ML20216B631
ML20216B631 | |
Person / Time | |
---|---|
Site: | Pilgrim |
Issue date: | 03/09/1971 |
From: | Chen G, Kinyon B, Pierson T ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY |
To: | |
Shared Package | |
ML20216B615 | List: |
References | |
CENC-1139, NUDOCS 9805180275 | |
Download: ML20216B631 (176) | |
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- REPORT NO. CENC 1139 SUBJECT CATEGORY:
" ANALYTICAL REPORT"
} ff. b O COMBUSTION ENGINEERING, INC.
NUCLEAR COMPONENTS DEPARTMENT C.E. CONTRACT 21466 0.E. APED PURCHASE ORDER 205-B1171 s '.:
ANALYTICAL REPORT FOR PILGRIM REACTOR VESSEL CERTIFIED by VENDOR APPROyjED Byd8/h>%N Date 2/7/7 /
FOR l T. M. Pierson "'?'" @ t'.!'TMt B. W. Kinyon *
- t N t o w.een.
G, G. Chen Y $$$UI2E2 1
9805180275 980505 PDR ADOCK 05000293 P PDR r
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I ABSTRACT i
This report contains the results of the detailed structural and thermal analyses necessary to establish the structural integrity of the Pilgrim Reactor Vessel for requirements of General Electric Specification 21A1110AB, Rev. 3, dated August 19, 1970, and compliance with rules of Section III, ASME Boiler and Pressure Vessel Code, 1965 Edition, June 30, ,
1966 Addenda, and Interpretations to ASME Boiler and Pressure l Vessel Code, Numbers 1332-4 1335-2,1336, and 1339-2.
PREPARED BY l h
T. M. Pierson
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G. G. Chen 0b W I Lead Structural Engineer Lead Thermal Engineer APPROVED BY k i u nA'*
W F. P. Hill, Jr. H. W. Dolfi N Supervisor Supervisor Project Analytical Group Contract Engineering Section
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This document is the property of Combustion Engineering, Inc. , Windsor, Connecticut, and is not to be reproduced or used to furnish any information for making of drawings or apparatus except where provided for by agreement with said Company.
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ACKNOWLEDGEMENT i ,
t Structural Analysis l J. Clem M. Goodwin
- A. Fife D. Massey J. Bass E. Wilson l Thermal Analysis '
M. Bairagdar Design G. St. Cin l R. Lumpkin l D. Howard 44 <
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DISTRIBUTION LIST Ewbank/ Sher /Dolfi/Alden/Halvorsen 1 F. P. Hill, Jr. 1 J. L. Pyle 1 G. E. St. Cin 1 General Electric - APED 10 Hartford Inspector 1 l NCD Library 1 Met Lab Library 1 4
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! TABLE OF CONTENTS l
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ABSTRACT ...............................................
1 1.000 INTRODUCTION .................................... 3 2.000 DESIGN CRITERIA ................................. 3 i 3.000 VESSEL GEONETRY ................................. 6 4.000
SUMMARY
OF DETAILED ANALYSIS .................... 8 4.100 Closure Region ........................... 8 4.200 Vessel Shell ............................. 10 4.300 Bottom Head - Support Skirt .............. 11 4.400 Nozzles .................................. 13
- 4. 500 Internal Brackets ........................ 21 4.600 Shroud Support and Attachments ........... 24 4.700 Basin Seal Skirt ......................... 27 m
4.800 Exte rnal At tachments . . . . . . . . . . . . . . . . . . . . . 28 5.000 REFERENCES ...................................... 32 Appendix A - Detailed Structural Analysis Appendix B - Detailed Thermal Analysis Appendix C - Design Drawings f
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1.000 INTRODUCTION The Pilgrim Reactor Vessel, designed and fabricated by Com-bustion Engineering, Inc., in accordance with General Electric APED Specification 21A1110AB, provides the pressure retaining boundary and support structure for the reactor core of a )
boiling water type nuclear energy steam generating system.
The vessel consists of a 224 inch I.D. cylindrical shell closed at the bottom with a hemispherical . head and at the top with a bolted closure. The unit is supported by a cylindrical skirt welded to the bottom head. Openings required for system op-eration and control are provided throughout the length of the cylindrical shell and in both heads.
This report consists of a summary of the results of detailed structural and thermal anelyses, shown in Appendices A and B, necessary to show compliance with rules of Section III, ASME Boiler and Pressure Vessel Code for a Class A vessel.
2.000 DESIGN CRITERIA Ability of the structure, as shown by the drawings of Appendix ,
C, to comply with the rules of Article 4,Section III, ASME j Boiler and Pressure Vessel Code for stress and cyclic life shows adequacy of the structure for the required design and operating parameters defined by General Electric - APED Speci-fication 21A1110AB. !
2.100 DESIGN PARAMETERS Design loading conditions defined by GE-APED Specification j
~
_2_1A1110AB include:
System Design Temperature ............. 575 F .
System Design Pressure ................ 1250 psig l Feedwater Design Pressure ............. 1475 psig Recirculation Design Pressure ......... 1370 psig Design Pressure Drop Across Shroud . . . . 100 psig Wa te r Le vel ( No rmal ) . . . . . . . . . . . . . . . . . . 520 inches Wate r Le vel (Re fueling ) . . . . . . . . . . . . . . . 958 inches Wate r Weight ( No rmal ) . . . . . . . . . . . . . . . . . 506 kips Wa te r Weight (Re fueling) . . . . . . . . . . . . . . 899 kips Seismic Load Factor (Vertical) . . . . . . . . 0.06 g's Seismic Load Factor (Horizontal) ...... 0.40 g's Design Life Objective ................. 40 years 3
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2.000 DESIGN CRITERIA 2.100 DESIGN PARAMETERS (Cont'd) l Pipe reactions are -defined for the Recirculation Inlet and j Outlet Nozzles, the Steam Outlet Nozzle, Feedwater Nozzle, l
and the Core Spray Nozzle. Since reactions for other nozzles
! have not been defined, they are assumed to not be significant.
2.200 OPERATING PARAMETERS System operating transients are shown by GE Specification 21A1110AB, GE Drawing 730E941, and include the following.
Transient Condition Occurrences No rmal Startup (100 0F/Mr) . . . . . . . . . . . . . . 120
! 50% Powe r Ope ratio n . . . . . . . . . . . . . . . . . . . . 14,600[',f Rod Worth Tests ........................ 400 Loss of Feedwater Heaters ,-
Turbine Trip at 2 5% Power . . . . . . . . . . . . . 10 ,,
Fee dwa te r He ate r Bypas s . . . . . . . . . . . . . . . 70 ,
Loss of Feedwater Pumps ................ 10 ,,
l Turbine Ge nerator Trip . . . . . . . . . . . . . . . . . 40 ,,
Re a c to r Ove rp re s s ure . . . . . . . . . . . . . . . . . . . 1 Safety Valve Blowdown .................. -2 ,
All o the r S c rams . . . . . . . . . . . . . . . . . . . . . . . 147) 5 Improper Start of Cold Reciro. Loop . . . .
Sudden Start of Cold Recirc. Loop . . . . . . . 5 Normal Shutdown 1000F/h r Cooldown (546-375 F)
Shutdown Flooding (375-330 F) 118 ',
1000 F/hr Cooldown ( 330-100 F) . . . . . . . . .
In addition, the vessel is expected to be subjkcted to 133 cycles of hydrostatic, pressure tests, threp of which will be at 125% of design pressure, and 130 at design pre ssure .
2.300 MATERIAL PARAMETERS In accordance with Article 4,Section III, ASME Code, ma-terials are evaluated with respect to Allowable Design Stress Intensity. Values of Design Stress Intensity (Sm) for materials used are:
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2.300 MATERIAL PARAMETERS (cont'd)
Sm at Sm at l Mate rial lo00F 5750F Reference l
SA 515-70 _
23.3 kai 19 15 ksi ASME III, Summer '66 SA 516-70 23.3 19.15 ASME III, Summer 866 l
ASTM A533 B-1 e 26.7 26.7 code case 1339-2 l SA 302B C 26.7 26.7 ASME III (1965)
SA 240 TP-304 20.0 15.8 ASME III (1965)
SB 168 23.3 23.3 code case 1336 l
ASTM A508-64 I 30.0 18.2 code case 1332-4 ASTM A508-64 II 26.7 26.7 code case 1332 4 w l SA 336 F-1 S 26.7 26.7 code case 1332-4 1 2
9 SA 182F304 g 20.0 15.8 ASME III (1965)
SB 166 23.3 23.3 code case 1336 SA 312 TP304 g 20.0 15.8 ASME III (1965) ;
SB 167 23.3 23.3 code case 1336 ASTM A540 B23(3) $ 43.3 36.3 code case 1335-2 ,
M l SA 193 B-7 $ 35.0 28.0 ASME III (1965) j i
3.000 VESSEL GEOMETRY 1
The Pilgrim Reacto: .essel consists of a 224 inch minimum I.D. l cylindrical shell closed at the bottom with a hemispherical ;
head and at the top with a bolted closure shell. j i'
The cylindrical shell consists of four courses of formed plates.
The upper and lower courses are 6-1/2" thick and the two inter-( mediate courses are 5-17/32" thick. The bottom head is welded l ' to the lower shell course and is 112" minimum inner radius. The upper segment is 3-1/4" thick and the lower, or dome, segment 1
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i 3.000 VESSEL GEOMETRY (Cont'd) is 7-1/4" min ~1 mum thickness. The support skirt, consisting of a tapered forging and a 2 inch thick by 198 inch 0.D. cylinder is welded to the transition between the bottom head segments.
I l The vessel flange is 250-1/2" 0.D. and is drilled for fif ty- '
j six bushed studs. A 1/4 inch thick skirt is attached to the flange 0,D. to support the Refueling Easin.
l The closure head 'is. 3-1/4" thick with a 250-1/2" O.D._ flange L at the mating edge. Holes are provided in the flange for the fif ty-six (56) 6-1/4" closure studs. Tao grooves are machined l in the . flange mating surface for the main closure 0-ring seals.
i Openings required for system operation, control, and. instrumen- -
tation are provided along the length of the vessel and in both
! heads. Location and description of these openings are listed below and indexed to the drawing shown on the following page.
Index Description Location l N-1 1 - 4" Vent Nozzle (Flanged) Top Head N-2 2 - 6" Spray / Instrument Nozzles (Flanged) Top Head N-3 4 --20" Steam Outlet Nozzles 604-1/2" N-4 2 - 2" Instrument Nozzles 547" N-5 4 - 12" Feedwater Nozzles (Liner) 468-1/4" N-6 2 - 10" Core Spray Nozzles (Liner) 454-3/4" N-7 1 - 3" CRD Return Nozzle (Liner) 440" L
N-8 2 - 2" Instrument Nozzles 425-1/2" l
N-9 10 - 12" Recir,culation Inlet Nozzles (Liner) 200" N-10 2 - 28/36" Recirculation Outlet Nozzles 145" N-11 2 - 4" Jet Pump Instrument Nozzles 134" N-12 1 - 2" Core AP Nozzle Bottom Head l N-13 145 - 6" Control Rod Drive Nozzles Bottom Head
- N-14 42 - 2" Flux Monitor Nozzles Bottom Head ,
N-15 1 - 2" Drain Nozzle Bottom Head
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3.000 VESSEL CEOMETRY ' (C WD,)
w N-1' 3 +L" N-2 Lifting Lugs , ,
h (4) ' . 6 1/4" UI'" 8N Studs Elev. 664 9/1# 1
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s Refueling Basin
-N-3 2ts@[I,a Gi" ;
-N 4 Stabilizer -O 3
- Brackets (4) 1 -N 5
-N 0
-N 7
-N-8 w
n" , , 227d"J.a _
g 52 Note: "N" numbers t' index nozzles.
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, See preceding page.
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_ 226ls 10.
- z' -N4 Shroud Support m - -NA0 s
\ -N-ll Elev. 113-7/16 -
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113% R
'N-12 3+g l N ' .13 -
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N-34' Support 7 4
Elev. O' - 0" . Skirt Elev. 16" -
f-ti-k~5 7
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I 4.000
SUMMARY
OF DETAILED ANALYSES ,
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Results of detailed analyses required to comply with rules of Article 4,Section III, ASME Boiler and Pressure Vessel Code for a Class A vessel are presented on the following pages.
The detailed analyses are shown in Appendix A. I 4.100 CLOSURE REGION i
4.110 Abstract Closure She//
Ability of the design of the gyg closure region to comply with rules of Article 4, Section '
- III, ASME Code (1965 Edition with addenda .through Winter 1966) is shown by calculations pre- ---
sented in this report.
4.120 Geometry C/..ru,.e / !
A*#f
- Clan 9 e l The structure included in the closure region' consists of the i i vessel and closure flanges with ,
I their hubs and adjacent shell sections, the closure bolts, Vene/ /
and the 0-ring seals. r/a,,,e / /
4.130 Significant Results N'ub -
Ability of the vessel shell __
design to comply with rules of Article 4,Section III, ASME V'"#!
Code is shown by the detailed ####/ h{-.
analysis.
Maximum primary membrane stresses calculated for tne closure I and vessel shells are 21 9 and 21.8 (26.7 kai allowable),
respectively. Primary local plus bending stress calcula-tions show maximum stress intensities of 33 8 ksi at the Closure Shell-Hub junction and 29 8 kai at the Vessel Shell-Hub junction. For both locations, the calculated stress intensity is less than the 40 ksi allowable for the material at design temperature.
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4.100 CLOSURE REGION 4.130 Significant Results_ (Cont'd)
Primary plus secondary stress intensity ranges of 67.8 ksi at the closure shell-hub junction and 74.4 kai at the vessel shell-hub junction are less than the 80.1 ksi allowable for-the material.
Results of calculation of bolt stresses shows:
Average Design Stress = 34.4 kai < 36.3 ksi allow, at 575 F Average Service Stress = 59.2 kai < 86.6 kai allow, at 1000F
= 41.2 kai < 73.6 kai allow. at 5460F Maximum Service Stress = 121.8 kai < 129.9 kai allow, at 100 F0
= 91.7 kai < 108.9 kai allow, at 3460F Evaluation. of cyclic life of the structure shows maximum usage factors of 0.21 in the closure shell, 0.77 in the vessel shell and 0.786 in the bolts. For each of these parts, the calcu-lated values are less than the allowable usage factor of 1.0..
4.140 Discussion of Analysis Although Article I-12,Section III, ASME Code does not re -
quire a minimum seal load for 0-rings, a load of 1000#/ inch was used in the analysis of the closure region. Continuity loads at gross changes in geometry were determined ~from the set of simultaneous equations obtained by equating free edge deformations of adjacent sections. Deformations of the bolt at the top of the closure flange were calculated by treating the bolt as a cantilever beam subject to an end shear and t moment. A friction load is applied to the mating surface.
The friction factor used is based on results of observations
- made during hydro test of similar vessels.
The evaluation of stresses and cyclic life of the bolts is in accordance with rules of Par. N-416,Section III, ASME Boiler and Pressure Vessel Code, except that the allowable number of load cycles is determined by the equation defined by ASME Code Case 1336. It should be noted that the required number of bolt-up operations for the bolts is 80 times even though the required cycles for the shell structure is 130.
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4.200 VESSEL SHELL _
4.210 Abstract-Ability of the vessel shell design to comply with rules of Article 4,Section III, ASME Code is shown by the detailed analysis.
4.220 Geometry The vessel shell consists of four cylindrical shell courses.
The upper and lower shell courses are 6-1/2" thick. The two middle courses a're 5-17/32" minimum thickness. The mid-radius of the shell courses is constant for the full length of the vessel.
Stresses at attachments to the vessel shell are included in analysis of the attachments, so are not considered in this analysis.
4.230 Significant Results The magnitude of stresses and effect on the cyclic life of the cylindrical shell sections due to mechanical loadings, operating transients, internal heat generation, and the thermal discontinuity at the water-steam interface are evaluated in this analysis. These loadings are superimposed on the structural discontinuity formed by the junction of shells of different thickness so as to give the maximum possible magnitude of stress. Rules of Article 4, Section-III, ASME Code are satisfied for all categories of stress and for cyclic life of the structure.
Maximum primary membrane stress intensity is 26 3 ksi which is-less than the allowable value of 26.7 ksi. Since there are no primary local or bending loads on the structure, the maximum primary stress intensity across the wall section is equal to the primary membrane . stress intensity.- This maxi-mum primary membrane stress intensity is 26.3 ksi which is.
less than the 40.05 kai allowable for the material.
Maximum primary plus secondary stress intensity range of 32.8 kai is less than three times the allowable design stress intensity value of 80.1 ksi.
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l 4.200 VESSEL SHELL 4.230 Significant Results (Cont'd) ,
Maximum usage factor is calculated as O.4353 which is less than the 1.0 allowable value.
4.240 Discussion of Analysis l
l Analysis of the vessel shell has been conservatively simpli-fled by assuming 'the maximum stresses due to gravity and seismic loads, internal heat generation, and thermal discon-tinuity (water-steam interface) occur at the change in wall.
sections. Stresses due to the gross structural discontinuity ,
l at the change in wall section are determined from solution of a continuity analysis of the structure. l
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! 4.300 BOTTOM HEAD - SUPPORT SKIRT l
l 4.310 Abstract l
l Comparison of the magnitudes of stress intensity and usage factors calculated for the structure with allowable values shows compliance with the rules of Article 4,Section III, ,
ASME Code. )
i 4.320 Geometry l
Included in the analysis ]/
l of the bottom head - + _
! support skirt region are f
the bottom head dome Y/'#j,fj'(j !
i segment, upper segment, support skirt forging, I
and support skirt cylinder. The support 4**e /#
skirt cylinder is .-
assumed fixed at the . IJuese* /
base plate. ' '1JUkt 11
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( 4.300 BOTTOM HEAD - SUPPORT SKIRT 4.330 Significant Results Ability of the bottom head-support skirt structure to satisfy l rules of Article 4,Section III, ASME Code is shown by the '
i detailed analysis presented in Appendix A of this report.
Primary membrane stress intensity calculations result in maxi-l mum values of 24.8 kai in the upper shell segment and 26.6 kai in the dome segment. Both of these values are less than the allowable stress of 26.7 kai. The primary membrane stress intensity of 10 3 kai in the skirt is less than the 19 1 kai allowable stress. Since primary local plus bending stresses are . equal to pr.4:ary membrane stress intensities l for all parts, these stress intensities are less'than the allowable values of 150% of the allowable membrane stress intensities.
l Maximum values of primary plus secondary stress intensity range at each significant location are:
l Upper segment at transition taper:
SI = 36. 5 ksi < 80.1 kai allow.
l Dome segment at edge of penetrations: l l SI = 71 9 kai < 80.1 ksi allow. I Support skirt forging at attachment to head:
SI = 36.9 ksi < 80.1 kai allow.
Support skirt forging at bottom of taper:
SI = 70.4 ksi < 80.1 ksi allow.
Support skirt at base plate:
SI = 54.8 ksi < 56.1 kai allow.
Results of the cyclic life evaluation of t. atructure shows the following usage factors:
Upper segment at transition taper U = 0 309 < l.0 Dome segment at edge of penetrations U = 0. 2 2 2 < 1. 0 Support skirt forging at attachment to head U = 0.265 < l.0 Support skirt forging at bottom of tapei- U = 0.079 < l.0 Support skirt at base plate U = 0. 079 < 1. 0 12 t
4.300 BOTTOM HEAD - SUPPORT SKIRT 4.340 Discussion of Analysis For analysis of the bottom heact-support skirt region, defor-raations of the upper shell section, the dome segment, and the support skirt are determined by use of the Seal-Shell-2 Computer Program. These three elements are connected by a ring element at their point of intersection. Continuity loads at the junctions of each of the elements with the ring are determined by equating deformations of each of the elements with those of the ring, and solving the resulting simultaneous equations.
Particular assumptions and methods used to represent the structure as a model for the Seal-Shell solution were as follows:
- 1. The stiffness of the bottom head dome segment was adjusted to compensate for the penetrations by modifying the elastic modull per equations for a flat plate with a rectangular array of holes as described in Welding Research Council Bulletin No. 80 (Reference 12).
2 The support skirt was assumed fixed at its attachment to the support plate.
. Stresses in the perforat'ed dome region were adjusted' from the isotropic segment stresses obtained from the Seal-Shell Solution by applying factors from Volume 19, Journal of Applied Mechanics (Reference 13).
Stresses in the attachment region of the support skirt were calculated directly from loads obtained from the Seal-Shell Solution using classical methods.
4.400 N0ZZLES Since nozzles provided in the vessel for system operation and control have been designed in accordance with the rules of Par. N-450,Section III, ASME Code, analytical requirements for each nozzle are dependent upon the necessity of a fatigue 1 analysis as determined by requirements of Par N-415.1, j
( Section III, ASME Code.
13 Q
4 4.400 NOZZLES The Feedwater, Core Spray, CRD Return, Recirculation Inlet, and RecirculatRa Outlet Nozzles are subjected to flow con-ditions of such severity as to require a fatigue analysis.
Although the CRD Nozzles are also in this category, their geometry is so different that they are discussed separately.
Nozzles subjected to vessel coolant only, and shown by satis-faction of requirements of Par. N-415.1,Section III, ASME Code to not require a fatigue analysis include the Vent, 6" Spray / Ins trument, Steam Outlet, 2" Instrument, Jet Pump Instrument, Core AP, In-Core Instrument, and Drain Nozzles.
4.410 Abstract Results of analyses presented in Appendix A of this report, and summarized in Figures 4.431 and 4.432 show ability of the nozzle designs to satisfy rules of Article 4,Section III, ASME Code.
. 4.420 Geometry The geometry of the nozzles can be separated into three basic design configurations. The first,' designated as Type A in this report, consists of a reinforced nozzle attached to the vessel shell with a full penetration weld.
A tapered transition is provided for the change from the reinforced section to the connecting pipe geometry. This nozzle configuration is used for most of the nozzles in the vessel. Variations in the basic configuration includes provisions for the thermal liners required for the Feedwater,
. Core Spray, CRD Hydraulic Return, and Recirculation Inlet Nozzles, and the flanged ends provided for the nozzles in the closure head.
The second design configuration, designated as Type B, consists of nozzles of uniform section attached to the vessel with a partial penetration weld. This design is used for the small instrument nozzles that are not sub-jected to significant pipe reactions.
The nozzles designated as Type C consists of the CRD Nozzles that are attached to the vessel with a partial penetration weld and extend into the vessel. '
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4.400 NOZZLES _
4.430 Significant Results Satisfaction of the rules of Article 4,Section III,-ASME Code for the design of all nozzles in the vessel is shown by the detailed analyses of Appendix A.
Design of all nozzles in the vessel comply with rules of Paragraph N-450,Section III, ASME Code for opening com-pensation. Therefore, as provided by Par. N-451, Section l
III, requirements of primary stress limits are satisfied' by the designs used.
Results of the detailed analysis of the Feedwater, Core Spray, CRD Hydraulic Return, Recirculation ~ Inlet, and Recirculation Outlet nozzles as shown in Figure 4.431.
l As stated in Paragraph N 451(a)Section III, ASME Code, compliance with the rules of Paragraphs N-415.1 and N-450 shows ability of nozzles to satisfy stress and cyclic life limits of' Article 4 of the Code. Thus analysis of the Vent, 6" Instrument / Head Spray, steam Outlet, 2" Instrument, Jet Pump Instrument, Core AP, In-Core Instrument, and Drain Nozzles is limited area reinforcement calculations and evaluation of. primary stresses outside of the limits of reinforcement. Results of these calculations are shown in Figure 4.432.
In addition to the analyses summarized in Figure 4.432, stress and cyclic life of the bolts and flanges for the Vent Nozzle and the 6" Instrument / head Spray Nozzle were determined from a detailed analysis based on continuity
. requirements of the structure. Results of the analyses were:
a) Bolt Area calculation per Article I-12,Section III,
. ASME Code shows 2.159 in* required versus 7.55 in*
available for the Vent Nozzles and 2.920 in a required ,
versus 14.014 inn available for the Instrument / Spray Nozzle.
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FIGURE 4*431 NOZZLES REQUIRING FATIGUE ANALYSIS Opening Compensation f 3 54/e E,./
Reinf. Area Nozzle '
Req'd. Avail. * ,#/
Feedwater 79.646' 82.9'80 4 bb s /- pf,/e, i Core Spray 73.846. 78.626 .4.c 4h CRD Hyd. Return 25.698'. 26.374 Recirc. Inlet 72.220 82.830 Recire. Outlet 193.08 .207.38 Typical Nozzle Type A ,
Stress and Cyclic Life Summary c Primary Stress P + S Stress O Intensity Intensity Usage i Nozzle y (Ks:.) Ranse (Ksi) Factor j 0} Max. Allow. Max. Allow. Max. ' Allow.
1 < 26.7 26.7 77.0 80.l ( 0~37b 1.000 3 12.7 2647 37.7 80.1 D 7 1.000 3 12 7 17.7 20.4 5'343' o.195 1.400 4 7.6 15.8 <20.4 48.8 *:o.195 1.000 .
1 < 26.7 26.7 57.5 80.1 6.377 1.00 Core 2 14.0 26.7 36.2 80.1 0.274 1.00 spray 3 14.0 15.8 36.6 48.0 0.437 1.00
- 4. 10.5 15.8 <36.6 4 8. 0 <:o.205 1.00 1 < 26.7 26.7 66.9 80.1 OgQ96 1.00 l CRD Hyd. 2 10.2 26.7 1654 80.1 Neg. 1.00 Return 3 10.2 15.8 27.0 48.0 0;413. 1.00 4 Neg. Neg. 0 413 1.00 1 < 26.7 26.7 33.1 80.1 0.r2,81 1.00 2
- 3 26.7 M.5 80.1 0. W l.00 Recirc.
Inlet 3 13.3 15.8 34.2 48.0 0.104 1.00 4 13.2 15.8 (Re f. 24) 0 970 1.00 1 < 26.7 26.7 29.6 80.lc .o,75 0 1.00 Recirc 2 13 5 26.7 33.4 80.1 o,563 1.00 Outlet 3 13 5 ' 15.8 20.4 48.0 0.469 1.00 4 LINER NOT REQUIRED 16
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4.400 N0ZZLES 4.430 Significant Results (Cont'd) b) Bolt stress and cyclic life calculations show:
Eval. Category Vent Inst / Spray Allow.
Avg. Oprn. Stress (Ksi) 19.4 29.3 2Sm = 56.0 Max. Oprn. Stress (Ksi) 43.8 35.2 3Sm = 84.0 Usage Factor (U) 0.493 0.493 1.0 c) Results of analysis of flange-safe end junction were:
Eval. Category Vent Inst / Spray Allow.
Primary Stress Int. (Ksi) 2.3 2.9 Sm = 15.8 Usage Factor 0.0268 0.0115- 1.0 Analysis of the Control Rod Drive Nozzles was accomplished by an interaction solution based on continuity of deforma- ,
l tions.
Satisfaction of primary stress requirements for the bottom head'in the region of the nozzles was shown by complying with the rules for area compensation, as defined by Para-graph N-450,Section III, ASME Code.' These calculations showed the available opening reinforcement area to be 35.911 in8 which is greater than the required area of 28.566 in2 Maximum primary stress intensities calculated for the drive housing and stub tube were 6.0 kai(23.3 kai allow.) and -
-5. 7 kai (12.0 kai compressive allow. ), respectively. Maxi-mum primary plus secondary stress intensity ranges were 36.4 kai (47.4 kai allow. ) for the housing and 54.7 kai (69.9 kai allow.) for the stub . tube. I The maximum usage factor calculated was 0.6000, which is {
, less than the 1.0. 1 i
18
4.400 N0ZZLES 4.440 Discussion of Analyses The method of analysis used for the Feedwater, Core Spray, CRD Hydraulic Return, Recirculation Inlet, and Recircula- l tion Outlet Nozzles was as follows: I
- 1. Satisfaction of primary stress requirements for the reinforced region of each nozzle is shown by calcu-lations verifying adequacy of opening compensation in accordance with the rules of Par. N-450,Section III, ASME Code.
- 2. Satisfaction of primary stress requirements for the '
nozzle outside of the reinforced section, the safe end, and the liner is shown by treating each of the com- ,
ponents as a long cylinder subject to the action of design operating conditions and applicable nozzle and liner reactions.
- 3. Primary plus secondary and peak stresses in each nozzle were determined from detailed solutions obtained by use of the Seal-Shell-2 Computer Program (Reference 10).
- 4. Evaluation of primary plus secondary . stresses and cyclic life for each nozzle was in accordance with require-ments of Par. N-414.4 and N-415.2,Section III, ASME Code.
Use of the Seal-Shell-2 Computer Program (Reference 10) for analysis' of the subject nozzles required that the nozzle structure be represented as a symmetrical model. This was accomplished by treating the vessel as a spherical shell of i radius equal to 1.5 times the actual cylindrical vessel radius. Stresses obtained from the Seal-Shell solution were then adjusted for the actual cylindrical vessel loads and deformations. A detailed description of the procedure, and {
derivation of the adjustment factors are presented in Ap- I pendix A. f Validity of the method of detailed analysis used is shown in Appendix A where calculated stresses are compared to test I data for a photo-elastic model and stresses calculated for each nozzle are compared to data for similar photo-elastic k- nozzle models.
19-
(
' 4.400 N0ZZIES ,
4.440 Discussion of Analyses (Cont'd)
Cyclic life of the Recirculation Inlet Nozzle Liner is deter-mined by the. methods defined by S. W. Tagart in Reference 24 and shown in the Nuclear Piping Code (B31.7) .
Analysis of the Vent and 6" Instrument / Head Spray Nozzles-considered the nozzles to be in a steam atmosphere for' all i operating conditions. Bolt loads and continuity loads at l
the flange-safe end junction were determined -from an inter- i action analysis in which the mating flanges were assumed to ,
be of the same geometry as the nozzle flanges. The bimetal joint was assumed to be at the nozzle end-reinforced section l junction. I l Stresses in the safe end of the Steam Outlet Nozzle are l calculated by applying attenuation factors from Reference l
l 3 to loads determined from the nozzle end-reinforced section Junction.
-Since the nozzle-safe end junctions of the 2" Instrument Nozzles consists of two cylinders of equal thickness and radius, and of approximately the-same conductivity, stresses are limited t'o those due to different thermal ~ expansion coefficients.
I Length of the Jet Pump Instrument and Core 6P Nozzles are I sufficient to allow attenuation of continuity loads. Thus, l analysis of thesa nozzles was accomplished by interaction
-solutions of two cylinders of constant thickness and radius but different elastic moduli.
e Requirements for the In-Core Instrument nozzle are limited to provision of .the required opening for installation of the nozzles by others. Thus, consideration of the. nozzle in the l
analysis was limited to requirements for complying with the rules of Paragraph N-4151,Section III, ASME Code, for cyclic life.
Since nozzle and piping material of the Drain Nozzle are the same, analysis of this structure was limited to evalu-ation of the nozzle-vessel intersection region.
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l 4.600 SHROUD SUPPORT AND ATTACHMENTS 4.640 Discussion of Analyses _ (Cont'd)
Cyclic life evaluation of the Shroud Support Plate at its junction with the Shroud Cylinder is accomplished by use of the method defined by S. W. Tagart in Reference 24 and shown in the Nuclear Piping Code, ASA-B31.7.
4.700 BASIN SEAL SKIRT
- 4. 710 Ab s tract Ability of the Basin Seal Skirt design to comply with rules 3 of Article 4,Section III, ASME Code, is shown by the detailed analysis of Appendix A.
4.720 Geometry ,
The Basin Seal Skirt is attached to the vessel flange and furnishes the support and seal for the refueling basin.
Analysis of this component includes consideration of the skirt cylinder and plate.
4.730 Significant Results Location of maximum stresses and cyclic usage factor was calculated in the skirt cylinder at its attachment to the flance. Maximum primary stress intensities at this loca-tion were 8.2 kai membrane (191 ksi allow. ) and 8.2 kai local.plus bending (28.7 ksi allow.). The maximum calcu- l lated primary plus secondary strecs intensity range was I 52.9 ksi (58.8 kai allow.). The resulting usage Rotation factor was 0.859 which 1.s less than the 1.0 allowable.
of the plate was determined as 0.003 degrees which is less than the 0.3 degrees allowed by specification.
4.740 Discussion of Analysis i The effect of vessel flange deformations on the basin skirt cylinder attachment was minimized by attachment of ;
the cylinder at the flange centroid. Flange deformations l were taken from Calculation S-101, " Closure Study." l t
l 27 f
l
l 4.800 EXTERNAL ATTACEMENTS
' l External attachments to the vessel include the. Stabilizer Brackets, Insulation Brackets, and Head Lif ting Lugs.
4.810 Abstract-Results of analyses, shown in Appendix A, of the Stabilizer ,
Brackets, Insulation Brackets, and Head Lif ting Lugs show l stresses and cyclic life of all parts to be within limits j defined by Article 4,Section III, ASME Code. {
4.820 Geometry
- i j
Four equally spaced stabilizer brackets are welded to the vessel shell for resistance to horizontal seismic and jet thrust loads. Each bracket consists of a lug welded to the vessel shell and two plate sections, welded to the lug and with pin holes for attachment to supporting structure.
Two rows of brackets are attached to the vessel cylinder for support of insulation. Each bracket consiets of an "L" shaped lug with the bottom leg welded to the vessel shell and a plate attached to the top of the vertical leg.
Four lugs are equally spaced around the closure head for l
use in handling of the closure head.
4.830 Significant Results Ability of the Stabilizer Bracket to comply with rules of Article 4, Se' ction III, ASME Code for stress and cyclic 3 l
life were shown by the analysis. Results of the analysis were as follows:
- 1. Maximum primary shear stresses are 15.7 kai in the bracket and 2.6 kai in the vessel. Allowable is i 16.0 kai, 2, Maximum torsion stresses are 1.9 kai in the bracket and 0.5 ksi in the vessel. Allowable is 21.4 ksi.
- 3. Maximum primary membrane stress intensities are 21.2 ksi for the bracket and 22.2 ksi for the vessel.
Allowable value is 26.7 kai.
28
- 4. 800 EXTERNE ATTACHMENTS 4.830 Significant Results (Cont'd)
- 4. Maximum primary local plus bending stress intensities are 27.4 kai in the bracket and 27.6 kai in the vessel.
The allowable value is 40.0 kai.
- 5. Maximum primary plus secondary stress intensity ranges are 27.4 kai in the bracket and 31.1 kai in the vessel.
The allowable value is 80.1 ksi.
- 6. Cyclic capability of the bracket structure is shown by complying with the rules of Paragraph N-415.1,Section III, ASME Code .
Compliance with rules of Article 4,Section III, ASME Code for stress and cyclic life capability of the Insulation Brackets was shown by analysis of this region. Specific ,
l results included: l i
- 1. Maximum primary shear stresses were calculated as 1.5 l l kai in the bracket (11.2 kai allow.) and 0.1 kai in the vessel shell (16.0 kai allow. ).
- 2. Maximum primary membrane stress intensities were negligible in the bracket and 24.4 kai in the vessel shell (26.7 ksi allow. ).
- 3. Maximum primary local plus bending stress intensities were calculated as 6.3 kai in the bracket (2G.1 kai allow.) and 24.4 ksi in the vessel shell (40.0 kai allow.).
- 4. Maximum calculated primary plus secondary stress in-tensity ranges were 6.3 kai in the bracket (56.1 kai allow.) and 24.4 kai (80.0 ksi allow.) in the vessel Shell.
5 Cyclic capability of the structure was shown by comply-ing with rules of Paragraph N-415.1,Section III, ASME Code.
Analysis of the Head Lifting Lugs showed that the design complies with rules of Article 4,Section III, ASME Code for stress and cyclic life capability.
29
, i
4.800 EXTERNAL ATTACHMENTS 4.830 Significant Results (Cont'd)
Maximum stresses were calculated as follows:
- 1. Maximum shear stress at the lug hole was 12.3 kai (16.0 kai allow.).
- 2. Maximum bearing stress on the lug hole was 16.4 kai (40 kai allows.).
- 3. Maximum primary membrane stress intensities were 12.3 kai (26.7 kai all'ow.) and 17.6 kai (26.7 kai allow.)
in the lug and shell, re spe ctively.
- 4. Maximum primary local plus bending stress intensities were 32.8 kai (40.0 ksi allow. ) in the lug and 23 0 kai (40.0 kai allow. ) in the head shell.
I 5 Maximum primary plus secondary stress intensity ranges were 31.6 kai (80.1 kai allow. ) and 23 0 kai (80.0 kai l allow. ) in the lug and head shell, respectively.
I
- 6. Adequacy of the structure for cyclic operation was shown by complying with rules of Paragraph N-415.1, l Section III, ASME Code.
4.840 Discussion of Analysis i
Analysis of the Stabilizer Brackets includes evaluation of shear tear and bearing stresses at the pin holes, primary stresses in the bracket, lug, and vessel wall, and cyclic stresses in each of the components. Stresses in the bracket and lug were determined from standard equations found in most structures text books. Stresses in the ves-sel wall were cniculated by methods developed by P. P.
Bijlaard and presented in Welding Research Council Bulletin No.107, Reference 14.
Stresses in the Insulation Bracket plate and lug were de-termined from equations available in most text books on structural analysis. Stresses in the. vessel shell were determined by methods developed by P. P. Bijlaard and shown 30
4.800 EXTERNAL ATTACHMENTS 4.840 Discussion of Analyses (Cont'd) in Welding Research Council Bulletin No.107 (Reference 14).
Half of the bracket loads were assumed to act as a con-centrated load at the centerline of the outer edge of each plate.
The Head Lif ting Lugs were designed.for a load equal to the total head weight applied to one lug at any angle in the plane of the lug and wit,h a maximum angle of 100 lateral to the plane of the lug. For analysis of stresses in the head, the lug was taken as an attachment of radius equal to the width of the lug plus two-thirds of the fillet welds.
1 l
31
- J
i 1
i i
5.000 REFERENCES
- 1. General Electric-APED Specifications 21A1110 AB, Revision 13, dated August 19, 1970.
2 " Nuclear Vessels" ASME Boiler and Pressure Vessel Code,Section III, 1965, including:
- a. Summer 1966 Addenda, dated June 30, 1966.
- b. Interpretation of ASME Boiler and Pressure Vessel Code Numbers 1332-4, 1335-1, 1336, 1339-2 and 1366.
- 3. Timoshenko, Theory of Plates and Shells, McGraw-Hill Book Co., New York, 1940, 4 Timoshenko, Advan'ced Strength of Materials, Parts I and II_, D. Van Nos trand Co. , New York, 1965.
- 5. Timoshenko, Theory of Elasticity, McGraw Hill Book Co. ,
New York, 1951.
6 h. J. O'Donnell, "The Effect of Local Flexib111 ties on Stresses in a Structure," Westinghouse Report Number Wf-?D-X(CE)-170, March 27, 1961.
7 W. J. O'Donnell, "The Additional Deflection of a Canti-lever Due to the Elasticity of the Support," ASME Paper 60-APMW-3, January 5,1960.
- 8. W. J. O'Donnell, " Stresses and Deflections in Built-in Beams," ASME Paper 62WA-16, September 11, 1961.
- 9. Matusz, O'Donnell, and Erdlac, " Local Flexibility Co- 3 efficients for the Built-in Ends of Beams and Plates," I ASME Paper Number 68-WA/PVP-6, August 1,1968 I
- 10. " Seal-Shell-2, A Computer Program for the Stress Analysis of a Thick Shell of Revolution with Axisymmetric Pres- I sures, Temperatures and Distributed Loads," AEC Research and Development Report WAPD-TM-398, 1963.
- 11. " Tentative Structural Design Basis for Reactor Vessels {
l and Directly Associated Components," Office of Technical Service, U. S. Department of Commerce Publication PB151987, De cember, 1958.
- 12. Mahoney, Salerno and Goldberg, " Analysis of a Perforated
{
Circular Plate Containing a Rectangular Array of Holes," l Welding Research Council Bulletin No. 80, Augus t, 1962. j
- 13. Horvay, "The ' Plane Stress Problem of Perforated Plates," j Journal of Applied Mechanics, Vol.19, September,1952, !
(KAPL Report No. P769). I l 14 Wichman, Hopper, and Mershon, " Local Stresses in Spheri- l cal and Cylindrical Shells Due to External Loadings," l l Welding Research Council Bulletin No. 107, August, 1965. !
- 15. Taylor and Lind, "Photoelastic Study of the Stresses Near l Openings in Pressure Vessels," Welding Rese 'ch Council !
Bulletin Number 113, April 1966. j 32 l
t
[ a
5.000 REFERENCES (Cont'd)
- 16. Galletly, " Analysis of Discontinuity Stresses Adjacent to a Central Circular Opening of a Hemispherical Shell," Department of the Navy, David W. Taylor Model Basin Report No. 870, 17 Mahoney and Salerno, " Stress A'nalysis of a Circular Plate Containing a Rectangular Array of Holes," Welding Research Council Bulletin No.106, July,1965
- 18. Roark, Formulas for Stress and Strain, McGraw-Hill Book Co., New York, 4th Ed.
19 Peterson, Stress Concentration Design Factors, John Wiley and Sons, New York, 1962.
- 20. Den Hartog, Advanced Strength of Materials, McGraw-Hill Book Co., New York.
- 21. Seely and Smith, Advanced Mechanics of Materials, John ,
l Wiley and Sons, 2nd Edition.
l 22 Peery, Aircraf t Structures, McGraw-Hill Book Co. , New York, 1950. I
- 23. Biach, " Instruction and Maintenance Manual, 1,680,000# l Tensioner," Biach Order #973.
l 24. Tagart, S. W., " Plastic Fatigue Analysis of Pressure Components," ASME Paper #68-PVP-3..
i I
l l
l 33
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APPENDIX A DETAILED STRUCTURAL ANALYSIS w
l l
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l APPENDIX A i
DETAILED STRUCTURAL ANALYSIS s 1
A.100 ABSTRACT ..................................... A-4 A.200 D IS C US S IO N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-4 i
A.300 NOMENCLATURE ................................. A-4 A.400 REFERENCES ................................... A-5 S-101 Closure Region ........................ A-6
! S-102 Vessel Shell .......................... A-100 l
l S-103 Bottom Head / Support Skirt ............. A-118 l l
S-200 General Nozzle Solution ............... A-160 l
S-201 Vent Nozzle ........................... A-186 S-202 6" Instrument / Head Spray Nozzle ....... A-205 S-211 S team Outle t Noz zle . . . . . . . . . . . . . . . . . . . A-227 1 I
S-212 Feedwater Nozzle ...................... A-2 54 l S-213 Core Spray Nozzle ..................... A-291
- S-214 CRD Return Nozzle ..................... A-327 1
S-215 2" Instrument Nozzle ( Upp e r) . . . . . . . . . . A-365 S-216 2" Instrument Nozzle (Lower) .......... A-37 9 S-221 Recirculation Outlet Nozzle ........... A-393 1
l S-222 Recirculation Inlet Nozzle . . . . . . . . . . . . A-421 l l S-223 Je t Pump Ins trument Nozzle . . . . . . . . . . . . A-472 l s' S-231 Core AP Nozzle ........................ A-489 S-232 In-Core Instrument Nozzle ............. A-503 S-233 Drain Nozzle .......................... A-511
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S-234 CRD Nozzle ............................ A-527 S-301 S tabilize r Brac ke t . . . . . . . . . . . . . . . . . . . . A-597 l \
l S-302 Basin Seal Skirt ...................... A-613 l
l S-303 Insulation Bracket .................... A-639 i
S-304 Head Lifting Lug ...................... A-647 .
1 S-401 Dryer Hold Down Brackets .............. A-655 l
j S-402 Guide Rod Brackets .................. A-663 l
l S-403 S te am D rye r B racke t . . . . . . . . . . . . . . . A-675 1
S-404 Feedwate r Sparger Bracke t . . . . . . . . . . . . . A-690 S-405 core Sp ray Brac ke t . . . . . . . . . . . . . . . . . . . . A-700 i
! S-406 Jet Pump Support Pads ................. A-708 l
S-407 Shroud Support ........................ A-720 1
Je t Pump Adap te r . . . . . . . . . . . . . . . . . . . . . .
S-408 A-781 S-409 Surveillance Bracket .................. A-794 l
l l
i l
i l
I I
j j
APPENDIX A DETAILED STRUCTURAL ANALYSES i A.100 ABSTRACT l
Ability of the' design of the Pilgrim Reactor Vessel to satis-fy requirements of Article 4,Section III, ASME Boiler and Pressure Vessel Code is shown by the detailed structural )
analyses presented herein.
A.200 DISCUSSION Analysis of each of the structural components shown in the Pilgrim Reactor Vessel Design Drawings presented in Appendix C for the design and operating parameters defined by General Electric - APED Specifications is presented in this appendix.
Evaluation of the structure is accomplished by complying with ,
the rules of Article 4,Section III, ASME Boiler and Pressure !
Vessel Code. Temperature data used in the calculations is l taken from Appendix B.
A.300 NOMENCLATURE Unless otherwise indicated in the specific calculation, the following nomenclature has been used.
A - Area of section (in8)
B - Bearing load (kips or kips / inch)
D - Flexural rigidity of section (in-lbs)
E - Elastic modulus (1bs/ina )
F - Load (kips / inch)
H - Radial shear load (kips / inch) l I - Moment of inertia of section (in 4) l M - Moment (inch-kips / inch)
N - Axial load (kips / inch)
P - Pressure (ksi) e
A.300 NOMENCLATURE (Cont'd)
R - Mid-radius of section (inches)
S - Stress intensity (ksi)
V or W - Vertical load (kips) a'- Outer radius of section (inches) i e - Eccentricity (inches) h.- Height of section (inches) ,
1 - Length of section (inches) l i t - Thickness of section (inches) a - Coefficient of thermal expansion (in/in/0F) l I a.or 6 - Radial deflection (in) l l A* or 6* - Rotation (radians)
Poisson's ratio (0.3) o - Normal stress (ksi)
T -
Shear stress (ksi)
! A.400 REFERENCES
! References indicated in the analysis of this appendix are shown in Part 5 00 of the report.
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Addenda through Summer 1966) is shown by calculations presented
)
)
in this report.
The structure included in the i l closure region consists of the 9 vessel and closure flanges with y /
/
their hubs and adjacent shell ;x -
sections, the closure bolts, , j and the 0-ring seals. Loading j conditions considered are as defined by General Electric APED l Specification (Ref. 1).
SIGNIFICANT RESULTS Stresses calculated for each significant location are listed in the summary on the following p.
page. Maximum calculated stresses and cyclic life for the shell structure are :
Pr! mary Membrane Stress Intensity: 21.9 kai < 26.7 kai allow.
Pri. + Sec. Stress Intensity Rg. : 74.4 kai < 80.0 kai allow, Usage Factor: 0.77 < l . 0 allow.
For the bolts, maximum service stress and usage factor are calculated as:
i l Maximum Service Stress: 121.8 kai < 129.9 kai Maximum Usage Factor: 0.786 < l.0 allow.
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COMBUSTION ENGINEERING, INCl * * ' NUMHP S-101 of Alc il59 ENGIN! ERIN 3 DEPARTMENT. CHATTANOOGA. TENN, SH ELT- N C. AID CHARGE NO 22.4" BWR cay, -1/.16/70 ny DOM oEscRenop CLOSURE REGION eggeg oxy, l/Jd/70 ny JEW: Q C.O DETAILED ANALYSIS C.1 Metho'd of Analysis The detailed structural analysis of the closure ' region is accomplished by calculation of loads and stresses in an analytical model consisting of structural elements that repre-sent the actual geometry as closely as possible. The analyti-cal model consists of:
- 1) Closure Shell and Hub - Axisymmetric Shell of Revolution as defined for use of the Seal-Shell-2 Computer Program (Ref, 10)
- 2) Closure Flange - Ring .
- 3) Vessel Flange and Bolt - Ring with Beam Appendage
- 3) Vessel Hub and Shell - Axisymmetric Shell of Revolution as defined for use of the Seal-Shell-2 Computer Program i
%=f (Ref. 10), j l External loads applied to the structure include internal pres- l sure, bolt load, seal leakage load, bearing load between the l flanges, friction load between the flanges, and thermal loads resulting from temperature distributions in the structure. Internal pressure (P) is taken as a uniform load acting on the surfaces of all parts within the pressure boundary., The pre s-sure boundary is taken as the inner surface of the shells and flanges and the inner 0-ring at .the mating surface. In addition to the bolt operating loads, use of stud tensioners for preloading requires that the bolt be elongated more than required for the preload. From tests by Biach, results of which are shown in the stud tensioner manual, (Ref. 23) the required overload is 1.33 times the required preload. Thus, the bolt tensioning load is: FPT = 1.33 Fp ; however, since the effective length, and stiffnesa of the ss idealized beam, and the distribution of the bolt end loads around the circumference are all changed, the continutty load equations derived for operating conditions are not applicable, n
COM2UOTION ENGINEERING, INC, NUM2EP -8"101 CENC IIM ENGINEERIND DEPARTMENT. CHATTANOOGA. TENN. CHEET L' b' CHARGE NO- 214." BWR ogy. 1/m/7o av. DOM ._ DEscRinsop CLOSURE REGION cuacx oxy, 1/26/70 av. JEW d Therefore, for the preloading operation, it is assumed that flan 6e deformations are not affected by end loads on the bolt, that the length of the bolt is to the spherical seat on the tensioner, and that the bolt and tensioner parts included in the assumed beam are of constant section equal to the bolt section. End loads on the bolt are then determined as direct functions of the mismatch in flange rotation. The seal leakage load (Po) is included to enable evaluation ~ of the structure in the event of leakags of the inner seal. The load is applied at the midpoint and is taken as a vertical
~1oad applied at the ' midpoint between the 0-rings and equal to the pressure load acting on the area between the 0-rings, or Po - P(Ro, - Ro1).
The bearing load (B) acting between the flanges, is assumed at the mid-radius between the 0-rings. This load is expressed in terms of pressure and bolt load by applying the require-ment for equilibrium of vertical loads, or B=(1/Rp)(FRp-fPRo3 D) - P o. The friction load between the flanges is equal to the friction factor times the bearing load, or ' HB = fB . The friction factor is determined from' hydro test results on a similar vessel (Millstone 224" BWR) where initial flange ' slippage, evidenced by the loud noise common to this condition, occurred at 500 psi. Calculation of the friction factor was Eccomplished by requiring continuity of the flanges at the 500 psi pressure and the bolt load detemined from the preload, and substitution of the resulting bolt load into the above equation. Thermal loads in the structure were derived from the coolant temperatures defined by specifications (Ref. 1) by combining the defined operating conditions into composite conditions as follows: a) Temperature of the structure during steady state opera-tion is taken ao equal to coolant temperature. _ _ _ - - _ - _ - - . - _ ^
D *IO ' A884= 1A COM;USTION ENGINEERING, INC, NUM1EP - SHEET O .bD ENIINEERINO DEPARTMENT. CHATTANOOGA. TENN. CHARGE NO- 214" BWR oxy,1/3d/70 my DGM . DEscRenop CLOSURE REGION eggeg oxy, 'l/M/70 ny JEW' V' b) Heatup rates of 1000F/hr or less are assumed to have the same range and rate of temperature change as the normal startup condition. The temperature distribution in the structure is determined from a finite difference sclution programed for the IBM 360 Comptter and described in Calcu)ation T-101 This condition is called "startup" and the required cycles are equal to the sum of the in-cluded cycles, c) ' Due to lack of similarity with any other condition, the shutdown flooding condition is treated as a separate con.- dition. Temperature distribution in the structure for this condition is determined from the finite difference solution of (b) above, d) Cooldown rates of 1000F/hr or less are assumed to result in the same temperature distribution as occurs at the end of shutdown. This temperature distribution, ob-tained from the same finite difference program as (b) above, is called " shutdown," and has a required number
** of cycles equal to the sum of the included cycles.
e) Heatup rates of greater than LOOOF/hr are assumed to be step temperature changes and are combined into a com-posite condition called " rapid heating." The structure is assumed to be at the minimum temperature of any of the included cycles, the surface in contact with the coolant is taken as the maximum temperature of the in-cluded conditions, and the required cycles are defined as the sum of the included cycles. f) " Rapid cooldown" is used to define conditions with cool-down rates greater than 100 F/hr. These temperature changes are treated as step changes with the structure assumed at the maximum temperature of the included con-ditions, the surface in contact with the coolant at , the minimum temperature of the included cycles, and the l required cycles equal to the sum of the included cycles, j Geometry of the structure is defined by the design drawings. Actual dimensions used are based on the following considera-
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O~N M* " # 1 l COMBUSTION ENGINEERING, INC. NUM EP q ENGINEERINS CEPARTMENT. CHATTANOOGA. TENN, CHEET f CHARGENO- 229" BWR DAT, 1/29/70 sy_ DOM oEncR Prior CLOSURE REGION CHECK DAT* I! SY JEW
- 1) For the continuity analysis, thickness of the closure l shell is taken as the machined thickness at the shell- I hub junction rather than the minimum drawing dimension, thus more nearly representing the actual stiffness of part. 'The minimum drawing dimension is used for calcu- l lation of stresses.
- 2) Thickness of the vessel shell used in the continuity ,
analysis is taken as 1/2" greater than the minimum j
- drawing dimension so as to more accurately represent i the actual stiffness of the part. This is justified by material ordering practices where plate thickne'as, af ter forming, is 1" greater than the minimum required wall section so as to allow for possible machining needed to satisfy code out-of-roundness tolerances. Since the ;
added thickness is divided' equally .on each side of the wall centerline, the maximum machining cut would be 1/2" thereby leaving 1/2" added thickness except in possible ! I local areas. Conservatism is assured.by using the mini-um drawing dimension for calculation of stresses.
- 3) Geometry of the closure and vessel hubs are obtained from full scale layouts of these sections.
- 4) In accordance with known' thread loading patterns and with tests performed by Biach (Ref. 23), the effective length of the bolt is assumed to extend into the vessel flange and the hub a distance equal to the shank radius.
- 5) The bearing load at the flange mating surfaces is treated as a point load acting at the midpoint between the 0-rings. Although the actual radius of the bearing load cer.troid changes with load changes, past attempts to include these radius changes have resulted in large increases. in complexity of the analysis without signi-ficant improvement in the accuracy of the results. In evaluating this assumption, it should be noted that the difference between the assumed dimension and the radius calculated for similar vessels is very small for most operating conditions. ,
- 6) The basin ceal skirt is neglected in analysis of the i closure region since comparison of the seal skirt stiff-ness with that of the closure parts shows the effect of the skirt on flange deformations to be insignificant.
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- COMBUSTION ENGINEERING, INC. NUM EP -
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EN::lNEERIN3 EEPARTMENT. CHATTANOOGA. TENN. SHEET M' M CHARGE NO 2.14" BWR oA7, 1/3s/70 my DOM otsCRsrTiop CLOSURE REGION
- CHECK DAT* 1 h o/70 sy. JEW 7
V Continuity' loads in the structure resulting from either self-constraint or constraint of adjacent parts are determined by equating deformations of adjacent elements. Basis of this solution are requirements for continuity of the structure at every point and equilibrium of internal and external forces. Loads required to maintain structural continuity are determined by equating edge deformations of adjacent elements when each element is treated as a free body subjected to the action of appligd loads and the unknown edge, or continuity, loads. The Seal-Shell-2 Computer Program (Ref.10) is used to deter-mine load-deformation relations for the element formed by the closure shell and hub. For this solution, the continuity loads, consisting of a radial shear (H1 #/in) and moment (M t in-#/in) are represented by a dummy. shear (GRN = 27RH1 = 10e#) and moment (GMN = 2FR Mt = 10e in-#) applied at the bottom edge of the element. Tha internal pressure load is applied as a uni- I form internal load (pi = 10 8 #/in a) and a blowoff load
,. (GZN " p1 va2 #) applied at the bottom edge. Deformation ~co- l 9 efficients for both general (axial gradient effects) and local (radial gradient effects) temperature gradients are included by entering temperatures at the surfaces, quarter points, and midpoints of each node. Influence coefficients for each load are calculated by multiplying the deformations obtained from the Seal-Shell solution by the ratio of actual load to the in-put load.
Deformations of the closure flange are calculated by use of standard equations (Ref. 4) for deformations of rings. Local deformations at the flange-hub junction are included as (Ref. 9) EK1 = = f (R/t)(1-p*) EK2 = = = 2.76 (1-p-2p*)/t EKa = = 7.6 (1-p*)/(t)
,. where t = t + 0.75r and f(R/f) is from Figure 5, Ref. 9 Al-though the threaded joint between the nut and bolt, and the
- bearing junctions between the nut and washer and the washer and flange do not conform to normal requirements for a fixed
COMBUSTION ENGINEEFtlNG. INC. N E EP 4E ENIINEERINS liEPARTMENT. CHATTANOOGA. TENN. CHEET *5U CHARGE NO- U BWR ' PAT, 1/db/70 my_ nnM DEscRsPrOp CLOSURE REGION M CHECM DAT* I SY JEW , joint, the structure is conservatively assumed fixed at this . point. Howe ve r, this conservatism is reduced by including the local flexibility effect for moment rotation, or EKB" " bha = 9.0077 I/d* where Z = bh*/6 = rd8/32; bh* = 3 d*/16 to convert from the ~ rectangular section of the reference to the actual round section. Radial deflection of the flange centroid due to temperature is calculated by using the nodal block average tempe rature . Rotations of the flange are determined from the mean vertical temperature gradient through the centroid. Slope of the top surface of the flange is taken as that re-sulting from the difference in axial growth between the bear-ing radius and bolt radius divided by the distance between the radii. Vessel flange deformations are calculated in the same manner as for the closure flange. Total deformations of the bolts at the top of the closure flange are obtained by adding bolt deformations to those of the flange where the bolt is treated as a beam cantilevered from the vessel flange and subjected to the action of combined axial and transverse loads. De for-mation coefficients for the bolt are obtained from Table VI, page 148, Ref. 18 as follows:
- 1. Case 13 -is used for combined tensile and shear loads.
- 2. Case 8 is used for combined tensile load and moment by assuming the beam length to be twice the effective bolt length and converting the compression load of the reference to a tensile load by use of relations on page 147 of the reference.
Since deformations of a beam subjected to combined axial and transverse loads are a function of the axial load, exact solution of the bolt deformations would require an iteration solution. However, evaluation of the coefficients for the range of bolt load normally expected for designs of this type shows a maximum variation of approximately 6 % from the average value, or: O
COMBUSTION ENGINEERING, INC, NUM;EP S-1OI '" E % 8I$1 ENGINEERIN D DEPARTMENT. CHATTANOOA. TENN. CHEET "44 b I7 cnARosno 2Z4" BWR DAr- 1 /36 /70 av..DO M _ g DESCRis riop CLOSURE REGION CHECK DATr 1/Jd/70 sy. JEW. _ %/ FT (assumed) 50 kips /in 70 kips /in 90 kips /in Gli = (1B- tanh U) 2253.8 2140.5 2032.8 100.71 Gic = (c hU) 95.299 90.275 Gaa e (k tanh U) 6.2529 5.9804 5.3372 where k = JFT /EI U=1k 3 Thus, using the load required to maintain sealing at design conditions (FT ) allows direct solution of the bolt deformation relations within the accuracy of the analysis. In evaluating
, bolt deformations with respect to assumptions made regarding y local flexibility effects and bolt load, it is interesting to compare the coefficients obtained from the equations used herein to those for a cantilever beam subjected to transverse loading only.
Loading Equations Gli Gia Gas i Axial plus transverse 2140.5 95.299 5.9804 Axial plus transverse 2768.8 114.13 7.1096 plus local effects Transverse loading only 2628.6 118.4 7.0796 From this it can be seen that even though including axial load and local flexibility effects is more theoretically cor-rect, accuracy of the solution is not significantly effected.- Equating edge deformations of adjacent elements gives a set of six simultaneous equations in terms of the applied loads and the unknown edge (continuity) shears and moments. For this analysis, these equations are solved by matrix algebra c using the IBM 360 computer.
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COMBULs10N ENGINEERING. INC. NUM ER.T*IOl N O! N EN21HEERIN3 CtPARTMENT. CHATTANOOGA. TENN. CHEET - CHARGE NO 2&(" BWR oar, 1/30 /70 ny._ DOM-- oEscntrnop CLOSURE REGION CHECM DAT,1/J9/70 av JEW . (- In addition to the normal operating conditions considered in the preceding continuity solution, the special condition of non-uniform bolt load, and change in load path, for the bolt tensioning operation must be included. Since the added flexi-bility of the bolt and tensioner eliminate requirements for radial continuity between the bolt and closure flange, con-tinuity loads in the structure are calculated by setting the shear load (Ha) and moment (Ma) a't this joint equal to zero a,nd solving the resulting two sets of two simultaneous equations., This solution conservatively assumes the tensioning load to be applied uniformly around the circumfer-ence rather than to only four bolts at a time. In determining the loads needed for continuity of radial dis-placements and rotations, the bolt load is treated as an applied load. Howe ve r, the bolt load actually consists of the bolt preload (Fp) and the bolt load needed to maintain vertical continuity between the top of the closure flange and i the bolt (Cut II), or U#" F = Pp (Eatm ) + V where V is calculated by equating vertical deflections EYaa = EYsa Thus, the contin'ulty bolt load is expressed as a function of the applied loads and includes deflections due to flange rota-tions, compression of the nut and flanges, tension of the bolt, and thermal growth of the flang'es and bolts. For the bolt tensioning operation, the load is applied directly to the bolt so the bolt continuity load is zero. Also, since the overpressure condition exceeds design pressure, separation of the flanges may occur so continuity bolt load is taken as zero for this condition. Continuity loads at the junctions of the shells and hubs are calculated by rationing the Seal-Shell. 2 Solution Output Loads at these points by the ratios of the actual applied loads to the dummy loads used in the solution. For convenience, the part of the calculated load at the closure nub edge due to the radial component of the pressure load is removed from the continuity load.
NUM!ER- 5-101 ( CN(- HH COMBUSTION' ENGINEERING INC. ' ~ ENGINEERIN3 CEPARTMENT. CHATTANooCA. TENN., CHEET CHARGE NO- 2 W BWR oxy, 1/fe/70 av DGM orsCRirriop CLOSURE REGION CHECK OAT, 1/24/70 av JEW p V As previously noted, operating bolt load consists of the bolt preload, adjusted for temperature effects, plus the continuity
- bolt load, or D#"-
F = Fp (Eatm ) + V where the bolt preload is defined as 'the load needed to main-tain gealing at design conditions. Thus, where the required seal' load is Fo = 1000 #/in from CE experience,. the design bolt load can be calculated directly from requirements for equilibrium of vertical forces. Then, solving for the pre-load where the operating bolt load is known gives the magni-tudo of preload for operation and hydro test. Loads applied to the bolts during tensioning are determined directly from graphs included in the tensioner instruction manual (Ref. 23). Operating bolt loads are calculated by substituting applied loads into the equation for the continuity bolt load. g,, . Vessel stresses were calculated at the four cuts indicated in Part C.8. Minimum thicknesses were used in all cases even though the nominal dimensions indicated on CE drawings reflect the more general values at critical cuts. Primary local + bending loads for this area are equal to General Primary loads as defined in Section III ASME Code { (Ref. 2). However, stresses due to discontinuities were in-cluded to . check for yielding at any point, thus guaranteeing the elastic action of the structure under Design Operation and Code Hydro Test conditions. These stresses were com-pared to the minimum yield point for tensile test'. specimens of the material. The following stress categories are evaluated for the. vessel
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and bolts as specified in Section III, ASME Code and customer specifications: j Vessel
- 1) General Primary Membrane Stress Intensity.
<' 2) Primary Local + Bending Stress Intensity. ! *" 3) Primary F Secondary Stress Intensity Range.
- 4) Peak Stress Evaluation.
1 l COMBUSTION ENGINEERINO, INC. NUM;EP t-t o l CENc nsi , ! EN!INEERIN3 CEPARTMENT. CHATTANOOGA. TENN, 6HEET 2- ID' . 2Z4" BWR 1/3o/70 ' CNARGE NO- ogy, ny_ DOM ; DEsCn PTiop ' CLOSURE REGION CHECK BAT, '1/30/70 sy. JEW f i Bolts i
- 1) Maximum Average Bolt Service Stress.
- 2) Maximum Bolt Service Stress.
- 3) Maximum Primary + Secondary Bolt Servic~e Stress.
- 4) Peak Stress Evaluation.
Primary + Secondary + Radial Thermal Stresses are also calcu-lated. Bearing stresses are evaluated for the washer and mating surface. 0-Ring separation is calculated as required l by customer specification. Finally, a comparison is made between the above ecnditions and ASME Code and customer limits. 1
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COMDUSTION ENGINEERING, INC. NUMDCR " * * *
--*~s.er ENGINECftlND DCPARTf4ENT. CHATTANOQ2A. TENN. GHEET N OF ~80 CHARGC NO DATP I' I7# DY M.
DECC Rit' TION - C Losu re Ree jio n .cNceg Day, f - to -? o oy 7 w - l C.o Debkd bdusts y l C.B _ Vessel M resses c l C.8.4 Peal Stress In4emsibes , , l c (c: 5' O ELemenh (O Cuk
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COMDUSTION ENGINEERING, INC. NUMDEP ENGINEERING DEPARTMENT. CHATTANOOGA. TENN. SHEET OF 48l' CHARGE NO- 22' # b DATr I * $8 ~70 BY N DESCR:PTiop b l05V f C- b89tOO CHECK DAir I~3o~70 BY 78 f.g) DeM d L ies
^ ro , C.& \/emd bodies.
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cot 43USTION ENGINEERING. INC. NUMDER d ' ' L6 NC- //14 CNGINCCRINS DEPARTMENT. CHATTANOOOA. TENN. OHEET N _CP A U cuAnan No.- 22.V 8 W R- l~to-70 oATv sy H DECr.mFTION Cl.CSUCE. k.8ilDo CHECK DATF I"M ""70 __OV- Y V { _C .o D1%M k.5\ws c.R %..iS+cekes >ro I C.S. 4 Ped-. S+ cess Tn6shes 4,, 4,.z s c., z ,-
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COMGUSTION ENGINECtING. INC. tiuuntn SiOI CN //39 EnosticcnlNG DEPARTMCt4T. Cli ATTA!400GA. TCl4N. CHECT OF CHAnGC No. Nb O pays- l - Id ~N OY N occc HPTIOtt CLOSUCC. h.8it On _. . CHECK DATF I ' I# ~7# OY IP 0.0 De.hdc3 kndests c.& b et h eises f" C.8. 4 Peaft. hss Tn6shes L 4,.z s c,z j J = 17. E l [-t.E.Menk O Ou.k .T. T., = J. o _ Pa.o%,, i4 cas e, g_, i mi g3, 4 57, Gamla'eh Me4 A 4ager
~ 2.% tjuv.t In (kaY t.Nd, he dre% meed::ho s 42ctor -
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< Sw,nco -1ss t il.B . - 16.3 u 1.0 16.t. c6.4 Su a at 1.4 6t o 2,, a go.'1 -14./ s q.o $ ort (Io 6 5. 0 l 17.0 2.6 /7.o -/ 5.1. a .'s
f COMBUSTION ENGINEERING, INC, NUM ER DIUI C D N (* //11 ENGINEEfttN3 oEPARTMENT. CHATTANOOGA. TENN. CHEET OF--- N*b CifARGE No- EU SM OAyr '\l'O-M _gy_ D oEscmer:Op O OWP- ffG40^ I - 3* -7a
/ CNEcx OAT- y- 7F b
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%h ! p@ in 4s4R %,g ' = [g 3 Nh *'A' 3 L's,3 1,67 1 (Ir ' -f 7( _
p Desty pesign Desqn ' Dest 1n S$eah Inner Q f N'~N'#^ Bot..e "Rnsioning gott Beloal Prussure.
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Ms - l45 4 4 - Y 9 4.70 -276.19 -147Al - 16 9.I 2. -\lG.s5 M4 8.07 15.75 o o o o 8.07 / 5'.7 3 4.4s f t.5% 6.45 11.5 8 i M 55 - 12AI. 110.88 -41.31 /62 66 - Z 5.Gl1 58.45 -/9. 3_2 23. to_ .II/.41 15. W - y o t .,ts u.o9 CTTs o o u o 0 Q o o o e o (Tr 5 2. - t/.3 9 36,9i -g 1.,11 (,2.6 C -2367 3255 - 6.t s 3d.93 - 8. 0/ %.o1 -1.Bo
& a b.t3 **' -3.74 + 4.06 o o /4.1s IL.91 3_S.E4
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COMOUSTION. ENGINEERING, INC. NUMDER 9,\01 CEMC //39 cNGINEERING DEPARTMENT. CHATTANOOGA. TENN. tlHEET 0F - A Nb CHARGE NO- NWG DAT'* .~ O~7 BY 78 nEsen:PTION O!MR BOO.S eggeg oxysr I~Io~70 sy Y d.0 D d ai'.cd A.3d vs:s pq ts dM YES$d. bTrdsSe.s f,= /2.,S/ l C-.B.t Pc 't STr eu In+ensches 1,, , s.n
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- n. u u 10. i s 2. M. ns n.oIs 6b5 TG1.Lb - 12 24 G - 3.117 /. /, 84.29 - 1 5 2. 4 9 - z% , %7.
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- 2. -14_,41 38.48 -31.41 S'I .%) -43.5 B St. Bio -3.1'1 10 15 -tit 3 3G,g3 145.o n 3 G ,4L
~#7 (4 tin l'I.*19 l'l .91 2 39 0 t L.13 2, ,}9
! $7' -3As L.35 - 6.49 t o.sg. -G.ot 9.15 -5.3o 8 59 -3.78 6.. i t -L.i1 3.93
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COMGUSTION ENGINEERING. INC, NUMDER 5 0t CENC v3f EH2tNCERIN3 DEPARmr.NT. CHATTANOOGA. TENN, gNEET N OF AU CHAW. /. NO.- bW DATP II"3e-70 l DESCRIPTION-- 0%re boon _gy % l ' eggeg ogy, ) -3 o -7o _ , y_ W l
- d.0 De$ai'.cd Ana\qsis psqt l C.S Vessel Smsses A ,= iz.38 f..B.+ Peg STree Infensches /,,, t.ss t,,
ru = r.O. g\rn Ei.emen4 @ cu r BI -
&_! K1, 6%4p ar3 g* _8 t 5 3 h3 ' bm % 4 11 . 49 A ll !
s = YN t ub%% >Ek + g k R, to in' r4 'f*hih" 5 ,* Es,3 /. 61. C' -k ik Hydi a Ilydro flydro sol + Q}',e BoU Prezure
%sionm1 l'reNal ~53h briercLa. b a. b a. b a. b al. lb 'w P o o 1. ss s a b F ll 9. 24 90.10 1 ts. 4.5I Ehe -765.fr -365. 8 8 -311.36 H3 20.%o ll.883 G,iW(
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I O COMDUSTIONI ENGIMEERING, INC. NUv3ER \D\ CEk\C //ff - Ef4GINCCRtt4G DEPARThCNT. CHATTANOOGA. TENN. SHECT OF A ~" CHARGE NO- 2 ZW I3 I.All"- DATF_' b"30~70 BY J DCOCRIPTION IN U- - O ~3#~7# CHECK DAT* BY C. C. Delinlcj Anai.pis, ..
- t. ,,5 g 0.3 Vcsse.\ hresses rt.- . o c. I C.ss Peat s,ress h4ms A = s.s,r 9s fa Ty b ; = c., C'o Eletno.n .y @ cut V As = 68/I r_,_
! Pd L'Tv 4 /o m v K a y A
- M "'
ai = g y, g - + Cv T From 2 0. ti : in A.1.2 ; l , Or A = 4.'l , %,,.4 = .o1 /. h,,,, * .'LS g ,. Pd*4 gt # W 4_ E6v + G'Ty b n g '. i v ' gq w At , M" s {-4 = o s ,*, p = . u. g_p , From Rei 11, Fi$ A, .1. l : 0~r- = I+1 . b E = ', o / K. = 5.o ' l . . N . s. .o 16vs = t.o (wQ gwg a.. a e m = 2.. o (a,M
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Desi7n BOL+ Tensicmim a lb R? sign 13aL+ Preload
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COMBUSTION ENGINEERING, INC, NUMDER L ##07 EN0tHEERIN3 DEPARTMENT. CHATTANOO2A. TENN, . CHEET 9 OF-
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CHARGE No b ~ d ""3 0
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DATR- -YN B DESCRIPTION
] ton CHECK DATF I"10"70 By Y l
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COMOUSTION ENGINEERING, INC. NUMDER C 01 CEMC Ng ENGINEEmHG DCPARTMENT. CHATTANOOGA. TENN. OHEET OF k ~bO CHARGE NO- bNS DAT 8" ' \- - l o - 7 0 gy. 78 . otscmPTsoN RUE' T# &N #jlOO _ CHECK DATF f o-70 gy W l C.0_Dc4atl_c3 Anabtsis r. = . oc r, ! 0.s Wssei Mresses ru .o c. C .S,4 Peal Snlass TA4ewsEss la= s.37G l4, /s es -
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COMBUSTION ENGINEERING, INC. NUM2EP $-/0t CCuc 1f3$ ENGINEERING DEPARTMENT. CHATTANOOGA. TENN. SHEET 47 OP 'Sb CHARGE No- b DAT* I~IO~10 BY I DESCRIPTIOP. 0205006 EstA inti CHECK DATF I'I#* Q - BY c.o De4-ard %agm . 5 c . 8 Ve.ssd S4ce.s,se.s C.B. 4 Pe.at. s+ cess Intensi+ie.s i E maamum aL4e.mahw) shess in4ewsthg al eachc.ut. ! is fabula+e 1 be.lous . ' j
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l l COMBUSTION ENGINEERING, INC. NUMDEP 101 C E MC. JlJi EH*lNEERINS DEPARTMENT. CHATTANOOGA. TENN. CHEET N OF- "U CHARGE N0 2W ISDW 'N e~70 i DEscRmrior Ok nnure Me W DATr BY13. cHEcx DAr,1 70 y( . ' my TP I A.O Oehalled Ad\0\l4 SIS QJ LL4 54ce t s e s
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4 Y APPENDIX B THERMAL ANALYSIS W l i I i 1 l L i
APPENDIX B THERMAL ANALYSIS i Report Title Pagc T-100-F General Description for Thermal Analysis B-3 Physical Properties B-16 Nomenclature B-19 Refe rences B-21. T-101-F Closure Region B-23 T-102-F Vessel Shell B-40 T-103-F Support Skirt B-43 T-212-F Feedwater Nozzle B-57 T-213-F Core Spray Nozzle B-68 . T-214-F Control Rod Drive Hydraulic System B-81 Return Nozzle T-221-F Recirculation Outlet Nozzle B-89 T-222-F Recirculation Inlet Nozzle B-98 T-234-F Control Rod Drive Nozzle B-125 i T-4'07-F Shroud Support B-134 1
COMBUSTION ENGINEERING, ~lNC, NUMDEP U"V" 4J 7 A Avv u ENGINEERIN2 DEPARTMENT. CHATTANOO2A. TENN, EHEET S"3 OF B-197 CHARGE NO. 21466 DAT, 10/1/69 sy Kinyon oExRinION GENERAL DESCRIPTION FOR CHECK DAT, 10/8/69 av Chen THERMAL ANALYSES
\ , ABSTRACT This portion of the thermal report contains the information which is common to all of the various analyses performed for determining temperature condition to be considered in the stress analyses. Phases considered are Methods of Analycis, Correlations for Film Coefficients, Fluid Flow, j General Assumptions, and Physical Properties. A table of i Nomenclature and a list of References are included. !
The thermal analysis for each specific area defines the transients and boundary conditions, and presents the nodal pattern assumed and the temperature conditions at the critical times in the transients. eb 1 l l l l k l
COMBUSTION ENGINEERING, INC. NUMBER CENC-1139 T-100-J B-l'47 ENGINEERING DEPARTMENT. CHATTANOOGA. YENN. SHEET OF CHARGE NO- 21#bb DAT, 10/1/69 oy Kinyon DEsCRirr:Op GENERAL DESCRIPTION FOR CHECK DATn 10/8/69 ey Chen THERMAL ANALYSES METHODS _OF ANALYSIS Digital Computer Solutions - Transient and steady state temperature distributions are determined by use of the finite difference re-laxation method as programmed for a digital computer. The general equations used are those developed by Hellman, et al, (1), which permit the calculation of film coefficients, flows, variable properties, and internal heat generation. One program applies to bodies of irregular shape or having boundary conditions that in-volve two- or three-dimensional heat flow while a simpler program is used for one-dimensional analyses. The body being analyzed is divided into a system of blocks or nodes. The general finite difference equation for the change in temperature of any node "j" in a time interval is: n=N T -T AT) = gg- I 3 1. j n=1 jn The term jRn represents the thermal resistance between node j and node n. The basic equation for thermal resistance is: R= f 2-where L is the length of the heat flow path, k is the thermal con-ductivity of the material, and A is the area normal to the heat flow path. In the case where the resistance between two nodes is composed of two different materials or there is a film coefficient to consider, , the I'esistances are simply added in series:
+ )Rn" n f + R) 3.
The thermal resistance of a film is Rf= 4. where h is the film coefficient and A is again the area normal to heat flow.
COMBUSTION ENGINEERING, INC. NUM!C CENC-1199 T-100-F B-5 ENGINEERINO DEPARTMENT. CHATTANOOCA. TENN. CHEET e, B-137 CHARGE NO- 21#b6 DAT, 10/1/69 ,y_ Kinyon DEsCnier:ON GENERAL DESCRIPTION FOR CHECK DAT, 10/8/69 ,y Chen i V THERMAL ANALYSES
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Occasionally, block geometry or material make up necessitate calcu - lating jRn as several resistances in parallel. In that case, the following form is applicable: 1 R- = Rt 1 + Ra + ... + R1 i . 5. The temperature of node "j" is calculated at successive time intervals AT using ATj from equation 1 as follows: T3 (T+AT) = T + AT) 6 l l The stability criteria for the temperature equation is: C AT < n=N y 7. E ~ RD L n=2 ?v i where specific theheat thermal capacitance and volume of node (Cj")j"s the product of density, Output at specified iterations or times consists of the nodal tem-peratures and any film coefficients, flows, or other special values computed. l Steady State Temperature Distributions as determined by the finite ! difference relaxation method utilize the following equation: n=N T l I + S "' R l T = ""1 d" l J n=N y 8. i I R n=1 j n I 1 where q "' represents internal heat generation. - The expression is equivalent to performing a heat balance about node "j".
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COMOUSTION ENGINEERING, INC. NUMDER CENC-1199 T-100-F ENGlHEERING DEPARTMENT. CHATTANOOGA. TENN. SH EET
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oF B-137 CHARGE NO- 21#6b 10/1/69 DAT, ,,Kinyon DESCRIPTION GENERAL DESCRIPTION FOR THERMAL ANALYSES CHEcx DATz_10/8/69 av Chen The computation proceeds from an initially specified temperature i i distribution through as many iterations as necessary to re'ach the point where the maximum change in temperature for any node from one racy. iteration to the next is less than a specified convergence ( accu j
< Mathematical Solutions - The basic differential equation (2) in Cartesian coordinates is d*T + d*T + d*T + qu' PC p 'M P @ dz' k k BT 9' i
1 Many specific solutions of this equation for various boundary con-ditions have been published (3, 4, 5, 6, 7). In general, these solutions may be applied to cylinders and plates subject to a temperature transient in the fluid, and to steady state conditions in fins and tube walls, generally without internal heat generation. For gamma heating, the internal heat generation term q'" varies exponentially with the distance from the surface. The steady state temperature equation for a flat plate in a gamma flux and cooled on the incident face is T 7 -T pp
=9 [1 - exp (-px) - x exp(-pt )] 10.
When cooled on the shielded face, the equation is: ttf Tx-T pp = px-exp(-p(t-x)] + exp(-pt) 11. The maximum thermal mismatch and conseque.itly the maximum thermal stress that a temperature transient could cause is to assume that the surface of a body or a thin member attached to a heavy body instantly assumes the fluid temperature, while the average tem-perature of the body has not changed. This conservative assump-l tion frequently shows such low stresses relative to the number cf M occurrences that a more exact analysis is not required. Mathematically, this is the condition of step change in fluid temperature with an infinite film coefficient. The average temperature as a function of time and slab thickness is given by: T=T g + (Tp -Tg ) 1-2 e -(n+1/2 f 9 Fo) . 12
" 8 (n+1/2 )
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COMBUSTION ENGINEERING, INC. NUM ER UMVMW - 1 "" ~ # ENGINEERIN3 DEPARTMENT. CHATTANOOGA, TENN, CHEET oF B-137 l eganag so, 21466 OAT, 10/1/69 ay Kinyon oEscamTION GENERAL DESCRIPTION FOR -cagen oxy, 10/8/69 sy Chen i '< THERMAL ANALYSES The temperature equation for this condition is:
.' exp(-(n+1/2)a Tr a
p0)' Sin (n+1/2)rx/t l T =T x o + (Tf -T ) 1-2 E n=o (n+1/2)r i . 13. l Fig.1 will give the average temperatures of two slabs for maximum temperature difference as a function of relative slab thickness. For a linear gradient terminated by a zero or reversed gradient, the maximum difference between surface and average temperature and between average temperatures of different thicknesses occurs at the end of the transient. The limiting value is given by: T' - T, = - ( AT/AT ) p Cp t */3k 14 This expression applies to flat slabs. For a cylinder cooled on the inside, this equation is: (AT/AT) p C y _ T - T, = - p 'R[InR/R - 3R * - R1 " 15. 2k ,R*-R* 4 o i When applied to adjacent sections of differing thickness, the temperature difference is over-estimated, as axial heat flow tends to reduce the difference. For a sudden temperature change with a finite film coefficient, the maximum difference between the surface and the bulk mean 4 temperature of a slab occurs at the time given by: a [exp(-U 2 Fo )) Nu (U a -Nu ) -=0 Z l 16 j n=o. U * (Nu" + Nu + U a) l l where U n are the positive roots of U tan U = Nu. A curve for the maximum temperature difference as a function of Nusselt j modylus and temperature ratio is shown in Fig. 2. Thermal gradients of thin-walled cylinder and cylinder subjected ) to a step change on the inside are approximated by flat slab l l gy equations. For linear temperature changec, Fig. 3 plots the ratio of T g - T for a cylinder vs a slab as a function of radius to l thickness ratio. i j
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COMBUSTION ENGINEERING, INC, NUMOER U LlW "14.3 9 T-1UV-F ENolNEERING DEPARTMENT. CHATTANOOGA. TENN, CHEET E*9 CF 3-137 CHAnos No. 21#bb DAT, 10/1/69 _ay Kinyon DESCRIPTION--- GENERAL DESCRIPTION FOR CHECK DAT, 10/8/69_ _sy_ Chen THERMAL ANALYSES
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., ,, g q-_ .-__. _4. . . _ ..y - . - g y . 3 . , ,._ .,,,. . . . . . .,g . 3 R a f10: Zink/c Rodin /Wa// 73/c.knen ee
COMBUSTION ENGINEERING, INC. NUMDER CENC-1139 T-100-F ENGINEERINS DEPARTMENT. CHATTANOOGA. TENN. SHEET b~l OF B-137 CHARGE NO. 21466 oxy, 10/1/69 ny Kinvon l uEscainlON GENERAL DESCRIPTION FOR CHECK DAT, 10/8/69 av Chen l THERMAL ANALYSES CORRELATIONS FOR FILM COEFFICIENTS Various correlations are used to evaluate the film coefficient for ' i transfer of heat across a metal-fluid interface. The value of the coefficient in general varies with temperature, temperature dif-ference, and flow. For most analyses, film coefficients are taken . as constant at an average value that over-estimates the stresses. I When more exact temperature distributions are needed, the effect i of temperature, temperature difference, and flow are included in j I the computation of the film coefficient for each iteration in the ! computer solution of the temperature distribution, j Turbulent Flow in Pipes and Annuli - The Dittus-Boelter correla- I tion (8) is the basic expression used for this condition:
- f Nu = .023 Re.e pp.4 17, l This equation evaluates fluid properties at the bulk temperature.
Colburn and Seider-Tate . correlations (8), which are modifications l that include evaluation of fluid properties at film or wall tem- l peratures, are used if the value is more conservative. , Laminar Flow in Pipes and Annu11 - The correlation for pipes (8) is:
' 1 )
DH Nu = 1.86(Re Pr 7)T (Mb)*14 18. 1 For annuli, the constant is increased by 33% (8). , Free Convection - Heat transfer between a body and a bulk fluid without change of phase is correlated (9) by equations of the form Nu = C Ra" 19. The values of the constants C and n vary with the physical arrange. - ment, the fluid, and the value of the Rayleigh modulus, which is the product of the Grashof and Prandtl moduli. These equations are based on steady state conditions, after natural convection flow has been established. In the analyses, however, the calculated coefficients are assumed to apply from the start of the conditions that induce free convection. Normally this is the conservative assumption. _ OA
COMBUSTION ENGINEERING. INC, NUMIEP CENO-LL39 T .Luu-r enGINEERIND NEPARTMENT, CHATTANOO2A, TENN, CHEET B-11 SP B-137 CHARGE NO- 21#bb DAT, 10/1/69 g Kinyon oEsen PTioN GENERAL DESCRIPTION FOR CHECK DAT,10/8/69 ' ey Chen THERMAL ANALYSES 1 TABLE 1 VALUES OF CONSTAWfS FOR FREE CONVECTION Characteristic Rayleigh
%rrangement Fluid Dimension Modulus C, n, Vertical Plates or Gas / Liquid Height < 10s .56 Cylinders .25 Gas " > 10e .12 " .33 Liquid > 10s .17 .33 Horizontal Plate, Hot, Facing Up, or Gas / Liquid Long Side < 10s .54 .25 Cold, Facing Down " " " " > 108 .14 .33 Reverse of Above " " " "
All .25 .25 Boiling and Condensing Vapors - During an increasing temperature transient, the saturated steam will condense on the head and ves- 'V sel wall above the water level. The correlation for film con-densation on a vertical surface (10) is taken to be 1
'gp (p-py )k* hfg (1 + .68 C p AT/h p g)'I h = .943 7 3,7 20.
This equation is valid for Pr > .5 and C p AT/hrg ( 1. The viscosi-ty is evaluated at an average temperature taken as Tw + 1/4 ATsat where ATsat is the difference between the saturation and the wall surface temperatures. When the pressure is reducing, as during a cooldown transient or j due to loss of pressure, the water will keep at the saturation temperature by a portion of it flashing to steam. The hotter walls will produce boiling at the surface. A correlation for boiling of saturated water (10) is given as: 1 1_ i p sat g/A E o h = .006 h pg, g (py -py) pp i.7 21. pg This gives the film coefficient at atmospheric pressure as 272 (ATsat)2 In addition to the heat transferred by the boiling, the turbulence due to the flashing to steam will transfer an additional amount of heat (10). Thus, the boiling film coefficient is high at all times, and generally may be considered as infinite. l
COMBUSTION ENGINEERING INC. NUMDER CENC-ll39. < T-100-F cNclNEERING DEPARTMENT. CHATTANOOGA. TENN. SHEER B-12 op_B-137 CHARGE NO- 21466 DAT, 10/1/69 _BY Kinyon oEscRwnop GENERAL DESCRIPTION FOR CHECK DATr 10/8/69 _av Chen THERMAL ANALYSES
!!ormal correlations for convective heat transfer apply for the steam when the wall is hotter., and for the water when the wall is cooler.
Enclosed Gaps - A correlation for heat transfer across an enclosed gap by: at various angles with respect to the horizontal (11) is given 1 Nu = C Ra5 Pr* 7*
- 22. i The values of C for various angles and the ranges of Rayleigh i moduli for which the correlations apply are given in Table 2. j t
i TABLE 2
. l Angle, Degrees C 0 (Horizontal) .069 1.5 x 105 < Ra < 7.5 x 108 30 .065 i
45 1. 5 x 10" < Ra < 2. 5 x 108 60
.059 1.5 x 105 < Ra < 2.5 x los i .057 1. 5 x 105 < Ra < 2.5 x 108 90 (vertical) .049 5 x 104 < Ra < 2.5 x 108 For Rayleigh moduli below the minimum, as occurs between the sleeves and heat in the control rod drive nozzles, convection is suppressed transfer is by straight conduction.
Water behind a nozzle liner, if flow is low, may be considered as being in.an enclosed gap. Heat transfer is a maximum at the top or bottom, and a minimum at the other position. The correlation ! for the maximum heat transfer coefficient as given in Table 2 is used, and the resulting temperature distribution assumed to be symmetrical about the axis. For rapid transients, the thermal inertia of the liner and the water has significant .effect in reducing thermal stresses, while for longer transients and steady state conditions only the thermal resistance is a factor. For the condition that has appreciable flow behind the nozzle liner, the fluid is taken as being at the ambient temperature of the nozzle fluid. This is conservative, but nearly correct, as the annulus. the water changes temperature very slightly in flowing through The flow in the annulus determines the film co-efficient, which generally is much lower than in the nozzle.
f COMBUSTION ENGINEERING, INC, NUMIES CENC.:1139 T-100.-F B-13 ENGINEERIN3 DEPARTMENT. CHATTANOOGA, TENN, EHEET ;, B-137 CHARGE NO: 21kbb DAT, 10/1/69 sy_ Kinyon 8 DESCRH' TION GENERAL DESCRIPTION FOR eggegoar, 10/8/69 sy_ Che n v THERMAL ANALYSES
\
Radiation - Radiant heat interchange is a factor at the support skirt-vessel junction and between the studs and the head flange. The expression for radiant heat transfer (12) is: q/A = .173 e (TA1) ( A*)
.(1gg) -(1gg) 03, Where the view factor is about 1, and A1 = A a, 1/c 1 + 1/c a-1 2*
When equation (23) is rearranged to solve for an equivalent film coefficient for radiation and. simplified by eliminating second order effects, the expression becomes: l q/A ~ gT ' h =. 5e{Ai+An[ l rad " Ti-Ta 1gg 25. (%v This simplified form, which is a convenient form for use in the computer difference program, gives an of 100 degrees error at an of lesstemperature average than 2% for of a temgerature 300 F. Metallic Joints - Thermal resistance at metal joints is considered for those surfaces in contact in air or steam, but not when water can wet the joint. Correlation of the conductance is by the dimensionless group, h P/kp, corresponding to the Nusselt modulus, being plotted against the "dimensionless" ratio P/B, pressure in pounds per square inch divided by the Brinell number, which is kilograms per square millimeter. Curves for various materials and surface roughness conditions are given in Reference 13. In general, the thermal resistance at the contact surfaces of the studs, nuts, and washers is very low, as the surfaces are relatively smooth and the pressures high. This gives a short heat path through the air filling the hollows, as well as a relatively large proportion of the surface in contact. When these hollows are filled with water, as at vessel flanges and rolled-in nozzle liners, contact resistance essentially disap-pears. Y
,o
COMBUSTION ENGINEERING, INC. NUMBERCENC-ll39 T-100-F ' ENGlHEERING DEPARTMENT. CHATTANOO2A. TENN. CHEET E-1 OF B-137 CHARGE NO. 21466 OAT, 10/1/69 By Kinvon . I oEsCninlON- GENERAL DESCRIPTION FOR CHECK DATF I O /A /b9 Dy Che_0_ THERMAL ANALYSES , FLUID FLOW 1 Pressure drops associated with coolant flow are determined by use , of Bernoulli's theorem, which in the general mothematical expres- ' sion is:
}
zi +
*+2 **8+ + ~
g
+H L 26 I
i The head loss, HL ,-is due to energy dissipation between points 1 , and 2 due to expansial s, contractions, turns and friction.
" Friction Factors for Pipe Flow" by L. F. Moody (14) is used in l determining the pressure drop due to friction with turbulent flow, ,
i. giving the factor "f" used in the equation , j AP = DH 2g 144 27. For laminar flow in a circular duct (15) the friction factor is given by i f = 64/Re 28 I 1 I and is an annulus, by ' f = 96/Re 29. Factors for coefficients for losses due to expansion, contrac-tions, and turns are given in standard handbooks and text books j l l (15, 16, 17). j l GENERAL ASSUMPTIONS l There are several general assumptions that apply to the analyses. l These are:
- 1. Physical properties are considered to be constant over {;
the range of temperatures considered.
- 2. Insulated surfaces are adiabatic.
- 3. No axial heat flow in the vessel wall or a pipe wall be-yond about 4 x wall thickness from the change in thick-ness.
( COMBUSTION ENGINEERING, INC. NUMIER CENC-1199. T-100-F ENGINEERIND DEPARTMENT. CHATTANOO2A. TENN. CHEET B-15 ;,B-137 CHARGE NO- 21466 oxy, 10/1/69 _,y Kinyon DEscarrr:ON GENERAL DESCRIPTION FOR CHECK DAT, 10/8/69 _sy Chen
%=v THERMAL ANALYSES 3
- 4. The attenuation factor, and consequently the gamma ray energy, is constant through the vessel wall thickness.
The physical properties considered in the thermal analyses in-clude density, specific heat, thennal conductivity and thermal expansion for all materials, with viscosity and heat of vapori-zation being additional factors for the water. The modulus of elasticity and emissivity are factors in structural materials. These properties are all variable with temperature, so that the value selected is average or one that gives'a conservative re-l sult. Where the variable' film coefficient option is used in computer calculations, the variation of the properties with tem-perature is included in the equations. l Considering insulated surfaces as adiabatic is a reasonable l simplification, as the heat flow through the insulation is a l sma11'part of the total heat flow involved in the transients. l Another factor is that when the stress range is being determined I the radial heat flow through the insulation produces thermal ef g , stresses that tend to cancel out, producing little net effect. Axial heat flow in a pipe or vessel wall with heat transfer from the surface is approximated (9) by the relation T -T
- T -T
= eXp(-zJh/kt) 30 H C The slope of the axial temperature gradient is a function of the thickness, conductivity, and film coefficient. The slope is 5%
as great at 3/kt/h wall thicknesses away from a heavier section, and less than 2% as great at 4Vkt/h wall thicknesses away, as at the junction. For a clad vessel wall six inches thick, the 2% l of the slope condition is reached in about 14.4 inches when the ' film coefficient is 200 BTU /hr-ft2 OP. l The gamma flux at the vessel wall comprises a spectrum of energies incident at various angles. As the attenuation factor is hi 6her i for low energy gamma radiation, the radiation reaching the outer surface contains a higher fraction of the more energetic gamma's, and the energy deposition rate is lower. Thus assuming the g gamma flux to be a beam of mono-energetic radiation normal to the surface over-estimates the temperature difference due to the gamma heating. l
COM3USTION ENGlN' EERING. INC. NUMIER_C D 1 M9. T-1.0_O - F ENGINEERING DEPARTMENT. CHATTANOOGA. TENN. SHEET B-16 op B-137 CHARGE nom.-- 21466 - oATE 10/1Z60 syKinyon DESCRIPTION- GEtERAL D_ESCRIPTION FOR _ . CHECK DATE 10/8/69;y_ Chen THERMAL ANALYSES PHYSICAL PROPERTIES l l ' The materials for which physical property values are needed in-clude carbon and low alloy steel, type 304 stainless steel, Inconel Type 600, air, liquid water, and steam. In Table 3 are shown values of the various properties at several temperatures l which cover the range required for the different analyses. For air and steam, the volumetric coefficient of thermal expansion l 1s taken as the reciprocal of the absolute temperature. This is { used in the Rayleigh modulus in the correlation for natural con-vection heat transfer. The values of the combined physical properties and' gravity constant, 8E P, for the fluids are
. pk j
i ! tabulated as the Rayleigh factor. 'For steam, the Rayleigh factor l is taken at the steam film temperature, which is midway. between ! the saturation temperature for the pressure during a cooldown and the wall temperature. I To establish the thermal capacitance of the metal nodes, the density and dimensions at 70F are used to determine the mass, and the specific heat selected for the temperature range. The density and specific heat vary more for liquid water than for I the structural materials, but the product is quire constant over the temperature range of interest, so that the thermal capacitance of water nodes can be considered constant, i The linear coefficient of thermal expansion and the modulus of elasticity of the metals are of interest in determining effective gaps at operating conditions. Differential expansions due to temperatures and pressures can produce large percentage changes in gap widths at thermal sleeves and in control rod drive nozzles, with correspondingly large changes in thermal resistances. l ! l j l \
COMBUSTION ENGINEERING, INC. NUMIER CENC-1139 T-100-F EN21NEERINS DEPARTMENT. CHATTANOOOA. TENN. CHEET b"17 MF 0~137 CHARGE NO- 21kbb DEsCRirTaop_ DATF 10/1/69 ayKinyon GENERAL DESCRIPTION FOR V THERMAL ANALYSES CHECK DATF 10/8/69_sy Chen i. T_ABLE 3 M_ajerial Symbol Property Temperatures ' Carbon and Low Alloy Steel
,(Refs. 18, 19) 70 200 400 6_00 a Avg. linear coeff, of 6.07 6.38 6.82 7.23 thermal exp. from 70 to temp, x10s, per op E Modulus of elasticity 27,9 27.7 27.0 l
x10-8, lb/1n a 25.7 ( k Thermal conductivity, 26.5 25.7 24.5 23.3 l BTU /hr-ft- F I c p Specific heat, BTU /lb i p Density, 1b/ft3 .114 .118 .125 .135 483. Type 304 Stiainless Steel (Refs. 19, 23)
- a Avg. linear coeff. of
- 9.11 9.34 9.59 9.82 thermal exp. fron 70 to !
temp, x10e, per F E Modulus of elasticity 27.4 27.1 26.4 x10-e, lb/in 2 25.4 k Thermal conductivity, 8.5 9.0 BTU /hr-ft OF 9.8 10.6 cp Specified heat, BTU /lb .108 .116 .124 p Density, 1b/ft3 .131 495. Inconel Alloy 600 (Refs. 19, 20) e Avg. linear Coeff. of 7.13 7.40 7.70 7.90 thermal exp. from 70 to temp, x10s, per op E Modulus of elasticity 31.7 30.9 30.0 x10 e, lb/1n 2 29.2 k Thermal conductivity, 8.3 9.0 10.0 BTU /hr-ft- F 11.1 cp Specified heat, BTU /lb .102 .109 .117 p Denalty, 1b/ft3 .123 528.6 hv l
COMBUSTION ENGINEERING, INC. NuuscaCENC-Il39 T-10_Q-J ENGtHEERING DEPARTMENT. CHATTANOOGA. TENN. SHEET E-10 OF B-197 CHARGE NO- 21#bb DAT,10/1/69 sy Kinyon oExa:Priop GENERAL DESCRIPTION FOR cNEcx OAT,10/8/69 eyChen_ THERMAL ANALYSES TABLE J (Cont'd) Material Symbol Property Tempel atures i Water (Refs. 2, 10, 21, 22) 70 200 400 600 ' p Density at saturation, 62.2 60.1 53.6 42.3 1b/ft3 , p Density at 1000 psia, ! 62.4 60.3 53.9 ' lb/ft3 p Vi scosity, 1b/ft-hr 2.3 .75 k .325 .210 Thermal conductivity, .348 .396 .383 .291 BTU /hr-ft-F cp Specific heat, BTU /lb-F 998 1.005 1.08 1.52 o Surface tension, lb/ft -
.0041 .0024 .0006 Pr Frandt1 modulus, 6.8 1.9 925 dimensionless 1.09 .
B Vol.'coeff. of thermal 130 400. 730. 960, expansion x10e, 1/op Ra/L3AT Raleigh factor x10 e, 238. 2270. 8320. 14100 1/fts-P (at 500F) AM (Ref. 2) 4 cp Specific heat, BTU /lb-F .240 .241 .245 .250 p Viscosity, 1b/ft-hr .044 .0519 .0626 k Thermal conductivity, .0721
.0149 .0181 .0225 .0265 BTU /hr-ft-F Pr Frandt1 modulus, .709 .693 .682 .680 dimensionless " ._
Rayleigh factor x10 *, Ra/L AT .59 .18
.072 -
1/ft*-F p Density, lb/ft l
.074 at one atmosphere l
Steam (Ref. 21) h fg Heat of vaporization, l 978 826 549 BTU /lb p Density, 1b/ft 8 .0297 .537 3.74 For Rayleigh factor: Pressure, PSIA 184. 325. 540 850. l Film temperature, F 460 485. 510 535. Rayleigh factor x10 *, Ra/L AT ! 35.2 105. 340. 890. 1/ft -F : { i l
, COMBUSTION' ENGINEERING, INC, NUMIEp UMU-11% T-100_-F ENalNEERIN3 DEPARTMENT. CHATTANOo?A. TENN. EHEET E"19 CF E-137 CHARGE NO- 21kbb DAT, 10/1/69 ' av Kinvon oEscairTioN GENERAL DESCRIPTION FOR cwEcx oxy,10/8/69 av Chen THERMAL ANALYSES Y
i NOMENCLATURE A Area, fta j B Brinell hardness number, kg/mm* C Constant, dimension 1 css { Cj Thermal capacitance of node j, BTU /F cp Specific heat, BTU /lb-F DH Hydraulic diameter, ft E Modulus of elasticity, 1b/in2 F Temperature, degress Fahrenheit f Friction factor, dimensionless g Acceleration due to gravity, 32.17 ft/seca or 4.17 x 108 ft/hre HL Head loss, ft h Film coefficient, BTU /hr-ft2-F k Thermal conductivity, BTU /hr-f t-F L Length or geometrical factor, f t N, n Indexing numbers, dimensionless n Exponent, dimensionless ( V P Pre s su re, lbs/ft2 or 1bs/in2 q Heat, BTU /hr q "' Heat generation, BTU /hr-ft 3 R Thermal resistance hr-F/ BTU; radius, ft. T Temperature, degrees Fahrenheit TA Temperature, degrees Rankine AT Temperature difference or increment, degrees Fahrenheit t Thickness, ft v Velocity, ft/sec x,y,z Length on coordinate axes, ft Greek a ft*/hr. Linear coefficient of thermal expansion,1/F; diffusivity, l Volumetric coefficient of thermal expansion,1/F E Emissivity factor, dimensionless l p Viscosity, lb/ft-hr j p Gamma attenuation factor, 1/ft { p Density, 1b/ft3 ! c Surface tension, Ib/ft j T,AT Time, time increment, hr
COMGUSTION ENGINEERING, INC. NUM0ER.SbbC.-1139 T-100-F i ENGINEERING DEPARTMENT. CHATTANOOGA. TENN, E O EH EET OF B-137 CHARGE NO. 21466 oxy, 10/1/69 uy_. Kin yo n oEscalPTION GENERAL DESCRIPTION FOR $ THERMAL ANALYSES CHECK DATr 10/8/69 sy Chen l t i; NOMENCLATURE (Cont 'd ) i Dimensionless Moduli Fo Fourier modulus, a T/t* l Gr Grashof modulus, L S g ATp */p 8 l ' Nu Nusselt modulus, h L/k * , Pr Prandt1 modulus,C p/k ! Ra Rayleigh modulus,p Gr x Pr Re Reynolds modulus, DH VP/4 , Subscripts ! b Bulk C Cold
- f Film; fluid ff Front face -
fg Evaporation ? H Hot i Index number; inside j Index number 1 Liquid n Index number o Zero; original; outside rad Radiation j sat Saturation { v Vapor [ w Wall
- I x, z Position on x, z axis l T At time T 9
r 1 _ i
l I COMBUSTION ENGINEERING, INC, NUMIER OENC-1139 T-100-F ENGINEERIN3 DEPARTMENT. CHATTANOOGA. TENN. SHEET B-21 _Or B-n7 cHARGK NO. 21466 oxy, 10/1/69 _ ny_.Kinyo n i osscRirTroy GENERAL DESCRIPTION FOR CHECK DAT,10/8/69 sy Che n' THERMAL ANALYSES
. r.
REFERENCES I
- 1. "Use of Numerical Analysis in Transient Solution of Two-
. Dimensional Convection",Heat Transfer by S. Problem K. Hellman, et with al. Natural and Forced ASME Paper No.
54-SA-53, 1954. 2
" Heat Transfer", by Ben,jamin Gebhart, McGraw-Hil Book Co.,
Inc., New York, 1961. .
- 3. " Conduction of Heat in Solids", by H. S. Carslaw and J. C.
Jaeger, Oxford University Press, 1948. l
- 4. " Temperature Distributions in Slabs with a Linear Temperature Rise at One Surface", by Anthony, M. L. Proceedings of the General Discussion on Heat Transfer, pp. 236-262, Institution {
of Mechanical Engineers, London, and American Society of Mechanical Engineers, New York, 1951. f l 1
- , y 5.
" Transient Thermal Stresses in Slabs and Circular Pressure Vessels", by M. P. Heisler, J. of Applied Mechanics, June 1953.
6
" Thermal Stresses in Spheres.and Cylinders Produced by Temperatures Varying with Time", by Kent, C. H., Trans. Am.
Soc. Mech. Eng., Vol. 54, No. 118, p. 185; 1932. 1.
- 7. " Tentative Structural Design Basis for Reactor Pressure i
i Vessels and Directly Associated Components (Pressurized, Water Cooled Systems)" PB 151987 U.S. Dept. of Commerce, Office of Technical Services. ! 8
" Heat Transmission" by W. H. McAdams, McGraw-Hill Book Co.,
New York, 3rd Ed., 1954 I i 9. " Heat Transfer Engineering', " by Hilbert Schenk, Jr., i Prentice-Hall, Inc., Englewood Cliffs, N.J., 1st Ed., 1959 i i 10 " Heat, Mass, and Momentum Transfer" by Warren M. Rohsenow l and Harry Y. Choi, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1961. t v i
. l i
l 1 l m
COMBUSTION ENGINEERING, INC. NUMDER CENC 1139 _T-100-F l ENGINEERING DEPARTMENT. CHATTANOOGA. TENN. OF B-137 EH EET CHARGE No. 21466 l oxyr 10/1'/69 av_Kinyon j DEmnieTioN GENERAL DESCRIPTION FOR CHECK DAT, 10/8/69 av Chen ! THERMAL ANALYSES ' REFERENCES
- 11. i
" Heat Transfer by Natural Convection in Liquids Confined by ,'
Two Parallel Plates Which are Inclined at Various Angles ' with Respect to the Horizontal", D. Dropkin and E. Somerscales Paper #64 HT-22 AIChE and ASME Heat Transfer Conference, ' August 1964. Trans of ASME, Series C,'Feb. 1965. '
- 12. " Chemical Engineers Handbook" Edited by J. H. Perry, r.
2nd Ed., McGraw-Hill Book Co., 1941.
- 13. " Thermal Conductance Across Metal Joints", by W. J. Graff, Machine Design, Sept. 15, 1960, pp. 166-172
- 14. " Friction Factors for Pipe Flow" by L. F. Moody, Trans.
i ASME Vol. 66, p. 671, 1944. - l i
- 15. " Fluid Mechanics" by Vie har L. Streeter, McGraw-Hill Book Co . , Inc . , New Yo' rk, 2nd Ed . , 1958. !
i {
- 16. " Marks' Mechanical Engineers Handbook", Edited by Theodore i
Baumeister, 6th Ed., McGraw-Hill Book Co., 1958
'17 . " Flow of Fluids", Technical Paper No. 410, Crane Co.,
Chicago, Ill., 1957.
- 18. " Physical Constants of Some Commercial Steels at Elevated Temperatures", British Iron and Steel Research Association, 1953.
19 "ASME Boiler and Pressure Vessel Code Section III - Nuclear Vessels", 1965 Edition - Revised. ASME, New York, N.Y. 20 AF TR 6145 Parts I, II, III International Nickel Co.
- 21. " Thermodynamic Properties of Steam", by J. H. Keenan and Frederick G. Keyes, John Wiley & Sons, Inc., New York, First Edition, 24th Printing.
- 22. "A Survey of the Thermodynamic and Phys { cal Properties of Water", by E. J. Wellman. M.S. Thesis, .Purdue University, 1950
- 23. " Metals Handbook", Vol. 1, 8th Ed.; American Society for "
Metals, Metals Park, Ohio, 1961. 4
l COM3USTION ENSINEERING, INC, suu:E,CENC-1139: T-101-F ENGINEERING DEPARTMENT. CHATTAN000A. TENN. SHEET b OF B-197 CHARGE NO- 21kbb DAT. 11/3/69 sy__ Che n og.c ,,,,, THERMAL ANALYSIS OF PILGRIM-y cageg oxy.11/5/69 sy_Ki n Von STATION CLOSURE REGION 1
SUMMARY
The thermal analysis of the closure region considers the end of heatup, shutdown flooding and the end of shutdowr.. The results are used in Calculation CE-S-lOl. TRANSIENTS The heatup transient is from 100F to 546F at 100F per hour, with the critical time at the end of heating. Cooldown is at
-100F per hour from 546F to 375F, when flooding st, arts. The temperatures of the water and steam drop to 330F in 10 minutes.
The shutdown transient then continues at -100F to 100F. The critical time is at the end of shutdown. The flanges are flooded at 1,81 hours, when the temperature has dropped to 348F. Maximum skin stresses occur at the moment of flooding of the flanges. Other transients are not as severe, as the film coefficient is very low during the cooling portion of a transient, when the metal is hotter than the steam. In the return to tempera-ture, there is condensation and a high film coefficient af ter the steam temperature rises above that of the wall. This is treated as a skin stress, using the temperature range. THERMAL MODEL Three-dimensional nodal pattern is used to cover a section included between the adicbatic planes of the bolt centerline and mid-way between bolts. Two layers are employed in the circumferential direction. Included in this model are head and vessel flanges, the adjacent head and wall sections, the bolt with the washer and nut, and refueling basin seal skirt. l Figures 1 and 2 show the nodal pattern for the upper and l lower flange sections. ' BOUNDARY CONDITIONS
'~~~ The film coefficient for the steam condensing on the inner surfaces of the flanges during heatup is considered as in-finite. During cooldown prior to flooding, the correlation
1 1 COMSULTION ENGINEERING, INC. NUM!EP CENC-1199 T-lOl- P ( i EN:lNEERIN's CEPARTMENT. CHATTANOOGA. TENN. CHEET b~ 4 OF B-137 CHARGE NO- 21466 11/3/69 oar. sy Chen otaCn:Prio, THERMAL ANALYSIS OF PILORIM CHECK DATr 11/5/69 sy Kinyon STATION CLOSURE REGION for natural convection is used, the value being calculated in l the program according to the instantaneous conditions. After flooding, the film coefficient is again considered as infinite due to local boiling. Heat transfer across the gap between the bolt and the head is mainly by radiation, while that across the gap between the vessel and the refueling basin seal skirt is by radiation and convection. Both are taken as temperature dependent in the p rogram. Conduction across the threads and between the nut, washer and the head is considered as having the same values as' solid metal. The thermal resistance between the flange surfaces in contact is reduced to a negligible amount by the contact pre ssure . The thermal resistance across the gap outside the seal region is taken as constant regardless of the slight variation in the air properties due to changes in temperature. CALCULATIONS The film coefficient in the shutdown transient prior to flood-ing is evaluated by Equation 19 of T-LOO. Due to the tempera-ture and pressure dependence of the steam properties, the equation for the temperature range between 546F and 348F is: h = 1.469 x 10 ~5 (T sat - 100)a. ave Btu /hr-ft 8-F These values are used to calculate film resistances which are then combined with the resistance through the cladding to compute the overall conductances between the steam and the interface. The equivalent film coefficient for radiation is evaluated by Equation 23 of T-100. Using e1 = c a = 0.8 for the studs and head flange, the equivalent film coefficient is: T + 460 T + 460 8' hr d = 0.001154 ( 100 ) +( 100 ) T T x ( A1gg+ 460) + ( ygg 3 + )460 Btu /hr-fth-F
COMZUSTION ENSINEERING, INC. NUM:EP UENU-11W T-101-F ENolNEERING DEPARTMENT. CNATTANOOGA. TENN. SHEET b OF B-197 cNAnoE NO 21466 OAT. 11/3/69 .ychen oEscat e THERMAL ANALYSIS OF PILGRIM- cagex oar. 11/5/69' eyKinyon STATION CLOSURE REGION 4 A higher emissivity value of 0.9 is taken for the painted surfaces of the basin seal skirt and the vessel, giving a constant of 0.001415 for the above equation. For simplicity, each node is only connected to the opposite node across the gap, using the smaller area and a view factor of 1. Convection is suppressed in the gap between the studs and the I head flange, and the relatively small conduction by the air l 1s neglected. The convective film coefficient for the gap between the vessel and the basin seal skirt is calculated in the computer using j h = 0.0626 ATl/* Btu /hr-ft"-F ! i This is derived from Equation 19, T-100. The AT is specified ! as the temperature between Nodes 139 and 353. I RESULTS l 5,, The thermal data for stress calculation are listed in Table 1. The time at which shutdown flooding occurs is 1.81 hours when the water is 348F. l 1 The cut locations are shown in the nodal layouts, and the Index identification is given in the stress report CE-S-101. The print pattern to identify the nodal temperatures is shown in Figures 3 and 4 The computer output from which these data are staken are presented following Figure 4 C gj c Ys (u... i: lb v
I l COMEULTION ENGINEERIND, INC. NUMIEP CENC-1139 T-101-F ENDNEERINS DEPARTMENT. CHATTANOOGA. TENN. CHEET b~ OF B-137 21466 j CHARoE NO_ OAT. 11 /3/69 sy. . C he n, { oEscairfio, THERMAL ANALYSIS OF PILGRIM CHECK DAT* 11/b/b9 BY KinVon STATION CLOSURE REGION TABLE 1 ,() AVERAGE TEMPERATURE, F, AND SLOPE OF O
\*, '
1 AXIAL TEMPERATURE GRADIENTS, F/IN c\
\
End of Shutdown End ofi Index Heatup Flooding. Shutdown Tai 450.0 511.9 204.2 Tea 354.0 530.4 309.8 Tas 483.0 506.0 168.6 Ta 422.9 517.4 235.0 T3B 487.A 505.2 162.2 f T3aB 476.9 508.1 173.5 d(9 .
- s y \ Tsap 420.0 523.1 235.0 yA T33B 496.9 502.6 151.7 Tasp 441.7 518.9 ,211.3 T s'- 453.9 513.7 198.4 T3 290.5. 536.0 353.O ma 1.271 -0.0879 -1.32 ms 1.83 -0.347 -1.986 Radial Temperature Distributions at Indicated Sections of Vessel Head and Vessel Wall End of Heatup for Vessel Head Temperature, F Cut No. {
T Ti T T T T 1/ 4 1/ 2 3/ 4 0 19 536.1 542.5 539.0 534.5 533.5 532.0 1 20 533.4 541.8 536.6 531.4 530.1 528.8 23 520.1 539.3 527.8 516.2
, 512.5 508.8 25 478.5 535.3 503.6 480.7 457.3 409.6
COMBUSTION ENGINEERING, INC. NUMBEP U M b " 11 " T-1U1-f ENGINEEftsNG DEPARTMENT. CNA1TANCOGA. TENN. SHEET b~ oF E-l'47
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( TABLE 1 (Continued) l End of Heatup for Vessel Wall ! j Temperature, F l Cut No. T Ty T j T j Tg T,7 w o W 487.3 536.8 505.2 481.3 465.1 458c. 3 3 M 492.6 537.1 508.3 486.9 472.9 467.R 4 499.4 537.6
/ 512.9 494.4 482.3 478.3 6
(i98.3$ 537.7 513.6 494.5 480.1 472.0 8 '50778 538.7 51 8.1 503.3 494.4 492.4 / Shutdown Flooding for Vessel Head Tempe ra tu"e , F Cut No. T T T T T To 1 1/4 1ra 3 /4
- 19 466.3 461.0 467.7 463 9 468.5 469.3 20 472.3 466.2 470.0 473.7 474.6 475.5 23 484.6 476.1 481.3 486.5 488.0 489.4 25 501.6 485.6 495.3 501.8 507.8 517.0 Shutdown Flooding for Vessel Wall Tempera ture , F Cut No. T T T T T Tg 1 g 0 505.7 488.3 500.0 508.1 513.1 515.1 3 504.1 487.8 498.9 506.4 511.0 512.6 4 501.8 487.0 497.0 503.9 508.1 500.4 6 485.9 495.8 502.8 507.4 509.4
( 8 498.6 484.5 494.2 500.7 504.5 505.4 l W l
COMBUSTION ENGINEERING INC. NUM"EP CENC-1139 T-101-F EN!!NEERIN3 DEPARTMENT. CHATTANOOOA. TENN. SHEET OF- B-137 2.1466 11/3/69 CHARGE NO DATu ,y Chen gEsCairrio, THERMAL ANALYSIS OF PILGRIM CHECM DATr 11/6/69 sy Ki nyon STATION CLOSURE REGION TABLE ) (rontinued) End of Shutdown for Vessel Head ' Temperature, F Cut No. 7 Ti T,p4 T T Tg 1/2 3j4 19 109.4 103.1 106.6 111.1 112.1 113.1 20 112.4 103.8 109.1 114.4 115.7 117.1 23 126.6 106.5 118.7 130.8 134.7 138.6 25 172.1 111.0 145.0 169.7 195.2 246.6 End of Shutdown for Vessel Wall Tempe ra ture , F Cut No. T T T T T j Tg 1 j j o l'51.7 109.3 142.6 168.0 185.4 192.7 3 lbs.7 108.9 139.1 161.7 176.6 182.0 j 4 148.0 108.3 133.9 153.3 165.8 170.0 6 149.1 108.1 133.1 1 52.9 168.0 176.4 8 138.7 107.0 128.1 143.3 152.5 154.5 l 4
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- ENelNEERING DEPARTMENT. CHATTANOOGA. TENN. SHEET OF B-197 CHARGE NO- 21466 oar.11/3/60 my Che n o m R Prl w THERMAL ANALYSIS OF PILGRIM CHECK DAT8 11/b/b9 EvEiDVon STATION CLOSURE REGION TABLE 1 (Continued)
Axial Temperature Distributions of Refueling Basin Skirt Temperature, F
, End of Shutdown End of X(In) Heatup Flooding Shutdown ~
0.9 402.9 527.7 253.7 2.45 403.3 527.9 252.8 4.30 408.0 527.0 246.9 6.75 414.1 525.6 239.5 > l 9.00 423.8 523.3 227.7 ' 11.55 443.0 518.5 204.9 1 w 14.70 449.8 516.7 196.4 i 18.90 447.3 514.7 193.6 l 4 22.90 410.7 518. 3 225.3 25.70 318.4 530.1 313.2 27.25 291.2 533.4 339.5 1
*The origin and direction of "X" is indicated in Figure 2 u
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v DEsCase THERMAL ANALYSIS OF PILGRIM CNECM DA't.11/5/69 .y Kinyon STATION CLOSURE REGION l { END OF SHUTDOWN (4.177 HOURS) - I h I I
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COM~'USTION ENCINEERING, INC . NUMIEP CENC-ll39 T-102-F ENGINEEnlNG DEPARTMENT. CHATTANOOGA. TENN. SHIET B- O o, n-347 CHARGE NO- 21Nbb DAT* INO/I# NY NM E#* DEscaterio, THERMAL ANALYSIS OF PILORIM CHECK DAT, ih8/70 gy Ch e ru STATION VESSEL WALL
SUMMARY
The thermal analysis of the vessel shell considers heatup and cooldown transients and gamma heating. The results are used in Calculation CE-S-102-F. TRANSIENTS Heatup 1.s at 100F per hour to 546F. Cooldown is at -100F per hour to 375F, flooding in a ten minute period during which the temperature drops to 330F, and then continuation of the -100F per hour rate. Transients having a small temperature range are considered as skin stresses, using the full AT, and are not tabulated in this analysis. Gamma heating is a factor only at power, as it is essentially zero at standby, The energy absorption at the surface is given as 8100 Btu /hr-ft3, and the average linear attenuation coe-ficient as 8.336 per fo'ot through the vessel wall. THERMAL MODEL The vessel wall is considered to be a vertical infinite flat slab, 5-1/2 and 6-1/2 inches thick, and with 7/32 inch thick cladding. This ascumption permits the use of one-dimensional models, and is conservative, as it neglects the axial heat flow between sections or at the water-steam interface. BOUNDARY CONDITIONS In the heatup transient and for the gamma heating calculation, the film coefficient for heat transfer between the water and the wall is taken as 500 Etu/hr-ft2-F, and the film coefficient I i for the surface that is condensing steam is taken as infinite. During cooldown, this surface is considered as insulated, while - the film coefficient for surfaces in contact with water is taken as infinite. This is due to the wall being hotter than the water during periods of reducing pressure or when the flooding occurs so there will be boiling. j CALCULATIONS ! At the end of the long heating and cooling transients, tempera-ture of the wall will be changing at the same rate as the fluid and the heat flux at the wall and through the clad is given by f ff p cp t. The values of the heat flux and the film and clad temperature drops are given in Results.
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COMZUSTION ENGINEERING, INC. NUM;EP CENC-1139 T-102-F { ENGINEERIND DEPARTMENT. CHATTANOOGA. TENN. SHEET bW OF B-137 . CHARGE NO- 21466 ,47,, f/ze/7o ,y Atriym l oEnca Priop THERMAL ANALYSIS OF PILGRIM eggeg ogy, //28/7o gy chert, l STATION VESSEL SHELL
.The maximum radial gradient in the wall occurs at the end of flooding, when 330F water rises against the 546F wall. Con-sidering the clad conductance as a film coefficient permits ,
i I calculation of a Nusselt modulus and consequently determination, ' by using Fig. 2 of T-100F, of the maximum difference between the interface and the average wall l temperatures. - i I Nu = 10.8 x 65
= (f) (f) = , 8 *M 24 = 13.4 I T3 -T From Fig. 2' AT = .62, and with a ATfluid equal to y i
fluid ftYpt 546 - 330, or 216F, T - Typ = 134F. gY RESULTS End of 100F Transient Thickness of section, inches
- 5-1/2 6-1/2 Heat flux at interface, Btu /hr-f ta 2750 3250 Heat flux at surface, Btu /hr-ft2 2860 3360 i 7 - Typ, F degrees '17.5 24.5 Typ - Tsurface, F degrees 4.6 5.5 T-Tsurface, F degrees 22.1 30.0 ATf11m, F degrees 5.7 6.7 !
Tcoolant - T, F degrees , 27.8 36.7 (at end of 100F/hr heatup) T T-T fluid due to gamma heating h . at core centerline, F degrees b [ ok 6.4 ,
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l Max, AT across water level, F degrees -~~' m 141 (T of wall above minus 7 of wall below) Max radial AT, T - Typ, F degrees 134 l t
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