View source for LR-N08-0033, CDI Report No. 07-17NP, Revision 4, Stress Assessment of Hope Creek Unit I Steam Dryer Based on Revision 4 Loads Model.

{{Adams
| number = ML080420469
| issue date = 01/31/2008
| title = CDI Report No. 07-17NP, Revision 4, Stress Assessment of Hope Creek Unit I Steam Dryer Based on Revision 4 Loads Model.
| author name = Bilanin A, Teske M
| author affiliation = Continuum Dynamics, Inc, PSEG Nuclear, LLC
| addressee name = 
| addressee affiliation = NRC/NRR
| docket = 05000354
| license number = NPF-057
| contact person = 
| case reference number = LR-N08-0033
| document report number = 07-17NP, Rev 4
| document type = Report, Technical
| page count = 129
}}

=Text=
{{#Wiki_filter:LR-N08-0033 ATTACHMENT 4 Hope Creek Generating Station Facility Operating License NPF-57 Docket No. 50-354 Extended Power Uprate Stress Assessment of Hope Creek Unit I Steam Dryer Based on Revision 4 Loads Model CDI Report No. 07-17NP, Revision 4

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information CDI Report No. 07-17NP Stress Assessment of Hope Creek Unit 1 Steam Dryer Based on Revision 4 Loads Model Revision 4 Prepared by Continuum Dynamics, Inc.
34 Lexington Avenue Ewing, NJ 08618 Prepared under Purchase Order No. 4500413356 for Nuclear Business Unit, PSEG Nuclear LLC Materials Center, Alloway Creek Neck Road Hancocks Bridge, NJ 08038 Approved by 6/4-11 5           J Alan J. Bilanin 40V 1\ 6-e- .
Reviewed by Milton E. Teske January 2008 This report complies with Continuum Dynamics, Inc. Nuclear Quality Assurance Program currently in effect.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Executive Summary A harmonic finite element stress analysis method is used to assess stresses on the Hope Creek Unit I (HC1) steam dryer resulting from acoustic and hydrodynamic loads. The harmonic stress analysis confers a number of useful computational advantages over a time-domain method including the ability to assess the effects of frequency scalings in the loads without the need for additional finite element calculations. ((
The analysis begins by developing a series of unit stress solutions corresponding to the application of a unit pressure at a MSL at specified frequency, f. Each unit solution is obtained by first calculating the associated acoustic pressure field using a separate analysis that solves the damped Helmholtz equation within the steam dryer [1]. This pressure field is then applied to a finite element structural model of the steam dryer and the stress response at frequency, f, calculated using the commercial ANSYS 10.0 finite element analysis software. This stress response constitutes the unit solution and is stored as a file for subsequent processing. Once all unit solutions have been computed, the stress response for any combination of MSL pressure spectrums (obtained by Fast Fourier Transform of the pressure histories in the MSLs) is determined by a simple matrix multiplication of these spectrums with the unit solutions.
This report provides details of the ANSYS 10.0 finite element structural model of the HC1 steam dryer and reviews pertinent modeling considerations. It also summarizes the framework underlying the development and application of unit solutions in the frequency domain and shows how these solutions are used to develop stress histories for general load conditions. Next, it reviews the assessment of these stresses for compliance with the ASME B&PV Code, Section III, subsection NG, for the load combination corresponding to normal operation (the Level A Service Condition). ((
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Results obtained from application of the methodology to the HC1 steam dryer using the Rev. 4 acoustic/hydrodynamic loads [2] show that at the nominal CLTP case (no frequency shift) the smallest alternating stress intensity stress ratio (SR-a) is 4.38. The most limiting maximum stress ratio (SR-P) anywhere on the steam dryer is 1.63 at the weld joining the skirt to the upper support ring. These results account for all the end-to-end biases and uncertainties in the loads model [2] and finite element analysis [15]. They also reflect the elimination of plant and sensor noise, based on 1000# data [16]. To account for frequency uncertainties in the finite element model, the stresses are also computed for loads that are shifted in the frequency domain between
+/-10%. The lowest alternating stress ratio is SR-a=3.22 and occurs on the junction between the inner hood and hood support. The most limiting maximum stress ratio, SR-P = 1.63.
In Revision 4 of this document, for those nodes having the lowest stress ratios at CLTP, the stresses are recomputed at EPU conditions using updated biases andq uncertainties summarized in Table 12. The noise removal strategy using the 1000# data is limited to the frequency range 80+/-5 Hz. The EPU dryer loads are scaled from CLTP loads using subscale test data which ii

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information results in higher loads than simply using the square of the steam flow speed. With the changes made in this revision the lowest stress ratio is due to a maximum stress, SR-P=1.58. The lowest alternating stress ratio at any frequency shift is SR-a=2.18. Given that the biases and uncertainties in the loads (Table 11) and finite element model (Table 12) are already accounted for, these stress ratios are expected to qualify the dryer with margin at EPU conditions.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Summary of Changes from Revision 3 to Revision 4 Revision 3 of C.D.I. Report 07-17P reflects changes due to information developed after release of Revision 3, as explained below.
: 1. Section 5.6 was added to detail the methodology used to estimate stress ratios at EPU conditions.
: 2. Use of the 1000# data to reduce noise in the MSL data was restricted to the frequency interval 75-85 Hz in estimating stress ratios at EPU conditions.
: 3. Revised bias and uncertainties incorporating recent work were incorporated into the EPU stress ratios.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table of Contents Section                                                                                                       Page Executive Summary........................................................................................11i Summary of Changes from Revision 3 to Revision 4..................................................                  iv Table of Contents...........................................................................................          V
: 1. Introduction and Purpose................................................................................I
.2. Methodology ............................................................................................          3 2.1 Overview.............................................................................................         3 2.2 ((Application to Real-Time Power Ascension ....................................................               S 2.3 Computational Considerations ....................................................................             6
: 3. Finite Element Model Description .....................................................................             9 3.1 Steam Dryer Geometry .............................................................................            9 3.2 Material Properties.................................................................................        11 3.3 Model Simplifications .............................................................................          11 3.4 Perforated Plate Model............................................................................          12 3.5 Vane Bank Model..................................................................................            13 3.6 Water Inertia Effect on Submerged Panels......................................................              14 3.7 Structural Damping ................................................................................          15 3.8 Mesh Details and Element Types ................................................................              15 3.9 Connections Between Structural Components ..................................................                 16
: 3. 10 Pressure Loading .................................................................................        23
: 4. Structural Analysis .....................................................................................         25 4.1 Static Analysis .....................................................................................       25 4.2 Harmonic Analysis.................................................................................          25 4.4 Computation of Stress Ratios for Structural Assessment......................................                29
: 5. Results ................................................................................................... 33 5.1 General Stress Distribution and High Stress Locations........................................               34 5.2 Load Combinations and Allowable Stress Intensities .........................................                54 5.3 Frequency Content and Sensitivity to Frequency Shift of the Stress Signals................ 71 5.4 Compensation for Additional FEM Bias and Uncertainty ....................................                    80 5.5 Compensation for Signal Noise Using 1000# Data............................................                   83 5.6 Extended Power Uprate Stress Ratios .........................................................              100
: 6. Conclusions............................................................................................        107
: 7. References .............................................................................................       109 Appendix A. Comparison of ANSYS Frequency Predictions Against Analytical Formulas for Flat Plates..................................................................................................11I Appendix B. Comparison of Transient and Harmonic Simulations for the Browns Ferry Unit 1 Dryer.......................................................................................................      114 Appendix C. Structural Modeling of Perforated Plates .............................................                123 v

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: 1. Introduction and Purpose Plans to qualify the Hope Creek nuclear plant for operation at Extended Power Uprate (EPU) operating condition require an assessment of the steam dryer stresses experienced Under the increased loads. The steam dryer loads due to pressure fluctuations in the main steam lines (MSLs) are potentially damaging and the cyclic stresses from these loads can produce fatigue cracking if loads are sufficiently high. The industry has addressed this problem with physical modifications to the dryers, as well as a program to define steam dryer loads and their resulting stresses.
The purpose of the stress analysis discussed here is to calculate the maximum and alternating stresses generated during Current Licensed Thermal Power (CLTP) and determine the margins that exist when compared to stresses that comply with the ASME Code (ASME B&PV Code, Section III, subsection NG). This step establishes whether the modifications done prior to commercial operations are adequate for sustaining structural integrity and preventing future weld cracking under planned EPU operating conditions. The load combination considered here corresponds to normal operation (the Level A Service Condition) and includes fluctuating pressure loads developed from Hope Creek Unit 1 (HC1) main steam line data, and steam dryer weight. The fluctuating pressure loads, induced by the flowing steam, are predicted using a separate acoustic circuit analysis of the steam dome and main steam lines [3]. Level B service conditions, which include seismic loads, are not included in this evaluation since no physical modifications were made to the HC 1 steam dryer for EPU operation.
((
(3)))   This approach also affords a number of additional computational advantages over transient simulations including: ((
(3)))  This last advantage is realized through the use of "unit" solutions representing the stress distribution resulting from the application of a unit fluctuating pressure at one of the MSLs at a particular frequency. ((
(3)))
This report describes the overall methodology used to obtain the unit solutions in the frequency domain and how to assemble them into a stress response for a given combination of 1

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information pressure signals in the MSLs. This is followed by details of the HC1 steam dryer finite element model including the elements used and overall resolution, treatment of connections between elements, the hydrodynamic model, the implementation of structural damping and key idealizations/assumptions inherent to the model. Post-processing procedures are also reviewed including the computation of maximum and alternating stress intensities, identification of high stress locations, adjustments to stress intensities at welds, and evaluation of stress ratios used to establish compliance with the ASME Code.
The results for Rev. 4 acoustic/hydrodynamic loads [2] in terms of stress intensity distributions and stress ratios are presented next, together with accumulative PSDs of the dominant stress components. The latter show that the load and structural response are dominated by a strong 80 Hz component and a significant 41 Hz signal.
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: 2. Methodology 2.1 Overview Based on previous analysis undertaken at Quad Cities Units 1 and 2, the steam dryer can experience strong acoustic loads due to the fluctuating pressures in the MSLs connected to the steam dome containing the dryer. C.D.I. has developed an acoustic circuit model (ACM) that, given a collection of strain gauge measurements [4] of the fluctuating pressures in the MSLs, predicts the acoustic pressure field anywhere inside the steam dome and on the steam dryer [ 1-3].
The ACM is formulated in frequency space and contains two major components that are directly relevant to the ensuing stress analysis of concern here. [
(2)
(3)))
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[II (3)
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(5)
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information (6)
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2.3 Computational Considerations Focusing on the structural computational aspects of the overall approach, there are a number of numerical and computational considerations requiring attention. The first concerns the transfer of the acoustic forces onto the structure, particularly the spatial and frequency resolutions. The ANSYS finite element program inputs general distributed pressure differences using a table format. This consists of regular 3D rectangular (i.e., block) nxxnyxnz mesh where na is the number of mesh points in the a-th Cartesian direction and the pressure difference is provided at each mesh point (see Section 3.10). These tables are generated separately using a program that reads the loads provided from the ACM software, distributes these loads onto the finite element mesh using a combination of interpolation procedures on the surface and simple diffusion schemes off the surface (off-surface loads are required by ANSYS to ensure proper interpolation of forces), and written to ASCII files for input to ANSYS. A separate load file is written at each frequency for the real and imaginary component of the complex force.
The acoustic field is stored at 5 Hz intervals from 0 to 200 Hz. While a 5 Hz resolution is sufficient to capture frequency dependence of the acoustic field (i.e., the pressure at a point varies gradually with frequency), it is too coarse for representing the structural response especially at low frequencies. For 1% critical structural damping, one can show (as indicated in the design record file, DRF-CDI-174) that the frequency spacing needed to resolve a damped resonant peak at natural frequency, fn, to within 5% accuracy is Af=0.0064xfn Thus for fn= 1 0 Hz where the lowest structural response modes occur, a frequency interval of 0.064 Hz or less is required. In our calculations we require that 5% maximum error be maintained over the range from fn- 5 Hz to 200 Hz resulting in a finest frequency interval of 0.0321 Hz at the low frequency end (this adequately resolves all structural modes up to 200 Hz). Since there are no structural modes between 0 to 5 Hz, a 0.5 Hz spacing is used over this range with minimal (less than 5%) error. The unit load, in (o, R), at any frequency, cok, is obtained by linear interpolation of the acoustic solutions at the two nearest frequencies, 0 i and o~i+1, spaced 5 Hz apart. Linear interpolation is sufficient since the pressure load varies slowly over each 5 Hz interval (linear interpolation of the structural response over these 5 Hz intervals would not be acceptable since it varies much more rapidly over these intervals).
Solution Management
[(3) 6

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Upon completion of each frequency calculation, ANSYS is instructed to export the stresses which are stored in text files. There is one file per MSL per frequency per real/imaginary component, and each file contains the complete stress state over all nodes on the dryer. This format is convenient from a solution point of view. However, it makes it difficult to extract the stress response at a node since, in order to do so, thousands of files must be opened and searched through thousands of nodes until the node of interest is reached. ((
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Structural Damping In harmonic analysis one has a broader selection of damping models than in transient simulations. A damping factor, z, of 1% critical damping is used in the structural analysis. In transient simulations, this damping can only be enforced 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% or less depending on the pinning frequencies. Outside the pinning frequencies, damping is higher. With harmonic analysis it is straightforward to enforce very close to 1% damping over the entire frequency range. In this damping model, the damping matrix, D, is set to D =2zK                                                  (7)
(0 where K is the stiffness matrix and co the forcing frequency. One can show that with this model the damping factor varies between 0.995% and 1.005% which is a much smaller variation than using the pinned model required in transient simulation.
Load Frequency Rescaling One way to evaluate the sensitivity of the stress results to approximations in the structural modeling and applied loads is to rescale the frequency content of the applied loads. In this procedure the nominal frequencies, cOk, are shifted to (l+X)cok, where the frequency shift, X, ranges between +10%, and the response recomputed for the shifted loads. The objective of the frequency shifting can be explained by way of example. Suppose that in the actual dryer a strong structural-acoustic coupling exists at a particular frequency, co*. This means that the following conditions hold simultaneously: (i) the acoustic signal contains a significant signal at co*; (ii) the structural model contains a resonant mode of natural frequency, cOn, that is near co*; and (iii) the associated structural mode shape is strongly coupled to the acoustic load (i.e., integrating the product of the mode shape and the surface pressure over the steam dryer surface produces a significant modal force). Suppose now that because of discretization errors and modeling idealizations that the predicted resonance frequency differs from (o* by a small amount (e.g.,
1.5%). Then condition (ii) will be viola'ted and the response amplitude therefore significantly diminished. By shifting the load frequencies one re-establishes condition (ii) when (1+ X)co* is near cOn. The other two requirements also hold and a strong structural acoustic interaction is restored.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Evaluation of Maximum andAlternating Stress Intensities Once the unit solutions have been obtained, the most intensive computational steps in the generation of stress intensities are: (i) the FETs to evaluate stress time histories from (5); and (ii) the calculation of alternating stress intensities. [
(3)]
The high computational penalty incurred in calculating the alternating stress intensities is due to the fact that this calculation involves comparing the stress tensors at every pair of points in the stress history. This comparison is necessary since in general the principal stress directions can vary during the response, thus for N samples in the stress history, there will be (N-1)N/2 such pairs or, for N=64K (the number required to accurately resolve the spectrum up to 200 Hz in 0.0 1 Hz intervals), 2.l1x 10 calculations per node each requiring the determination of the roots to a cubic polynomial. [
(3)))
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: 3. Finite Element Model Description A description of the ANSYS model of the Hope Creek Unit I steam dryer follows. This model is virtually identical to one developed for previous investigations using time domain-based analysis methods [7].
3.1 Steam Dryer Geometry A geometric representation of the Hope Creek steam dryer was developed from available drawings (provided by PSE&G and included in the design record files, DRF-PSEG-258 and DRF-175C) within the Workbench module of ANSYS. Field measurements taken by C.D.I. on an identical spare dryer for the cancelled Hope Creek Unit 2 were also used to develop this model (also contained in DRF-175C). The completed model is shown in Figure 1. This model includes modifications made to the HC1 steam dryer on-site, prior to commercial operation.
These are:
* Tie bars, outer hoods, and center end plates were replaced on the original dryer (FDI-041-79450).
* Reinforcement bars were added to the middle and inner hoods (HCI-KTI-415-7)
* Back-welding of the middle and inner hoods weld joint to their end plates (HCI-KTI-415-3 and -5)
The modified areas are shown in Figure 2.
0.00            100.00 (in) 50.00 Figure 1. Overall geometry of the HC1 steam dryer model.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Modified tie bars and end panels Additional hood reinforcements
                                                         '00,\
Figure 2. On-site modifications accounted for in the model and associated geometrical details.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 3.2 Material Properties The steam dryer is constructed from Type 304 stainless steel and has an operating temperature of 550'F. Properties used in the analysis are summarized below in Table 1.
Table 1. Material properties.
Young's Modulus    Density Poisson's Ratio (106 psi)   (Ibm/in 3) structural steel                       25.55       0.284          0.3 structural steel for perforated plates            15.33       0.227          0.3 structural steel with added water inertia            25.55       1.183          0.3 The structural steel modulus is taken from Appendix A of the ASME Code for Type 304 Stainless Steel at an operating temperature 550'F. The effective properties of perforated plates vand submerged parts are 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 the stress distribution due to the static dead weight load, the unmodified density of steel (0.284 lbm/in 3 ) is used throughout.
3.3 Model Simplifications The following simplifications were made to achieve reasonable model size while maintaining good modeling fidelity for key structural properties:
* Perforated plates were approximated as continuous plates using modified elastic properties designed to match the static and modal behaviors of the perforated plates. The perforated plate structural modeling is summarized in Section 3.4 and Appendix C.
* The drying vanes were replaced--by point masses attached to the corresponding trough bottom plates and vane bank top covers. 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 were obtained using a separate hydrodynamic analysis (see Section 3.6).
     % Fixed constraints were imposed at the underside of the steam dryer upper support ring where it makes contact with the four steam dryer support brackets that are located on the reactor vessel and spaced at 900 intervals (Figure 3). No credit was taken for the constraints from the reactor vessel lift lugs.
* Most welds were replaced by node-to-node connections; interconnected parts share common nodes along the welds. In .other locations the constraint equations between nodal degrees of freedom were introduced as described in Section 3.9.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Support brackets constraints 0.00                  100.00 (in)           X,11 50.00 Figure 3. Fixed support constraints.
3.4 Perforated Plate Model The perforated plates were modeled as solid plates with adjusted elastic and dynamic properties. Properties of the perforated plates were assigned according to the type and size of perforation. Based on [8], for an equilateral triangular pattern with given hole size and spacing, the effective moduli of elasticity were found. The hole pattern and thickness of the perforated plates was based on conservative estimates and field measurements of accessible plates.
Subsequent more recent detailed measurements have confirmed that the actual plates are at least 50% thicker. Therefore, since maximum and alternating stresses scale as 1/(thickness) 2 , the current analysis is conservative.
Tests were carried out to verify that this representation of perforated plates by continuous ones with modified elastic properties preserves the modal properties of the structure. These tests
-are summarized in Appendix C and 'c'mpare the predicted first modal frequency for a cantilevered perforated plate against an experimentally measured, value. The prediction was obtained using the analytical formula for a cantilevered plate and the modified Young's modulus and Poisson's ratio given by O'Donnell [8]. The measured and predicted frequencies are in close agreement, differing by less than 2%.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 3.5 Vane Bank Model The vane bank assemblies consist of many vertical angled plates that are computationally expensive to model explicitly, since a prohibitive number of elements would be required. These parts have significant weight which is transmitted through the surrounding structure, so it is important to capture their gross inertial properties. Here the vane banks are modeled as a collection of point masses located at the center of mass for each vane bank section (see Figure 4).
The following masses were used for the vane bank sections, based on data found on provided drawings:
inner banks:          6,545 lbm middle banks:         5,970 Ibm; and outer ban ks:         4,685 lbm.
These masses were applied to the base plates and vane top covers using the standard ANSYS point mass modeling option, element MlASS21. ANSYS automatically distributes the point mass inertial loads to the nodes of the selected structure. The distribution algorithm minimizes the sum of the squares of the nodal inertial forces, while ensuring that the net forces and moments are conserved. Vane banks are not exposed to main steam lines directly, but rather shielded by the hoods.
The collective stiffness of the vane banks is expected to be small compared to the surrounding support structure and is neglected in the model. In the static case it is reasonable to expect that this constitutes a conservative approach, since neglecting the stiffness of the vane banks implies that the entire weight is transmitted through the adjacent vane bank walls and supports. In the dynamic case the vane banks exhibit only a weak response since (i) they have large inertia so that the characteristic acoustical ly- induced forces divided by the vane masses and inertias yield small amplitude motions, velocities and accelerations; and (ii) they are shielded from acoustic loads by the hoods, which transfer dynamic loads to the rest of the structure. Thus, compared to the hoods, less motion is anticipated on the vane banks so that approximating their inertial properties with equivalent point masses is justified. Nevertheless, the bounding parts, such as perforated plates, side panels, and top covers, are retained in the model since they can individually exhibit a strong modal response. Errors associated with the point mass representation of the vane banks are compensated for by frequency shifting of the applied loads.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Point masses located at vane bank's center of mass Top and bottom nodes are connected to masses Nodes on top covers and bottom trough plates are connected to point masses Figure 4. Point masses representing the vanes. The pink shading represents where constraint equations between nodes are applied in the point mass implementation.
3.6 Water Inertia Effect on Submerged Panels Water inertia was modeled by an increase in density of the submerged structure to account for the added hydrodynamic mass. This added mass was found by a separate hydrodynamic analysis (included in DRF-175C supporting this report) to be 0.225 lbm/in 2 on the submerged 14

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information skirt area. This is modeled by effectively increasing the material density for the submerged portions of the skirt. Since the skirt is 0.25 inches thick, the added mass is equivalent to a density increase of 1.183 Ibm/in 3 . This added water mass was included in the ANSYS model by appropriately modifying the density of the submerged structural elements when computing harmonic response. For the static stresses, the unmodified density of steel is used throughout.
3.7 Structural Damping Structural damping was defined as 1% of critical damping for all frequencies. This damping is consistent with guidance given on pg. 10 of NRC RG-1.20 [9]. Note that no credit is taken for other significant non-structural dissipation mechanisms such as the hydrodynamic losses in perforated plates. Hence additional conservatism is reflected in the results.
3.8 Mesh Details and Element Types Shell elements were employed to model the skirt, hoods, perforated plates, side and end plates, trough bottom plates, reinforcements, base plates and cover plates. Specifically, the four-node, Shell Element SHELL63, was selected to model these structural components. This element models bending and membrane stresses, but omits transverse shear. The use of shell elements is appropriate for most of the structure where the characteristic thickness 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 the full 3D stress. The elements SURF 154 are used to assure proper application of pressure loading to the structure. Mesh details and element types are shown in Table 2 and Table 3.
Table 2. FE Model Summary.
Description     Quantity Total Nodes       93,951 Total Elements    126,322 Element Types        5 Materials            3 Table 3. Listing of Element Types.
Generic Element Type Name           Element Name                  ANSYS Name 20-Node Quadratic Hexahedron          SOLID 186          20-Node Hexahedral Structural Solid 4-Node Elastic Shell                  SHELL63            4-Node Elastic Shell 4-Node Linear Quadrilateral Shell     SHELL181           4-Node Finite Strain Shell Mass Element                          MASS21             Structural Mass Pressure Surface Definition           SURF154            3D Structural Surface Effect The mesh is generated automatically by ANSYS with adaptive refinement near edges. The maximum allowable mesh spacing is specified by the user. Here a 3 inch maximum allowable spacing is specified everywhere except in the following areas: drain pipes (2 inch maximum spacing); base plates (2.75 inches); perforated plates (2 inches); top tie rods (0.75 inches); and 15

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information the curved portions of the drain channels (1.5 inches). Details of the finite element mesh are shown in Figure 5. Numerical experiments carried out using the ANSYS code applied to simple analytically tractable plate structures with dimensions and mesh spacings similar to the ones used for the steam dryer, confirm that the natural frequencies are accurately recovered (less than 1%
errors for the first modes). These errors are compensated for by the use of frequency shifting.
3.9 Connections Between Structural Components Most connections between parts are modeled as node-to-node connections. This is the correct manner (i.e., within the finite element framework) of joining elements away from discontinuities. At joints between shells, this approach omits the additional stiffness provided by the extra weld material. Also, locally 3D effects are more pronounced. The latter effect is accounted for using weld factors. The deviation in stiffness due to weld material is negligible, since weld dimensions are on the order of the shell thickness. The consequences upon modal frequencies and amplitude are, to first order, proportional to t/L where t is the thickness and L a characteristic shell length. The errors committed by ignoring additional weld stiffness are thus small and readily compensated for by performing frequency shifts.
When joining shell and solid elements, however, the problem arises of properly constraining the rotations, since shell element nodes contain both displacement and rotational degrees of freedom at every node whereas solid elements model only the translations. A node-to-node connection would effectively appear to the shell element as a simply supported, rather than (the correct) cantilevered restraint and significantly alter the dynamic response of the shell structure.
To address this problem, constraint equations are used to properly connect adjacent shell- and solid-element modeled structures. Basically, all such constraints express the deflection (and rotation for shell elements) of a node, R 1 , on one structural component in terms of the deflections/rotations of the corresponding point, P2 , on the other connected component.
Specifically, the element containing P2 is identified and the deformations at P2 determined by interpolation between the element nodes. The following types of shell-solid element connections are used in the steam dryer model including the following:
: 1. Shell edge to shell edge connections with dissimilar meshes.
: 2. Connections of shell faces to solid faces (Figure 6a). While only displacement degrees of freedom are explicitly constrained, this approach also implicitly constrains the rotational degrees of freedom when multiple shell nodes on a sufficiently dense grid are connected to the same solid face.
: 3. 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 consists of having the shell penetrate into the solid by one shell thickness and then constraining both the embedded shell element nodes (inside the solid) and the ones located on the surface of the solid structure (see Figure 6b). Numerical tests involving simple structures show that this approach and penetration depth reproduce both the deflections and stresses of the same structure modeled using only solid elements or ANSYS' bonded contact technology. Continuity of rotations and displacements is achieved.
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: 4. Connections of solid elements to shells, e.g., connections of the tie bars to-the vane covers.
The use of constraint conditions rather than the bonded contacts advocated by ANSYS for connecting independently meshed structural components confers better accuracy and useful numerical advantages to the structural analysis of the steam dryer including better conditioned and smaller matrices. The smaller size results from the fact that equations and degrees of freedom are eliminated rather than augmented (in Lagrange multiplier-based methods) by additional degrees of freedom. Also, the implementation of contact elements relies on the use of very high stiffness elements (in penalty function-based implementations) or results in indefinite matrices (Lagrange multiplier implementations) with poorer convergence behavior compared to positive definite matrices.
ELEMENTS TYPE NUM                               0 Figure 5a. Mesh overview. The colors emphasize element type.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 5b. Close up of mesh showing hoods, reinforcement panels and tie bars. The colors emphasize element type.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information ELEMENTS TYPE NUM Figure 5c. Close up of mesh showing drain pipes and hood supports. The colors emphasize element type.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 5d. Close up of mesh showing node-to-node connections between closure panels, end plates, and hoods. The colors emphasize element types.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 5e. Close up of mesh showing node-to-node connections between the skirt and drain channels. The colors emphasize element type.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Shell nodes DOF are related to solid element shape functions Surface of solid element Figure 6a. Face-to-face shell to solid connection.
Shell nodes DOF are related to solid element shape functions Surface of solid element Figure 6b. Shell edge-to-solid face connection.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 3.10 Pressure Loading The harmonic loads are produced by the pressures acting on the exposed surfaces of the steam dryer. At every frequency and for each MSL, the pressure distribution corresponding to a unit pressure at the MSL inlet is represented on a three-inch grid lattice grid (i.e., a mesh whose
,lines are aligned with the x-, y- and z-directions) that is superimposed over the steam dryer surface. This grid is compatible with the "Table"t format used by ANSYS to "paint" general pressure distributions upon structural surfaces. The pressures are obtained from the Helmholtz solver routine in the acoustic analysis Li].
In general, the lattice nodes do not lie on the surface, so that to obtain the pressure differences at the surface, it is necessary to interpolate the pressure differences stored at the lattice nodes. This is done using simple linear interpolation between the eight forming nodes of the lattice cell containing the surface point of interest. Inspection of the resulting pressures at selected nodes shows that these pressures vary in a well-behaved manner between the nodes with prescribed pressures. Graphical depictions of the resulting pressures and comparisons between the peak pressures in the original nodal histories and those in the final surface load distributions produced in ANSYS, all confirm that the load data are interpolated accurately and transferred correctly to ANSYS.
The harmonic pressure loads are only applied to surfaces above the water level, as indicated
.in Figure 7. 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 are linearly combined to obtain total values which are then processed to calculate maximum and alternating stress intensities for assessment in Section 5.
(3)))* This is useful since revisions in the loads model do not necessitate recalculation of the unit stresses.
The results produced here utilize the Rev. 4 acoustic/hydrodynamic loads model described in
[2] to calculate the MSL pressure signals Pn(co) and associated biases and uncertainties.
23

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information NODES AN PRES-NORM S
1-          z   -  -    I   -  ---       y   P                           _11,'
                   -. 111088              .039978             .191044           .34211            .493176
                               -. 035555             .115511            .266577          .417643             568709 Frequency no. 372: 50.2 Hz NODES AN OPRES-NORM z
                     -. 538048           -. 288656            -. 039264         .210129          .459521
                               -. 413352             -. 16396           .085432         .334825            .584217 Frequency no. 544: 150.7 Hz Figure 7. Real part of unit pressure loading MSL C (in psid) on the steam dryer at different frequencies. No loading is applied to submerged parts (nodes at the bottom).
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
: 4. Structural Analysis The solution is decomposed into static and harmonic parts, where the static solution produces the stress field induced by the supported structure subjected to its own weight and the harmonic solution accounts for the harmonic stress field due to the unit pressure of given frequency in one of the main steam lines. All solutions are linearly combined, with amplitudes provided by signal measurements in each steam line, to obtain the final displacement and stress time histories. This decomposition facilitates the prescription of the added mass model accounting for hydrodynamic interaction and allows one to compare the stress contributions arising from static and harmonic loads separately. Proper evaluation of the maximum membrane and membrane+bending stresses requires that the static loads due to weight be accounted for. Hence both static and harmonic analyses are carried out.
4.1 Static Analysis The results of the static analysis are shown in Figure 8. Only a few locations exhibited high
*stress intensity levels. These locations include the skirt/upper support ring connection with stress intensity 8,775 psi, the trough thin section/vane bank end plate/thick closure plate junction with stress intensity 5,416 psi and the thin closure plate/inner hood junction with stress intensity 8,133 psi. All locations are near the steam dryer support brackets. Close up views of these locations are shown in Figure 9. Note that these locations have high stress intensity also when static and transient runs are combined, primarily due to static loading.
4.2 Harmonic Analysis The harmonic pressure loads were applied to the structural model at all surface nodes described in Section 3.10. Typical stress intensity distributions over the structure are shown in Figure 10. Stresses were calculated for each frequency, and results from static and harmonic calculations were combined.
To evaluate maximum stresses, the stress 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 to ASME B&PV Code, Section III, Subsection NG-3216.2 the following procedure was established to calculate alternating stresses. For every node, the stress difference tensors, Gnm = On -Om, are considered for all possible pairs of the stresses Gn and am at different time levels, tn and tin. Note that all possible pairs require consideration, since there are no "obvious" extrema in the stress responses. However, in order to contain computational cost, extensive screening of the pairs takes place (see Section 2.3), so that pairs known to produce alternating stress intensities less than 1,500 psi are rejected. For each remaining stress difference tensor, the principal stresses S1, S 2, S 3 are computed and the maximum absolute value among principal stress differences, Snm = max{IS1 - S21,HSI -S31,IS2 -S31},
obtained. The alternating stress at the node is then one-half the maximum value of Snm taken over all combinations (n,m), i.e., Salt = I max {Snm}. This alternating stress is compared against allowable values, depending on the node location with respect to welds.
25

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 51594 Figure 8. Overview of static calculations showing displacements (top, in inches) and stress intensities (bottom, in psi). Maximum displacement (DMX) is 0.052";lmaximum stress intensity (SMX) is 8,775 psi. Note that displacements are amplified for visualization.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 9. Close up of high static stress intensity (in psi) locations at closure plates and near support brackets. I 27

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information AN
                                                                      -p 11396 9972           1 2820 AN
              ...    - 1458        ,Y10201              4.l.1-27   -- 11658-- 13115 .
Figure 10. Overview of harmonic calculations showing real part of stress intensities (in psi) along with displacements. Unit loading MSL C for frequencies 50.2 Hz (top) and 150.7 Hz (bottom).
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 4.3 Post-Processing The static and unsteady stresses computed at every node with ANSYS were exported into files for subsequent post-processing. These files were then read into separate customized software to compute the maximum and alternating stresses at every node. The maximum stress was defined for each node as the largest stress intensity occurring during the time history.
Alternating stresses were calculated according to the ASME standard described above. For shell elements the maximum stresses were calculated separately at the mid-plane, where only membrane stress is present, and at top/bottom of the shell, where bending stresses are also present.
For nodes that are shared between several structural components or lie on junctions, the maximum and alternating stress intensities are calculated as follows. First, the nodal stress tensor is computed separately for each individual component by averaging over all finite elements meeting at the node and belonging to the same structural component. The time histories of these stress tensors are then processed to deduce the maximum and alternating stress intensities for each structural component. Finally, for nodes shared across multiple components, the highest of the component-wise maximum and alternating stresses is recorded as the "nodal" stress. This approach prevents averaging of stresses across components and thus yields conservative estimates for nodal stresses at the weld locations where several components are joined together.
The maximum stresses are compared against allowable values which depend upon the stress type (membrane, membrane+bending, alternating - Pmn, Pm+Pb, Salt) and location (at a weld or away from welds). These allowables are specified in the following section. For solid elements the most conservative allowable for membrane stress, Pm, is used, although bending stresses are nearly always present also. The structure is then assessed in terms of stress ratios formed by dividing allowables by the computed stresses at every node. Stress ratios less than unity imply that the associated maximum and/or alternating stress intensities exceed the allowable levels.
Post-processing tools calculate the stress ratios, identifying the nodes with low stress ratios and generating files formatted for input to the 3D graphics program, TecPlot, which provides more general and sophisticated plotting options than currently available in ANSYS.
4.4 Computation of Stress Ratios for Structural Assessment The ASME B&PV Code, Section III, subsection NG provides different allowable stresses for different load combinations and plant conditions. The stress levels of interest in this analysis are for the normal operating condition, which is the Level A service condition. The load combination for this condition is:
Normal Operating Load Combination = Weight + Pressure + Thermal
.. .The-weight and fluctuating pressure contributions have been calculated- in-this-analysis and       are ---
included in the stress results. The static pressure differences and thermal expansion stresses  are 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 in Level B and C cases, and are         not 29

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information considered in this analysis. N6 physical modifications were made to the HC1 steam dryer since commercial operation; therefore, seismic loading would not change.
Allowable Stress Intensities The ASME B&PV Code, Section III, subsection NG shows the following (Table 4) for the maximum allowable stress intensity (Sm) and alternating stress intensity (Sa) for the Level A service condition. The allowable stress intensity values for type 304 stainless steel at operating temperature 550'F are taken from Table 1-1.2 and Fig. 1-9.2.2 of Appendix I of Section II, in the ASME B&PV Code. The calculation for different stress categories is performed in accordance with Fig. NG-3221-1 of Division I, Section III, subsection NG.
Table 4.      Maximum allowable stress intensity and alternating stress intensity for all areas other than welds. The notation Pm represents membrane stress; Pb represents stress due to bending; Q represents secondary stresses (from thermal effects and gross structural discontinuities, for example); and F represents additional stress increments (due to local structural discontinuities, for example).
Type                     Notation     Service Limit Allowable Value (psi)
Maximum Stress Allowables."
General Membrane                    Pm             Sm                 18,300 Membrane + Bending                 Pm + Pb         1.5 Sm               27,450 Primary + Secondary              Pm + Pb + Q       3.0 Sm               54,900 Alternating Stress Allowable:
Peak = Primary + Secondary + F              Salt            Sa                13,600 When evaluating welds, either the calculated or allowable stress was adjusted, to account for stress concentration factor and weld quality. Specifically:
* For maximum allowable stress intensity, the allowable value is decreased by multiplying its value in Table 4 by 0.55.
* For alternating stress intensity, the calculated weld stress intensity is multiplied by a weld stress intensity (fatigue) factor of 1.8, before comparison to the.Sa value given above.
The weld factors of 0.55 and 1.8 were selected based on the observable quality of the shop welds and liquid penetrant NDE testing of all welds (excluding tack and intermittent welds, which were subject to 5X visual inspection) during fabrication. These factors are consistent with fatigue strength reduction factors recommended by the Welding Research Council, [10], and stress concentration factors at welds, provided in [11] and [12]. GE Purchase Specification for the HCGS Steam Dryer (21A9355 Section 9.2) called for liquid penetrant testing of all welds (excluding tack. and intermittent welds) along the entire length.!.or circumference., using..the.
guidance of ASME Boiler and Pressure Code, Paragraph N-6127.3. In addition, critical welds are subject to periodical visual inspections in accordance with the requirements of GE SIL 644 SIL and BWR V*IP-139 [13]. Therefore, for weld stress intensities, the allowable values are shown in Table 5.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information These factors (0.55 and 1.8) also conservatively presume that the structure is joined using fillet welds unless specified otherwise.          Since fillet welds correspond to larger stress concentration factors than other types of welds, this assumption is a conservative one.
Table 5. Weld Stress Intensities.
Type                    Notation     Service Limit Allowable Value (psi)
Maximum Stress Allowables:
General Membrane                   Pm           0.55 Sm             10,065 Membrane + Bending               Pm + Pb        0.825 Sm             15,098 Primary + Secondary            Pm + Pb + Q       1.65 Sm             30,195 Alternating Stress Allowables:
Peak = Primary + Secondary + F            Salt            Sa               13,600 Comparisonof CalculatedandAllowable Stress Intensities The classification of stresses into general membrane or membrane + bending types Was made according to the exact location, where the stress intensity was calculated; namely, general membrane, Pm, for middle surface of shell element, and membrane + bending, Pm + Pb, for other locations. For solid elements the most conservative, general membrane, Pm, allowable is used.
The structural assessment is carried out by computing stress ratios between the computed maximum and alternating stress intensities, and the allowable levels. Locations where any of the stresses exceed allowable levels will have stress. ratios less than unity. Since computation of stress ratios and related quantities within ANSYS is time-consuming and awkward, a separate FORTRAN code was developed to compute the necessary maximum and alternating stress intensities, Pm, Pm+Pb, and Salt, and then compare it to allowables. Specifically, the following quantities were computed at every node:
: 1. The maximum membrane stress intensity, Pm (evaluated at the mid-thickness location for shells),
: 2. The maximum membrane+bending stress intensity, Pm+Pb, (taken as the largest of the maximum stress intensity values at the bottom, top, and mid thickness locations, for shells),
: 3. The alternating stress, Salt, (the maximum value over the three thickness locations is taken).
: 4. The stress ratio due to a maximum stress intensity assuming the node lies at a non-weld location (note that this is the minimum ratio obtained considering both membrane stresses and membrane+bending stresses):
SR-P(nw) =min{ Sm/Pm, 1.5 *Sm/(Pm+Pb) }.
: 5. The alternating stress ratio assuming the node lies at a non-weld location, SR-a(nw) = Sa / (1.1
* Salt),
: 6. The same as 4, but assuming the node lies on a weld, SR-P(w)=SR-P(nw)
* fsw
* 0.55 31

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
: 7. The same as 5, but assuming the node lies on a weld, SR-a(w)=SR-a(nw)
* fsw / 1.8.
where fsw=l at all welds (when justified, fsw can be adjusted to reflect different weld types).
Note that in steps 4 and 6, the minimum of the stress ratios based on Pm and Pm&#xf7;Pb, is taken.
The allowables listed in Table 4, Sm=18,300 psi and Sa=13,600 psi. The factors, 0.55 and 1.8, are the weld factors discussed above. The factor of 1.1 accounts for the differences in Young's moduli for the steel used in the steam dryer and the values assumed in alternating stress allowable. According to NG-3222.4 in subsection NG of Section III of the ASME Code, the effect of elastic modulus upon alternating stresses is taken into account by multiplying alternating stress Salt at all locations by the ratio, E/Emodel=l .1, where:
E = 28.3 106 psi, as shown on Fig. 1-9.2.2. ASME BP&V Code Emodel = 25.55 106 psi (Table 1)
The nodes with stress ratios lower than 4 are plotted in TecPlot (a 3D graphics plotting program widely used in engineering communities [14]) to establish whether they lie on a weld or not. The appropriate maximum and alternating stress ratios, SR-P and SR-a, are thus determined and a final listing of nodes having the smallest stress ratios is generated. These nodes are tabulated and depicted in the following Results Section.
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T his Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information
: 5. Results The stress intensities and associated stress ratios resulting from the Rev. 4 acoustic/hydrodynamic loads [2] with associated biases and uncertainties factored in, are presented below. Section 5.1 tabulates the highest maximum and alternating stress intensities and presents contour plots of these stresses to indicate which points on the dryer experience significant stress concentration and/or modal response. Section 5.2 compares the stresses against allowable values, accounting for stress type (maximum and alternating) and location (on or away from a weld). The results are presented in terms of stress ratios and the locations with the lowest stress ratios are identified. Section 5.3 examines the spectral content of select nodes showing the presence of a strong 80 Hz signal in the stress response. In section 5.4, the bias due to finite frequency discretization and uncertainty associated with the finite element model itself, are factored in (they were not accounted for in sections 5.1 to 5.3). In section 5.5 the origins of the 80 Hz signal are briefly discussed together with procedures for compensating for this noise using 1000# data [16]. Section 5.5 tabulates the fictitious stress ratios resulting from background noise with no flow (the 100O0# data) and presents the final results obtained when the 1000# data is eliminated from the CLTP data. Finally section 5.6 reports the predicted stress ratios at EPU conditions. This section also reflects the most recent revisions of biases and uncertainties in the finite element model as well as a more conservative frequency-limited 1000# noise removal procedure.
In sections 5.1 to 5.5, results are presented both at nominal conditions (no frequency shift) and with frequency shift included. Frequency shifts are generally performed at 2.5% increments except in section 5.3 where they are performed at higher resolution (0.5%) for the nodes identified as having the lowest stress ratios.
Finally, the tabulated stresses and stress ratios are obtained using a 'blanking' procedure that is designed to prevent reporting a large number of high stress nodes from essentially the same location on the structure. In the case of stress intensities (section 5.1) this procedure is as follows. The relevant stress intensities are first computed at every node and then nodes sorted according to stress level. The highest stress node is noted and all neighboring nodes within 10 inches of the highest stress node and its symmetric images (i.e., reflections across the xz0 and y0O planes) are "blanked" (i.e., excluded from the search for subsequent high stress locations).
.Of the remaining nodes, the next highest stress node is identified and its neighbors (closer than 10 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. In Section 5.2, a similar blanking procedure is applied to the stress ratios rather than stresses. Thus the lowest stress ratio of a particular type in a 10" neighborhood and. .its symmetric images is identified and all other nodes in these regions excluded from listing in the table. Of the remaining nodes, the one with the lowest stress ratio is reported and its neighboring points similarly excluded, and -so on until all nodes are either blanked or have a stress 'ratio higher than 4.
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          .This Document-Does Not Contain Continuum Dynamics, Inc. Proprietary Information 5.1 General Stress Distribution and High Stress Locations The maximum stress intensities obtained by post-processing the ANSYS stress histories for CLTP at nominal frequency and with frequency shift operating conditions are listed in Table 6.
Contour plots of the stress intensities over the steam dryer structure are shown on Figure I11 (nominal frequency), Figure 12 (maximum stress over all nine frequency shifts including nominal), and Figure 13 (-7.5% frequency shift where the alternating stress response is strongest). The figures are oriented to emphasize the high stress regions. Note that these stress intensities do not account for weld factors but do include end-to-end bias and 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 concern. Instead, structural evaluation is more 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 factors.
Comparisons on the basis of stress ratios are made in Section 5.2.
The maximum stress intensities in most areas are low (less than 500 psi, or 5% of the most conservative critical stress). For the membrane stresses (Pm) the high stress regions tend to occur at: (i) the outermost portion of the inner hood near the connection to the closure plate; (ii)
   *the weld joining the skirt and the upper support ring near the supports; and (iii) the central base plate/vane bank junction. In all cases the stress is dominated by static stresses as evidenced by the small alternating stresses (less than 1500 psi) in the rightmost columns in the table. The closure plates and regions in the vicinity of where they connect to adjacent hoods or vane banks, experience high stresses since they restrain any deflection of the adjacent vane banks.'
The membrane + bending stress (Pm+Pb) distributions evidence a more pronounced modal response in all cases. However, the highest stress locations are still dominated by the static
   .component as is confirmed by the low alternating stress values in the right hand column of Table
: 6. Modal excitations are most pronounced on the hoods, perforated plates and skirt structure.
Comparison of the nominal (0% frequency shift) and -7.5% frequency shift results shows that different modes are excited in each case. For example, in the nominal case the central plate in the outer hood shows the strongest response on this hood whereas at the -7.5% shift the outer two portions exhibit the dominant response. Stress concentrations are visible near the hood supports, at the bottoms of the hoods, near the tops of the closure plates and along the skirt/drain channel welds.
The alternating stresses are, generally small at nominal operation with the highest reported value (1,821 psi) occurring on a non-weld location on the perforated plates and the highest value on a weld being only 1,625 psi at the bottom of a perforated plate. This is very close to the 1,500 psi cutoff value used in the alternating stress calculation so that alternating stresses can be safely summarized as being essentially marginal or negligible (i.e., having an associated stress ratio > 4) at zero frequency shift. These stresses are, however, sensitive to frequency shift and all five of the locations identified as having the highest alternating stresses over all frequency
**shifts    assume -their. highest values at- the --7.5%--shift. The alternating stress -intensity- contour plots essentially record the modes excited by this signal, which here are seen to be confined to perforated plates and inner or middle hoods which, though not directly exposed to the main MSL pressure fluctuations (like the outer hoods are) are of thinner construction and therefore exhibit a 34

This Document Does Not.Contain Continuum Dynamics, Inc. Proprietary Information significant response. The largest alternating stress is more than twice the nominal shift value further evidencing a strong frequency-dependence upon the load spectrum.
35

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 6a. Locations with highest predicted stress intensities for CLTP conditions with no frequency shift. Alternating stresses are only computed at nodes where stresses can exceed 1500 psi.
Stress                          Location                                    Location (in                   Stress Intensities (psi)
Category                                                         Weld      x        y        z     node      Pm     Pm+Pb        Salt Tm      outer portion of inner hood (top near closure plate)  No     109.0 -27.6        95.3  44886    5963 8481 <1500
        "      central base plate/inner vane bank/side panel        Yes    -118.8    14.4       7.5  85994    4062      5595      <1500 skirt/upper support ring                             Yes     118.7    -5.9      -2.0  91960    3967      5903      <1500 closure plate/top cover plate/vane side plate/       Yes     108.4   -45.9      95.9  91627    3719      4277      <1500 perforated plate inner hood backingbar/closure plate                  Yes    -108.4    38.4       8.1  87035    3673      3874      <1500 Pm+Pb      skirt/upper support ring                             Yes     118.8      0.6     -2.0  88325    2330      9575      <1500 outer portion ofinner hood (top near closure plate)   No     109.0   -27.6      95.3  44886    5963      8481      <1500 central base plate/inner vane bank/side panel        Yes    -118.8     14.4      7.5  85994    4062      5595      <1500 cover plate/outerhood                                Yes      59.1   101.4       7.5  93493    1437      5455      <1500 drain pipe/skirt                                     Yes      88.2     79.6    -20.5  91083    1925      5418      <1500 Salt    middle vane bank perforated entry plate               No      26.3   -54.4      48.5  71368     239      1867       1821 middle vane bank/perforated entry plate              Yes      38.9   -54.4      21.5  80204     286      1742       1625 inner hood                                            No      30.0   -35.8      51.7  43406     707      1614       1578
        "      outer hood                                            No        0.3    94.9     74.9  33378     267      1576       1570
        "       outer hood                                           No      -4.7     90.3     94.9  33995     267      1652       1567 Node numbers are retained for further reference.
Spatial coordinate are in the coordinate system, defined by the origin at the centerline of steam dryer 7.5" below bottom plates. The x-axis is parallel to the hoods, y-axis is normal to the hoods pointing from MSL AB to MSL CD, z-axis is vertical, positive up.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 6b. Locations with highest predicted stress intensities taken over all frequency shifts CLTP conditions. Alternating stresses are only computed at nodes where stresses can exceed 1500 psi.
Stress                        Location                       Weld % Freq.            Location (in)                  Stress Intensities (psi)
Category                                                             Shift        x          y         z     node    Pm      Pm+Pb        Salt Pm     outer portion of inner hood (top near closure plate)  No    -10       109.0      -27.6      95.3 44886    6433      9178 <1500 central base plate/inner vane bank/side panel        Yes    -10     -118.8         14.4      7.5 85994    4122      5664 <1500 inner hood backing bar/closure plate                 Yes   -7.5     -108.4         38.4      8.1 87035    4005      4184      <1500 skirt/upper support ring                             Yes      0       118.7        -5.9     -2.0 91960    3967      5903      <1500 closure plate/middle side panel/top cover plate/     Yes    -10     -108.4         45.9     95.9 85891    3852      4516      <1500 top perforated plate Pm+Pb    skirt/upper support ring                             Yes      0       118.8         0.6     -2.0 88325    2330      9575      <1500 outer portion of inner hood (top near closure plate)  No    -10       109.0      -27.6      95.3 44886    6433      9178      <1500 cover plate/outerhood                                Yes   -7.5       -59.1    -101.4        7.5 93288    1957      6607       2447 central base plate/inner vane bank/side panel        Yes    -10     -118.8         14.4      7.5 85994    4122      5664      <1500 drain pipe/skirt                                     Yes     +5         88.2       79.6    -20.5 91083    1973      5522      <1500 Salt   outer vane bank/perforated entry plate               Yes   -7.5          1.9       85.9     21.5 82290     213      3773       3699
    "     middle base plate/middle vane bank                   Yes   -7.5       -83.4        54.4      7.5 86424     414      3823       3630
    "     outer vane bank perforated entry plate                No   -7.5          3.8       85.9     34.9 61491     202      3610       3556
    "     outer vane bank perforated entry plate                No   -7.5          2.2       85.9     63.0 61581     230      3517       3475
    "     middle vane bank perforated entry plate               No   -7.5         95.6       54.4     80.6 69772     895      3440       3315 See Table 6a for coordinates description.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 6c. Locations with highest predicted stress intensities for CLTP conditions with -7.5% frequency shift. Alternating stresses are only computed at nodes where stresses can exceed 1500 psi.
Stress                         Location                                      Location (in)               Stress Intensities (psi)
Category                                                        Weld      x           y        z    node  Pm      Pm+Pb        Salt Pm      outer portion of inner hood (top near closure plate)  No     109.0      -27.6      95.3 44886 6283 8951           <1500 central base plate/inner vane bank/side panel        Yes    8.8       14.4      7.5 85994 4074 5604           <1500 inner hood backing bar/closure plate                 Yes    -108.4        38.4      8.1 87035 4005     4184       <1500 skirt/upper support ring                             Yes     118.7        -5.9     -2.0 91960 3929     5770       <1500 closure plate/middle side panel/top cover plate/     Yes    -108.4        45.9     95.9 85891 3774     4459       <1500 top perforated plate Pm+Pb     skirt/upper support ring                             Yes     118.8          0.6    -2.0 88325 2287     9359       <1500
       "     outer portion of inner hood (top near closure plate)  No     109.0      -27.6      95.3 44886 6283     8951       <1500
       "     cover plate/outer hood                               Yes     -59.1    -101.4        7.5 93288 1957     6607        2447 ft    centralbase plate/innervane bank/side panel          Yes    -118.8        14.4      7.5 85994 4074     5604       <1500 drain pipe/skirt                                     Yes       88.2       79.6    -20.5 91083 1932     5444       <1500 Salt    outer vane bank/perforated entry plate               Yes        1.9       85.9     21.5 82290  213      3773       3699
       "     middle base plate/middle vane bank                   Yes     -83.4        54.4      7.5 86424  414      3823       3630 outer vane bank perforated entry plate                No        3.8       85.9     34.9 61491  202      3610       3556
       "     outer vane bank perforated entry plate                No        2.2       85.9     63.0 61581  230      3517       3475
       "     middle vane bank perforated entry plate               No       95.6       54.4     80.6 69772  895      3440       3315 See Table 6a for coordinates description.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
                                                                                   &Y X
Pm [psi]
6000 5250 4500 3750 3000
                                                                               ,2250
                                                                               '1500 750 0
Figure 1Ia. Contour plot of maximum membrane stress intensity, Pm, for CLTP load. The maximum stress intensity is 5,963 psi.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
Y X
Figure 1 b. Contour plot of maximum membrane+bending stress intensity, Pm+Pb, for CLTP load. The maximum stress intensity is 9,575 psi. First view.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information X
LY Pm+Pb [psi]
9000 8000 7000 6000 5000 4000 2000 1000 0
Figure I Ic. Contour plot of maximum membrane+bending stress intensity, Pm+Pb, for CLTP load. Second view from below.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Y -
Salt [psi]
1700 1550 1400 1250 1100 950 800 650 500 350 200 50 Figure lId. Contour plot of alternating stress intensity, Salt, for CLTP load. The highest alternating stress intensity is 1,821 psi. First view.
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    . This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 1 le. Contour plot of alternating stress intensity, Salt, for CLTP load. This second view from below shows the high alternating stress intensity near the hood supports and on perforated plates.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
Y x
Pm [psi]
6000 5250 4500 3750 3000 2250 1500 750 0
Figure 12a. Contour plot of maximum membrane stress intensity, Pm, for CLTP operation with frequency shifts. The recorded stress at a node is the maximum value taken over all frequency shifts. The maximum stress intensity is 6,433 psi.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information X Z Y'A4 Figure 12b. Contour plot of maximum membrane+bending stress intensity, Pm+Pb, for CLTP operation with frequency shifts. The recorded stress at a node is the maximum value taken over all frequency shifts. The maximum stress intensity is 9,575 psi.
First view.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Y
x Pm+Pb [psi]
9000 8000 7000 6000 5000 4000 3000 2000, 1000 0
Figure 12c. Contour plot of maximum membrane+bending stress intensity, Pm+Pb, for CLTP operation with frequency shifts. This second view from beneath reveals high stress and modal response of the hoods, perforated plates and hood supports.
46

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information X
Salt [psi]
3500
* 3000 E    2500 IN2000 1500 1000
                                                                                        *500 0
Figure 12d. Contour plot of alternating stress intensity, Salt, for CLTP operation with frequency shifts. The recorded stress at a node is the maximum value taken over all frequency shifts. The maximum alternating stress intensity is 3,699 psi. First view.
47

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 12e. Contour plot of alternating stress intensity, Salt, for CLTP operation with frequency shifts. This second view from beneath reveals more of the high stress regions on the hoods and perforated plates.
48

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
Y Pm [psi]
6000 5250 4500 3750 3000 2250 1500 750 0
Figure 13a. Contour plot of maximum membrane stress intensity, Pm, for CLTP load with
            -7.5% frequency shift. The maximum stress intensity is 6,283 psi.
49

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
Y J
Figure 13b. Contour plot of maximum membrane+bending stress intensity, Pm+Pb, for CLTP load with -7.5% frequency shift. The maximum stress intensity is 9,359 psi.
50

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information X
Pm+Pb [psi]
W4 9000 8000 7000 6000 5000 4000 3000 2000 1000 0
Figure 13c. Contour plot of maximum membrane+bending stress intensity, Pm+Pb, for CLTP load with -7.5% frequency shift. Second view from beneath.
51

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
Y
                                                                                   'vI X
3500 3000 2500 2000 1500 1000 500 0
Figure 13d& Contour plot of alternating stress intensity, Salt, for CLTP load with -7.5%
frequency shift. The maximum alternating stress intensity is 3,699 psi. First view.
52

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information L        x Salt [psi]
D-   3500 3000 2500 2000 1500 1000 500 0
Figure 13e. Contour plot of alternating stress intensity, Salt, for CLTP load with -7.5%
frequency shift. Second cutaway view showing high stress locations on the hoods and perforated plates.
53

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 5.2 Load Combinations and Allowable Stress Intensities The stress ratios computed for CLTP at nominal frequency and with frequency shifting are listed in Table 7. The stress ratios are grouped according to type (SR-P for maximum membrane and membrane+bending stress, SR-a for alternating stress) and location (away from welds or on a weld).
For CLTP operation at nominal frequency the minimum stress ratio is identified as a maximum stress, SR-P=1.58, and occurs at the junction of the skirt and upper support ring. At this condition, the dryer stress state is effectively governed by maximum stresses and, more specifically, by the weight-induced static stress field. This is clear from Table 7a where all entries in the right hand column show negligible alternating stress ratios, SR-a>4. In fact all nodes on the steam dryer have alternating stress ratios higher than 4.0 so that no entries for this stress type appear in Table 7a. All remaining locations for maximum stresses are listed in Table 7a and depicted in the accompanying Figure 14.
The effects of frequency shifts can be conservatively accounted for by identifying the minimum stress ratio at every node, where the minimum is taken over all the frequency shifts considered (including the nominal or 0% shift case). The resulting stress ratios are then processed as before to identify the smallest stress ratios anywhere on the structure, categorized by stress type (maximum or alternating) and location (on or away from a weld). The results are summarized in Table 7b and show that the minimum stress ratio, SR-P=1.58, is the same as before and is still identified with a maximum stress. This is the smallest stress ratio encountered anywhere on the structure for any frequency shift at the CLTP condition. Because the alternating stress ratio at this location exceeds 4.0,. the minimum stress ratio does not change appreciably with frequency shift. For similar reasons, increasing the loads by (115%)2 (the approximate increase when proceeding to 115% CLTP operation) is unlikely to significantly alter the value of this minimum stress ratio.
The minimum alternating stress ratio at any frequency shift, SR-a=1.86, is less than one half the value at the zero shift case and occurs on the welded perimeter of the bottom perforated plate.
This increase in stress intensity is due to the dynamic modal response resulting when the forcing frequencies are scaled by -7.5%. In fact, virtually all of the lowest alternating stress ratios occur at this shift. Since the structure contains tens of modes per 1 Hz interval, the strong modal response at this shift is indicative of close coupling between the acoustic pressure variation and structural mode shapes at the dominant response frequency which, here, is 74 Hz (80 Hz shifted by -7.5%, with the 80 Hz signal being the dominant component in the stress response as discussed in section 5.3).
Because the worst case stress ratios (i.e., the minimum stress ratio over all frequency shifts) are most important for conservative structural assessment, the locations of all nodes having maximum stress ratios SR-P<2.0 are plotted in Figure 15e, and all nodes. having -alternating stress ratios SR-a<2.0 are plotted in Figure 15h. Note that all plotted stress ratios occur on welds since all stress ratios at non-welds are 2.84 or higher. These plots differ from the preceding ones where the smallest stress ratio in a 10 inch region is identified and all other nodes in this region excluded from display and tabulation. In the current plots, this blanking is not performed so that 54

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information a more complete picture of where stress ratios are low, is conveyed. These plots show that all stress ratios, SR-P<2.0 occur at: (i) the steam dryer supports and (ii) the closure plate/inner hood junctions. All alternating stress ratios, SR-a<2.0 occur at: (i) the welded perimeters of perforated plates and (ii) the junction between the middle base plate and middle vane bank. The same conclusion is inferred from Table 7b.
Because it shows the highest alternating stress response, the results are also tabulated for the
-7.5% frequency shift in Table 7c. However, all of the tabulated values already appear in Table 7b so that little new insight is gained. Also, depicting the nodes with the smallest stress ratios effectively duplicates the series of plots in Figure 15. Hence rather than repeating the series, the reader is referred to the preceding Table 7b and the corresponding figures to locate the important low stress ratio nodes.
In summary, the general picture that emerges is that at CLTP loads the frequency shifts significantly affect the minimum alternating stress ratios and reposition the high stress locations to different parts of the structure. However, these ratios are well above allowable levels and contain considerable margin for increase to EPU operation. The smallest stress ratio encountered anywhere on the structure at any frequency shift, SR-P=1.58, is identified with a maximum stress and shows negligible variation with frequency shift.
55

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 7a. Locations with minimum stress ratios for CLTP conditions with no frequency shift. Stress ratios are grouped according to stress type (maximum - SR-P; or alternating - SR-a) and location (away from a weld or at a weld). Bold text indicates minimum stress ratio of any type on the structure. Locations are depicted in Figure 14. Alternating stress ratios are all greater than 4.0.
Stress  Weld                              Location                             Location (in.)                       Stress Intensity (psi)   Stress Ratio Ratio                                                                        x         y       z       node      Pm       Pm+Pb        Salt SR-P     SR-a SR-P      No     1. outer portion of inner hood (top near closure plate)   109.01 -27.6       95.3    44886     5963       8481      <1500  3.07      >4 SR-a      No                                                             NONE  (All SR-a > 4)
: 2. closure plate/inner hood                                108.4      27.9   94.9    85409     4943       7239      <1500  2.04      >4
  ..       .. 3. central base plate/inner vane bank/side panel         -118.8      14.4     7.5    85994     4062       5595      <1500  2.48      >4
: 4. closure plate/middle side panel/top cover plate/       108.4    -45.9     95.9    91627     3719       4277      <1500  2.71      >4 top perforated plate SR-a     Yes                                                             NONE  (All SR-a > 4)
See Table 6a for coordinates description.
56

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 7b. Locations with minimum stress ratios for CLTP conditions with frequency shifts. Stress ratios at every node are recorded as the lowest stress ratio identified during the frequency shifts. Stress ratios are grouped according to stress type (maximum - SR-P; or alternating - SR-a) and location (away from a weld or at a weld). Bold text indicates minimum stress ratio of any type on the structure. Locations are depicted in Figure 15.
Stress Weld                           Location                         % Freq.        Location (in.)                  Stress Intensity (psi)   Stress Ratio Ratio                                                                   Shift      x         y        z    node     Pm      Pm+Pb        Salt SR-P SR-a SR-P    No     1. outer portion of inner hood (top near closure plate)   -10     109.0     -27.6 95.3     44886    6433      9178 <1500       2.84      >4 SR-a    No     1. outer vane bank perforated entry plate               -7.5         1.8      85.9    27.6 61564     211      3658       3603  7.50     3.43
  ..     .. 2. outer vane bank perforated entry plate                 -7.5        2.2      85.9    63.0 61581     230      3517       3475  7.81     3.56
: 2. closure plate/inner hood                                -10    -108.4     -27.9     94.9 88252    5612      8317       1764  1.79     3.89 F... 3. cover plate/outer hood                                -7.5      -59.1   -101.4       7.5 93288    1957      6607       2447  2.29     2.81
         . 4. central base plate/inner vane bank/side panel           -10    -118.8       14.4     7.5 85994    4122      5664      <1500  2.44      >4
: 5. inner hood backing bar/closure plate                  -7.5     -108.4       38.4     8.1 87035    4005      4184      <1500  2.51      >4 SR-a   Yes     1. outervane bank/perforated entry plate                 -7.5        1.9      85.9    21.5 82290     213      3773       3699  4.00     1.86 IT   2. middle base plate/middle vane bank                     -7.5     -83.4       54.4     7.5 86424     414      3823       3630  3.95     1.89
         . 3. perforated entry plate/vane bank top vertical plate   -7.5       99.4       54.4    94.4 82652     676      3450       3252  4.38     2.11 TV   4. middle base plate/middle vane bank                    -7.5      -26.2       54.4     7.5 93931     242      2936       2864  5.14     2.40 if   5. outer base plate/outer vane bank                      -7.5         0.0    -85.9      7.5 86643     216      2924       2746  5.16     2.50 See Table 6a for coordinates description.
57

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 7b (continued). Locations with minimum stress ratios for CLTP conditions with frequency shifts. Stress ratios at every node are recorded as the lowest stress ratio identified during the frequency shifts. Stress ratios are grouped according to stress type (maximum - SR-P; or alternating - SR-a) and location (away froma weld or at a weld).
Stress  Weld                          Location                       % Freq.        Location (in.)             Stress Intensity (psi)  Stress Ratio Ratio                                                                 Shift      x         y        z    node Pm     Pm+Pb       Salt SR-P     SR-a SR-a    Yes   6. end plate/perforated entry plate/middle side panel  -7.5      108.4     54.4      87.1 79914 880     2792      2639  5.41     2.60
   ..     .. 7. perforated entry plate/vane bank top vertical plate   -5      -12.1   -54.4       94.4 93858 485     2852      2632  5.29     2.61
          "    8. hood support/middle vane bank                      -7.5      -54.5     54.4      18.6 84068 401     2648 1 2604     5.70     2.64
          "   9. end plate/perforated entry plate/middle side panel  -7.5      108.4     54.4      48.2 79942 764     2687 1 2483     5.62     2.77 See Table 6a for coordinates description.
58

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 7c. Locations with minimum stress ratios at CLTP conditions with -7.5% frequency shift. Stress ratios are grouped according to stress type (maximum - SR-P; or alternating - SR-a) and location (away from a weld or at a weld). Bold text indicates minimum stress ratio of any type on the structure. Since all nodes in this table also appear in Table 7b, for depictions of the node locations refer to that table and the accompanying Figure 15.
Stress  Weld                             Location                               Location (in.)                       Stress Intensi (psi)     Stress Ratio Ratio                                                                       x           y        z      node      Pm       Pm+Pb      Salt   SR-P     SR-a SR-P     No     1. outer portion of inner hood (top near closure plate)   109.0       -27.6    95.3    44886     6283       8951    <1500    2.91      >4 SR-a     No     1. outer vane bank perforated entry plate                     1.8      85.9    27.6    61564      211       3658     3603    7.50     3.43 it    2. outer vane bank perforated entry plate                    2.2       85.9    63.0    61581      148       3517     3475    7.81     3.56
: 2. closure plate/inner hood                             -108.4        -27.9    94.9    88252     5281       7821    <1500    1.91      >4
              .3. cover plate/outer hood                                  -59.1     -101.4      7.5    93288     1957       6607     2447    2.29     2.81
 . "      "     4. central base plate/inner vane bank/side panel        -118.8         14.4     7.5    85994     4074       5604    <1500    2.47      >4
          . 5. inner hood backing bar/closure plate                 -108.4         38.4     8.1    87035     4005       4184    <1500    2.51      >4 SR-a    Yes     1. outer vane bank/perforated entry plate                     1.9      85.9    21.5    82290      213       3773     3699    4.00     1.86
          . 2. middle base plate/middle vane bank                     -83.4        54.4     7.5    86424      414       3823     3630    3.95. 1.89
: 3. perforated entry plate/vane bank top vertical plate      99.4       54.4    94.4    82652      617       3450     3252    4.38     2.11
: 4. middle base plate/middle vane bank                     -26.2        54.4     7.5    93931      242       2936     2864    5.14     2.40
: 5. outer base plate/outer vane bank                          0.0      -85.9     7.5    86643      216       2924     2746    5.16     2.50
   ..     .. 6. end plate/perforated entry plate/middle side panel     108.4        54.4    87.1    79914      813       2792     2639    5.41     2.60
   ..     .. 7. hood support/middle vane bank                          -54.5        54.4    18.6    84068      401       2648     2604    5.70     2.64
   ..     .. 8. end plate/perforated entry plate/middle side panel     108.4        54.4    48.2    79942      749       2687     2483    5.62     2.77 See Table 6a for coordinates description.
59

This .Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 14a. Location of smallest maximum stress ratio, SR-P, at non-weld for nominal CLTP operation. Number refers to the enumerated locations for SR-P values at non-welds in Table 7a.
60

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
Y x
Figure 14b. Locations of smallest maximum stress ratios, SR-P, at welds for nominal CLTP operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 7a.
First view showing locations 1, 2 and 4.
61

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
Figure 14c. Locations of smallest maximum stress ratios, SR-P, at welds for nominal CLTP
.operation. Numbers refer to the enumerated locations for SR-P values at welds in Table 7a.
Second view showing location 3.
62

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 15a. Location of minimum stress ratio, SR-P, associated with maximum stress intensities at non-welds for CLTP operation with frequency shifts. The recorded stress ratio is the minimum value taken over all frequency shifts. The number refers to the enumerated location for SR-P values at non-welds in Table 7b.
63

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 15b. Locations of minimum alternating stress ratios, SR-a, at non-welds for CLTP operation with frequency shifts. The recorded stress ratio at a node is the minimum value taken over all frequency shifts. Numbers refer to the enumerated locations for SR-a values at non-welds in Table 7b.
64

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
Y x
Figure 15c. Locations of minimum stress ratios, SR-P, associated with maximum stress intensities at welds for CLTP operation with frequency shifts. The recorded stress ratio at a node is the minimum value taken over all frequency shifts. Numbers refer to the enumerated locations for SR-P values at welds in Table 7b. This view shows locations 1-3.
65

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 15d. Locations of minimum stress ratios, SR-P, associated with maximum stress intensities at welds for CLTP operation with frequency shifts. The recorded stress ratio at a node is the minimum value taken over all frequency shifts. Numbers refer to the enumerated locations for SR-P values at welds in Table 7b. This view shows locations 2, 4 and 5.
66

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information z
SR-P (weld) 1.95 1.9 1.85 1.8 1.75 1.7 1.65 1.6 1.55 1.5 Figure 15e. Locations of minimum stress ratios, SR-P, associated with maximum stress intensities at welds for CLTP operation with frequency shifts. The recorded stress ratio at a node is the minimum value taken over all frequency shifts. This view displays all nodes with SR-P<2.0.
67

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information x
Y Figure 15f. Locations of minimum alternating stress ratios, SR-a, at welds for CLTP operation with frequency shifts. The recorded stress ratio at a node is the minimum value taken over all frequency shifts. Numbers refer to the enumerated locations for SR-a values at welds in Table 7b. First view showing enumerated locations 1, 2, 4-6, 8 and 9.
68

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Figure 15g. Locations of minimum alternating stress ratios, SR-a, at welds for CLTP operation with frequency shifts. The recorded stress ratio at a node is the minimum value taken over all frequency shifts. Numbers refer to the enumerated locations for SR-a values at welds in Table 7b. Second view showing locations 3, 6, 7 and 9.
69

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Y
SR-a (weld) 1.95 1.9 1.85 1.8 1.75 1.7 1.65 1.6 1.55 1.5 Figure 15h. Locations of minimum alternating stress ratios, SR-a, at welds for CLTP operation with frequency shifts. The recorded stress ratio at a node is the minimum value taken over all frequency shifts. This figure shows all nodes with SR-a<2.0.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 5.3 Frequency Content and Sensitivity to Frequency Shift of the Stress Signals As indicated previously, both the loads and stress signals contain a strong 80 Hz component and a second weaker, but significant 41 Hz component. This can be seen by examining the accumulative PSDs which are computed directly from the Fourier coefficients as Z((Onn where &(COO) is the complex stress harmonic at frequency, 0( k. 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 X(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 YX(CON) (where N is the total number of frequency components) and the RMS of the stress signal in the time domain is established.
The accumulative PSD at nominal frequency shift for the az stress response at node 80204 is shown in Figure 16. This node is selected because it exhibits a strong alternating stress response at the 0% frequency shift and clearly reveals the two main contributors to the stress response.. From the plot, the largest contribution occurs over the 80.0 Hz to 80.2 Hz frequency range and the second largest contribution is made over the 40.5 Hz to 42 Hz range. Examination of the other nodes reveal similar qualitative observations, through the relative jumps may differ and their significance compared to the initial static contribution can also vary. Similarly, when the load is shifted in the frequency space, a similar response results with the 80 Hz and [40.5 -
42] Hz rises suitably shifted. This is indicated in Figure 17 where the accumulative PSD for node 82290 at -7.5% and 0% frequency shifts are compared. This node exhibits a very weak response in the zero shift case. However, at -7.5% frequency shift, the node participates in a strong response. This behavior is consistent with a mode being excited by the 74 Hz signal
*(80Hz shifted by -7.5%)
Further insight into the modal response can be obtained by examining how the maximum and alternating stress intensities of selected nodes vary with frequency shift. This evaluation is made in Figure 18 for the following nodes:
Nodes 88325 and 88252: - these nodes have the lowest stress ratios associated with a maximum stress intensity at any frequency shift.
Node 80204 - this node has a high alternating stress at zero frequency shift (see Table 6a).
Nodes 82290 and 86424 - these nodes have the lowest alternating stress ratios over all frequency shifts (see Table 7b).
To generate these plots th6 frequency shifts are made in 0.5% increments thus achieving a finer resolution than for the 2.5% increments used to evaluate all the nodes. This is a useful 71

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information advantage of the harmonic approach since, once the unit solution stresses are computed, the stress response at any shifted frequency can be easily and quickly evaluated thus allowing this higher resolution (in frequency shift) plot to be obtained in a few minutes. In a time-domain approach each frequency shift entails a complete finite element time simulation requiring days to weeks of computation time. For node 88325 the highest stress intensity of 9,610 psi occurs at the -0.5% frequency shift which is only 35 psi (or 0.4%) higher than the 9,575 psi value at zero shift. The maximum and alternating stress intensities vary by approximately 600 psi when
-frequencies are shifted in the +/-10% range. For node 88252, the stress variation is slightly higher, but clearly shows no strong unresolved interior peaks.
Node 80204 shows two interior peaks, at -5.5% and 0% frequency shifts. These could be due to the excitation of one of many skirt modes present in the structure. Unlike the previous two nodes, the maximum and alternating stress intensities are now very close in magnitude due to the small static stress component. Both alternating and maximum stress intensities are relatively small as evident from the associated alternating stress ratio of SR-a>4. A much stronger frequency shift dependence is seen in the last two plots for nodes 82290 and 86424 (Figure 18d and e). Both plots show the peak (now resolved to 0.5%) at -7.5%. Further, in each case the behavior about the peak is accurately described by the frequency response of a single degree-of-freedom damped oscillator. For example, the half power points for node 82290 are +/-0.78%
about the -7.5% shift; the half power points for node 86424 occur at +/-1.14% about the peak frequency shift. Both are close to the +/-1% values expected for 1% damping. Differences are attributable to the presence of multiple modes in the stress response.
Since acoustic loads scale roughly with the square of the steam flow, it is reasonable to anticipate that under EPU conditions (where steam flow increases by 15%) the stresses would increase to by approximately (115%)2=1.32. Under this assumption the minimum alternating stress ratio would reduce from 1.86 to 1.86/1.32=1.41, which given that the applied loads already account for all end-to-end biases and uncertainties, still contains sufficient margin for sustained EPU operation. The stress ratios associated with maximum stress do not scale this way due to the large static component in these stresses. However, on the basis of Figure 18a-b (nodes having the highest maximum stress intensities, 88325 and 88252), one sees that other than the vertical displacement the alternating stress intensity and peak stress intensity curves have very similar forms. It is then reasonable to expect that adding the increase in alternating stress intensity, or (1.32 - 1)=0.32 times the alternating stress intensity, to the maximum stress intensity yields a rough estimate of the peak stress intensity at EPU operation. The peaks then become 9973 psi (for node 88325) and 8882 psi (node 88252) with corresponding stress ratios, SR-P-1.52 and SR-P=1.68 respectively, which are both still well within allowables. These simple scaling arguments, indicate that at EPU the minimizing stress ratio would be due to an alternating stress (SR-a=1.41) rather than a maximum stress.
72

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information a (node 80204) 450 400 ---------------------- -------------       -
U,      350   ------------------------------------     -       ------------------
CL 300          ---------------- ------------                    -----------
Cl) 250   - --------------------- -------------            ----------------
200   - --------------------- -------------    -       ------------------
E E
150   - --------------------- -------------    -
100 --------------            ------   -------
50 0                      50                     100                  150 200 Frequency [Hz]
Figure 16. Accumulative PSD of the azz stress response at node 80204 for nominal CLTP operation with zero frequency shift.
73

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information a    (node 82290) 1200 1000   -
800                           ----------
C/)
0-                                                                             -        -7.5% shift C,)                                                                    ......... no shift U,
600          ---------------- ----------             . . . .  . . . . .. -
al)
E         400   - --------------------- ----------
E 200                            ----------
: .........          ...................---... --                -     - ..- M - ....
0 0                      50                  100                               150                                    200 Frequency [ Hz ]
Figure 17. Accumulative PSD of the (Yzz stress response at node 82290 at -7.5% and zero frequency shifts 74

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 88325 1 104 8000    - ------------------------ -------------------    ---------------------- --------------------- -
0~
6000 w                                  ---       Maximum Stress Intensity C                                                      ..
Alternating       Stress intensity 4-.
C w
U, L.
4000 2000 I      .                 I.
0
                -10                      -5                       0                       5                      10 Frequency Shift [ % ]
Figure 18a. Variation of maximum and alternating stress intensities with frequency shift for node 88325.
75

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 88252 1 104 8000
                     ------------------.                                                                                                            .....L----
6000 cn                                                                Maximum Stress Intensity
                                    ......... Alternating Stress Intensity a)
C C,,
(0 a)
S.-
4000
                                  . .. . . . . . .* . . . . .. . . . . . . .  . . . . . . . . . . r . . . .. .  . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .
2000
                                                                                                                .......... R I                              I 0
                 -10                            -5                                                0                              5                                          10 Frequency Shift [ % ]
Figure 18b. Variation of maximum and alternating stress intensities with frequency shift for node 88252.
76

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 80204 2000 1800 1600 1400
   &0 1200
  .4-U) 1000 800 600 400
                 -10              -5                0                   5                10 Frequency Shift [ %
Figure 18c. Variation of maximum and alternating stress intensities with frequency shift for node 80204.
77

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 82290 4000 3500 3000 2500 CJ) 2000 (U
1500 1000 500 0
                -10              -5                0                   5                10 Frequency Shift [ % ]
Figure 18d. Variation of maximum and alternating stress intensities with frequency shift for node 82290.
78

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 86424 4000 3500 3000 0~       2500 (j~
C 0) 4-,
2000 C
w (0
a, L..
1500 1000 500 0
                -10              -5                0                   5                10 Frequency Shift [ % ]
Figure 18e. Variation of maximum and alternating stress intensities with frequency shift for node 86424.
I 79

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 5.4 Compensation for Additional F1tM Bias a nd Uncertainty Following Revision 2 of this report, an extensive vibration test [15] was performed on the spare Hope Creek Unit 2 steam dryer. The dryer was subjected to shaker excitation at eight different locations and the dryer responses measured using accelerometers at various points on the dryer for peak forcing frequencies in the range 0-250 Hz. The measured response data was compared against response predictions obtained with the ANSYS finite element model and the differences between measured and computed responses used to develop an estimate of the bias and uncertainty associated with approximations, mesh discretization and modeling idealizations in the finite element model. These approximations produce an overall uncertainty of 21.1%. In
*addition, the discrete frequency schedule used in the harmonic analysis is chosen to ensure a maximum error in response peak estimation of 5% which translates into a 5% non-conservative bias error. Note that as explained in [17], it is appropriate to reduce this bias error to 1.72%.
However, because the reduction from 5% to 1.72% is small, no credit for this reduction was taken and the 5% bias was retained in the results presented here and subsequent sections. In Revision 2 and prior versions, neither the 5% bias or 21.1% uncertainty were included in the end-to-end biases and uncertainties applied to the loads. Moreover, these additional bias and uncertainty values are absent in Sections 5.1 to 5.3 above. In the current section 5.4, the
,additional bias and uncertainty values are incorporated along with all the previous biases and uncertainties reflected in previous versions of this report. Thus all end to end biases and uncertainties in the loads and finite element model are fully accounted for in the results below.
In Table 8 the stresses and stress ratios for the nodes listed in Table 7a and b are recomputed with the additional biases and uncertainties for the finite element modeling and frequency discretization factored in. As expected the alternating stress ratios decrease slightly, between 9%
to 10%, due to the added biases and uncertainties. The ordering of the nodes according to stress
*ratio remains unchanged. The smallest maximum stress ratio decreases slightly from 1.58 in Table 7b to 1.56 in Table 8b.
80

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 8b. Locations with minimum stress ratios for CLTP conditions with frequency shifts. Stress ratios at every node are recorded as the lowest stress ratio identified during the frequency shifts. Stress ratios are grouped according to stress type (maximum - SR-P; or alternating - SR-a) and location (away from a weld or at a weld). Bold text indicates minimum stress ratio of any type on the structure. Locations are depicted in Figure 15.
Stress  Weld                     Location                   % Freq.          Location (in.)                    Stress Intensity (psi)    Stress Ratio Ratio                                                         Shift      x          y           z     node    Pm      Pm+Pb       Salt SR-P      SR-a SR-P     No     1. outer portion ofinner hood (top near       -10      109.0      -27.6       95.3   44886   6504      9279      1164  2.81     10.62 closure plate)
SR-a    No     1. outer vane bank perforated entry plate    -7.5         1.8       85.9      27.6   61564    221      4007      3952  6.85      3.13
: 2. outer vane bank perforated entryplate      -7.5         2.2       85.9      63.0   61581    247      3849      3807  7.13      3.25
            . 2. closure plate/inner hood                    -10     -108.4      -27.9       94.9   88252   5729      8490      1936  1.76      3.55
: 3. cover plate/outer hood                     -7.5      -59.1     -101.'4       7.5   93288   2010      6841      2683  2.21      2.56
: 4. central base plate/inner vane               -10     -118.8        14.4       7.5   85994   4143      5692      <500  2.43     >13.7 bank/side panel
: 5. inner hood backing bar/closure plate       -7.5     -108.4        38.4       8.1   87035   4100      4280      -1030 2.46      6.67 SR-a    Yes    1. outer vane bank/perforated entry plate    -7.5         1.9       85.9      21.5   82290    224      4133      4060  3.65      1.69
            . 2. middle base plate/middle vane bank         -7.5      -83.4        54.4       7.5   86424    424      4171      3978  3.62      1.73
: 3. perforated entry plate/vane bank           -7.5       99.4        54.4      94.4   82652    694      3761      3565  4.01      1.93 top vertical plate
: 4. middle base plate/middle vane bank         -7.5      -26.2        54.4       7.5   93931    249      3211      3140  4.70      2.19
: 5. outer base plate/outer vane bank           -7.5         0.0     -85.9        7.5   86643    223      3191      3011  4.73      2.28
: 6. end plate/perforated entry plate/middle    -7.5      108.4        54.4      87.1   79914    903      3041      2893  4.97      2.37 side panel
: 7. perforated entry plate/vane bank top         -5      -12.1      -54.4       94.4   93858    501      3111      2889  4.85      2.38 vertical plate
            . 8. hood support/middle vane bank             -7.5      -54.5        54.4      18.6   84068    431      2899      2854  5.21      2.41
: 9. endplate/perforatedentryplate/middle       -7.5      108.4        54.4      48.2   79942    782      2925      2725  5.16      2.52 1___ _ 1__side panel                               I         I          I            I      I       I        I_                         I _    I See Table 6a for coordinates description.
82

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 5.5 Compensation for Signal Noise Using 1000# Data The origin of the 80 Hz component is largely due to the amplification of sensor noise and MSL turbulence in the ACM. It can be identified with a 'sloshing' mode where the acoustic pressure varies from negative minimum at one pair of MSL exits to a maximum value at the opposite pair with a zero value near the top of the steam dome. This mode experiences comparatively little damping because it does not produce significant motion at the steam/water interface. Since neither sensor noise nor the non-coherent turbulence constitute acoustic sources, they should not be included in the ACM and associated acoustic loads. The ACM analysis however, does not distinguish between the acoustic and non-acoustic fluctuations in the MSL signals that could lead to sizeable, but fictitious 80 Hz acoustic loads and resulting stresses on the dryer that dominate the response. Removing these fictitious loads in a conservative manner using analysis alone has proven difficult since not only is it difficult to quantify how much of the 80 Hz signal is spurious, but also the remaining part that does represent an acoustic load is subject to amplification because of its proximity (in frequency) to the aforementioned lightly damped 80 Hz sloshing acoustic mode.
To address this problem, data were collected [16] with the system maintained at operating pressure (1000 psi) and temperature, but little (5-8% of CLTP) flow. The recirculation pumps were in operation so that the background plant noise and vibratidns were present. At these conditions the acoustic loads are negligible so that these data, referred to as the 1000# data, originates entirely from non-acoustic sources such as sensor noise and mechanical vibrations.
This information is valuable since it allows one to distinguish between the acoustic and non-acoustic content in the CLTP signal and therefore modify the CLTP loads so that only the acoustic component is retained. The 1000# strain gage signals are filtered in the same manner as
.the CLTP data and are fed into the ACM model to obtain the monopole and dipole signals at the MSL inlets. Since there is negligible flow, these signals are fictitious, i.e., the hoop strains measured by the strain gages are not due to pressure fluctuations, but rather due to noise.
However, under the supposition that these signals are acoustic in origin the hypothetical stresses due to these signals can nevertheless be computed.-
The stress ratios calculated for the 10004 data are summarized in Table 9 for no frequency shift (Table 9a) and with consideration of all frequency shifts (Table 9b). The alternating stress
-ratios are above 4.0 without frequency shift and above 3.58 when all frequency shifts are considered. This value is more than twice the lowest alternating stress ratio (SR-a=1.69) reported in Table 8b resulting from the CLTP data. Moreover, and remarkably, the three lowest alternating stress ratios in Table 8b and in Table 9b (1000# data only) occur at the same nodes on the dryer. This provides strong and direct evidence that the dryer is strongly responsive to system noise and that this noise is a significant contributor to the limiting alternating stress ratios. If one compares the three highest alternating stresses ratios in Table 8b and Table 9b,
*then it follows that noise accounts for approximately 55% of the stress.-
Examination of the accumulative stress PSD curves (Figure 19) for the two lowest alternating stress nodes in Table 9b confirm that the noise represented by the 1000# dAata induces a strong response at 80 Hz. Moreover, comparing against Figure 17 it is evident that the stress response 83

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information artificially induced by noise is a significant (approximately half) contributor to the total stress response as measured in terms of accumulative PSDs.
The stress ratios associated with maximum stresses do not vary significantly and are dominated by the static component associated with deadweight.
To compensate for the non-acoustic noise source represented in the 1000# data, the CLTP MSL inlet pressure signals are modified according to:
P(f)=P 0 (f)*max 0,1- -N(f)                                       (8)
L  Po(f)J where f is the frequency (in Hz), Po(f) is the MSL inlet pressure (monopole or dipole) at CLTP conditions before correction, P(f) is the corresponding post-correction pressure and N(f) and P0 (f) are averaged pressure amplitudes associated with the 1000# data and CLTP data respectively. Specifically, f+1 Po(f)=f       IPo(f)l df                                       (9) where IP0(f)I denotes the absolute value of the complex quantity. Hence P0 (f) is the average amplitude of the CLTP pressure in the +/-1 Hz interval about frequency, f. The same definition, but using the 1000# pressure signal, is used for N(f). Note that this modification leaves the phase information in the original CLTP signal unchanged.
The stresses obtained with this modified CLTP load (i.e., with the noise removed per (8)) are listed in Table 10 for no frequency shift and with all frequency shifts considered. All biases and uncertainties associated with the ACM loads and FEM analysis are accounted for in this table.
The smallest alternating stress ratio taken over all frequency shifts increases from SR-a=1.69 (Table 8b) to SR-a=3.22 and occurs at a different location, the junction between the inner hood and its hood support. Inspection of the results in Table 10b reveals several other items of interest. First, the smallest alternating stress ratio also occurs at a frequency shift of +7.5%,
whereas previously all low SR-a nodes assumed their smallest values at the -7.5% shift.
Moreover, all of the nodes having low alternating, stress ratios at the +7.5% shift lie on the same inner hood/hood support junction. All the other nodes with low alternating stress ratios have their lowest SR-a values at the -7.5% shift (which was the case previously - see Table 8b). The nodes in Table l0b identified with the -7.5% shift are the same as the first three nodes in Table 8b. Of considerable interest is the fact that these nodes are also the same as the ones listed in Table 9 for the 1000# data. This suggests that there may still be a significant component of background and/or sensor noise remaining in the modified CLTP signals that is driving the stresses, i.e., this noise is at least sufficiently strong for these nodes to appear in the stress tables with SR-a<4.
84

This Document Does Not.Contain Continuum Dynamics, Inc. Proprietary Information As previously, the smallest stress ratio of any kind is identified with a maximum stress at a weld. It occurs at the same location as before and assumes a value of SR-P=1.63 which is slightly higher than the SR-P=1 .56 value reported using the unmodified CLTP loads in Table 8b.
The frequency content is examined via accumulative PSD curves (see Figure 20) for the two nodes exhibiting the highest alternating stress ratios in Table 10b. Node 88023 exhibits a
.gradual rise in frequency content over the 39.5 Hz to 42 Hz range. A slight rise in the accumulative PSD of the stress is also evident about 80 Hz. The situation is reversed for the response at node 82290 where the 80 Hz signal produces the largest rise at the -7.5% shift whereas a relatively small response is noticed in the 39.5 z to 42 Hz range. Note too that frequency shifting produces a much stronger change near the 80 Hz rise than at the 39.5 Hz to 42 Hz. This behavior is also reflected in Figure 21 showing the change in maximum and alternating stresses as a function of frequency shift for the two nodes having the lowest maximum stress ratios and the two nodes having the lowest alternating stress ratios in Table 10.
These plots show that: (i) for the nodes with the low maximum stress ratios (Figure 21 a, b), the variation of stress with frequency shift is small because the contribution is dominated by deadweight stresses; (ii) for nodes having the lowest SR-a at the +7.5% frequency shift (Figure 21c), the variation of stress with frequency shift is fairly gradual and the maximum. and alternating stresses are closely aligned since the static contribution is small; and (iii) for nodes having the lowest SR-a at the -7.5% frequency shift (Figure 21d), the variation of stress with frequency shift shows a pronounced peak that is approximately four times larger than at other frequency shifts (this curve closely resembles the one in Figure 18Sd, except that the peak amplitude is lower).
It is germane at this point to allude to the 80 Hz filtering scheme employed in previous versions (Revisions 2 and prior) of this report. There it was argued that one could retain 10% of the dominant 80 Hz signal and still produce a conservative load estimate. With all frequency shifts included, and 90% of the 80 Hz signal removed using a narrow-band notch filter, the lowest alternating stress ratios occurred at nodes 88023, 88020 and 88026. Looking at Table 1Ob, these are seen to be the first three nodes with the lowest stress ratios at the +7.5% shift. In previous revision 2 of this report, the alternating stress ratios at these nodes were 3.58, 3.64 and 3.99 respectively. However, these results did not factor in the 5% frequency discretization bias nor the 21.2% FE modeling uncertainty. When this bias and uncertainty are factored in, the stress ratios become 3.26, 3.32 and 3.64 respectively which happen to agree very well with the results in Table 10b (respective values: 3.22, 3.29 and 3.61) - i.e., the respective stress ratios agree to within 1.3%. Thus for these nodes, the results obtained with the previous approach of filtering 90% of the 80 Hz component in the CLTP signal, are in good agreement with the ones developed here by compensating for noise on the basis of the 1000# data. The current approach
.also predicts other low stress ratio nodes at the -7.5% frequency shift. However, these nodes coincide with those that produced the highest response for the 1000# data (see Table 9b) suggesting that for these nodes there may still be strong contamination by background and sensor noise.  ---
It is also worth noting that similarly good agreement could have been obtained using the previous 80 Hz filtering approach, but with less filtering. In fact, for the same nodes considered in the previous paragraph (nodes 88023, 88020 and 88026), the alternating stress ratios at only 85

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 50% filtering are 3.23, 3.28 and 3.62 respectively which are virtually identical with thevalues in Table lOb and differ only slightly from the values obtained using 90% filtering of the 80 Hz signal. This can be explained by noting that once the 80 Hz signal is sufficiently attenuated, then other locations whose response contains significant contributions from other frequencies will become prominent. This is shown in Figure 22 which shows how the minimum stress ratios vary with the level of filtering. It shows that initially as the filtering level is increased from zero, that the minimum alternating stress ratio increases with filtering level. This is because the stress response for the lowest stress ratio nodes is dominated by the 80 Hz component so that filtering this component reduces stresses. Above 50% filtering however, the line of the smallest alternating stress ratio flattens out as nodes dominated by other frequency components (and thus are unaffected by the 80 Hz filtering) emerge as the alternating stress leaders.
In summary, the lowest stress ratio on the dryer is due to a deadweight dominated maximum stress, SR-P=l1.63. The lowest alternating stress ratio anywhere on the dryer is SR-a=3.22 and occurs at the +7.5% frequency shift. These values account for all end-to-end biases and correspond to CLTP loads adjusted to eliminate non-acoustic content using the 1000# data.
86

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9a. Locations with minimum stress ratios for 1000# load with no frequency shift. Stress ratios are grouped according to stress type (maximum - SR-P; or alternating - SR-a) and location (away from a weld or at a weld). Bold text indicates minimum stress ratio of any type on the structure.
Stress     Weld                   Location                      Location (in.)               Stress Intensity (psi)    Stress Ratio Ratio                                                        x         y         z    node  Pm      Pm+Pb       Salt SR-P      SR-a SR-P-      No     1. outer portion of inner hood           109.0   -27.6        95.3 44886 5812       8290     <500  3.15     >13.7
       .....         (top near closure plate)
SR-a       No                                                   NONE     (All SR-a > 4)
: 2. closure plate / inner hood            108.4     27.9       94.9 85409 4720       6916     <500  2.13     >13.7
              "     3. central base plate/inner vane        -118.8     14.4        7.5 85994 3981       5473     <500  2.53     >13.7 bank/side panel
                  . 4. closure plate/middle side panel/top  -108.4     45.9       95.9 85891 3576       4165     <500  2.81     >13.7 cover plate/top perforated plate
: 5. drainpipe/skirt                        88.2     79.6      -20.5 91083 1860       5244     <500  2.88     >13.7
: 6. inner hood backing bar/closure plate -108.4     38.4        8.1 87035 3415       3596     <500  2.95     >13.7
: 7. cover plate/outer hood                 59.1   101.4         7.5 93493 1385       4932      530  3.06     12.95 SR-a       Yes                                                  NONE     (All SR-a > 4)
See Table 6a for coordinates description.
87

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 9b. Locations with minimum stress ratios for 1000# loads with frequency shifts. Stress ratios at every node are recorded as the lowest stress ratio identified during the frequency shifts. Stress ratios are grouped according to stress type (maximum - SR-P; or alternating - SR-a) and location (away from a weld or at a weld). Bold text indicates minimum stress ratio of any type on the structure.
Stress  Weld                     Location                  % Freq.         Location (in.               Stress Intensity (psi)    Stress Ratio Ratio                                                       Shift      x         y         z    node  Pm      Pm+Pb       Salt SR-P      SR-a SR-P     No  1. outer portion of inner hood                 -10     109.0    -27.6       95.3 44886 6155       8780       645 2.97     >13.7 (top near closure plate)
SR-a     No                                                       NONE    (All SR-a > 4)
: 2. closure plate/inner hood                    -10   -108.4     -27.9       94.9 88252 5120       7586     1051  1.97      6.54
: 3. central base plate/inner vane               -10   -118.8       14.4       7.5 85994 4032       5541     <500  2.50     >13.7 bank/side panel
: 4. coverplate/outer hood                      -7.5      59.1    101.4        7.5 93493 1605       5647     1256  2.67      5.47
: 5. closure plate/middle side panel/top cover   -10   -108.4       45.9      95.9 85891 3674       4291     <500  2.74     >13.7 plate/top perforated plate
: 6. inner hood backing bar/closure plate       -7.5   -108.4       38.4       8.1 87035 3564       3726     <500  2.82     >13.7
: 7. drainpipe/skirt                            +2.5      88.2      79.6     -20.5 91083 1871       5279     <500  2.86     >13.7
: 8. drain pipe/skirt                            -10     117.5    -17.7      -20.9 89375 1570       4807     <500  3.14     >13.7 SR-a    Yes  1. outer vane bank/perforated entry plate     -7.5        1.9     85.9      21.5 82290  168       2295     2200  6.58      3.12
: 2. middle base plate/middle vane bank         -7.5    -83.4       54.4       7.5 86424  366       2312     2114  6.53      3.25
: 3. perforated entry plate/vane bank           -7.5      99.4      54.4      94.4 82652  591       2255     2047  6.70      3.36 top vertical plate See Table 6 for coordinates description.
88

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 1Oa. Locations with minimum stress ratios for CLTP conditions with 1000# load-based noise filtered and no frequency shift.
Stress ratios are grouped according to stress type (maximum - SR-P; or alternating - SR-a) and location (away from a weld or at a weld). Bold text indicates minimum stress ratio of any type on the structure.
Stress  Weld                       Location                           Location (in.)               Stress Intensity (psi)    Stress Ratio Ratio        -                                                     x        y          z    node  Pm      Pm+Pb       Salt SR-P      SR-a SR-P     No    1. outer portion of inner hood (top near          109.0    -27.6       95.3 44886 5975      8495      <500  3.06     >13.7 closure plate)
SR-a     No                                                        NONE   (All SR-a > 4)
              . 2. closure plate/inner hood                       108.4     27.9       94.9 85409 4832      7079       563  2.08     12.19
: 3. central base plate/inner vane bank/side panel -118.8     14.4        7.5 85994 4065      5596      <500  2.48     >13.7
: 4. closure plate/top coverplate/vane side         108.4    -45.9       95.9 91627 3677      4227      <500  2.74     >13.7 plate/perforated plate
: 5. drainpipe/skirt                                 88.2     79.6      -20.5 91083 1917      5400      <500  2.80     >13.7
: 6. inner hood backing bar/closure plate          -108.4     38.4        8.1 87035 3449      3658      <500  2.92     >13.7
: 7. cover plate/outer hood                          59.1    101.4        7.5 93493 1406      5084       649  2.97     10.59
: 8. drainpipe/skirt                                117.5    -17.7      -20.9 89375 1519      4641      <500  3.25     >13.7 SR-a    Yes                                                        NONE (All SR-a > 4)
See Table 6a for coordinates description.
89

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 10b. Locations with minimum stress ratios with frequency shifts for CLTP conditions with 1000# load-based noise filtered.
Stress ratios at every node are recorded as the lowest stress ratio identified during the frequency shifts. Stress ratios are grouped according to stress type (maximum - SR-P; or alternating - SR-a) and location (away from a weld or at a weld). Bold text indicates minimum stress ratio of any type on the structure.
Stress  Weld                    Location                 % Freq.        Location (in.)                Stress Intensity (psi)    Stress Ratio Ratio                                                     Shift     x          y         z    node   Pm Pm+Pb            Salt SR-P      SR-a SR-P.. No    1. outer portion of inner hood (top near   -10     109.0    -27.6        95.3 44886  6130      8734       614  2.99     20.14 closure plate)
SR-a     No                                                          NONE (All SR-a > 4)
: 2. closure plate/inner hood                -10    -108.4    -27.9        94.9 88252 5106       7567      1018  1.97      6.75
: 3. central base plate/inner vane           +10    -118.8      14.4        7.5 85994  4080      5609      <500  2.47     >13.7 bank/side panel
: 4. cover plate/outer hood                 -7.5      59.1    101.4         7.5 93493  1613      5664      1269  2.67      5.41
: 5. closure plate/middle side panel/top     -10    -108.4      45.9       95.9 85891 3730       4384      <500  2.70     >13.7 cover plate/top perforated plate
: 6. drain pipe/skirt                        +10      88.2      79.6      -20.5 91083 .1960      5543      <500  2.72     >13.7
: 7. inner hood backing bar/closure plate   -7.5    -108.4      38.4        8.1 87035 3655       3836       602  2.75     11.42
: 8. drainpipe/skirt                         -10     117.5    -17.7       -20.9 89375  1566      4786      <500  3.15     >13.7 SR-a     Yes   1. inner hood/hood support                +7.5           0    36.5       45.9 88023  940       2214      2130  6.82      3.22
: 2. outer vane bank/perforated entry plate -7.5        1.9     85.9       21.5 82290  193       2220      2117  6.80      3.25
: 3. inner hood/hood support                +7.5           0    35.2       57.1 88020  961       2145      2091  7.04      3.29
: 4. middle base plate/middle vane bank     -7.5     -83.4      54.4        7.5 86424  398       2232      2032  6.76      3.38
: 5. inner hood/hood support                +7.5           0    37.5       34.7 88026  793       1975      1902  7.64      3.61
: 6. perforated entry plate/vane            -7.5      99.4      54.4       94.4 82652  606       2028      1827  7.44      3.76 bank top vertical plate
: 7. inner hood/hood support                +7.5           0    33.5       68.2 88017  835       2051      1792  7.36      3.83 See Table 6 for coordinates description.
90

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information (node 82290) 600 500  - ------------ --------  -----------
a-        400  ---------------           ----------
CD,                                                                       -7.5% shift
                                                                   ......... no shift U)             ----------------------
300 E         200  ---------------          -----------
100  ---------------------    -----------
0 0                      50           100                          150                             200 Frequency [ Hz ]
Figure 19a. Accumulative PSD of the azz stress response for the 1000# data at node 82290 at
-7.5% and zero frequency shifts.
91

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information a         (node 86424) 600 500  - --------------------- ----------    -----------
CL 400  ---------------
C4,                                                                                --7.5% shift U)
                                                                               ......... no shift 300       ------------------ ----------    -----------
C.)                                                     d ....... ............................................
                                                          , i fl 0.
200                                     I,-              ---------------------------------
100  ---------------         ----------------
0 0                      50                         100                    150                   200 Frequency [ Hz]
Figure 19b. Accumulative PSD of the azz stress response for the 1000# data at node 86424 at
-7.5% and zero frequency shifts.
92

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information a      (node 88023) 400 350 CL 300                       sg.
0)
                                                                                                  *+7.5% shift no shift 250                                                         . .. ... .. ... .. .. .. ... ..
0)
E       200                                                                                         --------------------
E 150                             ------------------- :-----------                            --------------------- -
100 0                   50                             100                             150                         200 Frequency [ Hz ]
Figure 20a. Accumulative PSD of the cyzz stress response for CLTP conditions at node 88023 at
+7.5% and zero frequency shifts.
93

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information a zz (node 82290) 600 500  ---------------
LO 400 C,,                                                                                  -7.5% shift C,)                                                                  ......... no shift W) 300         ----------------                            -- -- --- -- - - . ---
200  ----------------------
E E3
                                             ......... 4 ........... ...........................................
100                                                             ------------------------
0 0                      50                     100                            150                           200 Frequency [ Hz]
Figure 20b. Accumulative PSD of the azz stress response for CLTP conditions at node 82290 at
-7.5% and zero frequency shifts.
94

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 88325 1 104 8000 6000
                                          -Maximum        Stress Intensity U)
                                     ......... Alternating Stress Intensity Ui) 4000                                                                                    ---
Ui) 2000 ml=mm~i ---------------------- ------------   ---------------------
m==m=*==m=
0
                   -10                   -5                  0              5                     10 Frequency Shift [ %]
Figure 21a. Variation of maximum and alternating stress intensities with frequency shift for node 88325.
95

This Document DoesNot Contain Continuum Dynamics, Inc. Proprietary Information Node 88252 8000 7000 6000 5000
                                       -   Maximum Stress Intensity                   I CD 4000                                       -Alternating Stress Intensity            ---
u 1) 3000 2000 1000      . . ..
                        *i     . . . a& . . . .. . . . . .. *....................       , . . . ..............
mm*=
w-      n                                         - -
0
                   -10                -5                     0                          5                       10 Frequency Shift [ %]
Figure 21 b.
Variation of maximum and alternating stress intensities with frequency shift for node 88252.
96

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 88023 2500 2000 C',
1500 U) 1000 500 0
                    -10           -5               0                 5               10 Frequency Shift [ % ]
Figure 21c. Variation of maximum and alternating stress intensities with frequency shift for node 88023.
i 97

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Node 82290 2500 SMaximum Stress Intensity m
                                              ......... Alternating Stress Intensity 2000 F 0~
1500 C
                           - - -- - - - - - -I-- - - - - - - - - - -                    - - - - -    - - - - -    -  - - - - - - - - -
C w
ci, 1000                           -.                                                    '
L.
500                                ,. _ _ . . . . . . . . . . . . .. . .  .        .   . .    . ., . *    . .   = = . .
0
                    -10                    -5                                     0                            5                       10 Frequency Shift [ % ]
Figure 21d. Variation of maximum and alternating stress intensities with frequency shift for node 82290.
98

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Reduced Point Set for Nodes with SR-a<4
                                              @ 0 and 90% Filtering 4.5 1~~~                                    liiii 4
3.5 58 S
i.; ......&deg;        ...........
3        S            -----------      ---                     ----------
: 0)               S E
2.5 S
0 0
0 2                                                              ----------
1.5                                                   ............
1
                         -0.2   0         0.2         0.4          0.6   0.8         1         1.2 Degree of Filtering Figure 22. Scatter plot of alternating stress ratio versus degree of filtering in the 80 Hz notch filter previously used in Revision 2 of this report. Each point corresponds to the lowest stress ratio at any frequency shift computed for a given node at a specified filtering level (previously 0.9 or 90% filtering was used). The set of nodes used to generate the plot is the reduced point set (i.e., all nodes are separated by at least 10 in) having stress ratios less than 4.0 at 0% or 90%
filtering. Note that the stress ratios in this plot were generated without accounting for the 5%
frequency discretization bias or the 21.2% FEM uncertainty. When these are included the stress ratios decrease by approximately 10%.
99

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information 5.6 Extended Power Uprate Stress Ratios (3))) In addition, it is desirable to scale the CLTP dryer loads to EPU conditions using a methodology that includes the effects of onset of standpipe oscillation should this actually be observed during power ascension in the plant. ((
(3)))
The methodology proceeds by recording pressure data on the main steam lines at 1 / 8 th scale that are at the exact scaled locations in the plant. These pressure data are recorded at CLTP and
*EPU conditions and are documented in [18] and [19] submitted to the staff on 04-30-2007 and 05-24-2007, respectively. ((
(3))) The resulting EPU stresses at these nodes are presented in Table 13. Note that a direct comparison between Table 10b and Table 13 is not possible since additional bias and uncertainty have been added to the EPU analysis as well as only removing the background noise with the 1000# data in the frequency interval 75-85 Hz.
However, it is clear that the minimum stress ratio for alternating stresses at EPU conditions is 2.18 indicating significant dryer stress margin at EPU conditions. At CLTP conditions, the minimum alternating stress ratio is expected to be greater than 2.18 and less than 3.22 if the same biases and uncertainties are applied as used for the EPU estimates.
The biases and uncertainties associated with modeling approximations were recomputed and are summarized in Table 12. In addition, the noise removal strategy using the 1000# data was limited to the frequency range: 80+/-5 Hz. All of these modifications were implemented in the results reported below.                                                                   I 100

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information The stress intensities and associated stress ratios for the nodes listed in Table 1Ob are recomputed at EPU conditions using the revised biases and uncertainties and reported in Table
: 13. The smallest stress ratio in Table 13 is SR-P=1.58 and is identified with a peak stress and occurs at the same location as obtained previously in Table 10b at CLTP. This behavior, together with the high alternating stress ratio at this location, is consistent with the dominance of local stresses by the static load. The lowest alternating stress ratio listed in Table 10b is reduced from 3.22 to 2.18 in Table 13. The smallest stress ratio occurs at a different node. However, the three nodes having the lowest stress ratios in Table 10b all have similar stress ratios (they differ by only 2.1%). These same nodes also have the lowest alternating stress ratios in Table 13 and, again, these stress ratios differ by less than 2.7%. Hence the reordering of lowest stress ratio nodes merely reflects the expected jostling among a tightly grouped (in terms of stress ratio) set of nodes. In terms of frequency shift, all nodes that had the smallest CLTP alternating stress at the -7.5% frequency shift, continue to have the lowest alternating stress ratios at the same shift for EPU. On the other hand, those nodes having the lowest CLTP SR-a values at the +7.5%,
have the 'smallest EPU SR-a values at the +5% shift.
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[II (3)1))
Figure 23. Pressure monopoles by the ACM at the entrances to the four main steam lines, for CLTP conditions: MSL A (top); MSL B (bottom).
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((I (3)))
Figure 23 (continued). Pressure monopoles by the ACM at the entrances to the four-main steam lines, for CLTP conditions: MSL C (top); MSL D (bottom).
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information LI (3)))
Figure 24. Bump-up factor from CLTP to EPU conditions at the entrance to the four main steam lines.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table 13. Locations with minimum stress ratios with frequency shifts for EPU conditions with 1000# load-based noise filtered only over the 80+/-5 Hz range. Stress ratios at every node are recorded as the lowest stress ratio identified during the frequency shifts.
Stress ratios are grouped according to stress type (maximum - SR-P; or alternating - SR-a) and location (away from a weld or at a weld). Bold text indicates minimum stress ratio of any type on the structure.
Stress  Weld                    Location                 % Freq.        Location (in.)               Stress Intensity (psi)    Stress Ratio Ratio                                                     Shift     x          y         z    node  Pm      Pm+Pb       Salt SR-P      SR-a SR-P    No    1. outer portion of inner hood (top near   -10     109.0    -27.6        95.3 44886 6342     9040       946   2.89     13.06 closure plate)
SR-a    No                                                          NONE (All SR-a > 4)
            "    2. closure plate/inner hood                 -10   -108.4    -27.9        94.9 88252 5501      6851      1581  1.83      4.34
: 3. cover plate/outer hood                  -7.5     59.1    101.4         7.5 93493  463      6250      1844  2.42      3.72
: 4. central base plate/inner vane             +5   -118.8      14.4        7.5 85994 4149      5290       286  2.43     23.98 bank/side panel
: 5. closure plate/middle side panel/top       -5   -108.4      45.9       95.9 85891 3801      5959      2099  2.53      3.27 cover plate/top perforated plate
: 6. inner hood backing bar/closure plate    -7.5   -108.4      38.4        8.1 87035 3920      4114       866  2.57      7.93
: 7. drain pipe/skirt                        +2.5     88.2      79.6      -20.5 91083 1995      5620       481  2.69     14.28
: 8. drain pipe/skirt                         -10    117.5    -17.7       -20.9 89375 1634      5066       693  2.98     .9.90 SR-a    Yes   1. outer vane bank/perforated entry plate  -7.5       1.9     85.9       21.5 82290  224      3256      3146  4.64      2.18
: 2. inner hood/hood support                 +5.0          0    35.2       57.1 88020 1377      3254      3100  4.64      2.22
: 3. inner hood/hood support                 +5.0          0    36.5       45.9 88023 1357      3291      3069  4.59      2.24
: 4. middle base plate/middle vane bank      -7.5    -83.4      54.4        7.5 86424  418      3197      3028  4.72      2.27
: 5. perforated entry plate/vane             -7.5     99.4      54.4       94.4 82652  607      2940      2726  5.13      2.52 bank top vertical plate
: 6. inner hood/hood support                 +5.0          0    37.5       34.7 88026 1150      2861      2719  5.28      2.53
: 7. inner hood/hood support                 +5.0          0    33.5       68.2 88017 1181      2947      2703  5.12      2.54 See Table 6 for coordinates description.
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: 6. Conclusions A harmonic steam dryer stress analysis has been used to calculate high stress locations and calculated / allowable stress ratios for the HCI steam dryer at CLTP load conditions using plant measurement data. A detailed description of the harmonic methodology and the finite element model for the HC1 steam dryer is presented. The CLTP loads obtained in a separate acoustic circuit model [2], including end-to-end bias and uncertainty [3], were applied to a finite element model of the steam dryer consisting mainly of the ANSYS Shell 63 elements and brick continuum elements. The resulting stress histories were analyzed to obtain alternating and maximum stresses at all nodes for comparison against allowable levels. These results are tabulated in Table 10 of this report. The minimum alternating stress ratio (SR-a) at the nominal frequency case is 4.38 whereas the minimum SR-a at any frequency shift is 3.22. The most limiting maximum stress intensity stress ratio (SR-P) at the nominal frequency case is 1.63. It remains 1.63 when all frequency shifts are taken. These results account for all end to end biases and uncertainties and reflect the elimination of non-acoustic signals based on the 1000# data
[16].
On the basis of these CLTP plant loads, the dynamic analysis of the steam dryer shows that the combined acoustic, hydrodynamic, and gravity loads produce the following minimum stress ratios:
Frequency             Minimum Stress Ratio Shift            Max.        Alternating Stress,        Stress, SR-P            SR-a 0% (nominal)           1.63           4.38
                               -10%              1.67           3.81
                              -7.5%              1.65           3.25
                                -5%              1.66           4.54
                              -2.5%              1.66           5.06
                              +2.5%              1.65           3.59
                                +5%              1.64           3.49
                              +7.5%              1.63           3.22
                              +10%               1.65           3.52 All shifts       1.63 - 1.67    3.22-5.06 Assuming alternating stresses scale approximately with the square of the steam flow speed, then at 115% CLTP the minimum stress ratios are estimated as SR-a=2.43 (alternating stress intensity) and SR-P=1.57 (maximum stress intensity).
In Revision 4 of this document, for those nodes having the lowest stress ratios at CLTP, the stresses are recomputed at EPU conditions using updated biases and uncertainties summarized in Table 12. The noise removal strategy using the 1000# data is limited to the frequency range 80+/-5 Hz. The EPU dryer loads are scaled from CLTP loads using subscale test data which results in higher loads than simply using the square of the steam flow speed. With the changes made in this revision the lowest stress ratio is due to a maximum stress, SR-P=1.58.' The lowest 107

This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information alternating stress ratio at any frequency shift is SR-a-2.18. Given that the biases and uncertainties in the loads (Table 11) and finite element model (Table 12) are already accounted for, these stress ratios are expected to qualify the dryer with margin at EPU conditions.
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: 7. References 1 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).
: 2. Continuum Dynamics, Inc. (2007). "Acoustic and Low Frequency Hydrodynamic Loads at CLTP Power Level on Hope Creek Unit 1 Steam Dryer to 200 Hz" C.D.I. Report No. 07-18P (Proprietary)
: 3. 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 (Rev. 0)" C.D.I. Report No. 07-09P (Proprietary).
: 4. Structural Integrity Associates (2007). "Hope Creek Main Steam Line Strain Gage Data:
MSL Channel Combinations."
: 5. ANSYS Release 10.0. URL http://www.ansys.com.               Documentation:     ANSYS 10.0 Complete User's Manual Set
: 6. Press, W. H., S. A. Teukolsky, et al. (1992). Numerical Recipes, Cambridge University Press.
: 7. Continuum Dynamics, Inc. (2007). "Stress Analysis of the Hope Creek Unit 1 Steam Dryer at EPU Conditions Using 1 / 8 th Scale Model Pressure Measurement Data (Rev. 2) " C.D.I.
Report No. 06-27 (Proprietary).
: 8. 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.
: 9. 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.
: 10. WRC Bulletin 432 (1998). "Fatigue Strength Reduction and Stress Concentration Factors For Welds In Pressure Vessels and Piping," WRC, NY, p.32
: 11. Pilkey W.D. (1997). Peterson's Stress Concentration Factors, 2 nd ed., John Wiley, NY,
: p. 1 39.
: 12. Lawrence F.V., Ho N.-J., Mazumdar P.K. (1981). "Predicting the Fatigue Resistance of Welds," Ann. Rev. Mater. Sci., vol. 11, pp. 401-425.
: 13. General Electric (GE) Nuclear Energy (2003). Supplement 1 to Service Information Letter (SIL) 644, "BWR/3 Steam Dryer Failure," September 5, 2003.
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: 14. Tecplot 10 (2004). URL: http://www.tecplot.com. Documentation: Tecplot User's Manuial Version 10 Tecplot, Inc. Bellevue, Washington October.
: 15. Continuum Dynamics, Inc., "Finite Element Modeling Bias and Uncertainty Estimates Derived From the Hope Creek Unit 2 Dryer Shaker Test," CDI Report 07-27P (rev. 0), Dec.
2007.
: 16. Structural Integrity Associates, electronic communication of the Hope Creek MSL SG data taken on November 14, 2007 at 17:43 (data file: 20071114174355.zip) with the plant at normal operating pressure and temperature (920 psig and 527 deg F).
: 17. Continuum Dynamics, Inc., Response to RAI 14.110      2 nd Follow Up, January 2008.
: 18. Continuum Dynamics, Inc., "Estimating High Frequency Flow Induced Vibration in the Main Steam Lines at Hope Creek Unit 1: A Subscale Four Line Investigation of Standpipe Behavior," CDI Report 06-16P, (rev. 2), April 2007.
: 19. Continuum Dynamics, Inc., "Revised Hydrodynamic Loads on Hope Creek Unit 1 Steam Dryer to 200 Hz," CDI Technical Note 07-01P, (rev. 0), February 2007.
: 20. Structural Integrity Associates, Inc. 2007. Hope Creek Strain Gage Uncertainty Evaluation and Pressure Conversion Factors. SIA Report No. HC-28Q-301 (Rev. 1).
: 21. Continuum Dynamics, Inc., "Vermont Yankee Instrument Position Uncertainty," Letter Report dated 01 August 2005.
: 22. Exelon Nuclear Generating LLC, "An Assessment of the Effects of Uncertainty in the Application of Acoustic Circuit Model Predictions to the Calculation of Stresses in the Replacement Quad Cities Units 1 and 2 Steam Dryers (Revision 0)," Document No. AM-21005-008.
: 23. Continuum Dynamics, Inc., Response to RAI 14.66 (c), January 2008
: 24. Continuum Dynamics, Inc., Response to RAI 14.79      3 rd Follow Up, January 2008.
: 25. Flugge, W. (ed.) (1962). Handbookof EngineeringMechanics, McGraw-Hill, p.61-62.
: 26. Blevins R. (1979). "Formulas for Natural Frequency and Mode Shape," van Nostrand-Reinhold Co., p. 261
: 27. ASME (2004). ASME Boiler and Pressure Vessel Code, Section III, Article A-8000, Stresses
   . in Perforated Flat Plates.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Appendix A. Comparison of ANSYS Frequency Predictions Against Analytical Formulas for Flat Plates The computed modal masses affect the response amplitude, and while these masses can be computed using the ANSYS finite element (FE) software, there are no modal mass measurements or analytical solutions they can be compared against. One recourse for assessing bias errors and uncertainties is to consider a geometrically simple structure (e.g., a flat plate) for which analytical solutions for the modal amplitudes, masses, and responses are available.
Predictions of these properties using an ANSYS FE model having the same elements and connections present in the steam dryer model can then be compared against these analytical results thus allowing one to estimate the errors in frequency as a function of response frequency.
Modal analysis was performed for: (i) a rectangular plate simply supported on all sides and with dimensions comparable to the vane bank side panel; and (ii) a rectangular plate clamped on all sides and with dimensions comparable to the section of the middle hood that experienced the lowest alternating stress ratios at SMT EPU conditions with +10% frequency shift. In all cases, the mesh has spatial resolution similar to that used in the steam dryer model and the same element type SHELL63 is employed. For the simply supported plate, simple analytical solutions are available for any aspect ratio. For the clamped plate case, tabulated frequency predictions are available only at selected aspect ratios. Thus, for this case dimensions were chosen to correlate most closely with the steam dryer dimensions while adhering to one of the tabulated aspect ratios.
The material properties used in the finite element model were: Young's modulus, E=25.55 106 psi; density, p=0.284 Ibm/in 3 and Poisson's ratio, v=0.3. Modal frequencies are readily obtained in ANSYS. Modal masses are more difficult to extract due to underlying assumptions regarding the normalization of modes and the absence of analytical modal mass information.
However, since any error in the modal mass will be reflected in the computed frequencies (the modal frequencies depend on the generalized stiffness for the mode and the associated modal mass), the errors in modal frequencies are a good estimate of the errors in modal masses. The comparisons between ANSYS and analytical modal frequency predictions follow below.
Simply SupportedPlate Analytical eigenfrequencies for a plate that is simply supported on all sides is given by [25]:
                                               /7FD(m2n2n 2   ph a      b) where D= 121h 2 ), E is the Young's modulus,.p is the density, h is the plate thickness, a and b denote the plate dimensions, and m and n are modal numbers. For the model of the vane bank side panel, h = 0.375", a = 8.5" .and b = 88.4375". Then: D = 13940.6 Nm, and the lowest.
frequencies and relative errors are (note: m and n are mode numbers):
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Table Al. Comparison of analytical and ANSYS predictions of natural frequencies for simply-supported plate.
m n Analytical frequency, Hz ANSYS frequency, Hz Rel. Error (%)
1 1               464.1                       462.4               -0.37 1 2               476.8                       474.8               -0.42 1 3               498.1                       495.5               -0.52 1 4               527.8                       524.4               -0.64 Thus the errors in computed frequencies are less than 1% and are due to mesh resolution.
ClampedPlate The middle hood is modeled with a plate, clamped on all sides and of thickness h=0.125" and side lengths, a=17.92" and b = 44.8". This corresponds to the section of plate immediately adjacent to the location of high stress in the SMT calculation at EPU with +10% frequency shift.
At this aspect ratio, b/a=2.5, the analytical eigenfrequencies are given by [26]:
4J22 Zb2Fp where D = 516.32 Nm and the coefficients ,*, the lowest frequencies and relative errors are shown in the table below.
Table A2. Comparison of analytical and ANSYS predictions of natural frequencies for clamped plate.
ij    ,Y     Analytical frequency, Hz     ANSYS frequency, Hz Rel. Error (%)
1  1   147.8              82.69                       82.98                0.35 1  2   173.9              97.29                      96.01                -1.32 1  3   221.5              123.92                     121.14               -2.03 1  4   291.9               163.3                     158.73                -2.8 The mesh used to calculate plate eigenfrequencies and the mesh on the steam dryer model are shown below.
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                                     /
10-00 "Left- mesh on the flat plate model for eigenvalue comparison calculations;right - mesh on the actual steam dryer FE model. The size of elements in both models is kept similar.
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Appendix B. Comparison of Transient and Harmonic Simulations for the Browns Ferry Unit 1 Dryer (3)]
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Figure 25a. (('3)l 117

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Figure 25b. ((
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(3)))
Figure 26a. (((3)))
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information (3)]j Figure 26b. ((
(3)))
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Er (3)jI Figure 26c. ((                                                                                 (3)))
(3)))
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information rE Figure 26d. [ [                                                                                (3)))
(3)))
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This Document Does Not Contain Continuum Dynamics, Inc. Proprietary Information Appendix C. Structural Modeling of Perforated Plates Modeling the perforated plates in the steam dryer assembly explicitly is computationally prohibitive and an alternative approach is adopted where the plates are characterized by modified material properties adjusted to match the key static and dynamic behavior. This Appendix summarizes the modeling method employed and its verification against measurements.
The perforated plates used in the steam dryer assembly are very thin, i.e. the ratio of thickness and pitch of perforation is less than unity so that the effective properties provided in ASME B&PVC, [27], for thick perforated plates cannot be used. Therefore, to model the steam dryer we have adopted the effective material properties reported by O'Donnell in [8] which
,directly apply to the bending of thin plates. In his work the effective properties are calculated by equating an average stress field over the periodicity cell in a perforated plate. Thus, for a given static loading the solid plate with the effective or modified material properties will yield a similar stress field as the perforated plate with original material properties. Comparisons are made against the values provided in ASME Code [27], as well as to experimental data where good agreement is obtained.
In order to apply these results to the steam dryer analysis the staggered 450 perforation was approximated with an equilateral staggered 600 perforation. The difference was judged insignificant for modeling purposes. The effective properties were therefore inferred from Fig. 8 (Young's modulus) and Fig. 9 (Poisson ratio) of [8].
Verification (3)))
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((
Figure 27. ((
(3)))
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Figure 28. ((                                                                        (3)))
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