstar w/BET

-MEAN Hstar Tube = 10.60 in w/BET

0 10 20 30 40 50 60 70

TS Radius, in

3D FEA H* Results16.0

r f

S 14.0uiI-I-

E 12.0.0

108.0

CI-

6.0

C

o6.0

4.0

E 2.0

"0--SSM Hstar w/BET

N.MEAN Hstarw/BET

d-iMEAN Hstar Tube = 3.30 in w/BET

Generic Model F Results3D TS DisplacementsCondition Specific TS InputNOP Tht= 620 IFNOP Pp. = 2250 psiNOP Psec 895 psi

SLB Pp = 2560 psiSLB P_55 = 0 psiSLB Thor = 450 IFDP Factor = 0.64TS Stiffness varies with TS RadiusDepth based CPRDepth based RCPLimited Contact Pressure Slope BasisApplied SIPC Safety Factor

F F I -I

I F F -I

Minimum H* value is determined based on leakagerequirements

I ! _ _ _ _ _

0.00 10 20 30 40 50 60 70

TS Radius, in

3D TS Displacements much less sensitive to variability

Comparison of 95% H* Results16.0

.14.0cli

E 12.00

1o~

10.0C.

o .8.0

6.0

4.0

E2.0

-4-SSM 3D Hstar w/BET

--I•-SSM Axisymmetric Hstar w/BET

Worst tube at 95%Probability

Worst tube at 95%Probability

0.0

0 10 20 30 40 50 60 70

TS Radius, in

Current H* Result's16.0

14.0C6I-I-

12.0.0

S10.0C.

0 8.0

0.2

in 6.0

SS4.0

E 2.0--

-4-ALSP Worst Case Tube Hstar w/BET

i .- 3D Whole Bundle Hstar w/BET

I. ________________________

Generic Model F ResultsCondition Specific TS InputNOP Twt = 620 OF

NOP P. = 2250 psi

NOP Pse_ = 895 psi

SLB P,, = 2560 psiSLB Pse = 0 psi

SLB Thor = 450 OFDP Factor = 0.64TS Stiffness varies with TS RadiusDepth based CPRDepth based RCPLimited Contact Pressure Slope BasisApplied SIPC Safety Factor

N

A-,

ALSP - Axial Linear Superpositioning modelBET - allowance for uncertainty in position of bottom ofexpansion transition.

F ! I____________________0.0

0 10 20 30 40 50 60 70

TS Radius, in

qontact pressure distributions for all operating cases compared and worstca:e results ateach radius used for H*,°VWorst case tube H* defined using SIPC, limiting TS sector, worst conditionreoult (ALSP).

Ihole bundle (95/50) analysis based on 5500 tubes in Model F bundle.

Comparison of Variability18

16

C_ 14

E 12

'10

10

.2Co o•8

CL

6

.E 4

Worst Case Generic Model FAxisymmetric TS Displacements• .••Tube CTE -1cTubesheet CTE +laTube E +1a

Tubesheet E -laCoefficient of Friction -la

.. . RCP -Ia or 0 psiTube Length Minimized

t- 3D Worst Case Value is 3.30 in (RCP = 0 psi)with a Final Tube Length of 4 in

-I \"I.."-'SSM Hstar w/BET

-U--Worst Case wIBET, Tube Length = 15 in

-*--Worst Case w/BET, RCP=O psi, Tube Length = 17 in

"I*t-ý ý -0 I--

0 10 20 30 40 50 60 70TS Radius, in

Sensitivity of ALSP Results to Variation in ParametersChanges with respect to Tube Length and

Value of RCP

Conclusions* 3D FEA model is reference basis for H** Realistic boundary conditions applied* Model of record, ALSP, is conservative with respect to

3D FEA* Both H* analysis models are consistent with established

theory and current literature and are supported by testdata

* Crevice pressure model Utilizes depth based approach* Tubesheet radius dependent stiffness has little effect on

H* but significant effect on uncertainties* Residual contact pressure variability determined

analytically; mean RCP tests in progress