ML091610111
| ML091610111 | |
| Person / Time | |
|---|---|
| Site: | Nine Mile Point  |
| Issue date: | 05/27/2009 |
| From: | Bilanin A Continuum Dynamics |
| To: | Constellation Energy Group, Office of Nuclear Reactor Regulation |
| References | |
| 7708631 08-24NP, Rev 1 | |
| Download: ML091610111 (52) | |
Text
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 5.3 Frequency Content and Filtering of the Stress Signals The frequency contribution to the stresses can be investigated by examining the power spectral density (PSD) curves and accumulative PSDs for selected nodes having low alternating stress ratios. The accumulative PSDs are computed directly from the Fourier coefficients as (n)=
k~
where a(cok) is the complex stress harmonic at frequency. cok. Accumulative. PSD plots are useful for determining the frequency components and frequency ranges that make the largest contributions to the fluctuating stress.
Unlike PSD plots, no "binning" or smoothing Of frequency components is needed to obtain smooth curves. Steep step-like rises in Z(co) indicate the presence of a strong component at a discrete frequency whereas gradual increases in the curve imply significant content over a broader frequency range.
From Parsival's theorem, equality between Z(coN) (where N is the total number of frequency components) and the RMS of the stress signal in the time domain is established.
The selected nodes are the ones having the lowest alternating stress ratios (at a weld) in Table 9b. These are:
Node 85723 - located on the inner hood/hood support/middle base plate junction.
The associated PSDs are shown in Figure 15a.
Node 89649 - located on the lifting rod brace/vane bank end plate connection.
The associated PSDs are shown in Figure 15b.
Node 101873 - located on the vertical weld where the outer closure plate connects to the vane bank. The associated PSDs are shown in Figure 15c.
Node 95172 - located on the weld joining the middle closure plate to the inner hood. The associated PSDs are shown in Figure 15d.
These are the nodes labeled 1, 2, 4 and 6 in Table 9b and accompanying Figure 14d-i.
In each case, since there are six stress components and up to three different section locations for shells (the top, mid and bottom surfaces), there is a total of 18 stress histories per component.
Moreover, at junctions there are at least two components that meet at the junction. The particular stress component that is plotted is chosen as follows. First, the component and section location (top/mid/bottom) is taken as the one that has the highest alternating stress. This narrows the selection to six components. Of these, the component having the highest Root Mean Square (RMS) is selected.
The first node (85723), is dominated by a broad peak centered at 71 Hz. The frequency shifted curves do not differ significantly from the non-shifted results. Judging from the PSD curves, it appears that in the non-shifted case there are two peaks about 71 Hz, with one - the low frequency one - being dominant.
When the signal is shifted, the forcing on the lower frequency mode is reduced and that on the higher frequency mode increases. Interestingly, the combined effect is to effectively shift the peak frequency upward even though the signal is 78
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information shifted downward (as is clear by comparing some of the other 'peaks). This is effect is readily explainable in the context of the complex multi-modal system being considered here. Frequency shifting has -a more pronounced effect on node 89649 which has a dominant frequencies at 13.2 Hz, 19.6 Hz and 136 Hz.
The lower frequency peaks which grows, but do. not shift significantly with the +10% frequency shift. The higher frequency peak appears to shift and attenuate with the frequency shift in the signal. The last two nodes both involve a closure plate and exhibit similar stress spectra. For node 101873 the dominant peak frequency is 122 Hz whereas for node 95172 the peak is centered about 116.5 Hz. In both cases the peaks do not shift significantly with frequency shift. This is indicative of a strongly responsive mode being forced to a different extent by the shifted, and non-shifted signals. The presence of such modes in the closure plates is clearly seen in Figure 12d. The peak frequencies for the last two nodes differ because each nodes lie on a different closure plates (101873 is on the outer closure plate and 95172 on the middle one)..
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 85723, a CO) 0-W' EE 350 300 250 200 150 100 noshift 50 0
0 50 100 150 200 Frequency [ Hz ]
Node 85723, a 250 105 104 N
il) no shift
-5ýk shift]
1000 100 10 1
0.1 0.01 200 250 0.001 0
50 100 150 Frequency [ Hz ]
Figure 15a. Accumulative PSD and PSD curves of the azz stress response at node 85723.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 89649, a 0
CO E
E 600 500 400 300 200 100 0
-- 4--noshift 0
50 100 150 200 Frequency [ Hz ]
250 Node 89649, a yy 10, 104 noshift N
101 0
to,W-(n 1000 100 10 1
0.1 0.01 0.001 200 0
50 100 150 250 Frequency [ Hz ]
Figure 15b. Accumulative PSD and PSD of the ayy stress response at node 89649.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 101873, a 400 350 Z
no shift
...10% shift N 300 d
n~
250 (1)
=
W 200 EEE 150 100 50 0
0 50 100 150 200 250 Frequency [Hz ]
Node 101873, a 10 5
1-no shift 104
-10% shiftI N
1000 CnL U.
100 1
Q-10 0.1 0.01 0.001 0
50 100 150 200 250 Frequency [Hz ]
Figure 15c. Accumulative PSD and PSD of the axx stress response at node 101873.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 96172, a.
400 I
350
,--*,-- no shift 300
..........10% shift CL 250 0I w 200 E
E 150 100 50 0
0 50 100 150 200 250 Frequency [Hz ]
Node 96172, i 10 5
Z no shift 104
+10% shift 1000 r* 100 ciO U) 10 CLi 10 0.1 0.01 0.001 0
50 100 150 200 250 Frequency [Hz ]
Figure 15d. Accumulative PSD and PSD of the axx stress response at node 95172.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
- 6. Conclusions A frequency-based steam dryer stress analysis has been used to calculate high stress locations and calculated / allowable stress ratios for the Nine Mile Point Unit 2 steam dryer at CLTP load conditions using plant measurement data.
A detailed description of the frequency-based methodology and the finite element model for the NMP Unit 2 steam dryer is presented. The CLTP loads obtained in a separate acoustic circuit model [4] including end-to-end bias and uncertainty for both the ACM [4] and FEA were applied to a finite element model of the steam dryer consisting mainly of the ANSYS Shell 63 elements, brick continuum elements and beam elements.
The measured CLTP loads are applied with compensation for background noise based on low power data taken at 25% power. The resulting stress histories were analyzed to obtain maximum and alternating stresses at all nodes for comparison against allowable levels. These results are tabulated in Table 9 of this report. The minimum alternating stress ratio at nominal operation is SR-a=2.92 and the minimum alternating stress ratio taken over all frequency shifts is SR-a=2.80.
The stress ratio associated with maximum stress intensities varies weakly with frequency shift and assumes a minimum value of SR-P=1.35 both with and without frequency shifting. EPU stresses are obtained by scaling the CLTP flow-induced stresses by the steam flow velocity squared, (UEPU/UcLTp) 2=1.388. Under this scaling the limiting alternating stress ratio at any frequency shift at EPU is SR-a=2.02. The limiting maximum stress ratio is dominated by static stresses and reduces to SR-P=1.28 at EPU.
Since flow-induced acoustic resonances are not anticipated in the steam dryer, the alternating stress ratios at EPU operation can be obtained by scaling the CLTP values by the steam flow velocity squared,.
Under this approach, the limiting alternating stress ratio becomes SR-a=2.80/1.388=2.02. For the nodes with the limiting maximum stress ratios at CLTP, the corresponding limiting value at EPU is SR-P=1.28. Given that the alternating stress ratio SR-a obtained at EPU remains above 2.02 at all frequency shifts together with the comparatively small dependence of SR-P upon acoustic loads, the Unit 2 dryer is expected to qualify at EPU conditions.
Frequency Shift Minimum Stress Ratio at CLTP Min. Alt. Stress Max. Stress, Alternating Stress, Ratio (SR-a)
SR-P SR-a at EPU 0% (nominal) 1.35 2.92 2.10
-10%
1.37 2.83 2.03
-7.5%
1.37 3.22 2.32
-5%
1.37 2.80 2.02
-2.5%
1.37 3.13 2.25
+2.5%
1.36 2.81 2.02
+5%
1.35 2.82 2.03
+7.5%
1.35 2.89 2.08
+10%
1.35 2.81 2.02 84
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information All shifts 1.35 - 1.37 2.81-3.22 2.02 -2.32 Limiting 1.35 2.81 2.02 85
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
- 7. References
- 1. EPRI (2008).
BWRVIP-194: BWR Vessel and Internals Project: Methodologies for Demonstrating Steam Dryer Integrity for Power Uprate. EPRI, Palo Alto, CA: 2008.
1016578.
- 2.
ASME Boiler and Pressure Vessel Code,Section III, Subsection NG (2007).
- 3. Continuum Dynamics, Inc. (2005). "Methodology to Determine Unsteady Pressure Loading on Components in Reactor Steam Domes (Rev. 6)." C.D.I. Report No. 04-09 (Proprietary).
- 4. Continuum Dynamics, Inc. (2008). " Acoustic and Low Frequency Hydrodynamic Loads at CLTP Power Level on Nine Mile Point Unit 2 Steam Dryer to 250 Hz, Rev. A" C.D.I. Report No.08-08P (Proprietary).'
- 5. Continuum Dynamics, Inc. (2007). "Methodology to Predict Full Scale Steam Dryer Loads from In-Plant Measurements, with the Inclusion of a Low Frequency Hydrodynamic Contribution," C.D.I. Report No.07-09P (Proprietary).
- 6. Structural Integrity Associates, Inc. 2008. Nine Mile Point Unit 2 Main Steam Line Strain Gage Data Reduction. SIA Calculation Package No. NMP-26Q-302.
- 7. ANSYS Release 10.0.
URL http://www.ansys.com.
Documentation:
ANSYS 10.0 Complete User's Manual Set.
- 8. Continuum Dynamics, Inc. (2007). Response to NRC Request for Additional Informati6n on the Hope Creek Generating Station, Extended Power Uprate, RAI No. 14.110
- 9. Continuum Dynamics, Inc. (2008). "Stress Assessment of Hope Creek Unit 1 Steam Dryer Based on Revision 4 Loads Model, Rev. 4" C.D.I. Report No.07-17P (Proprietary).
- 10. Press, W. H., S. A. Teukolsky, et al. (1992). Numerical Recipes, Cambridge University Press.
- 11. Structural Integrity Associates, Inc. 2008, "Flaw Evaluation and Vibration Assessment of the Nine Mile Point Unit 2 Steam Dryer for Extended Power Uprate Operating Conditions,"
Report No. 0801273.401.
- 12. O'Donnell W.J. (1973). "Effective Elastic Constants For the Bending of Thin Perforated Plates With Triangular and Square Penetration Patterns," ASME Journal of Engineering for Industry, Vol. 95, pp. 121-128.
- 13. Idel'chik, I E. and Fried, E. (1989). Flow Resistance, a Design Guide for Engineers, Taylor
& Francis, Washington D.C., p 260.
- 14. DeSanto, D.F. (1981). "Added Mass and Hydrodynamic Damping of Perforated Plates Vibrating in Water," Journal of Pressure Vessel Technology, Vol. 103, p. 176-182.
86
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
- 15. Continuum Dynamics, Inc. (2007). "Dynamics of BWR Steam Dryer Components," C.D.I.
Report No.07-11P
- 16. U.S. Nuclear Regulatory Commission, (2007). Regulatory Guide 1.20 "Comprehensive Vibration Assessment Program for Reactor Internals During Preoperational and Initial Startup Testing," March 2007.
- 17. WRC Bulletin 432 (1998). "Fatigue Strength Reduction and Stress Concentration Factors For Welds In Pressure Vessels and Piping," WRC, NY, p.32
- 18. Pilkey W.D. (1997).
Peterson's Stress Concentration Factors, 2 d ed., John Wiley, NY,
- p. 139.
- 19. Lawrence F.V., Ho N.-J., Mazumdar P.K. (1981). "Predicting the Fatigue Resistance of Welds," Ann. Rev. Mater. Sci., vol..1 1, pp. 401-425.
- 20. General Electric (GE) Nuclear Energy (2003). Supplement 1 to Service Information Letter (SIL) 644, "BWR/3 Steam Dryer Failure," September 5, 2003.
- 21. Tecplot 10(2004). URL: http://www.tecplot.com. Documentation: Tecplot User's Manual Version 10 Tecplot, Inc. Bellevue, Washington October.
- 22. Continuum Dynamics, Inc., Response to NRC RAI EMCB 172, June 2008.
- 23. Continuum Dynamics, Inc. (2008). "Stress Assessment of Browns Ferry Nuclear Unit 1 Steam Dryer with Tie bar Modifications "C.D.I. Report No.08-15P (Proprietary).
- 24. Continuum Dynamics, Inc., Response to NRC Request for Additional Information on the Browns Ferry Nuclear Plant Extended Power Uprate, RAI EMCB 201/162, part c, January 2009.
- 25. Structural Integrity Associates Calculation Package, 0006982.304, "Comparison Study of Substructure and Submodel Analysis using ANSYS,!' December 2008.
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This Document Does Not Contain Continuum Dynamics, Inc..,Proprietary Information
- Appendix A Sub-modeling of Closure Plates (3)))
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information The sub-modeled locations together with the calculated stress reduction factors are given in Table 10. For each location depictions of the shell and solid element-based sub-models are given together with the applied loads/moments and resulting stresses. This is followed by a summary of the linearization paths and the limiting linearized stresses.
The calculation of the stress reduction factor concludes the presentation for each location.
Table 10. List of sub-model locations Location x
y z
node Stress reduction factor Top Thick Plate/Side Plate/Closure 47.1
-108.6 88 101175 0.62 Plate/Top Plate Closure Plate/Middle Hood
-63.8 85.2 72.5 91605 0.71 Closure Plate/Inner Hood 28.8
-108.6 87 95172 0.86 Side Plate/Closure Plate/Exit Top
-47.1 108.6 74.5 100327 0.88 Perf/Exit Mid Top Perf Note: The side plate/closure plate connection involving nodes 101175 and 100327 is reinforced on the interior side with a 0.25" weld. The hood/closure plate weld involving nodes 91605 and 95172 is reinforced on the interior side with a 0.125" weld.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model Node 101175 The sub-model for this node located at the top of the vertical weld joining the closure plate to the vane bank is shown in Figure 16a and involves five different components. The extracted forces are shown in Figure 16b. The shell sub-model stress distribution is shown in Figure 16c with a maximum (i.e., the maximum taken over all components and surfaces - top, bottom and middle) stress intensity stress at the location of 3362 psi. The corresponding solid sub-model together with mesh details and the stress distribution resulting when the same loads used in the shell sub-model are applied, are shown in Figure 17. Finally, the stress intensity linearization paths and corresponding linearized stresses extracted from the solid model are shown in Figure 18 and tabulated in Table 11. The limiting linearized stress in the solid sub-model is 2088 psi.
Comparing this value against the one obtained in the shell sub-model (3362 psi) yields the stress reduction factor: 2088/3362 = 0.62.
Top plate, 0.25" Vane bank side plate, 0.375" Closure plate, 0. 125" Thick plate, 0.5" Perforated plate, 0.078" ]
0.000002.000
.,n) 1.000 Figure 16a. Shell sub-model node 101175.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 9 Time: 1. s 1211 012008 10:12 AM
- Force: 14.684 Ibf
- Force 2:2.5432 Ibf
- Force 3:60.408 Ibf
- Force 4: 29.682 Ibf
- Force 5: 6.6215 Ibf
- Force 6: 25.379 Ibf
- Force 7: 2.0671 Ibf
- Force 8: 41 024 Ibf
- Force 9: 5.7018 Ibf Moment 9 Time: 1. s 1211012008 10:13 AM
//
4 i f L
- Moment: 6.5096 Ibf in
- Moment 2: 8.1909 Ibf-in
- Moment 3: 5.6901 Ibf in Moment 4: 6.7147 Ibf in
- Moment 5: 3.8973 Ibfin
- Moment 6: 6.1644e-003 Ibfin
- Moment 7: 8.9112e-002 Ibf in
- Moment 8: 2.4226 Ibf in
- Moment 9:0.14082 IVfJ Figure 16b. Forces and moments.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Stress Intensity Type: Stress Intensity-Top/Bottom Unit: psi Time: 1 1211 012008 10:39 AM 20311 Max 3500 3150 2800 2450 2100 1750 1400 1050 700 350 11.75 Min 0
I f7 Livid§~. )XL 4,
0.000 2.000 (in) 1.000 Figure 16c. Shell sub-model stress contours. Stress intensity: 3362 psi.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Proposed additional weld
$7 0.000 2.000 (in) 1.000 0.000 2.000 (in) 1.000 Figure 17a. Solid model geometry.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 17b. Mesh overview. Mesh parameters: 748,327 nodes, 176,028 elements.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 17c. Stress intensity contours (total) in solid sub-model.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 18. Linearization paths for sub-model node 101175.
Table 11. Linearized stresses along the linearization paths shown in Figure 18.
Path Membrane + bending linearized stress intensity, psi AB 1605 AC 710 AD 689 AF 492 BE 2088 96
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model node 91605.
The sub-model for this node located on the weld connecting the closure plate to the hood is shown in Figure 19a and involves two different components - the hood and closure plate. The extracted forces are shown in Figure 19b. The shell sub-model stress distribution is shown in Figure 19c with a maximum (i.e., the maximum taken over all components and surfaces - top, bottom and middle) stress intensity stress at the location of 3176 psi. The stresses in the comers are neither singularities nor due to constraint forces (they arise regardless of where the model is supported). When the sub-model mesh is refined these stresses do not grow. Instead they essentially retain their coarse level values but extend over a smaller range (i.e., over one element). A mathematical explanation for this behavior indicates that the localized stress is due to the local imbalance (due to discretization error) in the applied shear loads. Thus to equilibrate the applied in-plane stresses on the edges a jump in element stress is required.
The same behavior generally occurs when non-equal shear stresses are applied near the comer.
The solid sub-model, mesh and stresses are shown in Figure 20 and, the stress intensity linearization paths and corresponding linearized stresses extracted from the solid model are shown in Figure 21 and tabulated in Table 12. The limiting linearized stress in the solid sub-model is 2254 psi, which, when compared against the one obtained in the shell sub-model (3176 psi) yields the stress reduction factor: 2254/3176 = 0.71.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information L~vLK2 2 I oo,.12
'1 Closure plate, 0.125" z
4,,I.x 0.000 3.000 (in) 1.500 Figure 19a. Shell sub-model node 91605.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 7 Time: 1. s 1211012008 2:52 PM
- Force: 8.2261 Ibf
- Force 2:22.492 a
- Force 3:18.258 IbV
- Force 4: 51.111 Ibf
- Force 5: 43.361 Ibf
- Force 6: 3.1687 Ibf
- Force 7: 46.837 Ibf Moment 7 Time: 1. s 1211 022008 2:52 PM
- Moment: 3.8738 Ib"
- Moment 2:6.34141
- Moment 3: 8.5514 Ibf'
- Moment 4: 3.6938 Ibf
- Moment 5:12.605 Ibf.
- Moment 6:11.556 Ibf
- Moment 7: 87125 Ibft 6d,A-2ý
< 'l L J
\\_
z;(~'. i 0.000 F'
3.000 (in) 1.500 0.000 3.000 (in) 1.500 Figure 19b. Forces and moments.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Stress Intensity Type: Stress Intensity -I Unit: psi Time: 1 1211f012008 2:56 PM 6854.3 Max 3500 3150 2800 2450 2100 1750 1400 1050 700 51.895 Min 0
LF z
Figure 19c. Shell sub-model stress contours. Stress intensity: 3176 psi.
100
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information I"
.*Proposed additional weld Figure 20a. Solid model geometry.
101
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 20b. Mesh overview.
102
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information NODAL SOLUTION AN STEP=1 SUB =1 TIME =1 SINT (AVG)
DMX =. 00998 SMN =14.524 SMX =5788 14.524 1298 25 0 3863 5146 656.013 1939 3222 4505 5788 NODAL SOLUTION STEP=1 SUB =1 TIME=1 SINT (AVG)
DMX =.00998 SMN =17.52 SMX =4327 Figure 20c. Stress intensity contours (total) in solid sub-model. Part of structure is removed in the lower figure to show internal stress distribution.
103
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 21. Linearization paths for sub-model node 91605.
Table 12. Linearized stresses along the linearization paths shown in Figure 21.
Path Membrane + bending linearized stress intensity, psi Al-BI 2254 Al-Cl 1891 Al-DI 1261 Al-F1 822 Cl-El 1899 A2-B2 2170 A2-C2 1154 A2-D2 1160 A2-F2 867 C2-E2 930 Bl-B2 2139 104
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model node 95172.
The sub-model for this node located at the top of the weld connecting the closure plate to the curved hood is shown in Figure 22a and again involves only two distinct components - the curved hood and closure plate. The extracted forces are shown in Figure 22b and the shell sub-model stress distribution is shown in Figure 22c with a maximum (i.e., the maximum taken over all components and surfaces - top, bottom and middle) stress intensity stress at the location of 3198 psi.
The solid sub-model, mesh and stresses are shown in Figure 23 and, the stress intensity linearization paths on the original and added weld are shown in Figure 24.
The corresponding linearized stresses extracted from the solid model are tabulated in Table 13. The limiting linearized stress in the solid sub-model is 2762 psi. The corresponding value in the shell sub-model is 3198 psi so that the stress reduction factor is 2762/3198 = 0.86.
r~
Hood, 0. 125 "
1 Closure plate, 0.125" Z
40 ý* I I I 0.000 3.000 (in) 1.500 Figure 22a. Shell sub-model node 95172.
105
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 6 Time: 1. s 12A1012008 10:33 PM
- Force: 4.3941 Ibf
- Force 2:13.957 Ibf
- Force 3:13.152 Ibf
- Force 4: 5.8579 Ibf
- Force 5:12.614 Ibf
- Force 6:19.54 Ibf Moment 6 Time: 1. s 1211012008 10:33 PM
- Moment: 3.3253 lbf-in
- Moment 2: 6.7324 Ibf in
- Moment 3: 38.492 Ibf in
- Moment 4: 4.9806 Ibftin
- Moment 5:12.813 Ibf in
- Moment 6: 2.5859 Ibf in S
0.000 Y
3.000 (in) 1.500 0,000 P
3,000 (in) 1.500 Figure 22b. Forces and moments.
106
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Stress Intensity' Type: Stress Intensity-Top1Bottom Unit: psi Time: 1 12f10,12008 10:42 PM 3200 3198 Max 2880 2560 2240 1920 1600 1280 960 640 320 39.598 Min
-0 Figure 22c. Shell sub-model stress contours. Stress intensity: 3198 psi.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information I
Proposed additional weld L
0.000 a W
3,000 (in) 1.500 Figure 23a. Solid model geometry.
108
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 23b. Solid mesh.
109
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 23c. Stress intensity contours (total) in solid sub-model.
110
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 24a. Linearization paths at the original weld for sub-model node 95172.
111
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 24b. Linearization paths at the additional weld for sub-model node 95172.
112
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 13. Linearized stresses along the linearization paths shown in Figure 24.
Path Membrane + bending linearized stress intensity, psi AB 1910 AC 2437 AD 1696 AE 2421 AF 639 A1-B1 2002 Al-Cl 2689 Al-DI 1837 Al-El 2696 Al-F1 1598 C-C1 2762 113
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Sub model node 100327.
The final sub-model involving the closure plate is for a node on the vertical weld connecting the closure plate to the vane bank. It is located 13.5 inches below the top of the weld. The shell element-based sub-model is shown in Figure 25a and involves four components. The extracted forces are shown in Figure 25b and the shell sub-model stress distribution is shown in Figure 25c with a maximum stress intensity stress at the location of 2744 psi. The solid sub-model, mesh and stresses are shown in Figure 26 and, the stress intensity linearization paths depicted in Figure
- 27. The extracted linearized stresses are tabulated in Table 14 and show a limiting linearized stress in the solid sub-model of 2406 psi. The stress reduction factor is 2406/2744 = 0.88.
Geometry 12i1112008 9:32 AM L1~
I Side plate, 0.375" Closure plate, 0.125" 1
Perforated plate, 0.078" "-
Perforated plate, 0.078" Z
ý:X 0.000 3.000 (in) 1.500 Figure 25a. Shell sub-model node 100327.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 10 Time: 1. s 1211112008 9:44 AM
- Force: 2.6676 Ibf
- Force 2: 9.5592 IbV
- Force 3: 4.0198 Ibf
- Force 4: 7.6292 Ibf
- Force 5:14.618 Ibf
- Force 6: 5.0388 Ibf
- Force 7:3.1685 Ibf
- Force 8: 8.9608 Ibf Force 9: 9.0228 Ibf
- Force 10: 2.967 Ibf Moment 10 Time: 1. s 1211 V2008 9:44 AM
- Moment: 2r7487 Ibf-in
- Moment 2: 4.1118 Ibfin
- Moment 3: 2.8888 IbVin
- Moment 4: 59596 Ibfin
- Moment 5: 22.463 Ibf in
- Moment 6:5.067 lbi
- Moment 7:1.23171
- Moment 8: 0.74244 lbfir
- Moment 9:0.41921 lbfij
- Moment 10:1 7222 Ibfj 0.000 3.000 (in) 1 500 Lx L+/-6 0.000 3.000 (in) 1.500 Figure 25b. Forces and moments.
115
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Stress Intensity Type: Stress Intensity-ToplBottom Unit: psi Time: 1 1211112008 9:51 AM 3000 2743.7 Max 2500 2250 2000 1750 1500 1250 1000 750 500 250 25.701 Min 0
/AJj~j~N~~
I Cl z
0.000 3.000 (in) 1.500 Figure 25c. Shell sub-model stress contours. Stress intensity: 2744 psi.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Proposed additional weld Figure 26a. Solid model geometry.
117
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 26b. Solid mesh. Mesh parameters: 567369 nodes, 133680 elements.
118
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information NODAL SOLUTION STEP=1 SUB =1 TIME=1 SINT (AVG)
DMX =. 004133 SMN =1.847 SMX =6458 0
1200 2400 600 1800 3000 Figure 26c. Stress intensity contours (total) in solid sub-model. Parts of the structure removed to show internal stress distribution (bottom).
119
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 27. Linearization paths at the additional weld for sub-model node 100327.
Table 14. Linearized stresses along the linearization paths shown in Figure 27.
Path Membrane + bending linearized stress intensity, psi AB 1589 AC 439 AD 724 BE 2406 AF 488 120
This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Appendix B. Sub-modeling of Lifting Rod Support Braces Using the same validated [24,25] sub-modeling approach outlined in Appendix B, the top lifting rod support braces were analyzed to determine the weld size required to meet EPU target stress levels. The weld of concern joins the support brace to the vane bank side plate and experiences a high stresses at its end. The stress is determined to be a combination of membrane and bending stresses with the former being artificially high in the global shell model at this location.
Recall that membrane stresses grow without bound as the mesh is refined as it converges to the mathematical stress singularity. Therefore to obtain realistic stress estimates the full 3D solid model must be considered.
The shell element-based sub-model is shown in Figure 28a and involves a total of six components.
The extracted forces are shown in Figure 28b and the shell sub-model stress distribution is shown in Figure 28c with a maximum stress intensity stress at the location of 3653 psi. Calculations on two different resolution meshes confirm that results do not change significantly. The solid sub-model, mesh and stresses are shown in Figure 29 and, the stress intensity linearization paths depicted in Figure 30. The extracted linearized stresses are tabulated in Table 15 and show a limiting linearized stress in the solid sub-model of 2683 psi. The stress reduction factor is 2683/3653 = 0.73.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information J
Geometry 1211 7/2008 7:30 PM
/'.ý ", "I" I Perforated plate, top, 0.078" I Closure plate, 0.125"
- --*Collar, 0.375" a"
I Perforated plate, middle, 0.078" Side plate, 0.375" In nAn
'*t*
Bace 0.75" 31 U.UUU 3.000 (in)
A 1.500 Figure 28a. Shell sub-model node 89649.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Force 13 Time: 1. s Items: 10 ofl 3 indicated 1 211 7/2008 7:52 PM
- Force: 745.32 Ibf Force 2: 484 23 Ibff Force 390 31 Ibf Force 4 131 62 Ibf Force 5 320,4 lbf I
Force 6!39.673 Ibf Force 7 518.31 Ibf
- Force 8: 17081 Ibf
- Force 9 16328 f
- Force 10: 21.196 Ibf Moment 13 Time: 1. s Items: 10 of 13 indicated 121l 712008 7:53 PM
- Moment: 11915 Ibf-in
- Moment 2: 24.139 IbVin
- Moment 3: 4,8309 Ibf in
- Moment 4:1.0338 Ibf6in
- Moment 5:11.918 IV in
- Moment 6: 4.8986 Ibf-in
- Moment 7: 5.7237 Ibf in
- Moment 8: 0.68337 Ibfin
- Moment 9: 2.3724 Ibfin
- Moment 10: 0.25244 IWin
\\* J~,l.
z wlt--Oý 11 0.(
Figure 28b. Forces and moments.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Stress Intensity 3 Type: Stress Intensity-Top/Bottom Unit: psi Time: 1 12117/2008 8:02 PM LJiVS ~
I I
3653.4 Max 3270 2886.6 2503.1 2119.7 1736.3 1352.9 969.43 586.01 202.58 Min 0.000 2.000 (in) 1.000 X
Figure 28c.
3653 psi.
Shell sub-model stress contours on the brace plate. Maximum stress intensity:
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This Document Does Not Contain Continuum
- Dynaic, Inc. Proprietary Information 0.000~
3 0 (in))
Figure 2 9a. Solid sub-Iodel.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 29b. Solid mesh overview. Mesh parameters: 477255 nodes, 153921 elements.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 29c. Stress distribution in the solid sub-model.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 29d. Stress distribution in solid sub-model (alternate view).
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 30. Linearization paths across the weld at the high stress location on the lifting rod support brace.
Table 15. Linearized stresses along the linearization paths shown in Figure 30.
Path Membrane + bending linearized stress intensity, psi Al-BI 1303 A1-D1 1773 Al-CI1 2683 A1-C12 2612 A2-B2 994 A2-D2 1352 A2-C21 916 A2-C22 583 129