GO2-08-108, NEDO-33419, GEXL97 Correlation Applicable to ATRIUM-10 Fuel, Non-Proprietary Version
| ML082250681 | |
| Person / Time | |
|---|---|
| Site: | Columbia  |
| Issue date: | 06/30/2008 |
| From: | Global Nuclear Fuel |
| To: | Office of Nuclear Reactor Regulation |
| References | |
| GO2-08-108 NEDO-33419 | |
| Download: ML082250681 (45) | |
Text
LICENSE AMENDMENT REQUEST FOR CHANGES TO TECHNICAL SPECIFICATIONS INVOLVING CORE OPERATING LIMITS REPORT AND SCRAM TIME TESTING NEDO-33419 GEXL97 Correlation Applicable to ATRIUM-10 Fuel Non-Proprietary Version
Global Nuclear Fuel A Joint Venture of GE. Toshiba, & Hitachi NEDO-33419 Revision 0 Class I June 2008 GEXL97 Correlation Applicable To ATRIUM-10 Fuel COPYRIGHT 2008 GLOBAL NUCLEAR FUELS-AMERICAS, LLC ALL RIGHTS RESER VED
Non-Proprietary Information NEDO-33419 Class I. Revision 0 Important Notice Regarding Contents of this Report The information contained in this document is furnished for the purpose of obtaining NRC approval of NEDC-33419P, GEXL97 Correlation Applicable To ATRIUM-10 Fuel, to support the Energy'Northwest Columbia pin application , The only undertakings of Global Nuclear Fuel-Americas, LLC (GNF) with respect to infofri-ation inthisdocument. are contained in contracts'betw een GNFý and Energy Northwest, ahd nothing contained in this d0curnent shall be construed as'c6hanging those 'contracts. The use of this'information by anyone other than those participating entities' and for any purposes other, than those for which it is intended is not, authorized- and with respect any unauthorized use, GNF makes no representation or warranty, and assumes no liability a's to the completeness, accuiracy, or usefulness of the information.
contained in this document.
INFORMATION NOTICE This document is a non popriet'ary version ofNEDC33419P, xchich has the proprietary information removed. Porliions4f ihedocument that have6 been removed are indicated by double open and closed brcket 'asshotwti here (( by.double ii
Non-Proprietiry fiformatioh NEDO-33419 Class U Revision 0 Document
Title:
GEXL97 Correlation Applicable To ATRIUM-10 Fuel June 2008.
ABSTRACT The GEXL97 correlation for determining the nininmum critical power ratio (MCPR) during normal and aiasie 0peiation for the boiling water reactor (BWR) and its development'is presenited 'for appli'catini t6ý'ihAREVA ATRIUM- 10 fufel des:ign: The basic GEXL correlation is-a Criticalcquality' and boiling, length correlation used to predict the occurrence of boiling transiti6n in BWR* fuel designs.* The database . to uup the development of the GE)XL97 C6rrelation consisted of calculated critical power data generated with the corrected SPCB critical power C 'irelation as encoded in AREVA's theaal -hydraulic model XCOBRA. The specific ATRIUM`-'10 IGEXL97'correlatio'n develop6dd for use in the core design and safety analysis process is intended to accurately predict the expected critical power performance of the fuel assembly design. In the core design process the GEXL97 correlation is used to determinefi.the-xpec'ed thermal 'inaigin'for the ATRIUM- 10 fuel in the operating cycle. Thermal margins for the Global Nuclear Fuel (GNF) bundles in the operating cycle will be determined based on the appropriate ,GEXL correlation for those fuel Sdesigris.i In the safety andiysis pr6cess the GEL97 correlation is to be applied to the ATRIUM- 10 fuel in the mixed core while'the ap'propriate GNF GEXL correlation will be applied to the GNF fuel (including the determination of an acceptable MCPR safety limit for the mixed core). Based on the supporting SPCB correlation generated database, it is concluded that the safety related conditions have been satisfied with respect to the development of an acceptable critical power correlation.
The overall uncertainty of the GEXL97 correlation in prediction of the critical power for ATRIUM-10 fuel is ((
ini
Non-Proprietary Information NEDO-33419 class I Revision 0 Revision Status.
Revision Description of Change 0 Initial Issue.June 2008 I. *~....I iv
NonProprietary Informati6h NEDO-33419 Class I Revision 0 TABLE OF CONTENTS Page
- 1. INTRODUCTION AND
SUMMARY
.......... ... ..................... ................................ 1-1
- 2. CRITICAL POWER DATABASE FOR GEXL97 .................................................... 2-1
- 3. DATA COLLECTION MATRIX AND CORRELATION PROCEDURES ........... 3-1 3.1 THE ATRIUM- 10 DATA COLLECTION MATRIX ..................................................... 3-1 3.2 CORRELATION PROCEDURE FOR GEXL97 ............ .......... :......................... 3-1
.3.3 GEXL97 CORRELATION .................................................. 3-3
- 4. CRITICAL POWER CORRELATION ................................. 4-1 4.1 FORM OF THE GEXL CORRELATION ............................................ ............. 4-1
.4.2 . GEXL97 APPLICATION RANGE . ................... .................... 4-3 4.3 CALCULATION OF CRITICAL POWER BY GEXL .................. ....... 4-4 4.4.... GEXL INPUT PARAMETERS............ ...................................... 4-5 4.4.1. B oiling L ength ..................................................................................... 4-5 4.4.2. Therm al Diameter............................................................................... 4-5 4.4.3. M ass F lux ............................................................................................ 4-6 4.4.4. P ressure.............................................................................................. 4-6 4.4.5. R -Factor.............................................................................................. 4-6 4.4.6. A nnularFlow Length .......................................................................... 4-6
- 5. ATRIUM-10 GEXL97 CRITICAL POWER EVALUATION .................................. 5-1
- 6. NOM ENCLATURE ....................................................................................................... 6-1
- 7. RE FEREN CES ............................................................................................................... 7-1 APPENDIX A. R-FACTOR CALCULATION METHOD ...................................... A-1 A .1 INTRODUCTION ................................................................................................ A -I A.2 R-FACTOR CALCULATION PROCESS .................................................................. A-I A.3 BUNDLE AVERAGE AXIAL DISTRIBUTIONS ....................................................... A-I A.4 R -FACTOR D ISTRIBUTION ..................................................................................... A -3 A.5 R-FACTOR CALCULATION EXAMPLES ...................................... A-3 A .6 FUEL ASSEM BLY R-FACTOR ................................................................................. A-4 V
Non-Proprietary Information NEDO-33419 Class. I Revision 0 LIST OF TABLES Table Title Page TABLE 2-.1. GEXL97 DATABASE FOR ATRIUM- 10 FUEL......... ............... . 2-2 TABLE 2-2. GEXL97 DATABASE DETAILS-... ............... . ... ......................... 2-3 TABLE 2-3.. ATRIUM- 10 MODELING DIMENSIONS . ..... ................... ..... I.... ........... 2-5 TABLE 3-1. ATRIUM-10 CRITICAL POWER DATA MINIMUM COLLECTION MATRIX (STEADY-STATE) .................. .............. ............ 3-2 TABLE 3-2. STATISTICAL
SUMMARY
FOR ATRIUM-10 GEXL97 .......... 3-3 TABLE.3-3. STATISTICAL
SUMMARY
'.GEXL97.......... ... FOR EACH AXIAL POWER SHAPE FOR ATRIUM-, 0
.. .3-GEX 7.........-... ............... .............. ............ 3-3 TABLE.4-1. GEXL97,CORRELATION COEFFICIENTS ............................ ........ 4-2 TABLE 4-2. GEXL97 ADDITIVE CONSTANTS FOR ATRIUM-1.0 FUEL ................. 4-6 TABLE 5-1. STATISTICAL
SUMMARY
FOR COMBINED GEXL97 AND SPCB:UNCERTAINTy. 5-4 TABLE 6-1. NOMENCLATURE .... * *. ........ ................. . 6-1 T ABLE 6-2. ACRON YMS ................ .. .................. ..................... .......................... ... 6-3 TABLE A-I. R-FACTOR CALCULATIONý'BYLATTICE POSITION;.. .............. l.......... A-6 TABLE A-2. ATRIUM FOR RobWR.INTEhRATION POWE RTL,SHAPE, . .. ... a-8 LIST OF ILLUSTRATIONS,_::
Figure Title,:. :'Page FIG-URE 2-`1. ATRIUM-' 1' ASSEMBLY 'ROD NUMBE ING SYSTEM ...................... . 2-4 FiG6URE22.-13BUNDL:E'AXIAL' POWAER SH'APES - REVA C-riCAL Pb EP DATA COLLECTION
......L........
.. .(..'...
- ...; ..:...'...:.'.:.i... .... ,........
. :2. .':... ........
....... 2 -6 FIGURE 3-1'. 'SPCB CALCLAT VS:'GEXL97 CLCULATED CITCAL POWER: ..........
FIURE,3-2'GEXL97MASSF-LUX TRENDS .. . . .... ! .. ....... .....
"FiG6URE-3'3*-3. OEXL907 PkESSiJi.E TR..ENDS, .... : ....... ' ............ ..... .......... ...... 3-5 FIG.RE3. GEX..977tar.eT SUB-COOL.NG TRENDS ...... .. .......... 3-5 FIGURE 4-1. GEXL97 R-FACTO* * .. ... ....... ....................................... 14-3 FIGURE 4,21 CRITICAL POWERITERATION7 SCHEME , ..:.:...:,...'.,.*:.ýý:!.:..:.. *'. ... 4-5 FIGURE4-36 REGIMES OF -TWOP.HASE..FLOW,;- ' ... ...... 4-8 FIGURE ,5-j., :F,E .QUENCYVERgSUSiECPR:JIi-.TQ RAM-FORATRI UM-4'O GEXL97.. ...... 5-4 FIGURE:5-2, COMI ARISON OF INTEGRATED PROBABIITY OF B@ILINCITRANSITION............ 5-5 FIGURE-A-1. ATRIUM1 0AXIAL SHAP,*s' ORRQDPOW*ER INTEGRATION (NORMALIZED)A-2 FIGURE A-2. IDENTIFICATION OF,RODS IN POSITIONS ADJACENT TO ROD, I............... A-5 FIGURE A-3. A TRIU M -10 LATTICE .................................................................................. A-7 Vi
Non-Proprietary Inf6rmiationn, NEDO-33419 Class I Revision 0
- 1. INTRODUCTION AND
SUMMARY
-This report summarizes the development of tie ATRIUM-10 GEXL97 correlation. The ATRIUM-10 GEXL97 correlation willibe used :to determine the critical power performance
..of the AREVA ATRIUM-10 fuel in a mixed core.of AREVA'and GNF fuel., This document describes the process used in the development of the GEXL97 correlation for prediction of critical power for ATRIUM- 10.fueland the determination of theoverall'dicertainty of that
- correlation in prediction. of the ATRIUM 10 critical power performance..
ATRIUMi10 calculated biundle' critical powbr'data was obtained from AREVA based on the SPCB correlatioii (kfer&dhcf '2,e3) as encoded in the AREVA thermal hydraulic model SXCOBRA. Subsequent to NRC approval,'AREVA identified an error-in thie SPCB correlation -applicable to ATRIUM- 10 fuel. The error involved ihe calculation 6f the local power pefn peaking-anie. distribution k-VA lE"*
' .... corct fo " the test' 'assemblies e:"I;
......I: efer uised to determine critical power perforha correctd the error (Reference 3), and the 'data used in this report are based on this error'correction.- The objective, of this' data' collction was't0 obtain quality data appropriate for GEXL analysis. The span of the data collectiofinencompasses cosine, top
'peaked, bottom peaked, and dou'bfe 'humped aiMl P&&powery shapes' inrder to .coxver the complete range 'of'expectied operati'or of th'e ATRIUM -10' fulb In ABWR core.' The data was used to develop a new GEXL correlation for the ATRIUM-10 design. This new GEXL correlation for ATRIUM- 10 fuel is designated as GEXL97. The new GEXL97 correlation uses the same functional form' as previ6us, GEXL coi-relatibns with different constants for the GEXL correlation coefficient parameters. This report provides the results of the GEXL97 correlation development,Jincluding .jthe overall uncertainty relative, to meastirementx.results.
The GE critical quality boiling length correlation,(GEXL) wa&sdeveloped to accurately
<pr'dict the6nset of.b6ilinig trnsition in boiling water reactoi (BWR) fuel. assemblies during both steady-state
..deteriiiiniig and reacior transient condition's." The GEXL correlation is necessary for tiheMCP,6 6perating limits resulting from'transient analysis, the MCPR limit ahalcis' and the core operating performance and, design.,he GEXL correlation isian safety integril part of the triiiisient analysis-iiethodology .It, is usedto confirm .t-he adequacy o9f the minimum' critical p6oier ratio (MCPR) operating limit, a d it,can be .used to., determine the
'time'of'ons~et 'fboiling .tansition inithe analysis of other events..' .
The GEXL correlation has. been used in the-Safety ailYal sis'p'rfcess foir GE fueledBWRs since 1974.. The GEXL~correlation. was developed to pt6vYide"a best estiniat~e predictibno'of the onset.ofbdiling transiti'oni' BWR fuel sseffibli's, .Th&GEXL correlation is based 'on the relationships -of Critical quality With: boilikg "I...'th t'e..ss.es.biidl'e'.ae."'age.
.. t'itic.'
quality' as atfunction of boiling length,' thertmal dianieter, syste pressur ,la'ttice geometry, local peaking pattern (R-factor), mass flux andaindular fibWleng"th.
The GEXL correlation Was originally developed based on'test data typical of 7x7 and 8x8 fuel assemblies. Over 14,000 data points having various numbers of rods, heated lengths, axial heat flux profiles, and rod to rod power distributions were used in the development of the original GEXL (GEXLOl) correlation. The boiling transition test data available at the time of the development of the GEXL01 correlation are provided in the original licensing 1-1
Non-Proprietary Information NEDO-33419 Class I. Revision 0 topical report (Reference 1). Further background on the development of the GEXL97 correlation is provided in Section.2.. .
The GEXL correlation requires the development of coefficients for the specific mechanical geometry of the fuel assembly design: The database supporting the development of theGEXL97 cori'elation is desc:ibed in Sections'2 and 3.
As described above, the GEXL correlation isa.critical quality-boiling length correlation.
In, the GEXL correlation critical quality is expressed, as a function of boiling: length, thermal diameter, mass flux, pressure,,R-factor, and annular:flow length.. The axial power profile is not explicitly included in the GEXL correlation, however, the axial power shape is used to calculate boiling length', annular floW length, and akial'y ari'dition of tality; and thus, is inherently included in-the critic.al power corre6lation.' The-e'act forti 0f the GEXL correlation'and the coefficients for ATRiIJM-10 fiel are provided in Sectionii4.'
The measure of the capability ofa boiliing transition prediction correlation is its ability to predict the collected data. The GEXL correlation has been demonstrated to be an a ccurate predictor of the data generated from theSPCB ATRIUM- 10 cilitical,power-correlation.ý Its capability for predicting 'ATRIUM-10*fuelis provided 'in Sections 3 and 5. Th6' nomenclature and references usedin this rep6ot are demfinstrated in Sections 6 and 7) respecf*vely., ý '. . . ,
- i< .- ; , ° .d :..... .7 , ,
The overall uncertain.ty of theGEXL97 correlation in prediction of the critical power; for ATRIUM-1 fuel is;((
2 :r.
1-2
NoiiProprietiry~lnformati6n, NEDO-33419 Class I Revision 0
- 2. CRITICAL POWER DATABASE FOR GEXL97 The current. form, of the GE critical qualityrboiding lengtkhcorrelation (GEXL) .was developed to provide an accuratemeans of predicting.the occurrence.of boiling transition in BWR fuel. The primary source of boiling transition data used in the development and verification of the GEXL ;cbrrelation are dry6ut tests at the GE ATLAS facility ift San Jose, California. The ATLASitestlodop gnerIates pressure,; flow-'nd temperature :conditions. that accurately simulate'the actual; operatingr6'actor'envitonment.: "
The data. for the GExL97. !deevelopmenti specific .to ATRIUM-10 fueI was generated using the SPCB correlation (Reference.2; 3). Specified rod-to-rod peakings, axial, power shapes, pressure, mass flux and sub-cooling were Used-in the AREVA thermal hydraulic'model XCOBRA with the SPCB correlation to determine critical power at dryout. No GEXL97 development daia~'was ene'red'ouist~id theSPCB correltion' rangeof applicability:.
ATRIUM- 10 fuel i.s. a:.-Oxl. fuel,bundlewith, a water channel design that displaces 9 fuel rods. It contains a total of.83..fulllelg.th fuifel rods aind 8,part length.rods. It has 27 unique fuel rod locations .(Figure 271 )withinthe 10X 1qlattice.for which diyout data was collected.
In Section 4, the final GEXL97 correlation forX ATRIUM-10 fuel is given, including additive constants. The database used in the development of the GEXL97 correlation for ATRIUM- 10
.fel is sumnairiz6d in Table; 2--`Y. This tabie shows'. theuber of 6alcul~ted critical power data points obtained using the SPCB critical power correlation for colsieh,- l'Iet, outlet, and double humped axial power distributions. It also shows the fuel pin dryout location that formed the basis of the 28 different sets of AREVA calculated critical power data. Table 2-2 shows the same information but further divides the data collected into subgroups of pressure, mass flux, and inlet sub-cooling.
The ATRIUM-10 modeling dimensions used in the AREVA generation of the SPCB dryout data as well as in the development of the GEXL97 correlation are provided in Table 2-3. The generated data was based on chopped cosine, top and bottom, and a double humped peaked axial power profile. The axial power profiles are shown in Figure 2-2.
2-1
Non-Proprietary Information NEDO-33419 SClass I. Revision 0 Table 2-1. GEXL97 Database for ATRIUM-10 Fuel Number of Critical Power Data Points Fuel Pin Data Set [ Dryout II[ Position I I I lI __________ __________ _________
' ..... . . . . .. - . , . ... . . . .. . . : "/ : i *" Ii . . . . .I 2-2
Non-Proprietary Information NEDO-33419 Class I Revision 0 Table 2-2. GEXL97 Database Details
- .... NominaThemal HydTaulic Conditions Collection Type Axial Pressure Mass Flux Inlet Subcooling' Shape _ __(psia): (MI/hr-ft2) (Btu/Ibm)
- ~~~~~ II
- li+i '
2-3
Non-Proprietary Information NEDO-33419 Class I Revision 0 1 2 5 7106
. 2,2 12 4;,4 3 4 16 ,17 20 3,5~
3,6 3, 002,3 2, 00 ------
7,8.ý 0000 00 78ý 80
.100
( ) - Part Length Rod xx - Unique Rod Position Line of Figure 2-1. ATRIUM-10 Assembly Rod Numbering System 2-4
NTnal Prop.iAT Iary1 inMormationi NEDO-33419 Class I, Revision 0 Table 2-3. ATRIUM-10 Mode'1ing Dimensions Characteristic Assembly Data sets 1 through 28 Lattice 10 x'10 Nominal ,Inside Width of Channel Er:[
Inside. Corner Radius of Channel "Er[* Al]
Rod Pitch Diameter of All Heated Rods' Er
(( 1].
Axial Heat Flux Profiles (4) of Full Length R ods l4Peak-to-Average Cosine 1.6 Peak-to-Average Bottom and Top
- . Peaked, 1.2 Peaked Double Humped Number of Full Length Heated Rods 83 Heated Length of Full-Length Rods 15,0 in. (381 cm)
Number of Part Lengthý Heated Rods 8 End of Heated Length ofPart Length Rods Er . .
Spacers ~ 8.'
Water Box Off-set Central, Displacing 9 Fuel Rods Wafer Box outer Area, [ -. ]
Water Box Outer Width' Water Box Outside Corner Radius Er.'[ .. . i))
Hydraulic Parameters Used in GEXL Correla Er . -. ..]
Active Char-el Flow Area, True *Hydraulic Diameter Er * , , .
True Thermal Diameter GEXL Hydraulic Diameter*
GEXL.-Thermal Diameter* -
Er 4
2-5
Non-Proprietary Information, NEDO-33419 Class:I Revision 0
((
1]
.Figure: 2-2. Bundle AxialPower Shapes.7 AREVA Critical Power Data Collection r -) i /111 I'
Cl *.I~-.~'It~.
- . t 2-6
" Non-Proprietary Information NEDO-33419 Class I Revision 0
- 3. DATA COLLECTION MATRIX AND CORRELATION PROCEDURES 3.1 THE ATRIUM-10 DATA COLLECTION MATRIX The ATRIUM- 10 data collection matrix is outlined in detail in Table 3-1. This matrix shows the minimum range of data required for the GEXL97 correlation development. The data was generated by AREVA based on the SPCB correlation (Reference 2, 3) as encoded in the AREVA thermal hydraulic model XCOBRA. ((
Er]
3.2 CORRELATION PROCEDURE FOR GEXL97 The procedure used for development of the ATRIUM- 10 GEXL97 correlation can be summarized as follows:
'Arang e o e datcovering aril" ie i n s :fofrm a of, gn'era~tedd dta esi development database. This is the majority of the data. A separate set of data was used as the verification database.
- The correlation coefficients were chosen to minimize the bias and standard deviation in correlating the data and to minimize any trend errors in reference to flow, pressure, sub-cooling, and R-factor.
" Once the optimum coefficients were determined, the apparent R-factors were calculated for each assembly. The apparent R-factor is defined as that R-factor which yields an overall ECPR of 1.0 for a given assembly. In this document, ECPR is defined as the ratio of the GEXL97 calculated critical power to the SPCB calculated critical power.
These steps were taken to optimize GEXL97 for the ATRIUM- 10 fuel design and to minimize the prediction uncertainty. This identical process is used when developing GEXL correlation coefficients for GNF/GE fuel designs using test data.
3-1
Non-Proprietary Information NEDO-33419 Class I Revision 0 Table 3-1. ATRIUM-10 Critical Power Data Minimum Collection Matrix (Steady-st'ate)
Collection Type:'
Number of peaking patterns:
Axial Heat Flux Shaipe:
R-factor:
Pressure:
Mass flux:r Inlet sub-cooling:
Collection Type:
Number of peaking patterns:
Axial Heat Flux Shape:
R-factor:
Pressure:
Mass flux:.
Inlet sub-cooling:
Collection Type:;
Number of peaking patterns:
Axial Heat Flux;Shape: ". ....
R-factor: -
Pressure: 2:
Mass flux::. . . ,
Inlet sub-cooling:
Collection'Type:
Number of peaking patterns: .. ,
xial Heat Flux Shape: ,.
R-factor:
Pressure:
Mass flux:
Inlet sub-'cooiing:
Collecti n Type:_
Number of peaking patterns:
xAial Heat Flux Shape-:!
-factor:-
Pressure:.- .
-,.. :nlet.sub.c.oling:, . . .. . . . . .. . .
Collection Type:
Number of peaking patterns:
Axial Heat Flux Shape:
R-factor:
Pressure:
Mass flux:
Inlet sub-cooling:- ]
3-2
Non-Proprietary lnfoirmation NEDO-33419 Class I Revision 0 3__.3 GEXL97 CORRELATION
. Figure 3-1 shows the ATRIUM-10 SPCB calculated critical power data versus. the calculated critical power for ATRIUM-10 fuel using the GEXL97 correlation developed herein. The final ATRIUM-10 GEXL97 correlation coefficients, and additive constants are shown in Section 4. The GEXL97 correlation is developed from the majority of the data that consists of (( )) points for 25 different local peaking patterns and 4 axial power shapes with R-factors ranging up to (( )). The overall statistics for the GEXL97 correlation are shown in Table 3-2 and Table 3-3. Figures 3-2 through 3-4 show. the ECPR, mean and standard deviation for mass flux, pressure, and inlet sub-cooling for the correlation database which included all collection types except high R-factor (discussed below), all axial heat flux shapes, and pin peaking patterns which were used explicitly in the GEXL97, uncertainty calculation (Er )) data points). The low mass flux data([]
Mlb/hr-ft 2), which had a mean ECPR ([1 ))) and small.
uncertainty (E[ ))), were also not included as part of the correlation development database. Figure 3-2 includes data for mass fluxes in the range of (( )) Mlb/hr-,
2 ft , Figure 3-3-includes data-for pressures in-the range of[ .))psia,and, Figure 3-4 includes data for inlet sub-cooling in the range of ,,))
, Btt/lb. These figures demonstrate that there are no substantial trend errors in the GEXL97 correlation and.
that the GEXL97 correlation closely replicates the SPCB correlation over the given ranges.
The GEXL97 correlation was separately assessed against high R-factor data with R-factor values up to E[ 1], and a mean ECPR of EE )) and a standard deviation of (( ))were obtained. [r
)) High R-factors! inthis range are generally obtained for controlled bundles, which are non-limiting bundles;, and, therefore these data are not included in the correlation statistics.
Table 3-2. Statistical Summary for ATRIUM-10 ýGEXL97 Total Correlation , Development Verification Database Database Database,
Number of data points Er Mean ECPR Standard deviation, T(%) _ ]
Table 3-3. Statistical Summary for Each Axial Power Shape for ATRIUM-10 GEXL97 Axial Power Shape ________,_____
Number of data points Mean ECPR Standard deviation,_ (%) ))
3-3
Non-Proprietary Information NEDO-33419 Class I Revision 0 Figure 3-1. SPCB Calculated vs. GEXL97 Calculated Critical Power
((
1]
Figure 3-2. GEXL97 Mass Flux Trends 3-4
Non-Proprietary Inforniation NEDO-33419 Class I Revision 0 Er Figure 3-3. GEXL97 Pressure Trends
- *J i.: ', *i :'* ,'* : *':.i*
- t *," ,:F*,
- I*:*.*
' . :ri (? **Th.: i: -*, '. *"
Er Figure 3-4. GEXL97 Inlet Sub-cooling Trends 3-5
Non-Proprietary Information NEDO-33419 Class I Revision 0
- 4. CRITICAL POWERCORRELATION 4.1 FORM OF THE GEXL CORRELATION .
As discussed in Section 2, the critical quality versus boiling length plane was chosen by GE as the coordinate system for correlating the boiling transition data described in Section 3.
This approach was chosen because (1) it yields goodprecision; (2) is conceptually simple to apply, and (3) will account for variations in the axial-heat fluxprofile. The critical quality -
boiling length correlation developed to predict the6critical power in BWR fuel assemblies is called GEXL.
The GEXL correlation, expressed in the most general terms, is:
Xc=f(LB, DQ, G P, RLA) (4-1) where:
Xc = Critical qualitý (dimensionless)
LB =Boiling length (in.) .
DQ = Thermaldiameter(in.)2 G = Mass flux (106 lb/hr-ft ) K....
P = Pressure (psia)
R = Bundle-R-factor (dimensionless) . ..
LA = Annular flow length (in.)
Because GEXL is a dimensional correlation, the above units must be used in specific analyses.
The explicit form of the GEXL correlation is:
((] (4-2) where the correlation parameters, V(I), and the coefficients, A(I), are shown in Table 4-1.
The additive constants are shown in Table 4-2.
4-1
Non-Proprietary Information NEDO-33419 Class I Revision 0 Table 4i*. GEXL97 Correlation Coefficients
((
4-2
Non-Proprietary Information NEDO-33419 Class I Revision 0 4.2- GEXL97 APPLICATION RANGE The GEXL97 correlation for ATRIUM-10 fuel is .alid over the range stated below:.
Pressure: Er Mass Flux:
- Inlet Sub-cooling:
R-factor:
The correlation database spanned all application ranges and is bounded by the SPCB correlation ranges of applicability.,,
A study' of the GEXL97 trends shows' that the' Pfact6r trend 'is (( fl over the entire range of expected operation ('see Figure 44)'
Er, , L ", : , ! i : .* ,, ! ; :* : : : . i ; . :
ýJ Figure 4-1. GEXL97 R-fatrTrends ":
)) Based on these 4-3
Nbon-Proprietaiy'Infornmiaiion NEDO-33419 ClassI Revision 0 arguments, the GEXL97 correlation can be used to perform critical power calculations.for these non-limiting fuel assemblies even though their mass .flux 'values may be gteater than the upper mass flux limit specified herein.
As described in Section 3.3, a separate evaluation was completed usingthe high R-factor data to show that the correlation is well behaved at high R-factor conditions. The general trend of the GEXL97 correlation critical power calculations for high R-factor conditions follows the-general trend of the AREVA predicted critical power performance for these highly peaked pin power profiles.
4.3 CALCULATION OF CRITICAL POWER BY GEXL For steady-state conditions, critical power is predicted by aniterative procedure. Given the pressure, flow rate, inlet sub-cooling, axial power shape and fuellattice design, a value for the critical power is assumed and the local quality and boiling length are computed for each axial node (24 nodes are assumed) using energy and mass balance relationships., The critical quality is also computed for each node using Equation 4-2. If, at any of the nodes, the local quality is greater than the critical quality, a lesser value for the critical power is assumed. If the local quality is less than the critical quality at all of the nodes, a greater value for the critical power is assumed. The iteration continues until the local quality is just equal to the critical quality at one of the nodes and is less at all other nodes. The power for this last iteration is the predicted critical power.
This process is illustrated in Figure 4-2 where the dashed/solid lines show the critical and equilibrium quality profiles for the first and last iterations. The equilibrium quality X is a function of bundle elevation z and is calculated from:
X(z) = [Q(z)/ W -(hf - hi,,)]/(hg - hf )(4-3)
In Equation 4-3, X = local quality; z = axial coordinate for elevation in the bundle; Q =
integrated power input to the coolant up to location z; W = bundle coolant flow rate; hf=
saturated liquid enthalpy; hi, = inlet liquid coolant enthalpy; and hg = saturated vapor enthalpy.
For design application the correlation is intended to iteratively determine the bundle power which satisfies the requirement that for some z, X = Xc and X < Xc for all other z. It also should be noted that the values of Xc, X and z at which (Xc - X) is a minimum, change with each iteration on bun4te power. . . .
4-4
Non-Proprietary Information, NEDO-33419 Class I Revision 0 10.40 0.351 0.30 I-0.25
< 0.20 0.15 0.05 0.10 0
-0.05 0 50 100 150. 200 250 300 350'
-U ,NDLE ELEVATIN..(cm)
Figure 4-2. Critical:Power Ite'ration'Schemie' The critical power ratio, (CPR) is the. ratio of the predicted critical power to the actual power of the particular fuel assembly, both evaluated at thesame pressure, mass flux and inlet sub-cooling.: The minimum critical. power ratio (MCp1R) is. defined as the minimum CPR for any fuel assembly. within a core and is the figure of merit to represent the reactor, thermal performance or margin.
4.4 GEXL INPUT- PARAMETERS This section describes thenecessary inputs to the GEXL correlation for the bundle critical power calculation' Based-on Equation 4-1,. there are six'input parameters required for the .calculation of critical power. These parameters are: -(.1) boiling length, LB; (2) thermal diameter; Do; (3) mass flux, G; (4) pressure, P; (5)-bundle R-factor, R; and (6) annular- flow length, L-A. These parameters. are discussed in more detail below. .. .. .
4.4'.. Boilingh Length Boiling length, LB, is 'the distance from theonset of thermodyna-'mic average bulk boiling to th.e pointthro
- calculatede. of boiling transition. eoilinglihgth isn0ot f direct input to GEXL,but it is ugh the enifg!y b-alance during the calculation of critical power described in Section 4.3. The boiling"length is dependent oh the core pressure, enthalpy at the fuel assembly inlet, normalized axial power shape, mass flux and bundle power level.
4.4.2. Thermal Diameter The thermal diameter, DQ, is a characteristic diameter defined in the heated length region as four times the bundle active coolant flow area divided by the total rodded perimeter, i.e.
the perimeter of the fuel rods and the water box. The rodded perimeter does not include the 4-5
Non-Proprietary Information NEDO-33419 Class I.', Revision 0 channel. The thermal diameter used in the GEXL97 correlation for ATRIUM-10 fuel is ((
)), and the active flow area is (( ..
Both parameters are assumed constant over the length of the fuel assembly. This thermal diameter is specific to the GEXL97 correlation and is calculated to be consistent with GNF-A engineering computer program (ECP) calculations.' [
- caculaion .*'(( ... ]
4.4.3. Mass Flux.
The mass flux, G, is defined as the (( )) coolant flow per unit flow area in the heated region.
4.4.4. Pressure The pressure, P, is defined as the system pressure, taken as the core pressure ((
4.4.5.. R-Factor.
The k-factor is a parameter that accounts f6r the effects of the fuel rod power distributions and the fuel aissemblf local spacer anid lfattice critical power characteristics. Its formulation for a given. fel rod location depends or (( .
1] A detailed description of the R-factor caicuiati~n hiethodis pr~v'ided iniAppendix A. 1n-atditidn, thdre is ýciiadditive constant aplied to ca~fue~l roc'locairfE
)) ForATRIUM4Oiothe additfie cbnistdaits afe p'rovided in-Table 4-2:. The bolded positions r'epr'esent'fluniqtie' rod' iocatioiS foirvhich data* vere gneitatbd in order to cover all symmetric locations.
Table 4-2. GEXL97 Additive Constants for ATRffUM7-10 Fuel,
- - - -77777 - 7 ---
___ ____ I ___-
4.4.6. Annular Flow Length Er1 4-6
Non-Proprietary Information NEDO-33419 Class.I Revision 0 4-7
Non-Proprietary Information NEDO-33419 Ckiss I Revision 0 1]
HEAT FIOWS TRANSFER STEAM REGIONSREGIONS TSAT I
CONVECTIVE SINGLE HEAT TRANSFER TO STEAM SUPERHEATED 100 PHASE STEAM
\:. J
- o 0
0o G
LIQUID DEFICIENT R EGION 0
- 0 0& 0'
/
00 00 O':0.
FORCED
.,o0-0 ANNULAR CONVECTIVE HEAT TRANSFER FLOW THROUGH z LIQUID FILM z
0 SLUG FLOW t
H NUCLEATE 0 BOILING H
-4
-4 0- BUBBLE SUBCOOLED FLOW BOILING TSAT 4-100%
4-0 TEMP QUALITY T
WATER SINGLE PHASE WATER CONVECTIVE HEAT TRANSFER TO WATER Figure 4-3. Regimes of Two-Phase Flow 4-8
Non-Proprietary Information NEDO-33419 Class I Revision 0
- 5. ATRIUM-10 GEXL97 CRITICAL POWER EVALUATION The GE critical quality-boiling length correlation (GEXL) was developed to be an accurate, best estimate predictor of boiling transition in BWR fuel. A large critical power test database was obtained as part of the development of the form of the GEXL correlation.
The data covered the full range of BWR steady-state operating conditions for which an accurate prediction of critical power is an important element of the safety analysis process.
The GEXL97 correlation was developed from data generated based on the SPCB critical power correlation (Reference 2, 3) encoded in the AREVA XCOBRA thermal hydraulic model. This section provides the results of statistical analyses performed to demonstrate the application of the final GEXL97 correlation to predict the ATRIUM-10 simulated critical power data.
A statistical analysis was performed for the ATRIUM- 10 correlation database consisting of 1] data points for ((
][
)). The data and analyses cover the range for which the ATRIUM-10 GEXL97 correlation is considered valid, as identified in Section 4. To facilitate the statistical evaluation of the predictive capability of the ATRIUM-10 GEXL97 correlation, ((
Figure 5-1 shows the frequency distribution of the calculated ECPR results for ATRIUM-10 and is a graphical representation of the ECPR results that were used to calculate the statistics shown in Tables 3-2 and 3-3. ((
)). The large total correlation uncertainty of (( )) used in the safety limit calculation provides additional conservatism.
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Nofi-Pr6prietary Infotmati6n NEDO-33419 Class I Revision 0 I j I' -
(1
.f..,
I ~ ~%'i~~ 1 5-2
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~1 -
I I j.;.
]1 5-3
Non-Proprietary Information NEDO-33419 Class'I Revision 0 Table 5-1. Statistical Summary for Combined GEXL97 and SPCB Uncertainty Mean ECPR Standard Deviation, c (%)
GEXL97 Correlation E[
Bounding Value for SPCB Correlation Combined Value (Using p = 1) ))
((
Figure 5-1. Frequency versus ECPR Histogram for ATRIUM-10 GEXL97 Small ECPR errors exist for the individual power shapes as shown in Table 3-3. These errors are not atypical compared to past experience and these ECPR errors are accounted for in the larger GEXL97 correlation uncertainty for the total database. The relatively small ((
)) of the outlet and double humped axial power shapes and somewhat larger, but (( )) of the cosine and inlet peaked data is what leads to the non-normality of the ECPR histogram for the total database.
The safety limit is determined by summing the probability that each rod is in boiling transition and determining the point where the sum over all the rods of the probability the rod is in boiling transition equals 0.1% of the total number of rods.
NRSBT = pi = 0.001NR, Allrods where: NR is the total number of rods pi is the probability rod "i" is in boiling transition 5-4
Non-Proprietary. Information NEDO-33419 Class I Revision 0 NRSBT is the number of rods subject to boiling transition For a rod "i" with a given critical 'powerratio, "CPRi", the likelihood of that rod being in boiling transition is given by the probability that the ECPR is greater than the CPR value:,
pi f(x)dx, CPRi where: f is the ECPR probability density function.
The impact of the non-normality can therefore be evaluated by comparing the integrated probability of boiling transition as a function of CPR value for the actual ECPR histogram and the assumed normal distribution. This comparison is shown in Figure 5-2.
Figure 5-2. Comparison of Integrated Probability of Boiling Transition For the nominial'c6nditions the limiting rod will beatflthe"safe~tjýli"Miit,' fhich is typically around 1.10. All other rods will have higher CPR values. From the, above figure it is clearly seen that the probability'difie rods being in boiling transition'is conservatively calculated when using the normal distribution.
When the uncertainties ,in plant operating parameters and power distribution are accounted for in the safety, limit methodology, the leading bundles that contribute to the safety limit will have a CPR distribution around the safety limit. From the above figure ,it is seen that the probability of boiling transition is (( )) predicted for CPR values greater than (( )) and non-conservatively for CPR values between ((
)). Since most of the rods that contribute to the safety limit will be in the range close to the safety limit, the overall impact of using the normal distribution will be conservative.
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Non-Proprietary Information NEDO-33419 Class I' Revision 0
- 6. NOMENCLATURE.
Tlie nomenclature and acronyms used iri'this reporare pr6vided below. The units shown here are general dimensions of the variables. Actual units required for dimensional calculations V (I) terms in Equation 4-2 are described in Section 4.
Table 6-1. Nomenclature Symbol Definition ,... Units.
A-- 'Bindle flow area .*:in 2(rn 2) :: .: .
A (1) Fuel type specific GEXL coefficients Values in Section 4 consistent with specific English units DH Hydraulic diameter in (in)
DQ Thermal diameter in (in)
F Number of active fuel rods dimensionless G Mass flux lb/ft2-sec (kg/m 2 -sec)
Gf Mass flux of the liquid phase alone lb/ft2-sec (kg/m 2-sec)
Gg Mass flux of the gaseous phase alone lb/ft2-sec (kg/m 2-sec) g Gravitational constant ft/sec 2 (m/sec 2) hf Saturated liquid enthalpy Btu/lb (kJ/kg) hg Saturated vapor enthalpy Btu/lb (kJ/kg) hi.
Inlet liquid enthalpy Btu/lb (kJ/kg)
Average liquid velocity = Wf/pfA = Gf /pf ft/sec (m/sec) if ig Average vapor velocity = Wg /pgA = Gg /pg ft/sec (m/sec)
Jf., Dimensionless liquid velocity dimensionless Jj. Dimen.nless.vp-rvelocity . ,J, ,dimensionless.
LA Annular flow, lenqgth inm.I LB Boiling length . n (r)!y. . ..
li Additive constant 'dimensionless ,
nj Number of rods in position j dimensionless nk Number of rods in position k dimensionless P Pressure psi (Pa) q Correction for adjacent low power rods dimensionless 6-1
Non-Proprietary Information NEDO-33419 L, Class I t Revision 0 Symbol I Definition Units Q(z) Integrated power input, to the coolant up to BTU/sec (Watts) location (z)
R, Bundle R-factor. dimensionless Ri R-factor-for anindividual rod diimensionless RFC R-factor at fully controlled dimensionless>
ri Local peaking factor for rod i dimensionless ri Local peaking factor for rod j dimensionless rk Local peaking factor for rod k,.: dimensionless T Total number of lattice positions" dime'nsionless V(I) GEXL correlation parameters Values in -Section 4 c6nsisient with specific Einglish~units.ý Bundlecd'Olfant floWrate -.. b/hT g/sec)
W Wf Liquid mass flow -- lb/hr (kg/sec),: .', i i.
}... ....
Wg ,V~ or gss~fliW-. . .... ,. : , *:,-, ... h .(kg/sec):
Wi Weighting factor for rods in position i ., :. dimensionless; wi Weighting factor for rods in position j:.': dimensibnless Wk Weighting factor for rods in position k dimensionless X Local quality dimensionless Xc Critical quality dimensionless XTR Annular flow transition quality dimensionless zc Axial coordinate for the point of critical ft (M) quality ZTR Axial coordinate for the point of transition to ft (m) annular flow z Axial coordinate for elevation in bundle ft (M)
Pf Liquid density lb/ft3 (kg/m3 )
Pg Vapor density lb/ft3 (kg/m3 )
6-2
Non-Proprietary Information NEDO-33419 Class I Revision 0
- 'Table 6-2. Acronyms. .
BWR Boiling Water Reactor CPR Critical Power Ratio defined as the predicted critical power to the actual power of the particular fuel assembly, both evaluated at the same pressure, mass flux and inlet sub-cooling ECPR ECP Engineering Computer Program GETAB General, Electric BWR Thermal Analysis.Basis GEXL GE critical quality-boiling length cprrelation, GNF Global-Nuclear Fuels GNF-At:,: Global Nuclear Fuels - Americas MCPR Minimum Critical Power Ratio defined as the minimum CPR for any fuel assembly within a core and is the figure of merit to represent the;reactor thermal pe-fo rm.mance or margin' .
NRC Nuclear Regulatory Commission '
SPCB ARE VA (formerly Framatome Advanced NuclearPowe). critical power corr#eatio` f6r'r ATRIUM- 10 fuel XCOBRA AREVA~therrial-hydraulicimodel SPC Siemens Power Corporation,:.
,C,*. 1 ' . -.
6-3
Non-Proprietary Information NEDO-33419 Class I Revision 0
- 7. REFERENCES
- 1. NEDE-10958P-A, General Electric BWR Thermal Analysis Basis (GETAB): Data, -
Correlation and Design Basis, GE. Proprietary Report, January 1977.
- 2. EMF-2209(P)(A), "SPCB Critical Power Correlation", Rev. 2, September 2003.
- 3. EMF-2209(NP), "SPCB AdditiVe Constants iforAT;RIUM-O Ful", Adde ndum 1, Rev. 0,' April 2008.
- 4. NEDC-32505P-A, R-Factor Calculation Method for GEl 1, GE12, and GEl3 Fuel, Revision 1, GE Proprietary Report, July 1999.
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-Non-Proprietary lhf0rmation NEDO-33419 Class It Revision 0 APPENDIX A.R,-Factor Calculation Method A.1 Introduction .
The R-factor is af' inpUt' to the GEXL'cb rrelation thdat'accoufits for the' effects Of the fuel rod power distributions and the fuel assembly and channel geometry on the fuel assembly critical power. Its f6rmulation for a: giv6n fuel rod locationdepends on the power of thatfuel rod, as well. as the power of the surrounding fuel rods. In addition, there islan additive cohstant applied to ea'chfel rid iocation'that is dependent on the fuel assembly and channel geometry. The complete R-factor methodology is documented in Reference 4..
A.2 R-factor Calculation Process Local two-dimensional fuel rod power distributions vary axially in BWR fuel assemblies due to axial variations in nuclear design, exposure, void fraction and control state. These factors are considered when calculating the axially integrated powers for individual rods. The two-dimensional distribution of integrated rod powers for a bundle is then used to calculate individual rod R-factors. The bundle R-factor for a particular bundle average exposure and control fraction is the maximum of all of the individual fuel rod R-factors. The steps used in the R-factor calculation process are as follows:
- 1. Obtain relative 2D rod-by-rod power distributions from TGBLA, which are a function of lattice nuclear design, average exposure, void fraction, and control state.
- 2. ((
- 3. Calculate an R-factor for each individual fuel rod. ((
- 4. The bundle R-factor is the maximum value of all individual rod R-factors.
- 5. Repeat these calculations for each desired bundle average exposure, control fraction and channel bow.
A.3 Bundle Average Axial Distributions A 25-node axial shape is used to define a bundle axial relative power shape for the purposes of calculating R-factors. This shape is a function of control fraction. Bundle axial Void fraction and bundle axial relative exposure shapes are used to determine two-dimensional radial distributions as a function of axial height.
A-1
Non-Proprietary Information NEDO-33419 Class-I Revision 0
- Er
- [E
- The bundle axial relative exposure shape is defined as that shape which is consistent with .the uncontrolled axial relative power shape assuming uniform fuel density; and
- The bundle axial void fraction shape is defined as a shape that is consistent with the uncontrolled axial relative power shape and gives a prototypical bundle average void fraction.
Figure A-I provides a summary of these normalized axial shapes for ATRIUM-10 fuel. The corresponding numbers are listed in Table A-2.
Er 1]
Figure A-1. ATRIUM-10 Axial Shapes for Rod Power Integration (Normalized)
A-2
Non-Pioprietary Inf6ofiration NEDO-33419 Class I Revision 0 A.4 R-factor Distribution
))(A-1)
A.5 R-factor Calculation Examples Using the procedures defined in the previous sections, R-factors are calculated for different lattice locations in a bundle as a function of fuel assembly exposure, control state and channel bow using Equation A-1. The following example is for a lOx 10 lattice (ATRIUM- 10).
Consider Equation A-1 for the various cases as shown in Figure A-2:
Corner Rod:
Applying Equation A-I to a comer rod (as in Figure A-2a),
(( ))](A-2)
A-3
Non-Proprietary Information NEDO-33419 Class I Revision 0 Side Rod:
Applying Equation A-I to a side rod (as in Figure A-2b),
(( )) (A-3)
Interior Rod:
Applying Equation A-1 to an interior rod (as in Figure A-2c),
Er ))(A-4)
If there is one unheated. lattice position (as in Figure A-2d),
Er )) (A-5)
If there are two unheated lattice positions (as in Figure A-2e),
)) (A-6)
If there are three unheated lattice positions (as in Figure A-2f),
)) (A-7)
A summary, of the R-faetor calculation method for each ATRIUM- 10 lattice position (as identified in Figure A-3) is given in'Table A-i1.
A.6 Fuel Assembly R-factor The fuel assembly R-factor is determined in accordance with Equation A-8 for any specified fuel assembly exposure, control state and channel bow.
R=Max[Rj] taken over all i (A-8)
A-4
Non-Peoprietari I nformation NEDO-33419 Class I Revision 0 Water k) Box Figure A-2a Figure A-2d k i Watr Box Fk 00 Figure A-2b
(
k
,. k 'I k Water Box Figure A-2c Figure A-2f Figiure A-2. identificatiionofkRods' in Positions A:djacentito Rodi, A-5
Non-Proprietary Information NýEDO-33419 Class I Revision 0 Table A-1. R-factor Calculation by Lattice Position Lattice Apply 'Use P._Position Figure, Equation...
(1,1) . A-2a A-2 (1,2) A-2b A-3,-
(1,3) A-2b. A-3 (1,4) A-2b A-3 (1,5) A-2b. A-3 (1,6) A-2b °A-3 (1,7) A-2b A-3 (2,2) A-2c A-4..
.(2,3) A-2c A-4 (2,4) .A-2c A-4 *
(2,5)" "A-2c A-4 (2,6) . A-2c A-4 (2,7) A-2c A-4 (3,3) A-2c A-4 (3,4) A-2c A-4.
- (3,5) "A-2c ': A-4 (3,'6) A-2c A-4
'(3,7) A-2c, A-4 (4,4). A-2d A-5
..(4,5) A-2e A-6,
'(4,6) 'A-2f A-7 (4,7) A-2e A-6 (4,8) A-2d A-5 (5,8) .. A-2e A-6 r;;,.:;(6:,8) - ~A-2f 'A-7 (7,8) A-2e A-6 (8,8) A-2d A-5 A-6
Non-P o.Prietary Information NEDO-33419 Class I Revision 0 Line of Symmetry
/
1,1 3,
1,33 1,4 ,5 16 1, 1,3 12 1,2 1,3 2, 3,3 2,4 2,4; 1,3 1,4 1,7 1,5> 223 1,6 1,6 2, 2,6 3,, 4.,7;iLJ 4,6 ater Box . 1,5
"..2.3
... 1, 4,8'" .....5,8 % 6..8. .. ...7"....
8....
1,7 1,4 2, , 2 6 ,
1,3 1,3 1.. .2. 1..3 .. 1... 1,6..... .. . 1.... .. .14. ..
1,2 1,1 Part Length Rod . . - 'Additive ConsGtants Label Figure A-3. ATRIUM-10 Lattice A-7
Non-Proprietary Information NEDO-33419 Class I Revision 0 Table A-2. ATRIUM-10 Axial Shapes for Rod Power Integration A-8