ML092460595
| ML092460595 | |
| Person / Time | |
|---|---|
| Site: | Nine Mile Point  |
| Issue date: | 08/28/2009 |
| From: | Continuum Dynamics |
| To: | Constellation Energy Group, Nine Mile Point, Office of Nuclear Reactor Regulation |
| References | |
| 7708631, TAC ME1476 CDI Report 09-26NP, Rev 0 | |
| Download: ML092460595 (67) | |
Text
ATTACHMENT 2 ATTACHMENT CDI REPORT 09-26NP (NON-PROPRIETARy)
(NON-PROPRIETARY)
STRESS ASSESSMENT ASSESSMENT OF NINE MILE POINT POINT UNIT 2 STEAM DRYER STEAM DRYER AT CLTP AND EPU CONDITIONS, CONDITIONS, REV. 0 Nine Mile Point Nuclear Station, LLC August 28, 2009
DocumentDoes ThisDocument This NotContain DoesNot Dynamics,Inc.
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CDIReport CDI No. 09-26NP 09-26NP J' ,
, , Stress Assessment of StressAssessment Mile Point Nine Mile ofNine Point Unit Steam Dryer Unit 22 Steam Dryer-atat CLTP CLTP and and EPU EPU Conditions Conditions Revision 00 Revision : .'
Preparedby Prepared by Continuum Dynamics, Inc.
Continuum'Dynamics, Inc.'
34 Lexington Avenue 34Lexington Avenue Ewing, NJ
, Ewing, NJ 08618 08618 Prepared under Purchase Prepared under OrderNo.
Purchase Order 770863 i. for No. 7708631 for' Constellation Constellation
, . Energy Group Energy Group Nine Mile Point Nuclear Station; LLC Nine Mile Point Nuclear Station, LLC P. 0.
P. Box 63 O. Box 63 Lycoming, NY Lycoming, NY 13093
-13093 Approved by Approved by
,/11 ,Q-J~
((#~ p .. '.,
Biianin'- \
Alan J.1. Bilanin Alan Reviewed by Reviewed by
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Milton E.
Milton E. Teske August 2009 2009 report complies This report This ~ithContinuum complies with 'DYna~ics', Inc.
Continuum Dynamics, Nuclear Quality Inc. Nuclear Assurance Program Quality Assurance Program currently currently in effect.
This bocUmerit Document Does Not Contain Continuum DYnamics, Dynamics, Inc. mc. Proprietary Information Proprietary Information Executive Summary The finite element model and analysis methodology, methodology, used to assess stresses induced by the flow of steam through the steam dryer at Nine Mile Point-Unit Point'Unit 2 (NMP2), (NMP2) , are described and applied to obtain stresses at CL CLTP conditions. The analysis is cC)llsistentwith TP condition.s. consistent with those carried out u.s. for dryer qualification in the U.S. qualification to EPU conditions and complies complies with a standard analysis procedure procedure [1] supported by the EPRI BWRVIP.and BWRVIP. and currently under review by the USNRC. The resulting stresses are assessed for compliance compliance with ASME B&PV Code 2007 [2],Section III, with. the .ASME TIl, combination corresponding to normal operation (the Level A Service subsection NG, for the load combination Service Condition).
The analysis is carried out in the frequency dpmain, domain, which confers a number of useful computational advantages advantages over a time-accurate time-acc}lfate transient analysis including the ability to assess the effects of frequency scaling in the loads witho,ut, without fhe tb.e need for additional finite fmite element calculations. (( (( .
(3)))
(3))) The analysis develops a series of The analysis of corresponding to, unit stress solutions correspopding to the application applicatio~ of a unit pressure at a MSL at specified specified frequency, f. f. Each unit solution is obtained by first calculating calculatinig the associated assoCiated acoustic pressure field using a separate analysis that solves the damped Helmholtz Helmholtz equation within the steam dryer
[3]. This pressure pressure field is then applied to a finite fmite element. stXuctural model of the steam dryer and elem~nt, structural the harmonic stress response response at frequency, f, f, is calculated calculated rising Using the commercial ANSYS 10.0 10.0 finite element element analysis software. This stress response.
response ' constitutes the unit solution and is stored as a file for subsequent subsequent processing. Once all unit solutions have been computed, the stress response for any combination combination of MSL pressure pressure spectrums (obtained by Fast Fourier Transform of the pressure histories in the MSLs) is determined determined by a simple matrix multiplication of these spectrums with the unit solutions.
Results obtained from application application of the methodology methodology to the NMP2 steam dryer show that at nominal CLTP operation (no frequency frequency shift) the minimum alternating alternating stress ratio (SR-a) anywhere on the steam dryer is SR-a=3.00. The loads' loads used'to used-to obtain this value account for*all for all the end-to-end uncertainties in the 'loads end-to-end biases and uncertainties loads model [4] and finite element element analysis. It is is noted that:
(i) The signals account account for the revised biases and uncertainties uncertainties in the 60-70 Hz and 70-100 Hz frequency ranges. For various reasons the ACM was not recalibrated recalibrated over the new frequency ranges (such a recalibration is resource-intensive resource-intensive and would lead to a new revision of the ACM). As a result, the biases and uncertainties uncertainties in the new intervals are overly conservative conservative and higher than they would otherwise otherwise be, had such a recalibration recalibration of of the ACM been performed. .
(ii)
(ii) It is known that the signals used to estimate acoustic loads contain significant significant non-acoustic contributions referred to collectively collectively as plant noise (e.g.,
(e.g., pipe vibrations).
However, to expedite qualification, no noise removal has been performed for the analyses contained herein. .' ' ..' '
ii
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Inc. Proprietary Information" Both Both of of these these loadload details details increase increase conservatism conservatism in in the the analysis.
aIlalysis. Moreover, Moreover, to to account account for for uncertainties in the modal frequency predictions of the finite element uncertainties in the modal frequency predictions of the finite element model, the stresses are model, the stresses are also also computed computed for for loads loads that that are are shifted shifted inin the the frequency frequency domaindomain by by +/-2.5%,
+/-2.5%, +/-5%,+/-S%, +/-7.5%
+/-7.5% and and +/-10%.
+/-10%.
The minimum alternating stress ratio encountered at any The minimum alternating stress ratio encountered at any frequency shift is found to frequency shift is found to bebe SR-a=2.89 occurring at the -5% shift. The stress ratio due SR-a=2.89 occurring at the -5% shift. The stress ratio due to maximum stresses (SR-P) isto maximum stresses (SR-P) is dominated dominated by by static static loads loads and and isis SR-P=1.34 SR-P=1.34 both both with with and and without without frequency frequency shifts.
shifts.
Since Since flow-induced flow-induced acoustic acoustic resonances resonances are are not not anticipated anticipated in in the the steam steam dryer, dryer, thethe alternating alternating stress stress ratios ratios at at EPU EPU operation operation can can bebe obtained obtained by by scaling scaling thethe CLTP CLTP values values by by the the steam steam flow flow velocity squared, (UEPulUcLTPi=1.1782=1.388. Under velocity squared, (UEPU/UCLTP)2=l.1782=l.388. Under thisthis approach, approach, the the limiting limiting alternating alternating stress stress ratio ratio becomes becomes SR-a=2.89/1.388=2.08.
SR-a=2.89/1.388=2.08. Given Given thatthat the the alternating alternating stress stress ratio ratio SR-a SR-a obtained obtained at EPU remains above 2.08 at all frequency shifts together at EPU remains above 2.08 at all frequency shifts together with 'the comparatively small with 'the comparatively small dependence dependence of of SR-P SR-P upon upon acoustic acoustic loads, loads, the the Unit Unit 22 dryer dryer isis 'expected
'expected to to qualify qualify at at EPU EPU conditions.
conditions. .
In In order order to to achieve achieve these these stress stress ratios, ratios, the the closure closure plate plate requires requires modification modification and and weldswelds onon the lifting rod braces require reinforcement. For the closure plates the lifting rod braces require reinforcement. For the closure plates reinforcement strips reinforcement strips are are added added to to stiffen stiffen the the closure closure plates.
plates. Also, Also, thethe top top 18 18 inches inches of of the the welds welds connecting connecting the the closure closure plates plates to to the vane banks and to the hoods are reinforced by adding a weld on the the vane banks and to the hoods are reinforced by adding a weld on the inner side of the closure inner side of the closure plate.
plate. For For thethe lifting lifting rod rod braces, braces, increasing increasing the the weld weld size size from from 1/4114 in in to to 1/2 112 in in meets meets the the target target stress stress ratio.
,I ii 11
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.Table of Contents Section Section , Page Page E xecutive Summary Executive Summ ary ................................................................. .................................................,.... ,., .....1.....i
.. ;.......................................... ~ .............. ,................................................ i T able of C ontents ................................................................................................................
Table Contents ................................................................................................................ :.......... iii ..........
- 1. Introduction and Purpose
- 1. Introduction ................................................................
Purpose ............... .......................................
~ ............................................... ~ ... ;................ :......... " ............. 11
- 2. Methodology Methodology ................
............ 3 2 .1 O 2.1 verview ...............................................................................................................................
Overview ............................................................................................................................... 3 2.2 ((..............................
2.2 (( ......... C n i e a i n ...........
' ( 3 )
..... ........................... .... ...... :... 5
)) .............................................................
, 5 Computational Consider~tions 2.3 Compt;1tational Considerations.................................. ......... I.......................;.... 6
- 3. Finite Element Model Description ................... ..............................................................
- ........................................................ :................. 9 3.1 Steam Dryer Geometry Geometry ...........................................................................
.......................... ........~ ............................. *........ 9 3.2 Material Material Properties Properties ............................................................
............................................................................................................... ........ 12 12 M odel Simplifications 3.3 Model Simplifications .................................................................................
................ 12 12 3.4 Perforated Perforated Plate Mode.1., .. ~ ........ ;:: .......... ~ ......... ,........................... I........................................
Model ............................... :........................ :............. . ~ 1313 3.5 Vane Bank Model .............................................................
- ................................................. 15 15 3.6 Water Inertia Effect on Submerged Submerged Pane'is Panels ...........
- ............................... ,.. :.......................... 16 16 3.7 Structural Damping ..............................................
) ',' .':............................
. 16 16 3.8 Mesh Details and Element Types ............. :.................................................................
..................................... ,....... 16 16 Connections Between Structural 3.9 Connections Structural Components ................................................................
Components .................................................................... 16 16 3.10 Pressure Loading ...............................................................................................................
.......................................................................................................... 28
- 4. Structural .................................................
Structural Analysis .................................................................................................................... 31 31 4.1 Static Analysis ....................................................................................................................
........ ......................................... 31 31 H armonic Analysis 4.2 Harmonic Analysis ..............................................................................................................
.......................................................................................................... 31 31 P ost-Processing ...................................................................................................................
4.3 Post-Processing ................................................................................................................... 37 37 4.4 Computation Computation of Stress Ratios for Structural ...............................................
Structural Assessment ................................................... 37 Element Sub-modeling 4.5 Finite Element Sub-m odeling .............................................................................................
......................................................................................... 40 55.. Results R esu lts .......................................................................................................................................
.................................................... ................................................................................... 48 48 5.1 General Stress Distribution and High Stress Locations Locations ............................
...................................................... 49 5.2 Load 5.2 Load Combinations and Allowable Allowable Stress Intensities ...................................................
........................................................ 63 5.3 Frequency Frequency Content and Filtering Filtering of the Stress Signals .......................................................
................................................. 85 85 66.. Conclusions Conclu sions ...............................................................................................................................
............................................................................................................................... 92 77.. References R eferences .................................................................................................................................
................................................................................................................................. 93 Appendix A Sub-modeling and Modification Modification of Closure Plates ............................................
Plates ................................................. 95 Sub m odel Node model Node 101175 ......................................................................................................
......................................................................................................... 100 100 Sub m odel node 91605 ............................................................................................................
model ............................................................................................................ 107 107 Sub m odel node 95172 ............................................................................................................
model ........................................................................................................... 115 115 Sub m odel model node 100327 ..........................................................................................................
100327.......................................................................................................... 124 124 iii 111
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- 1. Introduction
- 1. Introduction and Purpose Purpose ,
Plans Plans to qualify qualify the Nine Mile Mile Point Point nuclear nuclear plant plant for operation' at Extended Extended Power Uprate Uprate (EPU) operating operating condition require an assessment assessment of the steam dryer stresses experienced dryer ,stresses experienced under under the increased ~oads. The increased loads. The steam steam dryer dryer loads loads due due to pressure' fluctuations fluctu,ations in the mainmain steam lines' "
steam lines (MSLs) are potentially potentially damaging damaging and the cyclic cyclic stresses stresses from these loads can produce fatigue cracking if loads are sufficiently cracking sufficiently high. The industry addressed this problem industry has addressed problem with physical modifications modifications to the dryers, dryers, as well well as a program to define steam steam dryer dryer loads loads and and their their resulting stresses.
stresses. .The purpose purpose of the stress analysis' discussed here is to calculate stress analysis' calculate the the maximum maximum and alternating alternating stresses generated generated during during Current Current Licensed Licensed Thermal Power Power (CLTP)
(CLTP) and Extended Extended Power Uprate Uprate (EPU) and to determine the margins margins' that exist when compared compared to stresses stresses that' comply comply with the ASME Code (ASME (ASME B&PV Code, Section S~ction III, III" subsection subsection NG).
The stress analysis of the modined modified NMP2 steam steam dryer establishes establishes whether whether the' existing'and existing' and proposed proposed modifications modifications are adequate for sustaining structural integrity integrity and preventing preventing' future weld cracking cracking under planned planned EPU operating operating conditions. The load combination combination considered considered here corresponds corresponds to normal operation (the Level Level A Service Service Condition) and includes includes fluctuating pressure loads loads developed developed from NMP2 NMP2 main steam line data, and weight. The fluctuating pressure loads, induced by the flowing steam, are predicted using a separate separate acoustic circuit circuit analysis of the steam dome and main steam lines [5]. Level B service B service conditions, which which include seismic loads, are not included included in this evaluation.
((
(3))) This approach (3))) approach also affords a number of of additional computational additional computational advantages advantages over transient simulations including: ((
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This last This last advantage advantage is realized through the use of "unit" solutions representing realized through the use of "unit" solutions representing the stress distribution resulting from the of a unit fluctuating pressure at one of the MSLs at a particular frequency. ((
application ofa (3)))
(3)))
This report describes the overall methodology used to obtain the unit solutions in the frequency domain frequency domain and and how how toto assemble assemble them into a stress response for a given combination of of pressure pressure signals in the MSLs. This is followed by details of the NMP2 steam dryer finite 1
This Document Document Does Not Contain Continuum' Dynamics, Inc. Proprietary Continuum'Dynamics, Proprietary Information Information element model including the elements elements used and overall resolution, treatment of connections connections between elements, between elements, the hydrodynamic model, the implementation implementation of structural structural damping and key idealizations/assumptions inherent to the model. Post-processing procedures idealizations/assump?pns inherent to, th~ model., Post-processing procedures are also reviewed including the computation incl~ding computation of maximum and alternating stress intensities, identification identification of high stress locations, adjustments adjustments to stress intensities intensities at welds and arid evaluation of stress ratios used to establish compliance with the ASME establishcompliance ASMR C~de.Code. The results in terms of stress intensitY intensity distributions '
and stress ratios are presented next together with ~ith PSDs' PSDs-of of the dominant' stresscomponents.
stress' components ..
fuIn ~rder order to to meet target EPU l~vels (i.e.,.
EPU stress levels (i.e., an alterna:ting alternating stress 'ratio of 2.0), two components required modification:
modification: the closure closure plate welds and the lifting rod s'lipport support braces. In In' the former case, stiffening simultan~ously increase stiffening strips or ribs are added to the closure plate to simultaneously mcrease '
the frequency and lower stresses [6]; also the closure plate attachment attachment weld is strengthened by placing an additional weld on the the' interior side' side of the junction where the closure plate meets the hood hood or or vane vane bank.
bank. For t):le the lifting rod braces, existing. 1/4 praces, the existing, 114 in weld is increased 1/2 in.
inc~eased to 112 Both modifications involve the use Of Both modifications of highly aetailed detailed solid element-based element-based sub-models sub-moqels of these locations locations to accurately assess the local stresses. '
- 1 .
2
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- 2. Methodology Methodology 2.1 Overview Based on previous analysis undertaken undertaken at Quad Cities Units 1 and 2, the steam steam dryer can experience strong acoustic acoustic loads due to the fluctuating pressures pressures in the MSLs connected to the steam dome containing containing the dryer. C.D.!.
C.D.I. has developed developed an acoustic acoustic circuit model CACM)
(ACM) that, given a collection of strain gage measurements measurements [7] of the fluctuating pressures in the MSLs, predicts the acoustic pressure pressure field anywhere anywhere inside the steam dome and on the steam steam dryer [1,
[1, 3-3-
5]. The ACM is formulated in frequency frequency space and contains two major components components that are relevant to the ensuing stress analysis of concern here. ((
directly relevant directly (3)))
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Computational Considerations 2.3 Computational Focusing on the structural computational aspects of the overall approach, there are a number structural computational of numerical and computational considerations considerations requiring requiring attention. The first ftrst concerns the transfer of the acoustic acoustic forces onto the structure, particularly particularly the spatial and frequency frequency resolutions. The ANSYS ftnite finite element element program inputs general distributed differences distributed pressure differences using a table format. This consists of regular 3D rectangular (i.e., block) nxxnyxn nxxnyxnzz mesh where net is the number of mesh points in the i-th Cartesian nO. Cartesian direction and the pressure difference difference is provided at each mesh point (see Section 3.10). These tables are generated separately separately using a program program that reads the loads provided from the ACM software, distributes distributes these loads onto the finite element element mesh using a combination combination of interpolation interpolation procedures procedures on the surface and simple diffusion schemes off the surface (off-surface loads are required by ANSYS to ensure proper surface (off-surface interpolation of forces), and written to ASCII files for input to ANSYS. A separate load file is written at written at each each frequency frequency for for the the real real and and imaginary imaginary component component of the complex complex force.
The acoustic field fteld is stored at 5 Hz Hz intervals intervals from 0 to 250 Hz. While a 5 Hz resolution is sufficient to capture capture frequency frequency dependence dependence of the acoustic field (i.e.,
acoustic fteld (i.e., the pressure pressure at a point varies gradually gradually with frequency), it is too coarse for representing the structural response especially at low frequencies. For 1% 1% critical structural damping, one can show that the frequency spacing neededneeded to resolve a damped resonant peak at natural frequency, fn, fn' to within within 5% accuracy 5% Af=0.0064xfn.
accuracy is Llf=O.0064xf n . Thus for ffn=10 structural response modes n=lO Hz where the lowest structural occur, a frequency frequency interval interval of 0.064 Hz or less is required. In calculations we require that In our calculations 5% maximum error be maintained over the range from fn= fn=55 Hz to 250 Hz resulting in a finest fmest frequency interval interval of 0.0321 Hz at the low frequency end (this adequately adequately resolves all structural structural modes up to 250 Hz). Since there are no structural structural modes between between 0 to 5 Hz, a 0.5 Hz spacing is used over this range with minimal (less than 5%) error. The unit load, fn(0), in <<(0, R),
R), at any
)
wk, is obtained by linear interpolation of the acoustic frequency, (Ok, acoustic solutions at the two nearestnearest frequencies, coi(Oi and coi+l, (Oi+ 1> spaced 5 Hz apart. Linear interpolation interpolation is sufficient since the pressure load varies slowly over the 5 Hz range (linear interpolation of the structural structural response would not be acceptable acceptable over this range since it varies much more rapidly over the same interval). Details regarding the frequency resolution resolution have been provided provided in [9].
Solution Management Management
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Structural Damping Structural Damping In harmonic harmonic analysis one has a broader selection of damping models than in transient transient simulations. A damping damping factor, z, of 11% % critical damping is used in the structural analysis. In In transient transient simulations, simulations, this damping can only be enforced enforced exactly exactly at two frequencies (where the damping model is "pinned"). Between these two frequencies the damping factor can by considerably smaller, for example 0.5% 0.5% or less depending depending on the pinning frequencies. Outside the pinning frequencies, frequencies, damping is higher. With harmonic analysis it is straightforward straightforward to enforce very close to 11% % damping over the entire frequency range. In this damping model, the damping dampIng matrix, D,is D, is set to .
D=-K (7),
D=D=2zK 2z K ,(7) 0)
where K is the stiffness stiffuess matrix and 03 the forcing frequency. When comparing 00 the comparing the response' obtained with this model model, against that for a constant constant damping ratio, the maximum difference difference at any frequency frequency is less than 0.5%, which is far smaller than the 100% 100% or higher response variation variation obtained obtained when using the pinned model required in transient simulation.
LoadFrequency Load Frequency Rescaling One way to evaluate the sensitivity of the stress results to approximations approximations in the structural modeling and applied applied loads is to rescale the frequency frequency content of the applied loads. In this procedure the nominal frequencies, ook, cOk, are shifted to (1 (l+X,)0k,
+A)ook, where the frequency shift, A, X, ranges between +/-10%, +/-1O%, and the response response recomputed recomputed for the shifted loads. The objective of the frequency shifting can can be explained explained by way of example. Suppose that in the actual dryer a strong structural-acoustic structural-acoustic coupling coupling exists at a particular frequency, 00*. co*. This means means that the following conditions hold simultaneously: (i) (i) the acoustic signal contains a significant signal signal at 00*;0o*; (ii)
(ii) the structural structural model contains a resonant resonant mode of natural frequency, con, oon, that is near co*;
00*; and (iii) the associated associated structural structural mode shape is strongly coupled to the acoustic load (i.e., (i.e., integrating integrating the product of the mode shape and the product of the mode shape and the surface pressure surface pressure over the steam dryer surface produces a significant modal significant modal force).
force). Suppose Suppose now that because because ofof discretization discretization errors and modeling idealizations that idealizations that the predicted predicted resonance frequency differs from 00* 0o* by a small amount (e.g.,
1.5%). Then condition 1.5%). condition (ii) (ii) will be violated and the response amplitude therefore significantly significantly diminished. By diminished. By shifting shifting the the load load frequencies frequencies one one re-establishes re-establishes condition (ii) (ii) when (1+ (1+ X)co*
A)OO* is 7
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Proprietary Information near con, (On' The other two requirements requirements also hold and a strong structural structural acoustic interaction is restored.
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Evaluation Evaluation of Maximum and andAlternating Alternating Stress Intensities Intensities Once the unit solutions have been obtained, the most intensive computational computational steps in the generation generation of stress intensities intensities are: (i) the FFTs to evaluate evaluate stress time histories from (5); (5); and calculation of alternating (ii) the calculation alternating stress intensities. ((
" i (3)))
The high computational computational penalty incurred in calculating altern'ating stress intensitIes calculating the alternating intensities is due due-.,
to the fact that this calculation comparing the stress tensors at every pair of points ill calculation involves comparing in the stress history. This comparison is necessary since in in-general general the principal principal stress directions directions can vary during the response, thus for N samples in the stress history, there will be (N-l)N/2 (N-1)N/2 such pairs or, for N=64K (the number number required to accurately accurately resolve the spectrum up to 250 Hz in 0.01 Hz intervals), 2.1x10 calculations per node each requiring the detern;tination~fthe 2.1 x 1099 calculations determination of the roots to' to "':
a cubic polynomial. (( :i . .
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- 3. Finite Element Model Description Description A description of the ANSYS ANSYS model of the nine Mile Point Unit 2 steam dryer follows.
3.1 Steam Dryer Geometry A geometric geometric representation of the Nine Mile Point Unit 2 steam steam dryer was developed developed from available available drawings (provided by Constellation Energy Group and included in the design record file, DRF-C-279C)
DRF-C-279C) within the Workbench module module of ANSYS. The completed model is shown in Figure 1. This model includes includes on-site modifications modifications to the Nine Mile Point Unit 2 steam dryer.
These are as follows.
On-Site Modifications On-Site Modifications (i)
(i) The top tie rods are replaced replaced with thicker ones.
(ii) Inner side plates plates are replaced replaced with thicker ones.
(iii) Middle hoods are reinforced with additional strips.
(iv) Lifting rods are reinforced reinforced with additional additional gussets.
(v) Per FDDR KGI-0265 the support conditionsconditions are adjusted to ensure ensure that the dryer is supported 100%
supported 100% on the seismic blocks.
These additional modifications modifications have been incorporated incorporated into the NMP2 steam dryer model and are reflected in the results presented in this report. The affected areas are shown in Figure 2.
Modifications Planned/or Modifications Plannedfor EPU Operation EPU Operation To meet the target stress stress ratio at EPU, reinforcement reinforcement of the closure plates and increases in in selected selected weld sizes are recommended. Analysis Analysis shows that the original closure plates experience experience a strong response from forcing of one of its structural structural modes. These structures have been modified using stiffening strips to simultaneously simultaneously reinforce them and shift their frequencies away from significant significant acoustic loads [6]. Analysis of these components components is summarized summarized in Appendix A.
analyzed using sub-models Modifications to welds are analyzed sub-models to minimize computational cost. These These analyses are performed at the following locations as discussed further in Section Section 4.5: (i)
(i) the lifting rod support braces; (ii) closure plate welds and (iii) the ends of selected tie bars. In addition, previous previous analyses of geometrically geometrically identical and similarly loaded locations locations have been applied at these locations and in the locations where reinforcements reinforcements are implemented.
Reference Frame Frame The spatial coordinates used herein to describe describe the geometry and identify limiting stress locations are expressed in a reference frame whose origin is located at the intersection intersection of the steam dryer centerline centerline and the plane containing the base plates (this plane plane also contains contains the top of of the upper support ring and the bottom edges of the hoods). The y-axis is parallel to the hoods, the x-axis is normal to the hoods pointing from MSL C/D to MSL AlB, A/B, and the z-axis is vertical, positive positive up.
9
This Document Does Not Contain Contain Continuum Dynamics, Inc. Proprietary Continuum Dynamics, Information Proprietary Information 0.00 Wz 100.00 (in) 50.00 geometry of the Nine Mile Point Unit 2 steam dryer model.
Figure 1. Overall geometry 10
This Document Does Not Contain Continuum Continuum Dynamics, Dynamics, Inc. Proprietary Proprietary Information Information Figure 2. Modify the figure to eliminate eliminate inner hood strips. On-site modifications accounted for On-site modifications for in the model and associated geometrical details.
11 11
This Document Does Not Contain Continuum Continuum Dynamics, Inc. Proprietary Proprietary Information Information 3.2 Material Properties The steam dryer is constructed from Type 304 stainless steel and has an operating temperature of 550'F.
550°F. Properties used in the analysis are summarized below in Table 1. 1.
- 1. Material Table 1. Material properties.
Young's Modulus Density Poisson (106 psi)
(106 (!bm/in33))
(lbmlin Ratio stainless steel 25.55 0.284 0.3 structural steel with added water 25.55 0.856 0.3 effect inertia effect The structural steel modulus is taken from Appendix Appendix A of the ASME Code for Type 304 Stainless Steel at an operating temperature temperature 550'F.
550°F. The effective perforated plates effective properties of perforated submerged parts are discussed and submerged discussed in Sections 3.4 and 3.6. Note that the increased effective density for submerged components is only used in the harmonic analysis. When calculating calculating the stress distribution due to the static dead weight load, the unmodified density of steel lbm/in 33) is used throughout.
(0.284 Ibmlin Inspections of the NMP Unit 2 dryer have revealed Inspections revealed IGSCC cracks in the upper support ring (USR) and skirt. A separate separate analysis of these cracks [12] has been performed to determine (i) they will propagate further into the structure and (ii) their influence upon structural whether: (i) structural response response frequencies and modes must be explicitly accounted accounted for. To establish (i) the stress calculated in the global stress analysis is used in conjunction with the crack geometry geometry to calculate the stress intensity factor which is then compared to the threshold stress intensity. For the USR and skirt cracks the highest stress intensity factors are 1.47 ksi-in° ksi-ino. 5 and 2.75 ksi-in°.
ksi-in°55 0 55 respectively; both values are below the threshold value (3 (3 ksi-in ksi-in°. )) implying that fatigue crack growth will not occur.
To determine (ii) the change in modal response frequencies due to the presence of a flaw is predicted predicted by analytical means (in the case of the USR) or using finite element analysis (for the skirt). In each case, the flaw size used in these calculations calculations is increased to ensure conservative conservative estimates (for example, in the case of the skirt flaws extending up to 12 V2 the panel width are considered). For the USR, the change in modal frequencies due to the presence of the cracks is less than 0.5%. For the skirt, using a conservative conservative estimate for the crack to panel width of 0.3 (the measured value is less than 0.17) the change in modal frequency is also less than 0.5%. In In both cases such small changeschanges in modal frequencies are considers negligible and are readily accounted for when performing performing frequency frequency shifting.
3.3 Model Simplifications Simplifications simplifications were made to achieve The following simplifications achieve reasonable reasonable model size while maintainingmaintaining good modeling modeling fidelity for key structural structural properties:
- Perforated Perforated plates were approximated approximated as continuous plates using modified elastic elastic properties designed designed to match the static and modal behaviors behaviors of the perforated plates. The 12
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structural modeling perforated plate structural modeling is summarized summarized in Section 3.4 and Appendix C of of
[13].
- " The drying vanes were replaced by point masses attached to the corresponding trough bottom plates and vane bank top covers (Figure 4). The bounding perforated plates, vane bank end plates, and vane bank top covers were explicitly modeled (see Section 3.5).
- " The added mass properties of the lower part of the skirt below the reactor water level hydrodynamic analysis (see Section 3.6).
were obtained using a separate hydrodynamic
- [)
((
- Four steam dryer support brackets that are located on the reactor vessel and spaced at 90° 900 intervals were explicitly modeled (see Section 3.9).
- Most welds were replaced by node-to-nodenode-to-node connections; interconnected parts share connections; interconnected common nodes along the welds. In other locations the constraint equations between between nodal degrees Section 3.9.
degrees of freedom were introduced as described in Section 3.4 Perforated Perforated Plate Model The perforated perforated plates were modeled as solid plates with adjusted adjusted elastic and dynamic properties. Properties properties. Properties of the perforated perforated plates were assigned according to the type and size of of perforation. Based on [14], for an equilateral square pattern with given hole size and spacing, effective moduli of elasticity were found.
the effective The adjusted adjusted properties for the perforated plates are shown in Table Table 2 as ratios to material properties of structural steel, provided in Table 1. 1. Locations perforated plates are classified Locations of perforated classified by steam entry / exit vane bank side and vertical position.
Tests Tests werewere carried carried out out to verify that to verify that this representation representation of perforated perforated plates plates by continuous ones with modified elastic properties preserves properties preserves the modal properties properties of the structure. These tests are summarized are summarized in Appendix C of [13]and compare compare the predicted first modal frequency for a cantilevered cantilevered perforated perforated plate against an experimentally experimentally measured measured value. The prediction was obtained for 40% and 13% open area plates (these are representative obtained for 40% and 13% open area plates (these are representative of the largest and lowest lowest open area ratios of the perforated open area ratios of the perforated plates at NMP2, plates at NMP2, as seen in in Table 2)2) using the analytical formula formula for aa cantilevered plate and the modified Young's cantilevered plate Young's modulus and Poisson's ratio given by O'Donnell [14].
O'Donnell [14]. The measured and predicted predicted frequencies are in close agreement, agreement, differing differing by less than 3%.3%.
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Figure 3.
Figure 3. (([
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Information
, Table Table, 2. Material pt:operties properties of perforated perforated plates.
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3.5 Vane Bank Model Model The vane bank assemblies consist of 'many many vertical angled plates that are computationally computationally expensive to model explicitly, since a prohibitive prohibitive number of elements would be required. These These parts have significant weight which is transmitted through the . surrounding structure, structure, so it is is important important. to capture capture their gross inertial properties. Here the. the.-vane
- vane banks are modeled as a po~nt masses .located at the center of mass for each vane bank section (Figure 4).
collection of point The following masses were were, used for the vane bank sections, based on data found found on provided provided dra\\,ings:'
drawings: . . .. . .'
. inner banks, 1618 Ibm, 4 sections sections per bank;.
baDk; .
middle banks, 1485 1485 lbin, lbm, total 4 sections per bank; and. and outer banks,1550 lbm, 3 sections per bank.
banks, 1550 Ibm, .I These masses were applied to the baseplates base plates and..vane covers~sing and.yane top covers using the.
the standard ANSYS stan<;lardANSYS point mass. modeling modeling option,-:element option,:element MASS21.
MASS21. ANSYS distributes'th~
automatically distributes ANSYSautomatically the point mass inertial loads to the'nodes,ofthe inertial,loads the -nodes of the selected.
selected.structure. distribution algorithm minimiz~sthe structure. The distribution minimizes the sum of the squares of the nodal inertial ensuring that the net forces and momen~s' f6rces, while ensuring inertial forces" moments conserved... Vane banks are not exposed to main steam lines directly, but rather shielded are conserved shielded. by the hoods.
the hoods. . .' .
The collective stiffness of the vane vane banks is expected to be small. small. compared compared to the surrounding support structure neglected in the model.
structure and is neglected mode1. In In the static case it is reasonable to expect expect that this constitutes a conservative conservative approach, since neglecting the stiffness of the vane banks implies that.that the entire entire weight is transmitted, through .the adjacent
~hrough .the adjacent vane bank walls and supports. In the dynamic case the vane banks exhibit only a weak weaK: response response since (i) they have large large inertia characteristic ac~ustically-induced inertia so that the characteristic. acoustically-induced forces diYideddivided by the vane masses and and inertias inertias yield small amplitude motions, velocities and accelerations; accelerations; aria and (ii) they are shielded from acoustic loads by shielded frorp. ,by the hoods, which transfer, dynamic which transfer. dynamic loads to the rest of the structure.
structure. Thus, compared to t<? the hoods, less motion is anticipated anticipated on the vane banks so that vane. banks.
15 15
This Doc~ent Document Does Not Contain Contain Continuum Dynamics, Inc. Proprietary'Infonnation ProprietaryInformation approximating their inertial properties properties with equivalent point masses is justified. Nevertheless, the bounding parts, such as perforated perforated plates, side panels,, and top covers, are retained plates, sidepanels,aJid retained in the model. Errors associated associated with the point mass representation representation of the vane banks are compensated compensated for by frequency shifting of the applied applied loads.
3.6 Water Inertia Effect on Submerged Panels Water inertia was modeled modeled by an increase in density of the submerged submerged structure to account for the added hydrodynamic hydrodynamic mass. This added mass was found by a separate hydrodynamic analysis (included (included in DRF-C-279C supporting supporting this report) to be 0.143 Ibmlin lbm/in 22 on the submerged submerged skirt area. This is modeled by effectively effectively increasing increasing the material density for the submerged submerged portions of the skirt. Since the skirt is 0.25 inches thick, the added mass is equivalent to a increase by 0.572 density increase Ibm/in 33 . This added water mass was included in the ANSYS model by 0.572lbmlin appropriately modifying the density appropriately density of the submerged structural structural elements when computing harmonic response. For the static stresses, the unmodified unmodified density density of steel is used throughout.
3.7 Structural Structural Damping Structural Structural damping was defmed defined as 11% % of critical damping for all frequencies. This damping consistent with guidance given, is COAsistent given,on on p~.
pg. lO 10 of NRC RG-1.20 [18]. [18].
3.8 Mesh Details and Element Types Shell elements were employed emiployed to model the skirt, hoods', perforated plates, 'side and end end plates, trough bottom plates, reinforcements, reinforcements, base plates and cover plates. Specifically, the foUr- four-node, Shell Element SHELL63,' SHELL63,' was' was selected' selected to mo'delmodel these structural components.'-components.' This This element mod~ls models bending and membrane membrane 'stresses, but" but' omits transverse shear. The use of shell transverse shear.'
elements is appropriate appropriate for most of the structure where the characteristic characteristic thickness is small is' 'small compared to the other plate dimensions. For thicker structures, such as the upper and lower support rings, solid brick elements were used to provide provide the full 3D stress. The elements ~lements SURF154 SURF154 are used to assure proper application application of pressure pressure' loading to the structure:
structure. 'Mesh Mesh details' details element types are shown in Table 3 and Table 4.
and element 4.
. The mesh automatically 'byANSYS thesh is generated automatically by ANSYS with~refinement wIth'refinement near edges. The The maximum maximUm mesh spacmg allowable inesh spacing is specifiedby specified by the'user.
the 'user: HereHere a 2.5 inch maximum allowable spaciiigis' spacing is. ."
specified specified with refinement
'refinement up to 1.5 i.5 inch in the following areas: drain pipes, tie rods, the curved curVed portions of the drain channels channels and the hoods. Details of the finite element element mesh are shown in Figure 5. 5. 'Numerical
'Numerical experiments experiments carried out using the ANSYS code applied to simple analytically tractable analytically tractable plate structures with dimensions and mesh spacings similar to the ones used steam dryer, confirm for the steam. * * \
confinn that the natural frequencies are accurately
. : 1 "
accurately recovered recovered (less than 11%
~
- errors for the first modes modes). These
):These errors errors are compensated compensated for by the .
use 'of frequency
'offiequency Shifting.
shifting.
3.9 Connections Connections Betweei. Between Structural Components Components' Most connections between
.*Most between parts are modeled as node-to-node node-to-node connections.
connections. This is the
- manner (i.e., .within the finite correct lIlanner element framework) of 'joining rmite dement joining elements elements away from discontinuities. At joints joints between between shells, this approach approach omits the additional stiffness stiffness provided provided by th~ extra weld material.,
the material.. Also, locally 3D effects are more pronounced. The latter effect is accounted for using weld weld' factors. *'TheThe deviation in stiffness due to 'weld weld material is negligible, negligible, since weld dimensions are on the order of the shell sheli thickness. The' cons~quences The consequences upon 'modal 16 16
This Document Does Not Contain Continuum Continuum Dynamics, Inc. Proprietary Information frequencies and amplitude amplitude are, to first order, proportional proportional to tIL*
t/L where t is the thickness and L a characteristic shell length. The errors committed by ignoring additional weld stiffness characteristic stiffness are thus small and readily compensated compensated for by performing frequency shifts.
When joining shell and solid elements, elements, however, the problem arises of properly constraining the rotations, since shell element nodes contain both displacement displacement and rotational degrees of of freedom at every node whereas whereas solid elements model only the translations. A node-to-node connection would effectively appear appear to the shell element element as a simply supported, rather than (the cantilevered restraint and significantly alter the dynamic response of the shell structure.
correct) cantilevered To address this problem, constraint constraint equations are used to properly connect connect adjacent adjacent shell- andand solid-element modeled structures. Basically, all such constraints solid-element constraints express the deflection (and rotation for shell elements) of a node, R 1, 1 , on one structural component in terms of the deflections/rotations of the corresponding deflections/rotations corresponding point, P 2 , on the other connected component.
P2, Specifically, the element Specifically, element containing P P22 is identified identified and the deformations at P2 P2 determined determined by interpolation between the element nodes. The following types of shell-solid interpolation shell-solid element element connections are used in the steam dryer model including the following:
- 1. Connections of shell faces to solid faces (Figure 6a). While only displacement degrees of
- 1. of freedom are explicitly explicitly constrained, this approach approach also implicitly implicitly constrains the rotational degrees degrees of freedom when multiple shell nodes on a sufficiently dense grid are connected connected to the same solid face.
- 2. Connections of shell edges to solids (e.g., connection of the bottom of closure plates with the upper ring). Since solid elements do not have rotational degrees of freedom, the coupling approach consisted of having the shell penetrate coupling approach penetrate into the solid by one shell thickness thickness and then constraining constraining both the embedded shell elementelement nodes (inside (inside the solid) and the ones located on the surface of the solid structure (see Figure 6b). Numerical Numerical tests involving simple structures structures showed that this approach and penetration depth reproduce reproduce both the deflections deflections and stresses stresses of the same structure modeled using only solid elements or ANSYS' ANSYS' bonded contact contact technology. Continuity of rotations and displacements is achieved.
The use of constraint conditions rather than the bonded bonded contacts advocated by ANSYS for connecting independently meshed structural connecting structural components confers better accuracyaccuracy and useful numerical advantages advantages to the structural structural analysis of the steam dryer including better conditioned conditioned and smaller matrices. The smaller size results from the fact that equations and degrees degrees ofof freedom are eliminated rather than augmented (in Lagrange multiplier-based methods) by additional implementation of contact elements relies on the use of additional degrees of freedom. Also, the implementation of very high stiffness elements (in penalty penalty function-based function-based implementations) implementations) or results in indefinite matrices (Lagrange multiplier implementations) implementations) with poorer convergence convergence behavior compared compared to positive definite definite matrices.
The steam dryer rests on four support blocks which resist vertical and lateral displacement.
The support blocks contact the seismic seismic blocks welded to the USR so that 100% 100% of the dryerdryer weight is transmitted transmitted through the seismic blocks per the FDDR KG1-265. KGI-265. Because the contact region between between the blocks and steam dryer is small, the seismic blocks are considered free to 17 17
This Document Does Not Contain Continuum Dynamics, Dynamics, Inc. Proprietary Information Proprietary Information rotate about the radial axis. Specifically nodal constraints (zero relative displacement),
displacement), are imposed over the contact area between between the seismic seismic blocks and the support blocks. Two nodes on each each support block are fixed as indicated indicated in Figure 7. One node is at the center of the support block surface surface facing the vessel and the other node is 0.5" 0.5" offset inside inside the block towards the steam dryer, halfway to the nearest upper support ring node:
node. This arrangement approximates the nonlinear contact condition where where the ring can tip about the block.
18 18
This Document Does Not Contain Continuum Continuum Dynamics, Inc. Proprietary Proprietary Information Information U
CE CE Point masses Masses are connected to -
top and bottom supports Gussets to lifting rods connections I
k- I Skirt to support A
f Skirt to f rings support gs connections Simply Simply supported supported restraints
/
Figure 4. Point masses representing representing the vanes.
vanes. The pink shading represents where constraint constraint equations between nodes are applied (generally (generally between between solid and shell elements, elements, point masses
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and nodes and (( (3)))) .
Table 3.
Table 3. FE Model Summary.
Description Description Quantity Total Nodes 1 159,793 Nodes!
I Total Elements 1 124,496 1
- 1. Not including additional additional damper nodes and elements.
Table 4. Listing of Element Types.
Generic Generic Element Type Name Element Element NameName ANSYS Name 20-Node 20-Node Quadratic Hexahedron Quadratic Hexahedron SOLID SOLIDI18686 Hexahedral Structural Solid 20-Node Hexahedral Solid 10-Node Quadratic Tetrahedron IO-Node Quadratic Tetrahedron SOLID SOLIDI18787 10-Node Tetrahedral IO-Node Tetrahedral Structural Solid Solid 4-Node Elastic Shell SHELL63 4-Node Elastic Shell Mass Element Element MASS21 Structural Mass Pressure Surface Definition SURF154 SURF 154 3D Structural Structural Surface Effect Effect Damper element COMBIN14 COMBINI4 Spring-Damper Spring-Damper 19 19
This Document Does Not Contain This Contain Continuum Dynamics, Inc.
Inc. Proprietary Information Figure 5a. Mesh overview.
overview.
20 20
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Information Figure 5b. Close up of mesh showing showing on-site modifications.
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Document Does This Document This Not Contain Does Not Contain Continuum Inc. Proprietary Dynamics, Inc.
Continuum Dynamics, Information Proprietary Information 5c. Close up of mesh showing Figure 5c. pipes and hood supports.
showing drain pipes supports.
22 22
Continuum Dynamics, This Document Does Not Contain Continuum Dynamics, Inc.
Inc. Proprietary Information Information Figure 5d. Close up of mesh showing node-to-node node-to-node connections connections between various plates.
plates.
23 23
Dynamics, Inc. Proprietary Information This Document Does Not Contain Continuum Dynamics, Information between the node-to-node connections between Figure 5e. Close up of mesh showing node-to-node the skirt and drain skirt and drain channels; hood supports and hoods; and other parts.
24
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information 5f. Close up view of tie bars.
Figure 5f. bars.
25
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Information Shell nodes DOF are related to solid element shape functions Shell elements Surface Surface of solid element element Figure 6a. Face-to-face Face-to-face shell to solid connection.
Shell nodes DOF are related to solid element shape functions Surface of solid element element Figure 6b. Shell edge-to-solid edge-to-solid face connection.
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Contain Continuum Dynamics, Inc. Proprietary Information Document Does Not Contain This Document Information Upper support Dng
,Free rotation axis Seismic block .-. ~
Support block FIxed displacement nodes Figure 7. Boundary conditions. Inside node is half way between halfway 1Jl~ck between outer surface of support block support ring.
and upper suppon 27 _
This Document Document Does Not Contain Continuum Continuum Dynamics, Inc. Proprietary Information Information 3.10 Pressure Loading Loading The harmonic loads are produced produced by the pressures acting on the exposed surfaces of the steam dryer. At every frequency frequency and for each MSL, the pressure distribution corresponding to a distribution corresponding unit pressure pressure at the MSL inlet is represented oil lattice grid (i.e.,
on a three-inch grid latti,ce (i.e., a mesh whose lines are aligned with the x-, y- and z-directions) z-directions) that is superimposed superimposed over the steam dryer surface. This grid is compatible compatible with the 'Table' format used by ANSYS to 'paint' general pressure distributions upon structural structural surfaces. The pressures are obtained from the Helmholtz Helmholtz solver routine in the acoustic analysis [3].
In general, the lattice nodes do not lie on the surface, surface, so that to obtain, obtain the pressure differences at the surface differences surface it is necessary to interpolate interpolate the pressure differences differences. stored at the lattice nodes. This is done using simple linear interpolation between the 8 forming nodes of the lattice containing the surface point of interest. Inspection of the resulting pressures lattice cell containing pressures at selected selected nodes shows that these pressures vary in a well-behaved manner between the nodes with prescribed pressures. Graphical depictions resulting pressures and comparisons between depictions of the resulting'pressures between the peak pressures in the original nodal histories and those in the final surface load distributions produced in ANSYS, produced confirm that the load data are interpolated ANSYS, all confirm, interpolated accurately and transferred transferred correctly to ANSYS.
correctly The harmonic pressure loads are only applied applied to surfaces above the water level, as indicated in Figure 8. 8. In addition to the pressure load, the static loading induced by the weight of the steam dryer is analyzed separately. The resulting static and harmonic stresses stresse's are linearly combined combined to obtain total values which are then processed to calculate maximum and and, altemating alternating stress intensities for assessment in Section 5.
((
(3))) This is useful since revisions in the loads (3))) This is useful since revisions model do not necessitate necessitate recalculation of the unit stresses.
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This Document Document Does Not Contain Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Information NODES NODES AN J\N PRES-NOFU1
-. 101592 .040991 e X f'. .468738
-. 030301 .11 V .397447 ..540029 5400 29 Figure 8a. Real part of unit pressure loading MSL A (in psid) on the steam dryer at 50.1 50.1 Hz. No loading is applied to the submerged surface and lifting rods.
29 29
This Document Does Not Contain Continuum Dynamics, Inc.
This Inc. Proprietary Information J\N NODE NODESS PRES-NORM PFE,-NQ:FiM
-. 3918-. 2006 :-/ e .394932
-. 299897 -. *.295671 .494193
.4941 93
.2 95671 pressure loading MSL A (in psid) on Figure 8b. Real part of unit pressure the steam on the dryer at steam dryer at 200.45 Hz.
200.45 Hz.
surface and lifting rods.
No loading is applied to the submerged surface rods.
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This Document Does Not Contain Continuum Continuum Dynamics, Inc. Proprietary Information
- 4. Structural Structural Analysis The solution is decomposed decomposed into static and harmonic parts, where the static solution produces the stress field induced by the supported structure subjected to its own weight weight and the harmonic accounts for the harmonic stress field due to the unit pressure of given frequency in one solution accounts of the main steam lines. All solutions are linearly combined, with amplitudes provided provided by signal measurements in eacheach steam line, to obtain the final displacement displacement and stress time histories. This decomposition facilitates the prescription of the added mass model accounting decomposition accounting for hydrodynamic hydrodynamic interaction and allows one to compare the stress contributions arising from static and harmonic harmonic loads separately. Proper evaluation of the maximum membrane and membrane+bending membrane+bending stresses requires that the static loads due to weight be accounted accounted for. Hence Hence both static and harmonic analyses are carried out.
4.1 Static Analysis The results of the static analysis analysis are shown in Figure 9. The locations locations with highest stress include the inner vane bank connection connection to inner base plate near support brackets with stress intensity 9,598 psi. There are four locationslocations with artificial stress singularity, which are excluded from the analysis. The static stresses one node away are used at these locations locations as more realistic realistic estimate of local stress. These locations connections of the inner end plate to the inner locations are at the connections inner base plate at the ends of the cut-out, as shown in Figure 9c.
Harmonic Analysis 4.2 Harmonic The harmonic pressure loads were applied applied to the structural structural model at all surface nodes described in Section 3.10 3.10.,.. Typical stress intensity distributions over the structure structure are shown in Figure 10. Stresses were calculatedcalculated for each each frequency, and results from static and harmonic calculations were combined.
calculations To evaluate maximum stresses, the stress harmonics harmonics including the static component are transformed into a time history using FFT, and the maximum and alternating stress intensities for the response, evaluated. According According to ASME B&PV Code, Section Ill, III, Subsection Subsection NG-3216.2 the following procedure procedure was established to calculate alternating stresses. For every node, the calculate .alternating stress difference difference tensors, ma(= (n o~ On - Om , - re, are considered considered for all possible pairs of the stresses an ac and am cym at different different time levels, tn and tin. tm. Note that all possible pairs require consideration consideration since there are no "obvious" extrema extrema in the stress responses. However, in order to contain contain computational cost, extensive screening of the pairs takes place (see Section 2.3) computational 2.3) so that pairs known known to produce alternating alternating stress intensities intensities less than 500 psi are rejected. For each remaining stress difference difference tensor, the principal stresses 8S1,1, S822,, S 833 are computed and the maximum maximum absolute value among principal principal stress differences, differences, Sn=-max{ISiS-S Som = max {lSI - S21, 21,IsI-s lSI - S31, IS22 --S3[},
31,[S S31}, obtained. The alternating alternating stress at the node is then one-half one-half the maximum value of Snrn S. taken over all combinations (nm), i.e.,
combinations (n,m), Salt =tmax{Som}.
i.e., Salt = max fSm. This alternating alternating stress is compared against allowable 2 n,m n,m values, depending on the node location with respect to welds.
31
Document Does Not Contain Continuum This Document Proprietary Information Continuum Dynamics, Inc. Proprietary Information AN NODAL SOLUTION STEP=l STEP=1 SUB =1=1 TIME=l TIME=1 USUM USUM (AVG)
(AVG)
RSYS=O DMX =.068847
=.505E-03 SMN =.505E-03 SMN SMX =.068847 soEo.008099
.SOSE-03 "°!.053a6 .6 15 .068847
.0612511
.008099 .0688117 calculations showing displacements (in inches). Maximum Figure 9a. Overview of static calculations Maximum displacement (DMX) is 0.069". Note that displacements displacement are amplified for visualization.
32
Document Does This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Information AN J\N Z
l-x o
0 PP 4000 1000 5000 5000 Figure 9b. Overview Overview of static calculations calculations showing showing stress intensities intensities (in (in psi).
psi). Maximum Maximum stress stress intensity (SMX)
(SMX) is 9,598 psi. Note that displacements are amplified for visualization visualization 33 33
Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information This Document Information
/
~.
~-,
- '_ -T-.....\
/,r-r -\ -- - \
I . 'J "
I' I, f \\ l
\.,
\"'--.J v) \.,~..
r=:
_//
'_ L-' " .........L,...
~D (
- ~ LJ - zI
~
~
1\
Figure 9c. Stress singularities. Model is shown in wire Figure frame mode for clarity.
wireframe 34 34
This Document Proprietary Information Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information NODAL SOLUTION J\N STEP=1185 SUB =1=1 FREQ=50.418 FREQ=50.418 REAL ONLY SINT (AVG))
(AVG DMX =.195193 SMN =.0815799 SMN =.08157 SMX =11642
.081579 1294 2zo7/ pr 9055 10348 11642 9055 10a. Overview Figure lOa. Overview of harmonic harmonic calculations calculations showing real part of stress intensities (in psi) along with displacements. Unit loading MSL A at 50.1 Hz (oriented to show high stress locations at the hoods).
35
Document Does This Document This Contain Continuum Does Not Contain Inc. Proprietary Continuum Dynamics, Inc. Information Proprietary Information J\N NODAL SOLUTION STEP=305 STEP=305 SUB =1 SUB =1 FREQ=200.446 FREQ=200.446 ONLY REAL ONLY SINT (AVG)
(AVG)
DMX DMX =
SMN .02 171 6
=.021716
=.177944 SMN =.177944 SMX =5=5801 801
.9 74644.744 12 7 4 P I P 4512 5157 5801
.177 4512 Figure 10b. showing real part Overview of harmonic calculations showing lOb. Overview part of intensities (in stress intensities of stress (in psi) psi) 200.5 Hz.
along with displacements. Unit loading MSL A at 200.5 Hz.
36 36
This Document Does Not Contain Continuum Dynamics, Dynamics, Inc. Proprietary Proprietary Information Information 4.3 Post-Processing Post-Processing The static and transient stresses computed at every node with ANSYS were exported into files for subsequent subsequent post-processing. These These files were then th,en read into separate customized separate customized software to compute compute the maximum and alternating alternating stresses at every node. The maximum stress was defmed defined for each node as the largest stress intensity intensity occurring during the time history.
Alternating Alternating stresses were calculated according were calculated according to the ASME standard standard described described above. For shell elements the maximum stresses were calculated separately separately at the mid-plane, where only membrane membrane stress is present, and at top/bottomtoplbottom of the shell, where bending bending stresses are also present.
For nodes that are shared betweenbetween several structural components components or lie on junctions, the maximum maximum and alternating stress intensities are calculated' calculated as follows. ,First, First, the nodal stress tensor is computed separately computed separately for each individual, component each. individual, component by averaging over all finite elements meeting at the node and belonging to the same structural elements structural component. The time histories of these stress ten sors are then processed to deduce the maximum and alternating ten,sors alternating stress intensities intensities for each structural structural component. Finally for nodes shared across multiple components the highest of the component-wise component-wise maximum and alternating stresses is recorded as the "nodal" stress. This approach preventsprevents averaging of stresses across components components and thus, thus yields conservative conservative estimates for nodal stresses at the weld locations where several components components are joined together.
The maximum stresses stresses are compared against allowable values which depend upon the stress type (membrane, membrane+bending, membrane+bending, alternating alternating - Pm, Pm+Pb, Salt) and location (at a weld or away from welds). These allowables are specified specified in the following section. For solid elements the most conservative allowable allowable for membrane stress, Pm, is used, although bending stresses are The structure is then assessed in terms of stress ratios formed by nearly always present also. The~tructure dividing allowables by the computed stresses at every node. Stress ratios less than unity imply that the associated associated maximum and/or andlor alternating alternating stress intensities intensities exceed the allowable levels.
Post-processing Post-processing tools calculate calculate the stress ratios, identifying the nodes with low stress ratios and generating generating files formatted for input to the 3D 3D graphics program, TecPlot, which provides provides more general and sophisticated plotting options than currently available general and sophisticated plotting options than currently available in ANSYS. in ANSYS.
4.4 Computation of Stress Ratios for Structural Assessment Assessment The ASME B&PV Code, Section ill, III, subsection NG provides different different allowable allowable stresses for different load combinations combinations and plant conditions. The stress levels of'interest of interest in this analysis are for the normal operating condition, which is the Level 'A A service condition. The load combination combination for this condition is:
Normal Normal Operating Load Combination Combination = = Weight Weight + Pressure + Thermal The weight and fluctuating pressure contributions have been calculated pressure contributions calculated in this analysis and are included in the stress results. The static pressure differences expansion' stresses are differences and thermal expansion small, since the entire steam dryer is suspended inside the reactor vessel and all surfaces are exposed to the same conditions. Seismic loads only occur occur in Level Level B and C cases; Band cases, and are not considered in this analysis.
37 37
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Allowable Stress Intensities Intensities The ASME B&PV Code, Section Section ill, III, subsection subsection NG shows the following (Table 5) 5) for the maximum allowable stress intensity (Sm) and alternating stress intensity intensity (Sa) for the Level Level A service service condition. The allowable stress intensity intensity values for type 304 stainless steel at operating operating temperature temperatUre 550°F550'F are taken from Table 1-1.2 and Fig. 1-9.2.2 1-9.2.2 of Appendix I of Section III, in the Section Ill, ASME B&PV Code. The 'calculation Calculation for different different Stress stress categories is performed performed in accordance accordance with Fig. NG-3221-1 of Division I, Section Section III, ill, subsection NG.
Table 5. 5. Maximum Allowable Maximum Allowable Stress Intensity Alternating Stress Intensity Intensity and Alternating areas Intensity for all areas' other than welds. The notation Pm represents membrane membrane stress; Pb represents stress due to bending; Q represents represents secondary secondary stresses (from thermal effects and gross structural discontinuities, discontinuities, for example);
example); and F represents additional stress increments increments (due to local structural structural discontinuities, for example).
Type Notation Service Limit Allowable Value {ksQ (ksi)
Maximum StressStress Allowables:
General Membrane Membrane Pm Sm 16.9 16.9 Membrane + Bending
, Membrane . Pm+Pb Pm + Pb 1.5 Sm L5Sm 25.35 Primary + Secondary Secondary Pm + Pb + Q Pm+Pb+Q 3.0 Sm 3.0Sm 50.7 50.7" AlternatingStress Alternating Stress Allowable:
Peak == Primary + Secondary + F Salt Salt Sa 13.6 13.6 When evaluating weld~,welds, e~ther either .the the calculated calculated or allowable allowable stress was adjusted, 'to to account for stress .concentration concentration factor*.and factor.and weld quality. Specifically:
Specifically: .
- " For maximum allowable stress 'intensity, intensity, the allowable value is decreased decreased by multiplying
, its value in Table Table 5 by 0.55. .
The weld factors of 0.55 and 1.8 selected based 1.8. were selected based on the. the, observable quality of the shop welds and liquid penetrant NDE testing of all welds (excluding (excluding tack and intermittent intermittent welds, which were subject to 5X visual inspection) during fabrication. These factors are consist~nt consistent with fatigue strength reduction factors recommended by the Welding Research Research Council, [19],[19], and stress concentration concentration factors at welds, provided in [20] and [21]. [21]. In addition, critical welds' are subject subject to periodical visual inspections in accordanceaccordance with the requirements requirements of GE SIL 644 SiL SIL and BWR VIP-139 [22]. Therefore, for .weld weld stress intensities, the allowable allowable values are shown shown in Table 6.
Table 6. . . , '
Thesee.factors These. factors (0.55 and 1.8) 1.8) also conservatively conservatively, presume that that'thethe structure is joined using fillet welds fillet welds unless specified otherwise.
ot~erwise. Since fillet' welds correspond cprrespond' to larger .stressstress concentration concentration factors than other types of welds, this assumption is a conservative one.
conservative
. ' ' 1 .
38 38
This Document Does Not Contain Continuum Continuum Dynamics, Inc. Inc. Proprieta~
Proprietary Information Information Table 6. Weld Stress Intensities.
Type Notation
,Notation Service Limit Allowable
-Allowable Value {ksQ (ksi)
Maximum Stress Stress Allowables.
Allowables:
General Gerieni.l Membrane Pm Sm 0.55 Sm. 9.30 9.30 Membrane + Bending Membrane Pm + Pb Pm+Pb 0.825 Sm 13.94 13.94 Secondary Primary + Secondary Pm + Pb + Q Pm+Pb+Q 1.65 1.65 Sm 27.89 Alternating Alternating Stress Allowables:
Peak = = Primary + Secondary*
Secondary-++ F Salt Salt Sa 13.6 13.6 Comparisonof Calculated Comparison Calculatedand andAllowable Stress Intensities A llowable Stress Intensities classification of stresses into general membrane or membrane The classification membrane + bending types was made according 'to 'to the exact location, where where the stress intensity was calculated;calculated; namely, general membrane.'
membrane; Pin, Pm, "for middle surface surface of shell element, and membrane + bending, Pm + Pb;: Pb,: for for.
other locations. For solid elements the most conservative, conservative, general general membrane, membrane, Pm, allowable is used'.
used:
structural assessment is carried out by computing The structural computing stress ratios between between the computed computed maximum and alternating alternating stress intensities, intensities, and the allowable levels. Locations where any of the ofthe stresses exceed allowable levels will have stress ratios less than unity. Since computation exceed allowable computation of of stress ratios and related quantities Within within ANSYS is time-consuming and awkward, a separate FORTRAN FORTRAN code was developed developed to computecompute the necessary necessary maximum and alternating stress stress Pm,ý Pm+Pb, and Salt, and then compare it to allowables. Specifically/the intensities,. Pm, Specifically,-the following quantities quantities were ccnnputed computed at every node,: node: . .
- 1. The maximum membrane stress intensity, Pm (evaluated
- 1. (evaluated at the mid-thickness mid-thickness location location for shells), . '
2: The maximum 2:' maximurr.l membrane+bending metnbrane+bending stress intensity, Pm+Pb, (taken as the large'st largest of the.
the' maximum maximum, stress intensity values at the bottom, bottom', top, and mid thickness locations, for shells), ,,'
shells), ' ' , ',
- 3. The alternating
- 3. alternating stress, Salt,Salt> (the maximum value over the three thickness locations lo~ations is taken).
~~. .
4i
- 4. The T4e stress ratio due to a maximum stress intensity intensity assuming the node lies,lies. at aa. non-weld non-weld location location (note that this (note that this is is the the minimum minimum ratio ratio obtained obtained, considering considering both membrane stresses membrane stresses and membrane+bending membrane+bending stresses): ,
. SR-P(nw) = min{ Sm!Pm, SR-P(nw)::::: Sm/Pm, L5 1.5
- Sm/(Pm+Pb) }.
- SmI(Pm+Pb) . ,
- 5. The
- 5. alternating stress ratio The alternating assuming the node lies at a non-weld location, rati<?,assuming SR-a(nw) ~=Sa SR,.a(nw) Sa / (1.1
- Salt),
Sait), .
- 6. The same as 4,
- 6. 4, but assuming the node lies on,a on-a weld, SR-P(w)=SR-P(nw)
- 0.55 SR-P(w)=SR-P(nw)
- 7. The
- 7. The same as 5, but assuming the node lies on a weld, as-5, SR-a(w)=SR-a(nw) / 1.8.
SR-a(w)=SR-a(nw) 39 39
This Document Document Does Not Contain tontaih Continuum Dynamics, Inc. Proprietary Information Information Note that in steps 4 and 6, the minimum of the stress ratios based on Pm and Pm+Pb, is taken.
The allowables allowables listed in Table 6, Sm=16,900 Sm=1~,900 psi and Sa=13,600 psi. The factors, 0.55 and 1.8, are the weld factors discussed above. The factor of 1.1 1.1 accounts accounts for the differences differences in Young's moduli for the steel used in the steam dryer and the values assumed in alternating stress According to NO-3222.4 allowable. According NG-3222.4 in* in-subsection subsection NG NO of Section III of the ASME Code [2], [2], the effect of elastic modulus upon alternating stresses stresses is taken into account by mUltiplying multiplying alternating alternating stress Salt at all locations by the ratio, ElEmodeI= E/Emodef l:I,.l, where: .
E = 28.3 10 1066 'psi, psi, as shown on Fig. 1-9.2.2. ASME BP&V Code 6
EmodeI Emodel = 25.55 106 psi (Table 10 (Table 1)
The appropriate maximum and alternating stress ratios, SR-P and SR-a, are .thus determined are.thus determined and .
a final listing of nodes having the smallest stress ratios is generated. The nodes with stress ratios .
lower than 4 are.plotted*in are plotted -in TecPlot(a TecPlot (a 3D 3D graphics plotting program widely used in i~ engineering engineering.
communities [23]), TQes~ These nodes are tabulated and depicted depicted in the following Results' Results Section Section...
Finally, at a limited number of weld locations (specifically the vertical hood reinforcement reinforcement strip), estimates of the 'nominal' membrane membrane+bending stresses is taken by finding membrane and membrane+bending the maximum stress at all of the sUJ,Tounding surrounding non-weld -element. nodes. This stress is then
'ele,ment. n04es. then multiplied by a weld factor of f=4.0 in accordance of£=4.0 accord~ce with the ASME code (Table NG-3352-1).
(Table NG-3352-1).
This is the appropriate appropriate weld stresse~ evaluated near, but off the weld weld factor for nominal stresses we14 and is toto' be distinguished be distinguished from from the 1.8 1.8 (fillet (fillet welds) or 1.4 (full penetration penetration w~lds) welds) weld factors applied to linearized-linearized- stresses evaluated on the weld. This stresses evaluated This processing processing of weld stresses i$ is consist~nt consistent with, with prior approaches prior approaches in industry (e.g..,
(e.g;; [24], specifically specifically Figure 6-46, pg. 112). 112). (Note that the that'the definition definition of 'nominal' stress is here understood understood as the characteristic characteristic stress in the plate or shell without the localized localized influence of reinforcements reinforcements or other discontinuities.
discontinuities. This definition is not not explicitly explicitly given in the ASME code which which was originally assembled before originally assembled. bef<?re finite element element modeling modeling methods were routinely used' and simplified or textbook calculation calculation methods were normative.
normative. However, Ho,Wever, thesethese, simplified simplified calculations calculations generally generally predicted predicted stresses st:t:esses that are in good agreement agreement with the finite finit~ element stresses away from junctions. Using junctjon,s. '*U sing neighboring neighboring node off- off-weld stresses to represent weld stresses represent the nominal stresses engineering application).
is thus reasonable for engineering 4.5 Finite Element Element Sub-modeling Sub-modeling In order to meet target stress levels at EPU in the NMP2 steam dryer modifications modifications are needed. These consist needed. These consist of stiffening th~
of stiffening the closure closure plates (see Appendix.
Appendix A) and reinforcing Welds -at reinforcing welds at two locations: (i)-the (i)'the top 18" of thewelds the welds connecting the closure plates to the hoods and'vane banks and (ii) the weld between the vane bank side plates and lifting rod support brace. These weld reinforcements weld reinforcements are developed using high resolution solid element-based element-baSed' sub-models sub-models of of these locations.
these locations. The use use of localized localized sub-models is motivated motivated by the need- need to maintain maintain computational costs at a feasible level. To this end the global steam 'dryer computational dryer model is predominantly comprised predominantly comprised of shell elements. 'These These elements are are* well suited for structures structures such as the as the steam steam dryer consisting consisting of shell-like components components and tend -to 'conservative to produce !conservative estimates of estimates of the the stresses.
stresses. In some cases however, such' as 'welded welded junctions junctions involving involving multiple components, shell element models can overestimate overestimate the nominal nominal stress intensities in the vicinity of the of junctions. In the junctions. such cases a more In such more refined refmed analysis using solid elements to capture the complete 3D complete 3D stress distribution, is warranted. Therefore, Therefore, to efficiently efficiently analyze complex complex 40 40
This Document Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information structures structures such as steam dryers, a standard engineering practice practice is to first analyze analyze the structure using a shell-based shell-based model.
model. Locations Locations with high stresses ate are examined in greater greater detail using 3D solid elements to obtain obtain a more definitive stress prediction.
prediction .
- t **
The solid element-based element-based sub-modeling sub-modeling follows the procedure procedure outlined in Appendix A (also
[25] and Appendix A of [26]) [26]) and validated in against both high resolution solid models of the full structure structure and sub-structuring sub-structuring results in [27] and [28]. Based on these models, the nominal stress intensities computed by the 3D solid element model are lower than those obtained with the shell-based FEA used to analyze the complete shell-based complete steam dryer by the stress reduction factors (SRFs) summarized summarized in Table 7. Note that the SRFs vary according according to location being dependent dependent on the individual geometry geometry and also the general loading characteristics. They are generally less than loading characteristics.
unity due to conservative conservative stress estimates in the shell-basedshell-based weld stresses. For example example the discontinuity stresses computed computed in a shell model at a weld joint between two orthogonal orthogonal members are often quite conservative conservative becausebecause the shell element depiction depiction does not provide provide any credit for the stress distribution associated with the specific weld geometry. Once the SRFs are obtained, the stress intensities predicted by the global shell element-based element-based analysis at these locations are first multiplied by these SRFs to obtain more accurate accurate estimates estimates of the nominal stresses. These are then multiplied by the 1.8 weld factor before before comparing against allowable allowable stress limits to obtain the alternating stress ratios.
Detailed Detailed 3D solid element sub-models are applied at both the weld reinforcements reinforcements and additional additional locations (see Table 7 for a complete complete list). For the closure plate the welds connecting connecting the closure plate to the vane banks and hoods experience significant significant vibratory stresses due to a plate response in the 125-135 125-135 Hz frequency frequency range. Though stresses remain remain well above allowable levels for all frequency shifts at both CLTP and EPU, the margin margin is below the target level (i.e.,(i.e., a stress ratio of SR-a=2.0 at EPU). Therefore, the closure plate was reinforced reinforced and a sub-model developed developed for each of the locations on the closure closure plates where stresses stresses exceeded exceeded target levels.
On each closure plate there are four such locations. The first two are on the vertical weld joining the closure plate to the vane bank. The first node is at the top of this weld and the second one lies 13.5" below below it. The other two locations are on the curved weld connecting the closure plate to the curved hood. Again the first location is at the top of this weld and the second one lies 14.5" below it. In both cases, the stresses at the top location result from a combination 14.5" combination of of membrane membrane and bending bending stresses whereas the stresses at the lower locations locations are predominantly due to bending. The stresses stresses are induced by a closure plate response dominated by a (1,2) response dominated (1,2) mode (i.e., the mode shape (i.e., shape resembles resembles the first mode of a beam in the horizontal direction and the second second mode in the vertical sense) which explains the high stress at the lower locations on the welds. Sub-model calculations at these locations locations show that to achieve the required target stress levels, an interior weld must be added along the top 18" 18" of each weld thus effectively effectively converting it from a single-sided to a double-sided fillet weld along this length. Additional Additional details are given given in Appendix A.
Sub-modeling is also applied to analyze the stresses in the lifting rod support brace where it Sub-modeling connects to the vane bank side plate [29]. [29]. A sub-modeling sub-modeling analysis of the high stress location shows that for the current WI 1/4"double-sided double-sided fillet weld the stress reduction is minimal. Repeating sub-model analysis with an increased the sub-model increased weld of 112" 1/2" resulted in a stress reduction factor of of 0.60. To meet EPU target stress levels it is recommended recommended to increase the weld to this size.
41
This Document Does This Document Contain Continuum Not Contain Does Not Dynamics, Inc.
Continuum Dynamics, Proprietary Information Inc. Proprietary Information The The other other locations locations where where sub-modeling sub-modeling'waswas performed performed are are listed listed as as locations locations 6-9 6-9 in in Table Table 77 and involve hood/hood support weld and the bottom of this weld where it meets and involve hoodlhood support weld and the bottom of this weld where it meets the base plate the base plate junction junction as as well well as as two two locations locations near near tie tie bar bar ends ends involving involving large large welds welds thatthat are are not not accounted accounted for for in in the the -shell
'shell model.
model. The The locations locations of of all all sub-models sub-models are are depicted depicted inin Figure Figure 11.11. Additional Additional details of sub-models evaluated for locations away from the closure-plate are given details of sub-models evaluated for locations away from the closure'plate are given in [29]. in [29].
1:.7 42
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 7. sub-model analysis.
- 7. Summary of stress reduction factors obtained using sub-model Location Reduction Stress Reduction
-t Factor do 1. Top of vertical closure plate/vane bank weld
- 1. 0.62 (Appendix A)
- 2. 14.5" 14.5" below location 3 on the same weld 0.71 (Appendix (Appendix A)
A)
- 3. Top of closure plate/hood weld 0.86
- 3. Top of closure platelhood weld 0.86 (Appendix A)
- 4. 13.5" 13.5" below location 11 on the same weld 0.88 (Appendix A)
- 5. Lifting rod support brace/vane
- 5. brace/vane side plate junction 0.60 [29]
(assuming an increased 112"1/2" weld) hood/hood support weld at junction 0.79 [25]
- 6. Bottom of hoodlhood with base plate
- 7. Hood/hood
- 7. support Hoodlhood support 0.77 [26]
[26]
- 8. Side plate/top plate
- 8. 0.70 [29]
I
- 9. Tie bar/top vane bank plate.
plate. 0.71 [29]
L ______________________________________________________
Note: For locations Note: 1-4 itit is assumed that an locations 1-4 has been an inner weld has been toto the the top top 18"18" of of the welds the welds joining the closure plate to the hoods or vane joining the closure plate to the hoods or vane banks, banks, thereby replacing the existing single-sided single-sided fillet weld fillet weld byby one one that is double that is sided. Also, double sided. Also, an an increased increased 1/2" W' weld is assumed weld is assumed for for location location 5. 5.
43
Information This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information l a. Closure plates and associated attachment welds examined with sub-model Figure lla. sub-model in Appendix A (note lifting rods and other components modeled with solid elements are omitted for perimeter are locations 1-4 in Table 7.
Sub-models on the perimeter clarity). Sub-models 44
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Contain Continuum Proprietary Information Information Figure lIb.
1lb. Location of node on inner hood/hood support/middle support/middle base plate weld analyzed with sub-model sub-model in [29]. Sub-model corresponds to location 5 in Table 7.
ft-x y
Figure 1Ic.
11ic. Location of node on hood/hood support/base support/base plate weld analyzed with sub-model sub-model in
[25]. Sub-model corresponds to location 6 in Table 7.
45
This Document Does Not Document Does Contain Continuum Dynamics, Not Contain Proprietary Information Dynamics, Inc. Proprietary Information Figure l1lId.
Figure Location of node on hood/hood
- d. Location sub-model analysis hoodlhood support weld analyzed with sub-model analysis corresponds to procedure in [26]. Sub-model corresponds procedure location 7 in Table 7.
in Table 7.
6ýLý Figure 11 e. Location of node on side plate/top plate weld analyzed lie. sub-model analysis with sub-model analyzed with analysis in Table Sub-model corresponds to location 88 in procedure in [29]. Sub-model 7.
Table 7.
46
This Document This Does Not Contain Document Does Continuum Dynamics, Contain Continuum Proprietary Information Dynamics, Inc. Proprietary Information Figure IIf. analyzed with sub-model 1If. Location of node on tie bar/top vane bank plate weld analyzed sub-model analysis procedure corresponds to location 9 in Table 7.
procedure in [29]. Sub-model corresponds 7.
47
This Document Does Not Contain Continuum Dynamics, Contain Continuum Proprietary Information Dynamics, Inc. Proprietary Information
- 5. Results The stress intensities and associated stress ratios resulting from the Rev. 4 acoustic/hydrodynamic loads [4] with associated biases and uncertainties acousticlhydrodynamic uncertainties factored in, are presented below. The bias due to finite frequency discretization discretization and uncertainty uncertainty associated with the finite element model itself,itself, are also factored in. In the following sections sections the highest highest maximum and alternating alternating stress intensities intensities are presented presented to indicate which points on the dryer experience significant stress concentration experience and/or modal response (Section concentration andlor (Section 5.1). The lowest stress ratios obtained by comparing comparing the stresses against allowable values, accounting accounting for stress type (maximum and alternating) and location (on or away from a weld), are also reported (Section 5.2). Finally the frequency dependence (Section dependence of the stresses at nodes experiencing experiencing the lowest stress ratios is depicted in the form of accumulative (Section 5.3).
accumulative PSDs (Section In each section results are presented presented both at nominal conditions (no frequency shift) and with frequency shift included. Unless specified otherwise, otherwise, frequency shifts are generally generally performed at 2.5% increments. The tabulated stresses and stress ratios are obtained using a 'blanking' 2.5% 'blanking' procedure procedure that is designed to prevent prevent reporting a large number of high stress nodes from essentially the same location on the structure. In the case of stress intensities this procedure is as follows. The relevant stress intensities are first computed at every node and then nodes sorted sorted according to stress level. The highest stress node is noted and all neighboring nodes within within 1010 inches of the highest stress node and its symmetric images (i.e., (i.e., reflections across the x=0 x=O and y=O planes) y=0 planes) are "blanked" "blanked" (i.e., excluded excluded from the search for subsequent high stress locations).
Of the remaining remaining nodes, the next highest stress node is identified and its neighbors (closer than 10 inches) inches) blanked. The third highest stress node is similarly located and the search continued in this fashion until all nodes are either blanked or have stresses less than half the highest value on the structure. For stress ratios, an analogous blanking procedure procedure is applied. Thus the lowest lowest stress ratio of a particular particular type in a 10" neighborhood symmetric images is identified neighborhood and its symmetric identified and all other nodes in these regions excluded excluded from listing in the table. Of the remaining remaining nodes, the one with the lowest stress ratio is reported and its neighboring neighboring points similarly excluded, and so on until all nodes are either blanked or have a stress ratio higher than 4.
The measured CLTP CLTP strain gage signals contain significant contributions from non-acousticnon-acoustic sources sources such as sensor noise, MSL turbulence turbulence and pipe bending vibration that contribute to the contribute hoop strain measurements.
measurements. The ACM analysis does not distinguish between the acoustic acoustic and non-acoustic non-acoustic fluctuations in the MSL signals that could lead to sizeable, but fictitious acoustic acoustic loads and resulting stresses on the dryer. One way to filter these fictitious loads is to collect data with the system maintained maintained at operating pressure (1000 (1000 psi) and temperature, but low power
[30]. By operating operating the recirculation pumps at this condition, the background background plant noise and vibrations remain present. At these conditions conditions the acoustic loads are known to be negligible so so that collected data, referred to as the low power power data, originate entirely entirely from non-acoustic sources sources such as sensor noise and mechanical vibrations. This information is valuable valuable since it allows one to now distinguish distinguish between the acoustic and non-acoustic non-acoustic content in the CL CLTP TP signal and therefore therefore modify the CL CLTPTP loads so that only the acoustic component is retained. In previous analyses of the similar dryers, these low power signals were subtracted.
48
This Document Does Not ContainContain Continuum Dynamics, Inc. Proprietary Proprietary Jnformation Information In the present implementation implementation however, no filtering using low power data is performed. The reason for retaining retaining noise in this particular case is to avoid protracted.
protracted review of the low power power subtraction process and to thus expedite qualification of the dryer. Thus, rather than attempting to justify the use of low power noise subtraction subtraction in this case, it was decided to use the CL CLTPTP signal (and by extension the EPU signals) directly directly without noise filtering. Therefore for all results presented presented herein, no noise filtering using low power power data has been performed.
The applied load includes includes all biases and uncertainties uncertainties for both the ACM (summarized (summarized in [4]) [4])
and the FEM. For the latter there are three main contributors to the bias. bias and uncertainty. The first is an uncertainty (25.26%) that accounts for modeling idealizations idealizations (e.g.,
(e.g., vane bank mass model), geometrical geometrical approximations approximations and other discrepancies discrepancies between the modeled and actual dryer such as neglecting of weld mass and stiffness stiffness in the FEA. The second contributor contributor is a bias of 9.53%
9.53% accounting accounting for discretization discretization errors associated with using a finite size mesh, upon computed computed stresses. The third contributor is also a bias and compensatescompensates for the use of a,finite
- a. finite discretization discretization schedule in the construction of the unit solutions. The frequencies frequencies are spaced such such that at 1%I % damping the maximum maximum (worst case) case) error in a resonance peak is 5%. The average error for this frequency schedule is 1.72%.
1.72%.
It is significant significant to note that the applied loads reflect revised bias and uncertainty uncertainty values over new frequency intervals: 60-70 Hz and 70-100 Hz. The higher bias and uncertainty uncertainty values in the 60-70 Hz range strongly influence influence the limiting stresses values, but are also overly conservative.
This is because when specifying specifying new frequency intervals intervals the ACM should be recalibrated recalibrated over these intervals before before calculating calculating the bias and uncertainty values. Because it is resource-intensive and would constitute further revisions to the ACM model (to Rev. 5) 5) this model re-calibration was not performed. Consequently Consequently the revised biases and uncertainties are higher than they would be if the ACM had been matched to data over the new intervals.
5.1 General Stress Distribution Distribution and High Stress Locations The maximum maximum stress intensities obtained by post-processing post-processing the ANSYS stress histories for CLTP at nominal frequency and with frequency shift operating conditions are listed in Table 8. 8.
Contour plots of the stress intensities over the steam dryer structure structure are shown on Figure 12 12 (nominal frequency) and Figure 13 (maximum stress over all nine frequency shifts including nominal). The figures are oriented to emphasize emphasize the high stress regions. Note that these stress intensities intensities do not account for weld factors but include end-to-end end-to-end bias and uncertainty.
uncertainty. Further, it should be noted that since the allowable stresses vary with location, stress intensities do not necessarily correspond to regions of primary structural necessarily correspond structural concern. Instead, structural evaluation is structural evaluation is more accurately accurately made in terms of the stress ratios which compare the computed stresses to allowable levels with due account made for stress type and weld. Comparisons Comparisons on the basis of of stress ratios are made made in Section 5.2.
The maximum stress intensities in most areas are low (less than 500 psi). For the membrane stresses (Pm) the high stress regions tend to occur at: (i) (i) the bottom of the central vertical side plate that joins the innermost vane banks (stress concentrations occur where this plate is welded to the inner base plates resting on the upper support ring); (ii) the welds joining the tie bars to the top cover plates on the vane banks; (iii) the seismic seismic blocks that rest on the steam dryer supports; and (iv) junctions junctions connecting connecting the bottoms of the hood supports. Except Except for the last location, the 49
This Document Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Information' stresses are dominated dominated by the static contribution contribution as cancan be inferred' inferred from the small alternating stress intenSities intensities (Salt) tabulated tabulated in Table 8 for the high Pm locations. From FigUre Figure 12a and Figure 13a 13a higher Pm regions are seen to be in the vicinity of the supports supports where all of the dryer ,.
deadweight is transmitted, the closure deadweight closure plates connecting connecting the inner hoods to the 'middlemiddle vane banks, and various localized concentrations concentrations such those along the bottom of the outer hood. hood.'
The membrane + bending stress (Pm+Pb) distributions distributions evidence a more pronounced pronounced modal response especially on the hood structures. ,The The two locations with the highest stress intensities of this type are the same pair having the highest membrane membrane stress and,and are dominated doniinated -by fHigh stress concentration deadweight. ,High -also-recorded concentration is -also* recorded on the top edge of this verticaLplate vertical plate where it joins to the inner vane bank. Other areas with high Pm+Pb stress concentrations concentrations (i) the tops of the:closure include: (i) the: closure plates where they are are-welded welded to a hood or vane bank end plates; (ii)
(ii) the skirt/drain channel welds;'
skirt/drain ch~el welds; (iii) the outer .cover plates connecting to the upper support ring ring and bottom of the outer hoods; and (iv) the common outer, common junction junction between each-hood, its between each'hood, its hood support (or stiffener), and the adjoining adjoining base plate (see Figure 13c). -,
The alternating stress, Salt, Salt> distributions are most pronounced pronounced on the outer hoods directly exposed to the MSL inlet acoustics, and on welds involving the closure plates. All hoods exhibit exhibit a strong response (e.g.,
(e.g., Figure 13d). The highest stress intensity at any frequency shift occurs at the middle hood. Though not exposed directly to the MSL acoustic sources, the interior interior'hoods hoods are thinner and their response is driven mainly by structural structural coupling coupling rather than direct direct forcing.
Numerous Numerous weld locations also show significant significant stress including including the bottoms of drain channels junctions between the hoods, hood and the jUnctions hood'-supports supports and base plates. These locationslocations are characterized by localized characterized localized stress concentrations concentrations as indicated indicated in Figure BeB3e and have emerged emerged as high stress locations in other steam-dryers also. Other locations with high alternating alternating stress stress" intensities include the tie bar/top cover intensities include the tie bar/top cover plate weld and plate weld welds involving and welds involving the the closure plate.
closure plate.
Comparing Comparing the nominal results (Table 8a) and results with frequency shifting it can be seen that inaximum maximum stress intensities, intensities, Pm and Pm+Pb, do not differ significailtly.
significantly. The highest highest alternating stress is approximately approximately 4.2%4.2% higher when frequency shifts are considered. For other nodes however the the variations are higher. As shown in the next section, all stresses are well within allowable levels. '
,i, "1
50 50
Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information This Document Table 8a. Locations with highest highest predicted predicted stress intensities for CL CLTP conditions with no frequency shift.
TP conditions Stress Location Location Weld Weld Location (in) node(a) node(a) Stress Intensities Intensities (psi)
Category Category x yy z Pm Pm+Pb Salt Salt Pm Inner Side Plate Inner No 3.1 119 119 0.5 37229 7475 8836 460
" Ext/Inner Base Plate Side Plate Ext/Inner Yes 16.3 119 0 94143 6913 9809 438 438
" Upper Upper Support Support Ring/Support/Seismic Ring/Support/Seismic Block Yes -6.9 -122.3
-122.3 -9.5 113554 6238 6238 911 911
" lei Bar lie Yes 49.3 108.1 88 141275 141275 5962 5962 807
" Hood Support/Middle Base Hood Support/Middle Base Plate/Inner Yes _ 39.9 -59.5 0 101435 5352 101435 5488 1638 1638 Backing Backing Bar/Inner Bar/Inner Hood Hood Pm+Pb Side Plate Side Plate Ext/Inner Base Plate Yes 16.3 119 0 94143 6913 9809 438
" inner Side Plate Inner No 3.1 119 0.5 37229 7475 8836 460
" Side Plate/Top Side Plate Plate/Top Plate Yes 49.6 108.6 88 ' 93256 2505 8542 -1129 1129
" Middle Base Plate/Inner Middle Base Plate/Inner Backing Bar Out/Inner Backing Bar Out/Inner Yes Yes -39.9 -108.6
-108.6 0 84197 441 7227 1433 1433 Backing Bar/Inner Hood Backing Bar/Inner Hood
" Side Plate/Top Side Plate Plate/Top Plate Yes 17.6 119 88 '91215 91215 898 7174 ' 1337
,7174 1337 -
Salt Middle Middle Hood Hood No -68.9 69.6-69.6 41;6 41.6 31054 1717 2759 -2728 2728
" Hood Support/Inner Support/inner Hood-Hood- - --- Yes 36.2 36.2' 50.8 -99529 0 50.8' 99529 975 ,2316 2316 2290
" Outer Hood - No -97.3 -50.7 62 62 78572 770 770 2160 2116
""_.._Middle Middle Hood No
--No -67.1 70.9 54.5 31441 1517 2099 2099 2016
"" Hood Support/Inner Support/Inner Hood Yes 39.1 0 23 99515 842 2064 1977 Notes.
(a) Node numhbr. are-retained Node numbers are-retained fnr for fiirther further reference.,
refPrion- . , _
(1-9) Appropriate (1-9) Appropriate stress stress reduction factor for the welds and modifications modifications listed in Table 7have applied,~ The number Thave been applied; number refers to the particular particular location and corresponding corresponding stress reduction reduction factor in Table Table 7.
51
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Proprietary Information Information Table 8b. Locations with highest predictedpredicted stress intensities intensities taken overover all frequency shifts CLTP conditions.
Stress Location Weld Location (in) node(a) node(a) Intensities (psi)
Stress Intensities % Freq.
Category x y z Pm Pm+Pb Salt Salt Shift Pm Inner Side Plate No 3.1 119 119 0.5 37229 7490 9003 634 10 it Side Plate Ext/Inner Ext/Inner Base Plate Yes 16.3 119 0 94143 9809
" Side Plate Base Plate Yes 16.3 119 6918 478 5
" Ring/Support/Seismic Block Upper Support Ring/Support/Seismic Yes -6.9 -122.3 -9.5 113554 6688 6688 1342 55
" Tie Bar Yes -49.3 -108.1 88 143795 6077 6077 877 S5
" Support/Middle Base Plate/Inner Hood Support/Middle Plate/Inner Yes 39.9 -59.5 0 85723 85723 5495 5819 1815 -10 Backing Bar/Inner Bar/Inner Hood Hood Pm+Pb Side Plate Ext/Inner Base Plate Yes 16.3 119 0 94143 94143 6918 "9809 9809 478 00 I Inner Side Side Plate No 3.1 119 0.5 37229 9003 634 55
" Inner Plate No 3.1 119 0.5 37229 7490 i Side Plate/Top Plate Yes 49.6 108.6 88 93256 2526 ' 8571 55
" Side Plate{Top Plate Yes 49.6 108.6 88 93256 2526 1215
" Middle Base Plate/Inner Plate/Inner Backing Bar -Yes
-Yes -39.9 -108.6-
-108.6- 0 84197 84197 470 7712 1683 5
-- Out/Inner Backing Bar/Inner-Hood Out/Inner Backing Bar/Inner-Hood , - . I - __-.- -, __
" " Side Plate{Top Plate/Top Plate Yes 17.6 119 88 91215 91215 920 7332 1585 55 0 "
Salt Salt Middle hood No -68.6 69.6 43.7 31149 1717 1717 2953 2914 2.5
"" Outer hood .. ..
- No -97.3 -50.7 62 78572 .- . 969 2674 2622 5, 5_
" Closure plate -No
--No 46.2 -108.6 88 16192 3697 16192 5410- ' 2561 5410 10 10
" Support/Middle Base Plate/Inner Hood Supportl.Middle,Base Plate/Inner Backing Yes -39.9 0 0 85723 4695 4849 ' 2378 ~5
-5 f . '
- Hood( 6)
Bar/Inner Hood(6) , , .. -
" Closure plate Closure. No -70.8
-70.8' 85.2 71.9 17691 17691 271 2394 2355 . -10
-10 Notes.
(a) Node numbers nUnibers are retained for further reference.
(1-9) Appropriate stress reduction (1-9) Appropriate reduction factor for the welds and modifications listed in Table 7 have been applied. The number to the p.umber refers 'to location and ~orrespoilding particular location corresponding stress r~dlictioIi reduction factor f3:c!or in Table 7. " ,
52 52
This Document Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Information z
Y Pm [psi]
7500 6750 6000 5250 4500 3750 3000 2250 1500 1500 750 0o Figure 12a. Contour plot of maximum membrane membrane stress intensity, Pm, for CLTP load. The maximum stress intensity is 7475 psi.
53 53
Document Does Not This Document Not Contain Contain Continuum Continuum Dynamics, Inc. Proprietary Dynamics, Inc. Proprietary Information Information z
YJ X Pm+Pb [psi]
9000 8000 7000 6000 5000 4000 3000 2000 1000 1000 0o membrane+bending stress intensity, maximum membrane+bending Figure 12b. Contour plot of maximum intensity, Pm+Pb, CLTP Pm+Pb, for CLTP intensity is 9809 psi. First view.
load. The maximum stress intensity 54 54
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information This X
yY Pm+Pb [psi]
9000 8000 8000 7000 7000 6000 5000 4000 3000 3000 2000 1000 0o Figure 12c. Contour Figure 12c. Contour plot of maximum maximum membrane+bending membrane+bending stress intensity, Pm+Pb, for CLTP CLTP load.
load. This This second second view from belowbelow shows shows the high stress intensities intensities at the hood/stiffener/base hoodlstiffenerlbase plate plate junctions junctions and drain channel/skirt channel/skirt welds.
55 55
Contain Continuum Dynamics, Inc. Proprietary Information This Document Does Not Contain Infonnation 11%
z Salt [psi]
2750 2500 2250 2000 1750 1750 1500 1250 1250 1000 1000 750 750 500 250 Salt, for CLTP load. The maximum Figure 12d. Contour plot of alternating stress intensity, Salt' alternating stress intensity is 2728 psi. First view.
56 56
This Document Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Proprietary Information y
Y
~x Salt [psi]
2750 2500 2250 2000 1750 1500 1500 1250 1250 1000 1000 750 500 250 Figure 12e. Contour plot of alternating stress intensity, Salt>
Salt, for CLTP load. Second view showing details of the outer hood and closure plate.
57 57
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Continuum Dynamics, Information z
Pm [psi]
7500 6750 6000 5250 4500 3750 3000 2250 1500 1500 750 o
0 Figure 13a. Contour Contour plot of maximum membrane membrane stress intensity, Pm, for CLTP operation with frequency frequency shifts. The recorded stress at a node is the maximum value taken over all frequency frequency shifts. The maximum stress intensity is 7490 psi.
58
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
Pm+Pb [psi]
9000 8000 7000 6000 5000 4000 3000 2000 1000 1000 o0 Figure 13b. Contour plot of maximum maximum membrane+bending membrane+bending stress intensity, intensity, Pm+Pb, for CLTP operation with frequency frequency shifts. The recorded stress at a node is the maximum value taken over all frequency shifts. The maximum maximum stress intensity intensity is 9809 psi.
First view.
59
Dynamics, Inc. Proprietary This Document Does Not Contain Continuum Dynamics, Proprietary Information Information p
yY
~x-/X Pm+Pb [psi]
9000 8000 7000 6000 5000 4000 3000 2000 1000 1000 0o membrane+bending stress intensity, Pm+Pb, for CLTP Figure 13c. Contour plot of maximum membrane+bending beneath reveals stresses shifts. This second view from beneath operation with frequency shifts. on stresses on channel/skirt support/base plate junctions, outer cover plate and drain channeVskirt the hood support/base welds.
60 60
This Document Document Does Not Contain Continuum Continuum Dynamics, Dynamics, Inc. Proprietary Information Inc. Proprietary Information z
Salt [psi]
3000 2750 2500 2250 2000 1750 1500 1250 1000 750 500 250 Figure 13d.
Figure 13d. Contour plot of alternating stress intensity, Salt, for CLTP operation with frequency shifts. The recorded recorded stress at a node is the maximum value taken over all frequency shifts. The maximum alternating alternating stress intensity is 2914 psi. First view.
view.
61
This Document This Document Does Continuum Dynamics, Inc.
Does Not Contain Continuum Inc. Proprietary Proprietary Information a
z Y
salt [psi]
Salt [psi]
3000 2750 2500 2250 2000 2cxx) 1750 1750 1500 1500 1250 1250 1000 1000 750 500 250 250 Figure Figure 13e.
13e. Contour plot plot of alternating alternating stress stress intensity, intensity, Salt, Salt' for CLTP CLTP operation operation with frequency frequency shifts.
shifts. The recorded stress at a recorded stress a node node is the maximum maximum value taken over over all frequency frequency shifts. Second view from below.
shifts. below.
62 62