ML20212Q626
| ML20212Q626 | |
| Person / Time | |
|---|---|
| Site: | Big Rock Point File:Consumers Energy icon.png |
| Issue date: | 08/29/1986 |
| From: | Campbell R, Maslenikov O, Salmon M NUCLEAR TRANSPORT & STORAGE, INC. |
| To: | |
| Shared Package | |
| ML20212Q619 | List: |
| References | |
| 86-1548, NUDOCS 8609050320 | |
| Download: ML20212Q626 (77) | |
Text
{{#Wiki_filter:. s ATTACHMENT Consumers Power Company Big Rock Point Plant Docket 50-155 THERMAL STRESS FATIGUE ANALYSIS OF BIG ROCK POINT EMERGENCY CONDENSER OUTLET N0ZZLE August 29, 1986 8609050320 860829' ~ PDR ADOCK 05000155 P PDR. 78 Pages IC0886-0139-NLO4
a Technical Report No. 86-1548 THERMAL STRESS' FATIGUE ANALYSIS OF BIG ROCK POINT EMERGENCY CONDENSER OUTLET N0ZZLE Prepared for Consumers Power Company Big Rock Point Nuclear Station Charlevoix, Michigan Prepared by R.D. Campbell M. Salmon
- 0. Maslenikov l NTS Engineering
- 6695 East Pacific Coast Highway Long Beach, California 90803 August 1986
. . _ , _ _ , . , ,_ _--e . - - - - - - -w - - - - - -- --
TABLE OF CONTENTS Section Title Page 1 INTRODUCTION . . . . . . . . . . . . . . . . . 1-1 2
SUMMARY
OF RESULTS . . . . . . . . . . . . . . 2-1 3 SELECTION OF N0ZZLE ............. 3-1 4 THERMAL ANALYSIS . . . . . . . . . . . . . . . 4-1 i 4.1 Computer Code . . . . . . . . . . . . . . 4-1 4.2 Analytical Model ............ 4-1 4.3 Thermal Transient ........... 4-4 4.4 Thermal Results . . . . . . . . . . . . . 4-5 5 STRESS AND FATIGUE ANALYSIS ......... 5-1 5.1 Description of Finite Element Model . . . 5-1 5.2 Computer Code . . . . . . . . . . . . . . 5-2 5.3 Loading Events and Stress Results . . . . 5-2 5.4 Fatigue Analysis ............ 5-5 REFERENCES APPENDIX A i
1 1548 4
- 1. INTRODUCTION I
NUREG-0828 describes issues that require resolution for continued opera-tion of the Big Rock Point Nuclear Power Station. Issue 90 requests tnat a fatigue analysis be conducted for one nozzle and one pipe element in the primary coolant pressure boundary. This report describes a thermal stress fatigue analysis conducted for the emergency condenser outlet nozzle. A piping element fatigue analysis is being conducted by the utility staff. There were three candidate nozzles considered for fatigue analysis, the steam drum feed =ater nozzle, the emergency condenser outlet nozzle, and the emergency condenser condensate return nozzle at the steam drum. The steam drun: feedwater nozzle shown in Figure 1-1 is eight inches nominal pipe size, and experiences a negative thermal transient during plant scram that initiates at about 370* F and goes to about 125' F in about 30 minutes. The nozzle is constructed of A105 Grade II carbon steel and is welded into a carbon steel steam drum. An austenitic stainless steel thermal shock liner is attached to the nozzle that protects the nozzle from severe thermal shock. The emergency condenser outlet nozzle shown in Figure 1-2 is four inch nominal pipe size. The nozzle is type 304 L stainless steel and welds
- into a carbon steel water box in the emergency condenser. A carbon steel piping stub is attached to the nozzle and there is not a thermal shock liner employed in this nozzle. Upon reactor scram, the nozzle experiences a sudden positive transient from about 126' F to about 592*
4 F, then a slow decay in the temperature to about 210' F in about three 3 hours. 1-1
. 1548 The condensate return nozzle, shown in Figure 1-3, is four inches nomi-nal pipe size and is very similar in geometry to the feedwater inlet nozzle with the exception that the nozzle is constructed of an Inconel alloy as opposed to carbon steel. A stainless steel thermal shock liner is used in the nozzle. It experiences the same thermal transient as the emergency condenser outlet nozzle.
Other loadings on the nozzles are operating pressure of 1435 psig and piping reaction loading from dead weight and restraint of thermal expan-sion. Consumers Power provided dead weight and thermal expansion loads-from their piping analyses. Stresses resulting from pressure and normal operating piping loads are small in comparison to stresses produced by thermal shocks, thus, the selection of a nozzle for detailed fatigue analysis is based upon the severity of thermal stress. The objective of the study was to determine the fatigue usage for the most critical nozzle. The anticipated number of transient cycles determined by Consumers Power for each of the candidate nozzles are specified in Reference 5 to be: Emergency Condenser Outlet Nozzle. - 126 cycles Condensate Return Nozzle - 126 cycles Steam Drum Feedwater Nozzle - 288 cycles The governing usage factor must account for the severity of the thermal transient as well as the total number of cycles. 1-2
l I w v I i 9.125" I.D. 15.469" 0.D. -
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l Figure 1-1. Steam Drum Feedwater Nozzle 1-3
l , 3 r l I
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i I + 4.500" 0.D.-* l l i i Figure 1-2. Emergency Condenser Outlet Nozzle i 1-4 L i
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- FLOW 5.00 ".I.D. 9.25 " 0.D.
f v v Figure 1-3. 4" Condensate Return Nozzle 1-5 t
i 1548
- 2.
SUMMARY
OF RESULTS A finite element thermal stress analysis and a fatigue usage calculation in accordance with NB3222.4 of the ASME code, Reference 1, was conduct-ed. The most critical nozzle was determined to be the emergency con-denser outlet nozzle. The heat transfer and stress analysis models were axisymmetric about the nozzle centerline. An axisymmetric model is justified since the dominant fatigue producing stress is from axisym-metric thermal transient loading. The maximum stress range occurs at the junction of the stainless steel nozzle and carbon steel water box on the inside surface. Cyclic loadings applied to the axisymmetric model included the thermal transient resulting from a reactor scram, pressure loading and thermal expansion loading from attached piping. The finite element stress calculations were conducted using ifnear elastic material models and the results were modified to account for strain concentrations due to in-elastic response. Specifically, the local thermal stresses were modf-fied to reflect the modified Poisson's ratio as specified in NB 3227.6. The finite element model was sufficiently accurate to compute primary, secondary and peak stresses resulting from thermal, pressure and exter-nal piping loading assuming idealized geometry. In order to account for the notch effects in the weld the K ,i K2 and K3 stress indices from Table NB 3681(a)-1 of the code were used for the case of a branch con-l nection. The stress indices were used as stress concentration factors and were applied to all components of stress. l Resulting stress components on the inside surface from the three loading l events, including stress concentration factors were: l i i , 2-1 l l
- _ _ _ . _ _ - -_ - . . _ - . . - . - - - - _ _ _ _ . . . - - - _ . . . _ , _ _ - - . _ _ _ _ . . ~ . . . . . . _ _ _ __ _ _ _ . . _ _ _ _ _ _ - . _ _ _ _ _ _ _ . _ .
1548 St KSI S2 IKSI) S3 IKSI) S12 IKSII (Radial) (Meridonal) (Hoop) (shear)
-9.70 -289.32 -242.16 -5.91 The principal stresses are:
oy = -9.S8 a 2
= -289.44 o3 = -242.16 The alternating stress intensity computed from principal stress differ-ence is:
Sa = 1/2 -289.44 - (-9.58 = 139.93 ksi Applying the ratio of the cold to hot modulus, the alternating stress intensity for fatigue evaluation is: Sa=[E h (Sa) Sa = h (139.93) = 155.97 ksi i The allowable number of cycles was interpolated from Figure 19.2-1 of the code to be 427. Seismic reaction of the attached piping were not factored into the fatigue analysis. For the SEP plan,ts, only a safe shutdown earthquake 2-2
^
1548 is specified which is classified as a Level D service loading event. The ASME code does not require Level D service loads to be considered in the analysis for cyclic operation. All assumptions made in the analysis are considered to be conservative, thus, the calculated design life of 427 cycles is considered to be con-i servatfve. The fatigue curve of Figure I 9.2-1 is a very shallow plot of log of al ternating stress vs. log of number of allowable cycles. A small decrease in stress will significantly increase the number of allowable cycles. The principal conservatisms inherent in the fatigue analysis result from two sources:
- 1. The maximum temperature of the transient was assumed to be the steam temperature entering the emergency condenser. The thermal shock ramp was also assumed to occur in four
! seconds,the time required to change one volume of water in the l water box at the maximum flow rate of 217 gpm. A detailed I thermal systems analysis would likely show a reduction in emergency condenser outlet temperature and a reduced ramp rate.
~
- 2. The film coefficient used fn the thermal analysis was appro-priate for the outlet pipe in the nozzle. At the point of l critical stress, the bulk flow velocity is less and the resul-ting film coefficient and corresponding thermal shock should be less, al though, local turbulence may result in a film coefficient nearly as high as that used in the analysis.
l , t 2-3 l
. 1548
- 3. The use of stress indices for branch connections in conjunc-tion with finite element analysis may be conservative for evaluating notch effects in the weld. The weld region may have been ground flush prior to the application of weld over-lay, in which case, smaller stress indices are more appropri-ate.
If the allowable number of cycles calculated are anticipated to be exceeded during the plant lifetime, the alternatives other than replace-ment are:
- 1. Conduct a systems thermal analysis to more accurately deter-mine the thermal transient experienced by the emergency con-denser outlet nuzzle. Update the thermal stress fatigue analysis with the transient defined by the systems analysis.
A scaling of existing finite element stress results can approximate the increased fatigue life without the necessity of rerunning the detailed thermal and stress analysis over.
- 2. Perform in-service inspection per the requirements of Section XI of the code and perform a flaw evaluations if cracks are found. If no cracks are found, flaw evaluation procedures may be used to determine the next required inspection interval, assuming a minimum size undetected flaw. Depending upon the timing of the scheduled ISI, this may be a preferred option.
Any unscheduled ISI should be compared in cost to Option 1. 2-4
1548
- 3. SELECTION OF N0ZZLE A direct comparison of the scram thermal transients for the feedwater and condensate return nozzles in the steam drum indicates that the condensate return nozzle experiences a much more severe thermal tran-sient both in temperature change rate and in the magnitude of tempera-ture change. Both nozzles are of similar design except for the dissimi-lar materials in the condensate return nozzle. Based on a simple comparison of the temperature transient range, the thermal stress in the feedwater nozzle is expected to be about 50% or less than the thermal stress in the condensate return nozzle. In the range of the number of applied cycles, the design fatigue curve would project a design life nearly ten times as great for the feedwater nozzle. Thus, the feedwater nozzle was eliminated as a candidate for further consideration.
The condensate return nozzle and the emergency condenser outlet nozzle both experience identical thermal transients. The emergency condenser outlet nozzle does not have a thermal shock liner, thus, would exper-ience the greatest surface stress, but, it was not clear by examination of geometry and thermal transients that the attachment of the shock liner in the condensate return nozzle would not experience a more severe fatigue environment when cor.sidering the gross temperature differences i between the shock liner and the nozzle and appropriate stress concentra-
- tion factors for the corner weld joint of the liner to the nozzle. It was therefore decided to conduct a thermal analysis of the two nozzles, using a coarse mesh model, and compare the temperature responses before selecting a final candidate nozzle for detailed thermal stress fatigue analysis.
Thermal models of the two candidate nozzles are shown in Figure 3-1 and 3-2. The basis for selecting the final nozzle was a comparison of temperature differences for two basic conditions. i 3-1
1548
- 1. Surface temperature vs. temperature at center of wall
- 2. Bulk temperature between the attached pipe and the nozzle or between the nozzle and the vessel wall.
A third condition was examined and that was the temperature difference between the thermal shock liner and the condensate return nozzle. Thermal stresses were then approximated by the simple equation: 3 ,EaAT 1-v where S is thermal stress, psi E is Young's modulus, psi a is the instantaneous coefficient of thermal expansion, in/in
'F AT is the above stated temperature difference v is Poisson's ratio.
For cases where dissimilar metals are involved, the equation is stated as: E(a,T,-aT) bb S= 1-v where subscripts a and b denote the materials a and b T is temperature, 'F a is as defined above 3-2
1548 l These equations are very approximate for complex geometries but serve as ' a gage for se'ecting the most critical nozzle. As expected, the emer-gency condenser outlet nozzle would experience the largest thermal stress by a significant margin and was selected for a detailed finite element thermal-stress-fatigue analysis. l l 3-3 l
. N0DAL POINT TYP.
BOUNDARY TYP. N0DE 1 TYP. CONDUCTOR I I
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TYP. CONDUCTOR l BOUNDARY N0DE 2 Figure 3-1. Condensate Return Thennal Model l l 3-4 l
BOUNDARY N0DE TYP. CONDUCTOR n o o . . - - - -
% TYP. CONDUCTOR BOUNDARY NODE TYP.
W , . . TYP. CONDUCTOR
*N0DAL POINT o e <
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l l l l l Figure 3-2. Emergency Condenser Outlet Nozzle 3-5
. 1548 l
- 4. THERMAL ANALYSIS 4.1 Computer Code The thermal transient analysis for the emergency condenser outlet nozzle subjected to a scram transient was conducted using the computer code ITAS (Reference 2) on an IBM PC-AT. ITAS (Interactive Thermal Analysis System) is a general purpose finite difference code for steady state and transient analysis of conduction, convection, and radiation heat trans-fer problems. The transient conduction capability of ITAS was utilized in the thermal analysis of the emergency condenser outlet nozzle. This capability has been independently verified by comparison to solutions by other finite element and finite difference codes.
4.2 Analytical Model The thermal mesh was constructed to be compatible with the mesh used in the finite element stress model. Figure 4-1 shows the detailed thermal analysis model. Nodal point numbering on the thermal model corresponded with nodal point numbering on the stress model. The model is symmetric about the nozzle centerline. The water box to nozzle junction is of three-dimensional geometry; however, for purposes of calculating thermal gradients applicable to the axisymmetric finite element stress model, the water box portion of the model is conveniently modeled as a flat annular plate. Node 260 is a boundary element that represents the fluid temperature in the emergency condenser water box and outlet nozzle. All surface nodes which are in contact with water are connected to node 260 by a conduct-ance representing the film coefficient for water flowing in a pipe. The conductance is defined by: . 4-1
1548 C = RA where h is the convective film coefficient and A is the effective sur-face area of the node. The film coefficient, h was computed for water flowing in a pipe (Refer-ence 3), from the equation: 0 0 6 = 0.023 Re .8 Pr .3 where Re is the Reynolds number (Dimensionless) Pr is the Prandt1 number (Dimensionless) k is the thermal conductivity of the water hr ft UF D is the diameter of the pipe, ft. Maximum flow specified by Consumers Power Company was 217 gom early in the transient. The film coefficient, h for 217 gpm flow, was computed to be 1986 Btu /hr ft2 .F in the nozzle. A value of 2000 was used in the analysis. 1 Surface nodes that are connected to node 260 are defined as arithmetic nodes which have no capacitance, i.e., all heat that enters flows out. j All interior nodes and nodes on the air side of the nozzle are repre-l sented as diffusion nodes, i.e., nodes that have thermal capacitance l equal to their mass times their specific heat. Adiabatic surfaces (no heat loss or gain) were defined at the termination points of the model and on the air side of the model. 4-2
, 1548 Constant thermal properties are required in the ITAS analysis. Proper-ties for 100* F were used which will result in conservative predictions of temperature gradients. This can be demonstrated by examining trans-fent response charts as shown in Figure 4-2. Figure 4-2 plots the maximum value of the difference between the thermal shocked surface temperature and the mean wall temperature, as the Fourier Modulus for varying values of a parameter containing the thermal diffusivity, (a).
As the thermal diffusivity, (a), increases, the difference between the thermal shock surface temperature and the mean wall temperature (To-Tavg) of the slab decreases. The temperature difference (To-Tavg) is a direct measure of thermal stress. Thermal diffusivity values were taken from the ASME code, Section 3 appendices, Reference 1, and for both the stainless steel nozzle and carbon steel water box show an increase with temperature. The arithmetic nodes and diffusion nodes are connected with conductors defined as: C = [kA-- where k is the thermal conductivity, Btu /hr ft *F A is the area of the conductivity path, ft2 L is the length of the conductor, f t. Values of conductivity were taken from the ASME code, Section 3 appen-dices. All geometric properties of the thermal model are defined by considering the nozzle axis as an axis of revolution and computing areas and volumes using circular coordinates. 4-3
. 1548
)
l l A mesh generation routine was written to generate the ITAS model proper- l ties with coordinates exactly compatible with the finite element stress model. Checks were then made by hand to verify that all different algorithms for generating conductances and capacitances by computer were l Correct. 4.3 Thermal Transient The emergency condenser outlet nozzle is subjected to a typical thermal transient shown in Figure 4-3' during a reactor scram. The temperature recording device in the line connecting the emergency condenser outlet to the steam drum condensate return nozzle limits out at 400* F and the transient peak beyond 400* F was conservatively upper bounded at the 592* F emergency condenser steam inlet temperature. There is undoubted-ly some cooling of the condensate before it leaves the emergency con-denser, thus, the transient used in this analysis is conservative. Temperature recordings are not definitive enough to know the exact rate of temperature increase from 126* F to 592* F. For purposes of the thermal shock analysis, the rapid temperature rise was conservatively assumed to occur in four seconds. This is the approximate time required t to clear the residual water in the water box at the maximum flow rate of 217 gpm. During normal operation, the emergency condenser remains essentially at ambient temperature, thus there are no significant cyclic stresses created by temperature changes in the dissimilar metals used in nozzle and water box construction or by restraint of piping thermal expansion. The scram transient is the only significant stress producing transient event. l 4-4 l
i 1548 4.4 Thermal Results ; i From previous screening runs on coarser models, it was determined that the maximum thermal stresses would occur during the first minute. Therefore, the detailed model transient was run for a total of one minute. The explicit solution option of ITAS was utilized wherein the code selects the time step to assure both stability and accuracy. The minimum stable time step is the minimum value of the capacitance of a node divided by the sum of the conductances leading into the node. A time step smaller than the minimum stable time step is selected for analysis. Isotherms were plotted for 3 sec, 6 sec, 9 sec,12 sec,15 sec,18 sec, 21 sec, 30 sec, 45 sec and 60 seconds. These plots are shown in Figures 4-4 through 4-13. These isotherm plots were used to select thermal transient cases for stress analysis. From the plots it is observed that the maximum bulk temperature differ-ence between the carbon steel water box and the stainless steel cladding occurs at about 12 seconds. The maximum bulk temperature difference between the nozzle and attached pipe occurs at about 12-15 seconds. Frcm the thermal contour lines, the maximum bulk temperature difference , between the stainless steel nozzle and the carbon steel water box is not severe and occurs at between about 15-18 seconds. The maximum tempera-ture difference between the surface and the average of the nozzle will occur in the first 15 seconds, thus, time slices selected for finite element analysis were 9 seconds,12 seconds,15 seconds and 18 seconds. 4-5
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1548
- 5. STRESS AND FATIGUE ANALYSIS 5.1 Description of Finite Element Model An axisymmetric finite element model of the emergency condenser outlet nozzle was constructed with the axis of symetry along the nozzle axis.
The cyclic fatigue producing stresses are almost totally dominated by the scram thermal transient and an axisymetric representation of the nozzle is justified as sufficiently accurate to compute peak thermal stresses on the inside surface. As will be shown, the most critical region in the nozzle is at the weld joint between the nozzle and the water box. Asymetric pipe bending loads produce very low stresses and the treatment of the asymetric loads as equivalent axisymetric loads does not comprise accuracy in computing fatigue life. The water box is modeled as a spherical shell with radius equal to twice the radius of the cylindrical water box. With this modeling feature, the membrane stresses in the spherical water box model produced by pressure will be equivalent to the hoop stresses produced in the cylin-4 drical water box by pressure. The finite element model is shown in Figure 5-1. Boundary conditions are applied on the termination points to represent the structural behavior of a continuous model. At the termination of the water box model, nodes 281 to 289, the nodal points are restrained so that displacements must follow a radial path from the center of the spherical surface. Rotation of the free end is not allowed. At the termination of the pipe model, nodes 266-271, rotation of the pipe is restrained. l 5-1
1548 Material properties are varied with temperature. Material properties were obtained from Reference 1 and include the modulus of elasticity, E, and coefficient of thermal expansion, a. 5.2 Computer Code The computer code SUPERSAP (Reference 4) was used to conduct the stress analysis. SUPERSAP is a derivative of the SAP IV computer code that has been adapted for use on micro and mini computers. It was developed and is maintained by Algor Interactive Systems. The program was utilized on an IBM PC-AT micro computer system. Sample problems for thick cylinders subjected to severe thermal transients have been compared between SUPER-SAP, ANSYS and NTS' MODSAP computer program with all results agreeing. The heat transfer capability of SUPERSAP was limited to steady state solutions, thus, SUPERSAP was used for the' stress analysis only. 5.3 Loading Events and Stress Results Three sources of loading iere applied to the nozzle model, pressure, external piping reaction and thermal transients. Pressure of 1435 psig was applied to the inside surface of the nozzle and water box. As discussed previously, the radius of the spherical model of the water box was taken as twice the water box cylinder radius so that pressure in-duced stresses in the water box model would be representative of actual pressure induced stresses, i.e., the maximum pressure stress in a cylin-der is: where o=f i 5-2
1548 p = pressure r = radius of cylinder t = thickness of cylinder whereas in a sphere the pressure induced stress is computed from: pr
*
- TUC Thus, for the same pressure p, a sphere of twice the radius of a cylin-der will result in the same stress.
Stress intensity contours for the pressure case are shown in Figure 5-2. Stress intensity is defined as the maximum difference between the three principal stresses and is used for comparison to allowable stresses in the ASME code. Note that only surface pressure was applied. The axial force on the pipe due to pressure was included with the equialent axial force for piping reactions. The maximum stress intensity occurs in the nozzle corner and is about 20 ksi. This is a local stress whereas average membrane stress is con-siderably less. Nozzle loading from the attached piping and from the axial component of pressure were simulated by applying an axial unit load of 100 kips to the nozzle. Results were then factored to represent the contribution from pressure and from pipe reactions due to restraint of thermal expan-sion. Table 5-1 shows the calculated nozzle loads for the emergency condenser outlet nozzles. The worst case loading was used. Note that loading due to dead weight is not considered in a fatigue analysis since it is non-
- 5-3
1548 i
; cyclic. The equivalent axial nozzle load due to pressure was computed to be 14.81 kips and the equivalent axial nozzle load due to piping reactions was computed to be 15.85 kips. The equivalent axial load for piping reactions was computed by equating the pipe stress produced by the equivalent axial load to that produced in the piping from the equiv-
] alent bending moment plus the pipe axial load. Results of the 100 kip unit load case were then scaled by factors of 0.148 and 0.156 to deter-mine the stress contributions from pressure induced axial force and piping reactions, respectively. Figure 5-3 shows the stress intensity contours for the 100 kip axial load. Scaling these results to actual loading results in maximum stress intensities of about 3.3 ksi and 3.5 ksi, respectively, for pressure and
- piping reaction loading.
Thermal stress analysis runs were made for times of 9,12,15 and 18 seconds. Stress intensity contour plots are shown in Figures 5-4 through 5-8. The maximum stress intensity occurs at the junction of the i nozzle to the water box at about 12 seconds. This stress is highly localized in the cladding while the bending stress through the water box wall is considerably less. A check on the primary plus secondary stress range reveals that the 3 Sm shakedown Ifmit is met. Thermal stresses at the carbon steel pipe stub to stainless steel nozzle are relatively low even though there is a significant temperature discontinuity. The positive thermal shock produces a severe temperature gradient through the nozzle wall and creates compressive thermal stresses on the inside surface. However, the difference in the average temperatures of the nozzle and the pipe stub creates positive bending stresses on the inside surface, thus, negating some of the effect of the through-the-wall temperature gradient. The net result is that the stress distribution, as shown by the stress contour plots in Figure 4-7, is not nearly as severe as that across the cladding. 5-4 e
--,,,,,,--,w,,-.--4_.,-..,-..,,,n,,a,.,m,,,y-w,,,.,,,,,,--,-,,--,._. - - , - - - . . - . . - . , , - ..,..n,-.,-,,_.. . - , . . , , , , , , , , - . , , _ _ - , , , _ . , _ , - . . , ,
, 1548 I
1 The junction of the w'ater box to nozzle was selected for the detailed fatigue analysis. Detailed stress output was obtained at this location for elements in the region of highest stress intensity shown in the thermal stress contour plot for 12 seconds. Stress output is contained in Appendix A along with the detailed fatigue calculations. 5.4 Fatigue Analysis A fatigue analysis in accordance with NB 3222.4 of the code, Analysis for Cyclic Operation, was conducted. During emergency condenser opera-tion, all of the loadin'g events analyzed are applied simultaneously. Actually, the maximum piping reaction stress will occur at a later point in time than the maximum thermal stress, but, the pipe reaction stress is so small that assuming simultaneous occurrence has only a mildly conservative effect on the calculated fatigue life. During non-opera-tion, the emergency condenser is stress free, thus, a single type of cycle occurs, one from zero stress to a peak stress and returning to zero stress. i t For combined pressure, piping reaction and thermal stress conditions, two conditions must be evaluated. First, the range of primary plus secondary stress must be compared to three times the code allowable stress of 3 Sm. Maximum primary plus secondary stress occurs on the outside surface of the SA 105 carbon steel water box. For the SA 105 Grade 11 water box, at a temperature of about 500* F maximum, Sm from l the ASME code is 19.4 ksi. I If 3 Sm is not exceeded, shakedown to elastic action is demonstrated and the elastica 11y computed stresses are used for fatigue analysis. In ; j order to determine the range of primary plus secondary stress intensity, l 5-5 i I - ______
1548 stress components through the wall must be linearized and the stress intensity computed from the equivalent linear stress components. The linearization is done by computing an equivalent linear bending moment that will result in the same through the wall bending moment as produced by the nonlinear stress distribution in the wall defined by the finite element stress resul ts. The equivalent linear bending stress is computed as: 6M b"7 t where M is the bending moment per unit arc length through the wall from the calculated stress distribution and t is the wall thickness. The moment, M, is computed by taking moments about the center of the vessel wall as: M=Iojj Aj rj where oj ) is the stress component,1, in element j, Aj is the area of the element j normal to stress component,1, rj is the distance form the center of the vessel wall to the center of element j Note that the linearization is conducted for all components of stress. The average membrane stress components, 779, in the wall must also be computed from the calculated finite element resul ts. The average membrane stress og is computed from:
# A 1,j i 1* EA j where the terms are as previously defined. The average membrane plus
! equivalent linear bending stress components are then combined and the l 5-6 l
- 1548 stress intensity computed on the surface for comparison to the 3 Sm shakedown Ifmit.
The maximum stress intensity from membrane plus bending was computed to be 29.9 ksi which is significantly les.; than the 3 Sm limit of 58.2 ksi. The local thermal stress must be modified in accordance with the requirements of NB 3227.6 to reflect a plastic Poisson's ratio. The effective Poisson's ratio is 0.484 as compared to 0.3 used in the elas-tic finite element analysis. The local thermal stress is computed in the finite element program as a function of: o=f(yfy) Therefore, local thermal stress was separated from the stress output and increased by the ratio: R= 1 - 0.3 1 - 0.484 The critical stress occurs in the weld joint between the water box and nozzle. The finite element analysis will compute stresses from pres-sure, piping reactions and thermal transients with accuracy for the idealized geometric surface but will not reflect localized stress con-centrations that arise from the irregular welded surface. Appropriate stress concentration factors are usually derived empirically from exper- , iment or experience. For this analysis, the K stress indices applicable to piping branch connections were applied to the computed stresses. The appropriate indices from Table NB 3681(a)-1 of the code are: Pressure, Ki = 2.0 l 5-7
1548 Piping Reaction, K2 = 1.75 Thermal Stress, K3"I7 Note that the K3 index is applicable to thermal stresses resulting froai bulk temperature mismatch between the nozzle and the water box wall or between the cladding and the water box wall and the equivalent linear through-the-wall thermal gradient and is not applied to local thermal stress. However, examination of the stress contours reveals that the thermal stress results primarily from the large temperature difference between the stainless steel cladding and the carbon steel water box. Therefore, the K3 index was applied to the total thermal stress. The stress indices were applied to all components of stress, i.e., the stress concentration is considered applicable in all directions of
, stress.
The alternating stress intensity for comparison to the fatigue curve, Figure 1 9.2-1, of the code was computed by summing up stress components at the inside surface of the nozzle to pipe weld joint. The inside surface stress components included the effects of the modified Poisson ratio for the local thermal stress and the weld stress concentration effects computed by applying the Ki , K2 and K3 indices. Stress compo-nents were then resolved into principal stresses and the alternating stress intensity, Sa, was computed as: l Sa = 1/2 (stress intensity range) l The computed alternating stress intensity was 139.9 Irsi. Before entering the fatigue curves, the stress intensity must be scaled by the ratio of the cold modulus of elasticity, E, for which the c 5-8
1548 fatigue curves are referenced, to the hot modulus, Eh , used in the stress analysis. The resulting stress intensity for fatigue evaluation is: Sa=[E h (139.9) Sa = h (139.9) = 156 ksi From Figure I 9.2-1 of the code, applicable for austentic stainless steels, the allowable number of fatigue cycles is 427. Appendix A contains selected stress output from the computer analysis and detailed calcul.itions for the fatigue life, i f 5-9
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1548 Table 5-1. Nozzles Loads - Emergency Condenser Outlet from Cyclic Thermal Expansion FORCE (LBS) MOMENT (FT/LBS) F F F x y z M x fy M EAST N0ZZLE 21 -145 66 245 -827 -583 WEST N0ZZLE 5 242 13 -699 -51 982 Fy is axial, Fx+F are z shear My is torsion, M, + M gare bending Equivalentmoment=(M x 2,gy 2 , g,2)1/2 West nozzle is governing case. 1 4 f 5-10 6
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- . ....- 23:
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see ...-- res ! is. ... -- n i i l l l l l l Figure 5-1. SUPERSAP Nozzle Model- Node pt. Numbering 5-11
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4 Figure 5-2. Stress Intensity From Internal Pressure 1 1 20.57
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1548 REFERENCES
- 1. ASME Boiler and Pressure Vessel Code, Section III, Division I, Subsection NB and Appendices, 1983.
- 2. Warriner, R.F., " Users Manual, Interactive Thermal Analysis System, I/TAS," Version 1, Revision 1.1, April 18, 1984.
, 3. McAdams, W.M., Heat Transmission, 3rd Edition, McGraw Hill,1954.
- 4. "SUPERSAP, Finite Element System for Stress, Dynamic, and Heat Transfer Analysis," Algor Interactive Systems, Inc., Pittsburg, PA.
- 5. Popa, N., Consumer Power Internal Correspondence NSP7-86, " Emergency Condenser Usage Factor," August 4, 1986.
9 i R-1
D e e APPENDIX A FATIGUE CALCULATIONS D n - - - , --
TITLE Fe- '" W O" PAGEboFd JOS NO./f! ? T I E Coast He*ev SY DATE HKD. SY Md6 DATE2blA Gt3) 493 6651 COMMENTS e v At.uA u ou or rrem A.rocu Thersta l slre ru ns w ore cedueled a-f 9,12, 15,19 an d 2-( sec. Ers m N chers w/s.,s,f cm 4 u v f fois (f,- h ] ,t(St. f s),(Ts ~.fi ) , me r, A u m
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TITLE E* aeh
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7 el 6 5 East ac < Coast Me ar SY OATE 7- CHKD. SY 7d 4 O ATE"M' Spotems Lon0 Beatn. CA 90003 l ( (213)493 6651 COMedENTS YkYP$.$Pb o Y4 W UI L & SM QCQ k +4enJ m J t = it sw, , pns, n m W W <p J LJ anu lo=/ r, g, p,;. L,s a yk. ( lo.1 m m u.t b Le -F. c % 4 f-<w avn ( y.u u s m p)v .rkb sd kdah ~~+A J gifr rIn h < l C 1 l l . l 1
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- P, b 142 m; g 105 106 107 108 109 110 111 112 I4I i
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,, _127 -1.76EAE_ci s.canir+o6 1.091oE+61 _1_oa7%E+on 1.to7?E+61 138 -3.8953E-01 8.6655E+00 1.0790E+01 -3.0965E-01 1.1190E+01 141 1.8814E-02 8.4219E+00 1.0528E+01.-1.0695E+00 1.0643E+01 141 -2.64217-01 L iE12E+00 1. oEa tE2.Q1_ 3 39CL4E-o f t_0777F+01 157 3.4121E-01 6.9571E+00 9.3110E+00 -2.2203E+00 9.6450E+00 158 3.2713E+00,_6._1340E+00_ 1.0419E+01 -4.8019E+00 1.07EEE+01 -
CUT. UT 15 _*STEL FOR J-V. FA:I
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- 53G1EtCC -
84 1.9031E+00 3.2753E+00 2.5962E+00 -3.2123E+00 6.5635E+00 97 2.7187E+00 4.3505E+00 3.9243E+00 -3.4664E+00 7.1222E+00 tA * *442E+DO _4 6531E+00 _.3 332iE+00 -3.2043Eton - 'o85E*4Q. - ( 111 3.9723E+00 6.9143E+00 5.9845E+00 -5.018EE+00 1.0479E+01 112 2.7375E+00 6.9419E+00 5.6846E+00 -5.93EOE+00 1.2706E+01
-' *354E=D' ' 7793E+C0 _1 L139E+DQ_-2 6330Em01 2 3112E*OC.
114 -1.1934E-03 4.4154E+00 -3.4431E-01 -2.4882E-01 4.7737E+00 117 -1.5005E-01 2.0313E+00 -6.8478E-01 -8.6467E-01 3.0172E+00 tia t.nm4ir ^* A '368E*Do -1 M".Jt0E=D* -7 '546E-n' A K' air +^^ 121 -1.2590E-01 2.4*64E+00 -1.1978E-01 -1.4675E+00 3.9032E+00 122 2.1395E-03 4.4314E+00 3.9370E-01 -1.2769E+00 5.1128E+00 st- t_ne-nc nt 7: 1450 Etch A AM4E-^' -* ^4*wrion =. pin 6F+no 126 9.5104E-03 4.7719E+00 9.8393E-01 -1.8003E+00 5.9704E+00 129 1.6113E-01 3.8564E+00 1.5302E+00 -2.5857E+00 6.3444E+00 tun a_numar n, ._nnoot.co e_meeTr+nn .* ***4EsOQ- 6 6432E*CC. 133 4.7411E-01 4.7391E+00 2.5931E+00 -3.0027E+00 7.3658E+00 134 1.1919E-02 5.3517E+00 2.4086E+00 -2.4245E+00 7.2129E+00 t17 7 4304E=O' " ..5250E+00_ 3.8748E*06 -' *A38Eton a_*nott ,cct 138 -3.3442E-02 5.8290E+00 3.3293E+00 -2.1902E+00 7.3182E+00 141 3.7932E-01 7.5662E+00 5.2734E+00 -2.1881E+00 8.4144E+00
*A*--3:41A2E ^2 a.5233E*00W4&9E*00 -! ^574E*0^ L e377F *00.
157 1.7576E+00 9.0141E+00 6.8833E+00 -4.7699E+00 1.1986E+01 i 158 5.4666E+00 1.1133E+01 8.8341E+00 -7.5951E+00 1.6213E+01 CU73U7 15 LISTED FCA J-K FACE C.E.M N-l."O.T. 5 : 31 NCRMr 5:31 HCCP 5%G3 EnEAA TAU 11.-1NTENE:7f l 141 3.1711E-01 1.14*EE+01 8.1125E+00 -1.*:3sE*00 1.15:0E*01
--14a-.-A 510E E-02-6. 7749E +00.-5. 3607E+00 -6. 5333E-0 4.-0. 4560E +00 157 -4.03 EE*00 1.110*E+01 9.8*766E+00 -3.764EE+00 E.3331E+01 1-0 E.59~r!E-01 1.6430E+01 9.11*0E*00 4.19~5E-01 1.E113E+01 153 -1.113.3-01 -3. 3M32-01 5.6;6*3+00 4. 50.23E-01 6. 965 ~.E +M. -
o A-7 TITI.g Fwr - [LMe [MMPAGE _ OF b JOS NO. l[N., n.u .. ese m 6695 East Pace Coas' mga.av gy M CHMO.By W
- DATE #
feenneest OATE % Systems Lorg Beecn CA 90003 . at31 a93 6elt C04WENTS fd fu MI / * 'l
,J u s ..
**** DUT;UT FCR TYPE-4 ELEMINTS (GA0J" 1)
Lor.o case - 1 s: ALE - 1.0000E+00 ~FM E.R M AL. S Tf EU Os7 POT IS t-!STED F09 L-1-FACE-- St. L ELEM NORMAL SIG1 NO; MAL SIG2 FCCP 5:G2 SHEAR TAU 11 INTENSITY 5,s ____ ___________ ___________ _____, ___ ____ _ _ __ m ____ --- 13 7.171GE-01 -1.0~s212-01 -1.0610E+01 9.3119E-01 1.10065-01 b ' l-14 -4.1166E+00 -1.31762 7 01'-1.1481E*01 7.1E61E+00 1.194 2-0*., "~ A7 4. 3532E+0r.r 3.-2056,E,+01 -8. 6377E+0I-- 4.-0689E+00---9. T66"E+Crr- 3 K 15 -6.2790E+00 -9.5614E+01 -S.7602E+01 8.9612d+00 9.1319E*01 41 -4.5153E-00 -6.3176E+01 -5.91763+01 3.8701E+00 5.9159E+01 4 ,.,..7.I-.00 -i. 2133~ D. -;. M 052*0. ..iiTEE-QQ .E;ZZ-0. 55 -5.1306E+00 -2.9710E*01 -2.7975E+01 1.4664E-00 2.4759E+01 56 -1.0717E+01 -1.31:3E+01 -1.3671E-01 1. 34 *,9E +00 1.3047E+01
---69'=47757tE+00 =4.-6114E+00 -3.'1279E+00'*1rOO47E-Ot 17t604 E+00-70 -8.35"s2E+00 -2.0223E+00 -4.0079E+00 -2.0608E+00 7.5560E+00 .
83 -3.2911E+00 1.2446E+01 1.3508E+01 ~5.1388E-01 1.6817E+01 64 -;.3236;-00 ..;i-355*01 1. 05"4'*07- *2707472+00 . 5;3;E-Oi 97 -2.2879E-00 1.1237E+01 1.1181E+01 - 6. 5669E-01 1.4587E+01 98 -3.3337E+00 2.061*E+01 1.9654E+01 -1.42ESE+00 2.4118E+01 644 -4.346 E=Oi 2.3017E'+0i 2.4768E*01 -2.Oa6tE+00 4.5176Ev0T-( 112 -9.0103E-01 2.4571E+01 2.3727E+01 -5.2008E+00 2.7514E+01 113 -3.2031E+00 -1.3195E+02 -1.1511E+02 -1.8006E+00 1.1987E+02-ii4 6.437;E-0. 19",9E+02- 4 4vr4E*01 1.3;&iE+00 1.2025E-02 117 -5.5685E+00 -1.0013E+02 -8.8199E+01 -2.4510E+00 9.4687E+01 118 -1.1613E+00 -9.5911E+01 -8.5890E+01 2.0618E-01 9.4760E+01 121 -6.i147ETOO -e.22.40E-Oi -;-5672Ev01' 6r196&E-Gi L.7151E-vi 122 -2.5179E+00 -6.3658E+01 -5.4294E+01 -8.3762E-01 6.1163E+01 125 -4.1455E+00 -1.2913E+01 -6.2811E+00 -1.1809E+00 9.0795E+00 1:1 -2.5793E*00 -1.294tE*01--Sr2603E+vv 4.au?E+0L 3.-7300Ee 129 -4.5999E+00 -1.5003E+00 3.4324E+00 -1.1510E+00 8.4130E+00 130 -3.3289E+00 -1.7425E+00 3.7846E+00 -7.8669E-01 7.4375E+00
-t33--97t*84E-GO i.0619E+Gi 1.295tt+0i -E.iGteE-Gi 1.7iG3Evet-134 -3.0292E+00 8.8144E+00 1.2407E+01 -4.8909E-01. 1.5457E+01 137 -2.6658E+00 1.9564E+01 2. 0250E+01 ' 1. 6940E-01 2. 2917E+01 136 -1.1iW3E-GG i.st48E+0i 1.3623EvGi -4.OE42E-Gi 2.iEGOE*0t-
, 141 -9.0900E-01 2.4190E+01 2.4035E+01 -6.4182E-01 2.5131E+01 142 -9.1282E-01 2.5471E+01 2.4504E+01 -6.7155E-01 2.6418E+01
--137
-3.3t32t-Gi i.9207E*01 2.2176E+Gi -i.6550E+GG i.1968E*0t--
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1.8670E+01 2.2001E+01'-8.2770E+00 ' 2...2253.E+01 . . + CUTPUT IS LISTED FOR J-H FACE ELELNO~ CAL 5:31 NORMAL S1G2 HCCP .SIG3 SHEAR TAU 11...!NTENSITY. 141 -4.9966E-01 2.6779E+01 2.4124E+01 1.113CE+00 2.9364E+01
- 14 2_-4. 720G E-01 2.9950E+01. 1.5477E+01 . 8. a.681E-01._3. 0470E+01 157 6.5121E-01 6.67622 00 1.70662+01 -1.0464E-02 1.6414E*01 158 1.0318E+00 1.1190E*01 2.13752+01 4.6037E*00 1.1153E+01
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, l TITLE f* ** *' b - PAGED.hOF d JOS NO.
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~
5 Deadweight -24 -235 87 -44 180 -366 (100) Thermal 21 -145 66 245 -827 -583 I'**f*'T (B) O** d ' * * ( 6 Deadweight -84 -119 -33 26 -54 10 I * (105) Thermal 5 242 13 -699 -51 982 (C) 7 Deadweight -20 -138 239 1102 -1028 216 (100) "Merms1 314 775 -215 7295 -1304 4560 (D) 8 Deadweight 6 -426 2 -305 -118 -722 (100) Thermal -16 403 1012 6142 -8582 3419 (E) Nostle 1 - Steam Drum Nozzle - Main Feedwater Line - West Connection No 21e 2 - Steam Drum Hossle - Main Feedwater Line - East Connection . Hostle 3 - Steam Drum Nottle - East Lead From Emergency Condenser to Steam Drum Nozzle 4 - Steam Drum Nottle - West Lead From Emergency Condenser to Steam Drum
, Nozzle 5 - Emergency Condenser Nozzle - East Lead From pergency Condenser to'~
Steam Drum Mozzle 6 - mergency condenser Nostle - West Lead From Emergency Condenser to_ steam Drum Nozzle 7 - Emergency Condenser Nozzle - East Lead From steam Drum to Emergency Condenser Noazle 8 - Emergency Condenser Nottle - West Lead From steam Drum to mergency Condenser b
- . , - - - , . - _ . - - - - , - - ------..,n.. - . , - - - , . - - - , . - . - - . - . - , - . - - - - - , - - - - -
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TITLE F-u<, o<d 6s.*Vd,AaEA _ Form ao, uo. ga Motionel NTS Eng. nee ing DATE 7'N 4 CHKD. ,Y M//f DATEf 6695 East Pacit< Coas* Miga.av BY # Technecel Systems Long Beacn CA 908C3 (213;493 6651 COMMENTS
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(LiCC. A -3 4 CHKD.BY'#' .' '# Teemaical 6695 Ear paca< Ocar araav BY DATE DATE ' Systems Long Beac% CA 90803 G13) 493 665' COMMENTS TeMe I.9.1 SECTION III. DIVISION 1 - APPENDICES 1933 Eduon
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'n y-FIG. I-9.2.1 DESIGN FATIGUE CURVE FOR AUSTENITic STEELS, NICKEL-Chit 0MlUM-Ilt0N ALLOY, NICKEL-IRON-CHfl0MlUM ALLOY, ANO NICKEL-COPPER ALLOY FOR Q E }9 S. > 28.2 ksi, FOR TEMPERATURES NOT EXCEEDING 80lrF g
Q (For S, s 28.2 hsi, use Fig. I-9.2.2.)
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Table I-9.1 Contains Tabulated Vasmes and a Formula for Accurate Interpolation of TMs Curve 5 m 9 Yr 8 0 m 8 t. g w
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