ML20011E254
| ML20011E254 | |
| Person / Time | |
|---|---|
| Site: | McGuire  |
| Issue date: | 12/31/1989 |
| From: | ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY |
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| ML19310C691 | List: |
| References | |
| EPRI-NP-6614, NUDOCS 9002120370 | |
| Download: ML20011E254 (110) | |
Text
{{#Wiki_filter:!: Topics: EPRI NP-6614. [' Reactor safety Project 29417 Reactor licensing . Final Report .
, Electric Power Reactor transients December 1989 -
R: starch Institute LWR 1 a E ARROTTA-HERMITE Code Comparison
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1 Prepared by Combustion Engineering, Inc. Windsor, Connecticut D CF Ohhoh369
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I ' L p-n R - E P-O R T S U M M A R Y- ' SUBJECT _ Nuclear reload management :
' TOPICS . Reactor safety Reactor transients Reactor licensing LWR AUDIENCE Safety analysis engineers / Core design engineers 4
c~ ARROTTA-HERMITE Code Comparison This report documents the verification of the ARROTTA space-time kinetics computer program against a similar industry code for a PWR rod ejection accident, The ARROTTA code can be run l much faster and at a small fraction of the cost than any other :! known code of its class. i BACKGROUND The ARROTTA computer program is a multidimensional space-time kinetics program developed by EPHI for solving LWR transient problems in which - spatial effects in the core are significant, Because reactor core power distri- i butions and other quantities of interest are not amenable to measurement in power reactors under transient conditions, verification of computer code l predictions of such events generally rely on numerical comparisons of com- l puter codes. ! OBJECTIVE To verify the ARROTTA computer program for transient applications. l t APPROACH The computer program HERMITE, one of several codes in the industry avail- l able for this type of companson, was chosen to verify the ARROTTA code I for transient applications. An NRC approved topical report for the HERMITE l code exists, and the code has been used repeatedly in licensing applications.
,.:. The investigators found the common input options between the HERMITE j D and ARROTTA codes. They ran both codes and compared the results. i RESULTS The EPRI ARROTTA verification program is comprehensive. This study j
provides further reassurance of the program's capabilities for addressing space-time effects. The good agreement of the ARROTTA and HERMITE , results for the analyzed 3-D rod ejection event verifies the transient neu- { tronics, transient fuel temperature, transient control rod motion, and transient _ cross section treatments in the ARROTTA code. The ARROTTA code can, therefore, be reliably used for any rod ejection type transient, including transients up to hot, full power conditions. EPRI PERSPECTIVE This report not only verifies that the ARROTTA computer program can be used to analyze off normal conditions or accident situations but it also establishes an industry benchmark. The details of the analysis and input decks used by both the ARROTTA and HERMITE codes are given. Thus, EPRI NP 6614s Electric Power Research Institute
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[. others can repeat this analysis knowing th;t they are repr:senting th)- problem in the same manner as was done in this study. The ARROTTA
- code has state-of the art algorithms that give accurate results with a minimum of detail. Thus the code produces excellent results with re-duced running time and a factor of 10 lower cost than other codes of the same type.
PROJECT RP29417 EPRI Project Manager: Lance J. Agee Nuclear Power Division . Contractor: Combustion Engineering, Inc. i
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i For further Information on EPRI research programs, call ; EPRI Technical Information Specialists (415) 855-2411. I i I l i t
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L, \l ARROTTA-HERMITE Code Comparison NP-6614 Research Project 29417 .! Final Report, December 1989 Prepared by COMBUSTION ENGINEERING, INC. C-E Power Systems 1000 Prospect Hil: Road Windsor, Connecticut 06095 1 Principal Investigators j R E. Rohan j S. G. Wagner C-E Project Manager - J. M. Betancourt l l t' -- } c. i Prepared for . Electric Power Research Institute 3412 Hillview Avenue Palo Alto, California 94304 EPRI Project Manager L.J.Agee Nuclear Reload Management Program Nuclear Power Division
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nf Requests for copies of t'his report should be directed to Research Reports Center ;i ' p' h[4 , '.'(RRC), Box 50490, Palo Alto, CA 94303, (415) 965 4081 There is no charge for reports !
' - . requested by EPRI member utilities and atiiiiates. U.S. utWity associations,'U.S. government / .9 -
l agencies (federali state,'and local),; media, and foreign organizations with which EPRI has - a
$.f ' 1 ; an information exchange agreement On request, RRC will send a catat9 of EPRI reports
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w'N \ 9; R A 3 . Electric Power Research institute and EPRI are registered service marks d Electnc Power Research Institute, Inc. - j e . . .
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;Copynght @ 1989 Electnc Power Research Institute, Inc A8 nghts reserved - -
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This report was prepared by the organization (s) narned below as an account of work sponsored by the Electnc Jl t, Powcr Reseasch ins'itute, Inc (EPRI). Neither EPRI, members of EPRI. the organizahon(s) named below, nor any ,
- person acting on benait of any of them (a) makes any warranty, express or impGed, with respect to the use of any I information, apparatus. method. or process disclosed in this report of that such use may not infnnge pnvately ' I owned rtghts; or (b) assumes any liabhties witn respect to the use of, or for damages resulting trorn the use of.
s+ any information, apparatus, method, or process disclosed in this report
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' Combusbon Engineenng. Inc '4 Windret Connectcut J
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gm . i t r , s r . 4 ABSTRACT ThisJ report documents-.the verification of: EPRI's ARR0TTA space-time- kinetics computer program against a similar.-industry code. A three-dimensional space time . kinetics-calculation of a PWR rod ejection transient:was run using the ARR0TTA' code. The-results were compared against those' of Combustion Engineering's HERMITE 0'
- code. The transient used an' initial zero power condition and ejected a rod worth ,
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'of $1.16. Additionally, steady state cases were compared in support of the .-
l transient analysis' problem -definition. Excellent agreement was obtained in all- Tj phases of the- comparison -including steady. state and transient total core power, l peak assembly- power, core average fuel temperature, and maximum fuel temperature. i A complete. problem description.. including all of the ' input, is contained in an
- appendix.
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ACKNOWLEDGMENTS The following individuals and organizations are recognized for their contributions to this work. Mr. Kenneth Doran, S. Levy, Inc., who was responsible for running ARR0TTA and providing the results to the authors, and for his consultation on all aspects of the work. Dr. Laurance Eisenhart, S. Levy, Inc., for supplying needed information on the ARROTTA program of which he is the principal author. ! Dr. R. R. Lee, Leaders in Management, Inc. , who provided general guidance and consultation throughout the ef fort. Mr. R. P. Harr is, Combustion Engineering, Inc., for several helpful suggestions and discussions with the authors on the use of HERMITE. e V
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?ll ;GENERAli il 1:
.l.1 4 Objective and Background m
. Scope 1 ' Formatc 1 -3 ':
Summary; l-3 l
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- References- 1-4 ]q y .u-s 12- . CALCULATIONAL MODELS 2 - 4
" Introduction - 2 l'
" H: 'ARROTTA Key Features 2 14 I'i ', s HERMITE Key' Features 2 n Major Differences' Between Calculational Models 2-5
- Y LReferences' 2 '
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'3 " PROBLEM. SELECTION 3-1 Definition of Problem 3-1-- q
- Modeling Assumptions-
_ 3-1 l4 ANNLYSISRESULTS 4'- l
, Introduction- 4 a l -' :
I' JW . 4 s Steady-State Calculations 4-1 i
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! - .4 Transient Calculations .4-6 LSummary 4-21 References 4-21 j '.-
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/' LAPPENDIX A' HERMITE SENSITIVITY STUDIES A-1 APPENDIX B PROBLEM DESCRIPTION B-1 r i vil
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-. . . ILLUSTRATIONS u F1oure han 3-l' Core layout 3-2 4-1 - ARR0TTA-HERMITE Comparison All Rods Out, Hot Zero Power 4-2 4-2 ARROTTA HERMITE Comparison All Rods Out, Hot Full Vower 4-3 3 Core Average Axial Fuel Temperature Comparison at Hot Fell Power 44 4 ANOTTA HfiRMITE Comparison Rodded, Hot Zero Neer - 4 4-5 N'RSTTA HERMITE Comparison Static Ejected Kurth - 4-7 4 .ARROTTA HERMITE Comparison of Total Core Power 4-9 4-7 ARROTTA-HERMITE Comparison of Total Core Power 4-10
'4-8 AtlROTTA HERMITE Comparison of Peak Power Density 4-11 49 ARROTTA-HERMITE Comparison of Peak Power Density 4-12 4-10 ARROTTA HERMITE Comparison of Core Average Fuel Temperature 4-13 4-11 ARROTTA-HERMITE Comparison of Maximum Fuel Temperature 4-14
*~ ARR0TTA-HERMITE Comparison of Radial Power 4-12 Distributions at 0.20s 4-17
,3 4 13 ARROTTA HERMITE Comparisor. of Radial Power Distributions at 0.23s 4-18 4-14 ARR0TTA-HERMITE Comparison of Radial Power Distributions at 0.39s 4-19
'4-15' ARROTTA-HERMITE Comparison of Radial Power Distributions at 0.50s 4-20 A-1 HERMITE Comparison of 2x2 and 1x1 Mesh Structures A-2 ix
Fiaure D.gs a A 2- ARROTTA Comparison of 2x2 and lxl Mesh Structures A3 A3 HERMITE Sensitivity to Axial Mesh-Structure A5 A-4 HERMITE Sensitivity to Time Step Size A6 A HERMITE Sensitivity to Fuel Temperature Model A6 HERMITE Sensitivity to Fuel Temperature Model A7 '*'l A-8 A-7
.A-8 HERMITE Total Core Power Sensitivity to Theta HERMITE Core Aver-age Fuel Temperature A9 *]
i Sensitivity to Theta A 10 t A' 9' HERMITE Maximum Fuel Temperature Sensitivity to Theta A-ll A-10 ARROTTA HERMITE Comparison of Fuel Pellet ! Heat Capacity A-13 ; A Il ARROTTA HERMITE Comparison of Fuel Pellet l Enthalpy from 400-1500F A-14 i A-12' HERMITE Finite Element and Nodal Expansion .i A-13 ni e e n a No a Exp n n ransient Comparison' A 17 .1 3 8-1 ' ARROTTA Fuel Assembly Type and Control Rod Group Layout B4 B2 ARROTTA Input Listing B-19 ; B-3 HERMITE Input Listing B 27 4
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' Selected Transient Results 4 16 N. B 1. Problem Parameters B 3-I .B 2L . Composition 14 Fuel: Type 1 Cross Sections ~ B'5 W B 3' Composition 2 Fuel Type 2 Cross Sections B' 6 F B4 Composition 3+ Fuel Type 3 Cross Sections B7
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. Composition 4 Fuel Type 4 Cross Sections iB 8 "* B 6: Composition S Fuel Type 7 Cross Sections- B9-py B7 Composition 6 Fuel Type 8 Cross Sections B 10
{M , .B 8 ' , Composition 7 Fuel Type 9 Cross Sections - B ll S ' _B 9 : Composition. 8 Fuel Type.10 Cross Sections B 12: l
' B 10 : -Composition 9 Fuel Type 11 Cross Sections B 13 .
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- toapasition 14. Fuel ' Type 12 Cross. Se:tions
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SUMMARY
'The. ARROTTA computer c0de is a multi dimensional space time kinetics program 6
. developed for the Electric Power Research Institute (EPRI). by S. levy, Inc. -The ;
' code objective' is. to solve boiling water reactor (BWR) and pressurized water i reactor (PWR) transient problems where spatial effects in the core are +
'significant.. :The EPRI ARROTTA verification program is a comprehensive one, of f which this study provices further reassurance of the code's capabilities for r addressing space time effects.
l The -' objective of this study is- to verify the ' ARROTTA computer program for i
- transient ' applications., This. has been accomplished by comparing results from ARROTIA' to results from Combustion Engineering's HERMITE code for the same :
' problem. . Since reactor core power distributions and other quantities of interest are not amenable to cieasurement in power reactors under such conditions, ;
, verification of computer code predictions of such events must rely on numerical j p t intercoraparisons between computer codes. Fortunstaly, there are several computer ,
y, codes such tas' HERM11E which can be used for tnk comparison. HERMifE was cNson ,
. because of .its- licensing status with the Nuclear Regulatery Consiss1nce k. l T - app' roved topical report ior HERMITE exists And the code has been used naenteOy :
"in'. licensing applications.
k# h ; A.three-dimensional .(3-0) space time kinetics calculat%n of a PWR rod ejection ? ? transient';was run using both ARP/M% and HERMITE. Tht resu'.ts t # the two i transient' calculations were then compared.- The transient used an initial zero {
# power condition.and ejected a rod worth of $1.16. This is a rather severe test of ;
- the space time capabilities' of ARROTTA since ejected rod worths this large are ,
+ Lunusual and the transient is very rapid, resulting in a power increase of a factor j
~ of one million within- one third of a second. Additionally, steady state cases were compared in support of the transient analysis problem definition. Excellent ,
> '. agreement was obtained in all phases of the comparison including steady state and , ctransient total core power, peak assembly power, core average fuel temperature and
. maximum-fuel temperature.
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Jihe' principal lconclusionfrom.thisstudyisthefollowing: s M. t [- s The'goodiagreement of the ARROTTA and HERM11E- results for. the 34 rod- : ejection event analyzed serves' to verify the transient neutronics. transient'
, fuel temperature, , transient control rod motion and trantient cross section ,
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-treatments-in ARROTTA.' The ARROTTA code can, therefore, be reliably used for: ;
-J fany rod ejection' type transient, inc19 ding transients er to hot full power .- g
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6- .Section 1 GENERAL. E r . ..
"I 11.1' OBJECTIVE AND BACKGROUND ;
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(Thel objective of this study ' is. to' verify the ARROTTA ' cocputer program forz j transient ' applications, this has been accomplished by comparing results from:
.ARROTTA to results from Comrustion Engineering's (C E's) HERMITE code for the.same 7'. ' '
problet Space time' kinetics calculations are typically used to l analyze
- off-nominal conditions' or accident situations. Since reactor core power .
D ' distributions and other parameters of' interest are not-amenable to measurement in power reactors under such conditions, verification of computer code predictions of . ,
- such events must irely on numerical intercomparisons between con 9 uter codes. -
I< fortunately, . there 'are available a number of codes including Combustion f
~ Engineering's HERMITE code which are capable of this type of calculation. l &, 4i .,
The.ARROTTA code'was develcped for the Electric Power Research Institute (EPRI) by:
- S. levy, Inc. under Restarch Project (RP) 1935-n. ARR0iTA, which stands for - ,.
![ , l Ar'vanced Rapid Rnactor OpraWnal Tra1 stent tria?yznr. was developed to solve itf 6nsient problems- where statial%ffect r. in the. core are of signifimte. Among. f
't y : thD. class of transiets is the control rod efecth n accidmt ir prchsurized water '.
%2 1 8 mreactors ' (PWRs) . AMOTTA is built oh the Analytic Nodalization Method 'as j a
..dirveloped Grlt}UAWRt(Reference -1.'l) in EPRI Rp IGN 1. The therni hydraulics ?
g model; in UROTTA is tak; > directly fr9a tha DEkGE .cograu (Refennee 1 ?) as ,
, 1eveloped under EpRI PP 1761 18- I.'!RJT(A itself was nriginally f nitiated as AN11A l @ /under Research project 1936 4 at Srookhaven Eational Laboratory. I N ~' t w.
[ .The- HERMITE code was developed at combustion Engineering for the analysis' of 'I (, : tre.nsientsf in large pWRs where space time effects are important, This was [
, !. accomplished by means of a numerical solution to the multi-dimensional, few-group, j
, time dependent neutron diffusion equation including feedback effects from fuel i,
- temperature. moderator temperature, moderator density and control- rod motion. A ,
f4 ' . topical: report -(Reference.1,3) describing the code, its input, and its i b verification was submitted to the Nuclear Regulatory Commission (NRC) in March, , g 1976 1 f 9 F 1-1 ! 1 [ s
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e A . submittal was made at the same time as a separate C-E topical report (Reference d' l.4)'on the rod ejection accident. The NRC approval for both topical reports was . obtained in July, 1976. In their evaluation of the HERMITE Topical Report, the . NRC ' staff concluded that. *The subject report describes 'an acceptable neutron !
- kinetics computer code for solving the few group transient diffusion equations in +
one, two and P dimensions." In addition, they statedi "It has been used to . support the L. * ' Element Assembly Ejection Analysis Topical Report - (CENPD-190, January b % and may be referenced in future license applications ana , topical reports." i Since the ilERMITE Topical Report was approved, the code has undergone a number of incremental improvements and has.been applied to a variety of analyses. Key ! improvements include the addition of the Nodal Expansion Method (NEM) neutronics ;
'(References 1.5 and 1.6) and the inclusion of the TORC thermal hydraulics l calculation (References 1.7 and 1.8). Results of the comparisons of the Hodal i Expansion Method with C E's ROCS coarse mesh program employing the Higher Order >
- Difference (HOD) method and PDQ were described in 1983 in the ROCS /DIT Topical :
Report (Reference 1.9).- In its acceptance, the NRC observed that based on the l good agreement for two and three dimensional power distributions between the NEM
' and POD rethods and between N:M and H0D and fine mesh PDQ 7 calculations, they
[ find either wthod-(NEM or H00) acceptable for coarso mesh power distribution ' ( calculations, furtr.ac, the NRC recomnded th)1 C E rerform further verification ; when NDI is 'nrorptratt-d into the ROC 4 code ir, order tc be astored tMt eqvivdent /
-eticul'ational biases and uncertainties are obttine1 with RMS MM as compared to l I, R005-h00. Subsequently, NEM has been incorporatej itto R005 (laciuding assmbly ,
t discontinuity factors) and the additional recommended determination of biases and 'i uncertainties is in progress. C-E's experience with NEM has shun it, to be l
. superior to tos finite elemen rathod ued originally on batt theoretical and ,
. empirical grounds. !
HERMITE has. been applied over the years in a variety of licensing analyses on specific dockets. The major applications have included one-dimensional space time
" calculations for the loss of f'ow accident, time dependent reactivity insertion i
due to control rod motion, three-dimensional calculations for the steam line break accident and two dimensional (2 D) analysis of asymmetric steam generator events. I 1-2 a . t
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m . i 1.2 SCOPE .
'R This report describes a comparison between ARROTTA and HERMITE for a control rod
" ejection transient initiated from hot zero power conditions.- In addition to ,
comparing transient power levels and power distributions, several static
.$: comparisons of power, eigenvalue and rod worth are also presented.
- 1.3 FORMAT i Section 2 of this report outlines the principal features of ARROTTA and HERMITE.
and discusses differences which can impact the calculational results of the codes.- q Section 3 describes the transient of interest - a control rod ejection from hot : zero power conditions. Section 4 presents the results for the steady state and ! transient cases which comprise the study. Conclusions are given in Section 5. I Appendix - A presents HERMITE sensitivity . studies, while Appendix B provides a complete input description. l t 1.4
SUMMARY
f r The first task was to take the ARROTTA input deck and convert it to a HERMITE input deck. The major. effort in this area was in the cross section treatment. While the ARR0iTA and HERMITE cross section represent.atiw era quite different, ! the flexibility of the HERMITE reyesentation permitted the .wo c.odss to pretjece ; ^ essentially identical macroscopic c.rcss sectionf for the'same velues of mnderatot '
&nsity and fuel teniperature. Therefore, any differences in results are aat due to differences in tross section representeM ori.
' The thermal hydraulic modeh and input' for the two ccdes hiso differ. After some
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iranisulation and sensitin'tj stud!es, the HERM11E input was generated. which
, ,. showed acceptable steaoy state or/reement with ARE0TTA.
A series of steady state cares and one ditansional transients were run to make some basic assessments of the accuracy and consistency of the HERMITE and ARROTTA
;models.. These studies also provided guidance in the selection of options to be used in HERMITE for the three dimensional (3 D) transient. Overall, the l steady state ARROTTA HERMITE comparison showed very good agreement. -i p
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? , g , f h The final task was execution of the 3 D rod ejection transient in half core U geometry. :The agreements on core power, peak power, time of peak power and radial [ power distribution are all excellent. The core total power peaks, for~ example, ; f' differ by only 31 MW out of some 4300 MW (0.7%). . Th'e time of peak power differs b I ' by only 5 ms. Agreement in peak' core power is comparable to the total core power . ; agreement. t y p , The good agreement.obtained for the comparisons performed provides verification of-f . ARR0TTA for analyzing problems where there are significant transient neutronic and a b fuel temperature feedback effects. ! n , b ! [
1.5 REFERENCES
[. 1.1 K. S. Smith, "An Analytic Nodal Method for Solving the 2 Group, Multi- . dimensional, Static and Transient Neutron Diffusion Equations," Nuc. Eng. ! Thesis, Dept. of Nuc. Eng., MIT, Cambridge, MA., February, 1979. t 1.2. D. J. Diamond, H. S. Cheng, and L. D. Eisenhart, BEAGL Ol A Computer Code .
. for Calculating Rapid Core Transients Volume 1-Hodeling," EPRI NP 3243 CCM !
Vol. I, Electric Power Research Institute (1983).- l [: l .3 P. E. Rohan, S. G. Wagner, S. E. Ritterbusen, "HERM11E: A Multi dimensional [ Space-Time Kinetics Code for PWR Transients," Cebustion Engineering, Inc., CINPD 18% A, July, 1976. p 1.4 ' ' *CEA Ejection Analysis, OmM astfon Engineering, inc., CEN"e 190 NP A, July,
- 1976, 1.0 H. ' Finnenann, H. Raum, " Nodal Expansion Me%od for the Analysis of Spere-Time Ufects in LWRs," ErgIfdingi 91 l'(NS2 unlal.1111 Meetiro, Paris, Wavemberi
%79.
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. l.6. H. iinnemann F, Bennee4'r M. R. Wagner '"/ntericte Current Trichniques for Multmtmensicnal Nacter Calcuiutons," ALFkernenet.nie,1Q,123 (1977). , & l7 " TORC Codt A Computer Code for Determining th9 Thenni Margin of a Reactor
- l*
Ti (cre," Corabustion Engineering,1r .. CENrD-161 hP A, July,1975. v 1.8 "10RC Code: . Verification and Simplified Modelling Methods," Combustion : Engineering, Inc.,:CENPD 206 NP A, January, 1977. - l 1.9:."The ROCS and DIT Computer Codes for Nuclear Design," Combustion Engineering, inc., CENPD 266-NP A, April, 1983. ! i 4 P e b l4 - t
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! Section 2
.. CALCULATIONAL MODELS i
,=
ln -'2 1 INTRODUCTION This section summarizes principal features of the ARROTTA and HERMITE computer ; programs. This is followed by a discussion of the major differences between the codas which have a bearing on the comparisons and their results. 5 2.2 ARROTTA KEY FEATURES The ARROTTA code'(Reference 2.1) is designed to solve the three dimensional, ! time dependent diffusion theory equations in rectangular geometry including a thermal feedback effects. ARROTTA's geometric description of the core consists ; first of specifying the location of each assembly type in the XY plane and the
, associated mesh.in all three dimensions. The neutronic mesh is specified next. :
Each assembly mesh interval must contain ont: or more neutronic mesh intervals subject tc a maximum of 40 neutronic mesh intersals ir, each direction. The t ' therm 614) dray',1c mesh is f,pecified next. The thermal-hydraulir mea must b0
- come,ansurate with the assembly mesh but not necessarily with 'ho neutronic mesh. [
Again the. maximum nurrber or thermal-bydraulic mesh intervals in each dimension h . 4 0.- There are a number of features which can r.tnimize and simplify the geometric .i description of the core. The code can handle both F/Rs and BWRs with RCC or i cruciform type control rods. Features also enable the code to expand input , gry,etry from or.e sin to another such as grartar core to fuli core. The neutronic model uses the Analytic Nodalization Method (ANM) as developed for ,
.. . QUANDRY. This is a coarse mesh method which breaks the problem down into a one dimensional representation in each coordinate direction within each'
- coarse mesh node. With the assumption of constant cross sections within each ;
node, the one dimensional problems are solved analytically. The three one dimensional equation sets are linked through transverse leakage. The ARROTTA
. implementation of ANM also incorporates assembly discontinuity factors to better represent.the true heterogeneous reactor. Boundary conditions that can be used ,
include zero flux and zero current conditions on external boundaries. The initial condition for transients is that the problem is in the steady state. 2-1 !
m 1 n . i L h The thermal-hydraulic model in ARROTTA is taken directly from the BEAGL code. The fluid dynamics model considers inhomogeneous, non equilibrium two phase flow. The . flow equations are one dimensional in the axial direction and, therefore, do not [ consider cross flow between neighboring channels. The boundary conditions ' employed are specified inlet temperature and flow for each of the . i thermal hydraulic channels. Pressure, inlet temperature, and flow can be varied as functions of time during a transient, in all, five flow regimes are , t considered. ARROTTA essentially solves a four equation system: one mass balance .[ equation for the liquid-vapor mixture, two energy balance equations for liquid and , D vapor phases and an algebraic slip relationship. The momentum balance is not
- y. considered because it is decoupled from the energy equations and because the inlet l mass. flux is specified' for the core as a boundary condition. !
The fuel temperature model solves the radial heat conduction equation for each thermal hydraulic unit cell. The unit thermal hydraulic cell consists of a fuel pellet, gap, clad and surrounding moderator. Axial heat conduction is ignored, lhe heat source in the fuel pellet is represented as a parabolic function of I pellet radius with a free parameter that can be varied on input to govern the curvature of the rarabola. With this distribution and the assumption of uniform f themal condettivity and specific heat in the pellet the heat conducH on equation is se!ved W1ytically, The pellet c14d gap is modeled w P,h a gap conductivity. ; The heat conduction equation is aga % solved in the clad. A fraction of the heat can o'e deposited directly in the clad and coolant. ; ,t= The cross action treatment t'cgins with the concept of 'asserably types" which consis.L of.one or more axin material corapositf or.s suc's as tre bcttom reflector, fuel u,d top reflector, ine ass;mbly type concept h gone.ral enough to incluce baffles and radial refle,: tors n well . Cross sections are specified by composition. In each composition the macroscopic cross sections arc quadratic functions of void fraction for boiling water reactors (BWRs) and the relative change in moderator density with respect to a reference value for PWRs. Separate sets of quadratic coefficients are input for rodded and unrodded conditions. The moderator temperature dependence of each cross section type in each group is treated as a linear function moderator temperature. Fuel temperature dependence !
, is treated as a linear function of the square root of the absolute fuel temperature. The fuel temperature dependence is only allowed in group 1. The moderator and fuel temperature dependence is the same for both rodded and unrodded l macroscopic cross sections.
2-2
f, 4 y. To account for rod cusping, cross sections for partially rodded nodes are obtained
~ , by blending the unrodded and rodded cross sections using a factor which can be up :l to a third order' polynomial in the fraction of the node which is rodded. However, j
- i. ' in both the ARROTTA and HERMITE analyses a simple volume weighting was used. ,
, Kinetics parameters can vary by composition. Assembly discontinuity factors can i be composition, group and node-face dependent. Different sets of discontinuity
- factors can be used for rodded and unrodded conditions.
e L 2.3 .HERMITE KEY FEATURES i I Like-ARROTTA, the HERMITE code is designed to solve the time dependent diffusion- - [ theory equations in rectangular geometry including thermal feedback effects. HERMITE can solve one , two or three dimensional problems. The neutronics mesh i
.is specified separately for each of the three spatial dimensions with a
non uniform. mesh permitted. Thermal hydraulic channels are assigned to various ; regions of the neutronics mesh. Typically, though not necessarily, one { i . thermal hydraulic channel is assigned per fuel assembly. The axial i thermal-hydraulic mesh may be coarser than the neutronic mesh but they must share , p ' common mesh points. There are no fixed limits on the number of neutronic or thermal hydraulic mesh points. The code :reats PWR type control rods. (
'HfRMITI oHgihaily used a linear finite element ratod to scive the space tim, p' C ffurion aquation. Its r.Med previously, Yne bdal Expansi:m Hethod ha:; been j , . added and is the current standsrd method. The Nodal Eversion Method and the [
Analytical Nodalization Method are similtr in that both reduce the . threc dimensional spatial problem to one dimensional (1 D) reprMentatious in each ? of the three spatial directicas in each tode. In the Nadal Expansinn hthod, ; the n ore dimentional prob 1Lms are solved bj using a fcarie order polyn a al flux 3 representation. Th< three one-dirner:sional equation sets are lieked throt9n , c trsnsverse leakage. 1he time dependence is handled by use of a frequency [
' transformation. Dotridary conditions that can be used include vacuum and zero current on external boundaries'. The initial condition for transients is that the problem is'in the steady state. For one dimensional axial problems, there is also a finite difference method in the code, its results are equivalent to those from ,
the Nodal Expansion Method but it is much faster thar the Nodal Expansion Method ! for the' fine axial mesh typically used in reload analyses. 2-3
,m
, 'HERMITE has two thermal hydraulic models. The original model is a closed channel model where the mass balance, energy balance and equation of state are solved : cimultaneously. The boundary conditions employed are specified inlet temperature, - and flow for each of the thermal hydraulic channels. Inlet temperature, flow and , (I decay heat can be varied as functions of time during a transient. The second flow .
.i I model in HERMITE is taken from C E's TORC code. This is an open channel flow I
, model which is based on that of COBRA IIIC (Reference 2.2). The open channel flow . [ model can handle more' complex conditions and includes such features as flow balancing. The original closed channel'model is used for this study. ? I L p' The. fuel temperature model solves the radial heat conduction equation for each thermal hydraulic unit cell which consists of a fuel pellet, gap, clad and I , I' surrounding moderator. Adal heat conduction is ignored. The heat source in the ! [ fuel pellet is spatially constant across the pellet. The heat conduction equation y is solved by a finite difference technique which permits the thermal conductivity and specific heat to vary across the pellet. The pellet clad gap is modelled with
- a gap conductivity. For steady-state problems there is an alternative fuel ,
temperature modei-which correlates fuel temperature with linear heat rate and burnep. A traction of the hat can bt deposited directly in the coolant. , t a The cross si:ction trer4tment in HERMITE is tard upon the fiARM0W vystem used in i FD0'(Reference 2.3). This system permits microscq,ic and macroscopic cru s [ sections to'be functions of up to three independent variables. These variables can be number densities or other quantities such as moderator density or fuel ; temperature. In additito th v a is another ret of factors which multiply cross
' sections.and which can also t,e funct%rs of up to three variables. 1 hts treatment permits a very general representai. ion of cross section changes due te changes in {
moderator temperature, moderator density, fuel temperature or control rod , position. The code accepts one set of kinetics parameters. HERMITE also includes a depletion capability similar to that in the GAUGE code _{ (Reference 2.4). Depletion chains for individual nuclides are specified on input. 24
ll ,
/
2'. 4 MAJOR DIFFERENCES BETWEEN CALCULATION MODELS
'Since_ the problem of interest had already been set up for ARROTTA, the task at hand was to model the same problem using the same data in HERMITE. The differences between ARROTTA and HERMITE are generally small. for the purposes of 4a .this comparison. Only differences between the codes which were' considered or which impact results are discussed, 116
'The current version of HERMITE does not use assembly discontinuity factors, which have'become standard and widely accepted in steady state coarse mesh codes. Under a reasonable set of assumptions (face independence of the discontinuity factors) the HERMITE cross sections could be modified to incorporate the effect of discontinuity _ factors, with the only approximation being in the axial reflector regions, it was decided for this comparison not to use them because they added complexity to the problem set up and were not considered significant from the point of view of comparing and verifying the transient neutronic and thermal hydraulic aspects of ARROTTA.
ARROTTA accepts composition dependent kinetics parameters u.ereas HERMITE can accept only one set. For this problem, ARR0TTA and HERMITE both used the swe, ,, single set of kinetics parameters. [ Since it is the fuel temperature which limits the power increase during the 'l
- transient, the fuel temperature models in the two codes are impor*. ant. There are i some minor differences in the fuel temperature mode). f.RRDTTA is able to handle a I non uniform heat source within the pellet but assaes spatially constar.t thermal conductivity and specific hs.at, while HERH11E r;ar. hsndle a spatially varying conducthi+,y but assumes a spat tally constant heat source.
LAnother area of difference in the fuel temperature calculation is the way in which the.two codes derive the power in the representative fuel pin in each thermal _ hydraulic unit cell.- In HERMITE the code is given the number of fuel pins in'the fuel assembly as part of the input. With that the power in the average pin is easily derivable, in ARROTTA, the input quantities are unit cell pitch, the thermalihydraulic channel dimensions, and a factor which excludes the area not considered part of the fuel rod or coolant. This factor is interpreted to mean that the area of the gap around the assembly and the guide tube cell area is excluded. From the thermal-hydraulic channel mesh, the input cell pitch and ] l i 2-5
t i __ fraction of excluded area, an implied number of fuel pins in-a fuel assembly in ! ARROTTA is derived. This number implied from the ARR0TTA input and used in i, HERMITE is 282.36 pins. L The solution strategy for the neutronics and fuel temperature has an important ! l bearing on the results of the transient. Both ARROTTA and HERMITE first advance i p the neutronics from time tn to time i +1 n and then advance the thermal hydraulics. j { LThe thermal-hydraulics and neutronics are not solved simultaneously or implicitly. i Time step size studies described later in detail explored the effect of this : approximation. For the purpose of highlighting the differences between ARROTTA _! and HERMITE, a brief discussion of the transient aspect of the fuel temperature f model is provided. The general form of the transient fuel temperature equationsL I in both codes is i h=q(t)+otherterms 3
~
~ where q(t) is the heat source in the fuel. The discretized form of this equation ;
< ' ' in HERMITE is ,
.n
'yT1 n
= 1/2 (q" + q"'I) + other te w j i
?
Thh approximation 'is cquivalent to assuming that the beat source varies - f -linearl) in time from t n-1 to t n. A more gnieral form of '. tis aquatica is i n n t yI -)~ = e q" + ti-f) q"'I + other terms
]
o ; The default theta (e) value used in HLRMITE is 0.5. Another common approximation , is.e l. This second approximation is the one used in ARROTTA, based on the- : ARROTTA documentation. The sensitivity of-the HERMITE results to e is discussed in Appendix A.- A value of e=1 was used in the 3-D HERMITE calculation for compatibility with the ARROTTA calculation. In addition to the heat deposited in the fuel, ARR0TTA permits heat to be - deposited directly -in both the clad and coolant. HERMITE permits direct deposition only'in the fuel and coolant. For purposes of consistency and since ' the effect is not significant for this study, all heat was deposited in the fuel pellet in both codes. 2-6
f# , Ao - E : f j$ h- .-, F.' i
' Another area of minor difference is in the neutronic boundary condition where l' ARROTTA has a zero flux condition and HERMITE has a vacuum boundary condition.
,This difference is insignificant.
~
. u; ~ The water properties and fuel properties'in the two codes come from different j
, c. sources. A limited comparison has been made between them and the differences are small. s The HERMITE cross section treatment is very flexible. For these comparisons-this flexibility enables HERMITE to exactly duplicate the ARR0TTA cross ~ section i treatment after some preliminary manipulations. Conceptual differences in the l
- cross section treatment include polynomial fits in HERMITE compared to tabular
! data in ARROTTA. : i l
2.5 REFERENCES
l t 2.1 Laurance D. Eisenhart,'"ARR0TTA: Advanced Rapid Reactor _0perational Transient- . Analysis Computer Code Documentation Package," Volume 1: Theory and Numerical ; Analysis, and Volume 2: User's Manual, Electric Power Research Institute, retruary, 1989, , 2.2 D. . S. Rowe, ~ " COBRA-IliL: A Digital Computer Program for Steady State and ! 1ransient Thernal-Rydraulic Analysis of Rod Bundle Nuclear Fuel Elements," , BNWL 1595,' March, 1973. ; 2.3 M. = R. Wagner, GAVGE: A Two-Dimensional Few Group Neutron Diffusion-Oepletion i
- Program. for a Uniform Triangular Mesh," GA.8307, March,1968. .
?.4 R. L Breen, O. J. Marlowe, C. J. Pfeifer, "HtRMON): System for Nuclear- ; Reartor Depletion Camputation," WAPD-TM 478, January, 1965. ;
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h Section 3 PROBLEM SELECTION ; 1 3.1 DEFINITION OF THE PROBLEM The rod ejection accident in a PWR is postulated to be the result of the failure i of a control rod pressure housing leading to the rapid ejection of the control rod itself. The reactivity' insertion produces a transient and a relatively peaked power distribution. If the reactivity insertion is great enough, a prompt I transient leads to a large power increase which may result in DNB (Departure from Nucleate Boiling) and fuel damage. The transient is limited by the Doppler : reactivity and is terminated by a scram caused by flux signals. ; The main reactor parameters affecting the course and magnitude of the transient , are typically the ejected rod worth, the delayed neutror fraction, the precursor i half lives, the Deppler feedback, the prompt neutron lifetime and the power ; peaking. Additional parameters of generally less significance are the moderator I reactivity feedback, rod ejection time, trip time and trip reat civity. For this i 4 comparison it was not necessary to simulate the transient r-ut to the tiinc of trip. 7
' 3.2 MODELING ASSUMPTIONS The problem chcLen for this comparison was the ejection of a sir.gic control rod from the ret.ctor at hot zero power conditions. The problem is typical of a.large i modern PWR core. The hot zero power transient rather than the hot full power case 3 was chosen because it represents a more severe test of the computer programs. The rod worths are generally higher, leading to a prompt critical transient in this case. The power level anr1 fuel temperature increases are also greater.
Conclusions drawn from the hot zero power transient will apply to a hot full pcwer
- transient-of similar duration. 1 A more detailed description of the problem is presented in Appendix B including ,
both ARROTTA and HERMITE inputs. Figure 31 shows a core layout with the location of the various fuel types and control rods. The ejected control rod is located '! one assembly in from the right hand edge of the core along the major axis. As 3-1 i r
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- i such -it was modeled in half core geometry in both ARROTTA and HERMITE. The thermal absorption cross section of the rod to be ejected and its symmetric
partners was appropriately increased so that the ejected rod worth was $1.16 in
~
order to create a severe prompt critical transient. t P' ARROTTA was run with one neutronic mesh and one thermal hydraulic mesh per fuel I assembly. . These are the' typical mesh structures used in ARROTTA applications. ;
- 1o The baffle was also one fuel assembly (21.608-cm) wide. The minimum thickness of' i the radial reflector was also one assembly mesh (21.608 cm). There were sixteen j '
axial l planes with twelve 30.48 cm planes in the core and two 20 cm reflector L planes at both the top and bottom of the core. 1 4 HERMITE was run with a 2x2 neutronic mesh and one thermal hydraulic mesh per fuel [ t assembly. These are the typical mesh structures used in HERMITE applications. l The baffle was one fuel assembly wide which means it had two 10.804 cm neutronic - y t. mesh intervals in it. The radial reflector had a minimum of two mesh intervals of _ 10.804 cm each. Thus the HERMITE neutronics radial nesh was overywhere finer than ; {
- the- ARROTTA mesh. The HERM17E axial mesh structure vas . identical to that of ARROTTA. The thermal hydraulic mesh was also identical in the two codes, i b ,
g y. The' initial condition was steady state-operation with a number of control rods '
, inserted. The rod to be ejected was inserted approximately 9M. The red was ,
Jejected in abort 0.10 s at constant velocity. The init,ial power level was 0.001 l MW (which is referred to as "zero power' throughout this report).
] .
a
'The transient was followed out to 0.50 s. ARROTTA used 1 ms timesteps throughout ['
the transient. HERMITE used 10 ms timesteps throughout. i y Both moderator density and fuel temperature feedback were used. Since the initial power level is so low and the transient so rapid (-0.40 s) there is no significant
,_ _ _ moderator heating. The fuel temperature feedback is, therefore, the important phenomenon to model. ;
't i
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L , Section 4 3 ANALYSIS RESULTS b l V i ,
4.1 INTRODUCTION
r
- The steady state and transient comparisons between ARROTTA and HERMITE are l presented and discussed in this section. Preliminary sensitivity studies using l HERMITE are described in Appendix A. These sensitivity studies were used te
. choose modeling. options, such as timestep sizes and to explore the sensitivity of h the results. Similar sensitivity studies were performed for ARROTTA in a separate Y . study. . These are described in Reference 4.1. [
L 4.2 STEADY STATE CALCULATIONS ! E y ; I :The first comparison was at hot zero power, all t ods out. The purpose of this g case was to -assure consistent modeling of cross sections without feedback or-control rods effects. The axially integrated radial power distribution and ; eigenvalue comparisons are shown in fig 1re 4 1. Edited results demonstrate thd p the cross sections in both codes are the same. Agteement for this casa is 9001.
.i The next task was to run an all rods out problem at hot full power conditions. ;
The primary purpose.of.this test was to verify consistent treatment of thirmal L feedback and the associated. cross'section changes. The axially integrated radial ! power distribution and eigenvalue comparisons are shown in figure 4-2. The 1
- h. agreement is even better .than for the zero power case as one would expect because l** full power conditions.with thermal feedback tend to smooth differences. The axial .j power shapes also show excellent agreement. The fuel temperature comparison is of
?- particular-importance since it will impact the power peak during the transient, h figure'4 3 shows the axial distribution of the average fuel temperature for both I
_ code's . The maximum difference is about 23'F at a fuci temperature of 1460*F; / ; p 'From an engineering viewpoint this is good agreement. b A steady. state comparison for the zero power condition with control rods inserted at their initial conditions for the transient is shown in Figure 4 4. The l 4 agreement-is again good. ; 41 ' n-t
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til?34 -1.2137 1.1120 0.9487 Legend ARROTTA-
= 1 1151." : 1.2112 ' 3.1071 0.9401 1:ERMITE-
-0.1% 0.2% 0.4% 0.9% t--difference 4 t3/ Maximum D12ierence ' Standard- -;
y: Deviation k offective ARROTTA 1.008527 - Positive 1.65%
.k-effective HERMITE ^ 1.008222 Ne06tive ~2.24% 1.00%. ,
Dtiference 0.000305 , k
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Figure 4 1. ARR0TTA HERMITE Comparison All Rods Out, Hot Zero Power- .3
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g 'r
' 0.97PJ. 0.0665 - -1.0000 . 0.9790- 1.1665 *,.2309 0,9620 4i nl . ,
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0.6% 0.1% :j
;1.1063- 1.1361 1.0425' O.8063 Legend ARRoTTA i 4
1.1001' 1.-1346: -1.0390 0.0til HEhMITE-
- *0.2% . 0.1% ' _0.3% 0.6%- 6--differecco. [
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3 Seviation 's ?. <- W s k-offective ARRoTTA 0.994267. Poettive 0.934 &
# 'tf-~[ :k-effective HERMITE 0.994346 Nogettve' + 0. 66 % ' O.36% _ [
4
. Difference 0.00005
. i.
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'T Figure 4 2. :ARROTTA-HERMITE Comparison All Rods Out, Hot Full Power- 3
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- 2. Be . ' 2. 9% .
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"N,h[ , ' 7 0.8906 0.7592 0.0472 C.7666 6.9192 1.1162 :1.6219 a.2312 j
';;:c 'O.9142 0. 77 6 3 J-. 0.t644 0i7765 0.9217 1.1088 1.5987 1.2045 a k-@ N* *2. 6% - .-2.2%, ~*2.0% -1.3% -0.3% 0.14 1.6% -2.2%
y , . _ j' t t- + 0.1815 ,- 0,9533 0.8628 0.9178 ,0.7206 1.3366 1.8E44 4 . '0.0073' 0.9719 'O.8720- 0.9217 0.7187 1.3146 1.9116 r , .-1.8% + 1. 9 % - 1.1% ' -0.4% 0.2 % - 1.7%- 3.4% ; b; / 0'.6882; '0.7810 1.0007 1.1126 1.3338 1.1101 1.44t9 :
;0.6964 10 7506 1.4899 .1.1088. 1.3146 1.6710 1.426V- ,i
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+1.3%' -0. 4 % . 0.04 0.9% 2.0% 1.$4 i
. - 0.60 3 0'.3928 1.2410 1.2717 Nogend ARROTTA g-
'O.6847 _ 0.k945: 1.2311 1.2046 Etase!T! ;-;
-0.$4 - . 0 1% 0.6% 1.4% 4- alfference 4 A h
wen mum elftorence stenotra 7
- Deviation Q, 'k-of f ec*1ve ARMi% 0.WP7026 Positive 1.37% f
- k* effective H&kNITL: 0.kf6623 N*04t1** +3.31% 1.75%
pN.' *~ Diffotence 0.000503-
'(
_( h LFigure'4 4. ARROTTA HERMITE Comparison Rodded, Hot Zero Power m ,
} ? !!
j$ l k k. .,i" ' 3 n . 2tc r J
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g 45 - - I 2/L '. ,,
K , [e l ' A'stesdy state comparison for zero power conditions with the ejected rod out of : h ' the core was also run. The power distribution for this case is shown in Figure [ 4 5. This case together with the previous one determine the ejected rod worth.
~
- f. The eigenvalue and rod worth are summarized in Table 41. The difference in rod ,
worth in these calculations is approxin.ately 0.8 of a cent. To a first order ,! japprosimation, this difference could be expected to cause a 0.7% change in the ! heat deposited iaring the transient.
- Overall, the steady state agreement between ARROTTA and HERMITE is very good. I Such good agreement means that both codes start the tre.nsient from the same set of [
t ' cordit ions.' The -' static ejected worths also agree very well. Th2 numerical i
,T methods Ju the two codes have comparable accuracy. This is substantiated by the fact that the transient results compare very favorably as discussed in Section r 4.3. ;
i i 4.0 TRANSIENT CALCULA110NS i Based on the problem definition and the results of the steady state and sensitivity studies described in Appendix A, the 3 0, half core rod ejection i transient was run with HERMITC using 10 ms timesteps. This timestep size is typical for transients of this type in HEftMITE. Figures 4 6 and 4 7 display the { total core power as a function of time. The plots show exactly the same data, the. !
.only difference being that Figure 4 6 uses a toqarithmic scale to emphasize the early phase ~ of the transient, while Figure 4 7 uses a linear scale to emnhasize the peak power portion of the transient. ARROTTA results using 1 ms timesteps are 3 also shown for comparison. This is c'typichi timestep size in ARROTTA for this type transient. Agreement is excellent. ;
Figures 4 8 and 4-9 display, on logarithmic and linear scales respectively, the ,_{ peak power density from t'oth codes. The location of the peak power (assembly and sxial plane) is the same in both ARROTTA and HERMITE, Again, the agreement is , ) excellent. ,
.The core average and maximum fuel temperatures as a function of time are shown in Figures 4 10 and-4 11. The location of the maximum fuel temperature is the same in both codes. The difference in the two curves appears to be due to the 5 ms shift in the t.ime of the power peak rather than any other differences in accuracy -
of the two codes. .. 6 4-6 , 9 -_ __
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,, 0.1981 0.2391 0.2136 0.2193 0.2720- 0.2689 0.3637 0.5632 0.9249 1.103f 3.5846 2.3172 2.1972 f, 0.1633. 0.2314 0.2107 0.2182 0.2754- 0.2733 0.3685 0.5668 0.9304 1.0998 *. 5265 2.2612 2.1993 2.6% 2.9% 1.5% 0.1% -1.3% -1.6% ~1.3% -0.6% -0.6% 0.3% 1.2% 1.6% 0.3%
0.2105 0.3006 0.3079 0.2491 0.2690 0.0879 0.6416 0.0682 1.4764 1.9492 1.7273 0.2069 0.2949 0.3061 0.2505 0.2702 0.0898 .0.6429 0.8650 1.4636 1.9129 1.7099 1.7% 1.9% 0.6% -0.6% -0.5% -1.0% -0.2% 0.4% - 0.9% ' e.9% . 1.1% 0.2395 0.2939. 0.2997 0.3226 0.6640 0.9557 1.0460 1,egend ARRO1TA 0.2372 0.2828 0.2925 0.3237 0.6641 0.9459 1.0284- REmMITE 1.0% 0.3% -1.0% -0.3% 0.3% 1.0% 1.7% 4--difference Mexiuma Difference standern Deviation k-effective ARROTTA' O.99547 Positive 3.99% k-effective RERMITE 0.99503 Im0etive -2.60% 1.25% Difference 0.00044 Figure 4-5. ARROTTA-HERMITE Comparison Static Ejet.ted Worth 2
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cc oi.. , EIGENVALUE AND EJECTED R00 WORTH COMPARISONS- :
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- Ejected Rod Out -Change ini 5
- i k effective 'j 1 .
ARROTTA~ 0.987027 0.995479 -0.008452' 1.158. WW
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.HERMITE 0.986523- 0.995033 0.008510 1.~ 166 , . .
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i , O O.2 0.4 Time (seconds) Figure 4-6. ARROTTA-HERMITE Comparison of Total Core Power
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-& 5~ . ' 2, M ci_>t. in1.0 m J..~..> , u e. . . an ernbe. ratbre?
1;.n1 .
- f _ ... ~ M, v%--.= 1
~w
...' r
. _ ,_ ,,9
~,, ,.sc 3,.
,e
. ik M %y;,- - G.
4 ., L -. 2 ARR.O.TTAM HERMITE Compa..rison ; - - - <_. - V - %, . an.- %,v?W ~a w
~.
s 9 0- , ,. , . . , am,n ~ , w ; 1 , .
- sy .: p4. ;
~
,, 4 < ~
, '", % .. 'W
, n,f.
'h Ie'" ). c.y,,~.. _
,,," + ,, quj ,. 3 (
.- .. . y~.... ~.: ,.
an 9.u WWW9
~
^
'900f- iARROTTAi -
'y,,
v
.. ; z__; , - '; w., >*- - - J .,.,,,,2
'~-..k-g
- t , , pu;.. ,,
b5 9 m , .
%,. ,.+~
' . . .- 1
.q i ;;a g,l.a.,.'%-7j z- ,~
w2
,,, __ '/ N b'[.? OW > s W '
850;- 2'+ 1 HERMITE : u.
^. . d>e aj 7_- t
--mi
- 'P'
- l $1h %es
~
r e3 +P 9
,6 '
e
,,,,., .. ' C' l , l' Y '
s % a. 800 -. c.m: m . (,L,, -
- p. ..? ? '2 cms T.
&}'Q . u, ~
. v .
a' tm , -
- e. N_ .;.
~
s .
- m. ;W.;
. e.. v ~
,3 .g."; m m , -
o " '
= -
750 - -
. 2
. v -
. ~ .. = - -L -
e, g .- , ty"-. .
- 4 4 #
s ,4-eq5
.-m- . -
).e.,_ i m 1
=
bJ<e'
- C, 700 - . -
- w. - ,-
. ,. . .. n w e. ~ ~
a '
,4 *
+
) .'(,m. t <
A , 650 - ,
~ v
.,. , ^f
~
7 1 , y , r s _ ..w - ' m.- 4 a .' . 600- - c a, 'm::
+ a. .
Y . .
. ev r 550 , - ., i e 2_ M9 ..
s , 0-L O.2 ; O.4.5 -
-p
^N n
- n,
. - - - - * . 'Q :;. %'
.. Tim.e :(seconds),., , #s. .
. . . - _s.m:~['.
,A, ,
.s FigureI4411 ARROTTA-NERMITE' Comparison ofsMaximus Fuel Temperature _ - . . . "o,?%[?
p,. 4 n
- " * " ' ' ~
m.' s 4 e - ,7 .,,6 ,. i f'*" r 4 1 "
-q f _,{l ar m k x .- y
.m--
p.. . e.. j_ . , ~ ..
.-'f'*_
4 a y- {-
.+ s f e .
..,"= p g'l' *
;.j . < .*'4
- g a .c.. }.,;
,. i, i E e 'Un,,p h=- %,,,--'N
;u:,, . a J[., q_, .n.,
'~"",
m, p
;. - t _ + ,a'" ~ ,' ' r * ,,, * ...;" .
4 . ' * '. x ih.',.,,,,..}J f 5 ?O - g j-
.;l
=q
-'s*;
o ,, i.s
, _, ( . .,
~t-,
- ba
* .g' W
- I-c \
. ."' . m- [ n.. : #m. 7 Q, -,
r
.nt
.y:
,* AM' ~
W'-
.NP / &
ng'
' ~
- 3.;&.
st "^ $; t' :j.y m ug w.aw ' - - - - 3 -
- , ,;; , , , w;3
l"l y; ( ,
~
p Selected [trasient'resultsare.summarizedin'tabularforminTable4-2, h- ' Comparisons of ' normalized radial power. distributions.at several points during the
~
l V ' '
= transient'have been made. The,first comparison, Figure 4-12, was made-at 0.20 s,-
a point before significant heat is'added to the core. In both ARR0TTA and HERMITE w the peak fuel temperature has risen less than 0.1 'F. The assembly powers differ
,by almost a factor of 70'across the core. (Because of- the large variation in=
- power . numerical differences rather than % differences are shown.on the transient radial' power distribution comparisons.) The agreement between ARR0TTA and HERMITE is excellent. ~The second comparison is made at 0.23 s, the point where the-l relative power distribution = isxmost peaked. The agreement-shown in Figure 4 13-is again excellent. 'The -third comparison, Figure 414, is 'at the 0.39 s, a point near the peak _in. total core power and ' peak assembly power. The fourth comparison,.
< Figure 4-15, is at 0.50 s, the -last analyzed time in the transient. Again, the agreement is excellent.
2
.I[
l
- 4 1
ii
. .+ 9 1
a 4-15 i l l
g.o C%; 0:1 wcT' x , a- <
~
y ; j A. y J. (_ . - - , .1 s'! .l
.:V 2;;;l9 -W.1);y + l, ,4 kv ,4y , -
r ; g-x - n-V , w M., &
,, j If I
?
(,1 1 -1 4 '
' -l ': 1 > -
Table 4 21 : g -
- l R, m ? SELECTED TRANSIENT RESULTS-m,'
@ . x ,
- - il:j R :- m.'
( _
' Quantity:. ARR0TTAt- HERMITE: o .>
- l 65 .
f v .. S : ' , . . .:i y Maximumtotal:corepower.(MW): 4308: - 43395 q y , . . - -
. a l'i n.; , ; Time'of maximum' total core power (s)i 0.388 10.383 !- ': ' ,y ...* ; Maximum assembly. power density)(w/cc) . .2005' 2014 s
mI
.. e :;
~ _ _
7 . Time of max'imum assemblyLpower density:(s) '
.0.387' 0.382' a
i- 1Averagefuel.~ temperature-(*F) q
.2 s'- 557- 557- 1
.3 s 558 558= =;
.4's 584 589 ,
, -. 5 . s. 603t 605: S
- Maximum fuelitemperature ('f) q
.2 s. : 557.- :557 l
& .3.s ;562 565 e .
-.4's- 770: 804-4 5sl. 907- -911-4 '
)
f" -I k,,' g [ l.'l.. k' i L L ., f . W
)
N,
.,s
# f, O
t
)
[b i l .5 h
.t i ?
p 4 l :- -t . F- w - 4-16 1; 'ci, p 4 E
- :. l [ ,. -se .'; 8 Ia
.n
%^* N
, ~ 7" -::' , -
W:& . '
'. . mL ' , .
- +
l w y: - w s - L. , -& x p' @WQ7 s i;.' " ~- - 3j, ;.
.,m. .
Tr - g,
'1 .r h-
. , 2" . .J O! ' l&.
<i ; .sb, y Y '
+
B, r op
"},.
'n .
+ J h
e r, f g 0.1002- 0.1372 1 0.1962.. 0,1973 0.2369L P.1994 0.6556 ~ .1.0795 - 1.9355 L 2.3412 ? 3.4762 ' 4.0788 E5 1233 i
~
0.0751 ' O.0218 3 1 0.0775 - 0.0225 ~ ~ 0'.104 6 : 0.14 34 0' 2049 ' 0.2648 -0.2440 <0.1942 0.6709 1.09 4 8.' - le9601 ' - 2.3580 3.4893 :' 4.06651. 5.08921
- M
-0.0024 -0;0007 -0.0044 L -0,0062. -0.0087 0-0;0075' -010071_. -0.034 8 : -0.0153 -0.0153.-0.0246 .-0.0168 -0.0131 0.0124 ' 010341 "
0.1100- 0.1085 'O.1091-'O.1621 0.1657 l0.2226: 0.2502."0.3903- 0.6018e'1.1250' 1.5758- '2.6091 .!3.0174: -4.8857 5.1215 0.1131 011119 .0.1133 0.1691: 0.1123'.0.2308 022582 . 0.4007: 0.6139 1.1435 1.5912 /.2.6320 ' 3.0201 - 4.8403 05.0007 L
^
-0.0031 '-0.0034 -0.C04 2 -0.0070:-0.0066 -0.0082 -0.0080. -0.0104 -0.0121 -0.0184 '-0.0154 -0.0229' -0.0027'.'0.0454 '0.0408; 0.1385 0.1268 0.1440- 0.1416' O.1824 ['O.1579 0.3357 --0.4323 0.66681 0.6496 _1.5294 ..1.9739: 3.0171 3.4672 : 4.2554:
0.1407 0.1299 0.1490' O.1465- 0.1991- 0.1635" 0.3475- 0.4426 0.6783 0.6594 i.5467 'l 1.9785 3.0242 ? 3.4468 " 4.2175
^
-0.0022 -0.0031 -0.0050' -0.0049 -0.0067..-0.0056 -0.0108 -0.0103 -0.0115 -0.0098 -0.0173 "-0.0046 -0.0071 .0.0204 0.0379 p
0.1379 0.1898 0.1435 0.1466 0.1655 0.2572: 0.3291 . 0.5353 0.6142 0.9208 =1.1127- 157010' 2.3761- 3'.8133 3.1966 0.1392 0.1932 0.1471 'O.1512 0.1711?'.0.26561 0.3376 0.5481 'O.6241 0.9308_ 1.1203 1.7055 2.3646 3.7771 3.1580 1
-0.0013' -0.0034 -0.0036 -0.0046i-0.0056 -0.0084 '-0.0085 -0.0128 -0.0099 -0.0100 -0.0076 -0.0045 -0.0115 0.0362; 0.0386-0.2224 0.1719 0.1128 0.1914. 0.2412 0.3732- 0.4415 :0.7126' O.8111 1.0562< 1.0332 2.2436'13.3913 O.2243 0.1745 0.1158 0.1972- 0.2478i 0.3837 0.4495 0.7231 0.8152 -1.0556 1.0314 '2.2190.13.3399.
-0.0019 -0.0026 -0.0030 -0.0058 '-0.0066 -0.0105 -0.0080 -0.0103 -0.0041 'O.0006 -0.0018- 0.0246 ;0.0515
.pn . .
- 0.1805 0.2296 'O.2073 0.2129 0.2670 10.2656 0.3619 'O.5625 0.9263 1.1066 1.5530 2.3310 2.2001 ,
U 0.1835 0.2317 0.2108 0.2178 '.0.2747 -0.2724 0.3677 0.5661 'O.9306 1.10121 1.531? 2.2894 2.1868
-0.0030 -0.0021 '0.0035
-0.0049 f-0.0077 ~ -0.0068. -0.0058 -0.0036 -0.0043 0.0054 0.0218 0.0424 0.0133 0.2632 0.2917 0.3005 022444. 0.2658 0.0877 0.6427 028705 124832 1.9600 1.7378 0.2072 0.2951 0.3061-. 0.2502 0.2702.t 0.0890 0.6438 0.8663 1.4678 1.9193 1.7148-
-0.0040 -0.0034 -0.0056 -0.0053 -0.0044 ' -0.0013 e0.0011 0.0042 0.0154 0.0400 0.0230 0.2340 0.2787. 0.2865 0.322G 0.66"[6 0.9591 1.0506
~
-0.2373^ 0.2829 0.2928 0.3244 0.6656- 0.9483 _1.0312
-0.0033 -0.0042 -0.0063' -0.0024- 0.0020 0.0108 L 0.0194
. Maximum Difference Standard Legend ARROTTA Deviation HERMITE Positive 0.0515 : Difference Nega tive -0. 02 4 6 0.0155 Figure 4-12. ARROTTA-HERMITE- Comparison of. Radial Power Distributions at'0.20s
+
t, 2 -__._----..--__ a~- m:- _
, ,gs ;
d , ngewb, g_
- n. a' g . , .
4 C2
,f '5 1 ef 2 _
3g_Qs . ' 1 s
. . re s.
~ , , , 1
=
3~ ~ g' . . - 1 I, . - 515 t52 321 3 5'8 404 211 688 78 8 293 284 51 3 953
+ 100 100 220 110
.~ . 550 550 44'0 330
,. ,.7 7 1' 6 5 0' 5
- 064 936 716 936 pq 972 61 5 770 476 101 07 3 761 54 1 64 2 173 94 5 081 000 880 440 870 330 21 0 I
- 44 0 440 330 330 330 220 e s c
~
- n. . . - n 3 066 77 0
~
505 038 275 1 02' AE e 2 , 990 .- 693 802 747 651 4 94 292 853 TTr - 781 120 120 761 4 12 384 31 2 TI e 0. 4 40 000 000 330 220 3 20 770 OMf ym RRf t 330 330 330 220 220 220 110 REi AHD a s . 747 659. 396 374 4 59 239 3 11 24 8 090 d n
- 18 6 451 9 22 03 2 4 8 4 77 0 1 54 600 3 1 1 33 0 532 6 14 n o 7
.m , 330 660 990 e 770 000 550 990 e g i t 220 220 11C 110 1 10 110 110 e L u e
- - - - b .
i
&~
94 5 50 4 154 6 15 693. 967 956 207 376 650 734 6 15 38 5 375 7 25 0 1 9 r _ 550 0 00 861 531 t 362 79 1 24 1 120 s 990 550 550 110 00 0 11 0 4 40 000 i _
, 110 110 11 0 110 110 110 110 110 D .,
. r ,
'7 5' y 604 561 8 989 121 363 532 138 e
- 955 231 99 9 009 154 60 4 064 980 w .;
L 791 000 1 43 110 4 50 660 230 990 1 1 0 880 23 0 990 76 0 880 54 1 9 90 o . ,. - 2 P . 1 10 110 000 000 000 000 000 000 . - - - - - - l a , i 604 802 835 219 71 4 51 6 78 1 569 dn 1 515 1 42 681 4 4 9 230 263 23 1 751 ro 5 d , 571 01 1 671 1 20 121 660 4 4 0 660 ai 1 a - 660 660 660 660 770 550 660 660 dt 0 R na _ O00 000 000 000 000 000 000 000 ai 0 f
- - - - - - - t v o ,
S e
'8 68 D
4 28 275 264 208 4 40 792 934 n 94 4 0 00 220 582 198 1 75 78 1 1 42 .., 8 9 0 9 01 3 4 1 34 1 4 4 0 660 8 8 0 220 o ., 1 1 0 34 0 440 550 4 4 0 330 000 330 s - . i r 0O0 000 000 000 000 000 000 000 , ,
'- - 7 - - - - e a .
c p 8 9' '1 n 1 1 0 6 48 956 0 5 5' 4 39 604 264 e 61 m 637 3 4 0 088 550 6 7 0 34 1 87 8 230 330 781 526 670 504 670 62 6 89 0 r e 1 1 53 o , 220 220 330 330 330 220 220 220 f 00 C ., f E 000 000 0O0 000 000 000 000 000 i 00 D - T , ee I 1 0 9' 275 473 8 4' 6 055 077 758 4 73 n u vv M e 74 7 208 735 750 1 76 6 4 7 4 05 82 4 t ii R . s 900 230 56 0 560 4 4 0 670 4 50 780 t t E - 1 20 220 1 1 0 220 22 0 220 220 220 i i a H s. x sg - 9 000 000 000 000 000 000 000 000 a oe A
~
4 M PN T , 077 527 297 307 109 659 187 703 T a. O
~
64 8 526 286 51 5 1 75 274 055 373 900 670 8 9 0 670 990 1 1 0 0 00 330 R R 1 20 1 1 0 1 1 0 11 0 1 10 220 33 0 220 ,. A ; p q 000 000 000 000 000 000 000 000 a 4
. .f 396 671 956 1 65 033 736 891 1 87 4
1 39 64 60 4 253 603 1 4 3 3 1 v_ ,, 34 0 660 4 4 0 450 1 10 01 0 990 - 4g 11 0 1 1 0 1 1 0 1 10 1 1 0 220 220 4 ,. 000 000 000 000 000 000 000 "
- '- - - - - - e r .g
- g 04 4 04 4 912 834 7 70 385 286 3 6 3 527 1 4 2 033 91 2 781 2 64 u
g 000 01 0 4 4 0 4 4 0 770 2 30 000 - x 1 1 0 1 1 0 1 1 0 1 1 0 110 220 220 i .
- F .
w 000 000 000 000 000 000 000 , 3
- - - - - e -
747 264 572 3 85 891 01 1 3q 120 22 0 8 13 010 693 22 0 9 23 8 90 1 3 2 220 033 880 ~ 000 1 1 0 1 1 0 1 1 0 22 0 1 1 0 y 000 000 000 000 O00 000 93 4 781 1 4 3 594 4 7 2 923 8 0 2 7 8 1 7 70 01 0 3 4 0 33 0 000 1 '10 1 1 0 11 0 000 000 000 000 y Q 2 a ~ _ y , ig
.#< ,~ i
,4
* .. .e-s. -
- ' u;- -
~ . . %. - 1 l- -q' QW " ~
Q W
~
/
1 " 's~ s ..
-q e g. ch..
* - . , 7*
"",* ,. ; Q ,* vgp ^ -
. O_
7.;7 jf" , x ,-
;., ~ . ,
_. '~ , _ .L.,.i 3Q(.;;f r-e- q - a.
.s i f' '
~
gg Q'
- ~
1 - y
~
}; ,
, :s 0.0928 0.02651'.0.'li97 0.1608 052244 10.2193( 0.2554f;0.196S' 0;6655 11.0799 1.9099-.'2.2831' 3.350$ i ?3.9010. l 4.8849 's ,~ .
0.0965. 0.0276 J.1258 ~ 0.1693. 0.23572;0.2288 .0.2641~.0.2022 0.6816 :1.0953. I'9328
. -'2.2965 3.3567 J 3.8979 -: p 4.83a7 c
-0.0037 -0.0011 .-0.0061 I-0.0085 -0.0113 ~ -0.0095 ' -0.0087 L-0;0054 ' -0.01611-0.0154 -0.0229; -0.01347 -0.0062';0.0031 _0.0492- -
g 0.1359 0.1327 0.1310 0.1904-.0.1897 0;2469 e0.2692: 0.4073 0.6140 1.1273 1.5570' 2.54 57 c 2.9125 / 4.6441<. 4.8886- m 0.1407 0.1379-0.1370 0.1999 0.1985 0.2574 i 0.2768 :0.4192 :-0.6270 '1.1458 1.5713 2.5648: '2.9098' 4.6183 T 4.8323 ' " '
- -0.0048 -0.0052 -0.0060 -0.0095' -0.0000-0.0105 -0.0096 "-0.0119.'-0.0130 - 0.0185 -0.0143 '-0.0191 10.0027 -0.0258; 0'.0563' 0.1709 0.1555 0.1738 0.1669 : 0.2d90 0.1750 0.3622 0.4544 ' O.6867 - 0.6559 - 1.5i64 1.9329 ; 2.9208-' 3.3312 4.0774' O.1750 0.1605 .0.1811 -0.1738 '0.2179' 0.1820.. 0.3750. 0.4665 -0.6995 0.6659 1.5326 ,:1.9352 - 2.9227 - h3040 n . 4.0287 :
~
-0.0041 -0.0050. -0.0073 -0.0069 -0.0089 -0.0070 -0.0128~~0.0121 -0.0128 -0.0100 -0.0162 -0.0023 -0.0019 '-[ 0.0272 z '0.0487 } - g 0.1699 - 0.2324 0.1737 0.1730 0.1895~ 0.2857 6.3558 D.5659 0.6371 0.9368 1.1123: 1.6736 2 2;3143i.3.6865: 3.0817'.
0.1728 -0.2383 0.1794 0.1796 .O'.1971 0.2964' 0;3665: 0.5811 -0.6486 ,0.9478 1.1197- 1.6763 2.2994 , 3.6434 .3.0358; .
-0.0029 -0.0059 -0.0057. -0.0066 -0.0076'-0.0107--0.0107 -0.0152 -0.01151-0.0110. -0.0074 '-0.0027 0.0149 0.0431L: 0.0459- '
O.2714-'O.2079 0.1333 0.2197 0.2696 0.4061 .0;4688. 0.7423 0.8316' 1.0664 '1 02541 212011 - 3.3105-0.2758 10.2125 0.1378 0.2276 0.2785 0.4191 0.4788 0.7545 0.8368 .1.0661'.1.0229 2.1736' 3.2520
-0.0044 -0.0046 -0.0045 -0.0079 -0.0089 -0.0130 -0.0100 -0.0122 -0.0052 - 0.0003 - 0'0025 . 0.0275 ' 0.0585.
A - 0.2191 0.2761 0.2452 0.2465 0.3015 0.2918 - 0.3850 0.5868 '0.9535- 1.1254 1.5573 12.3110" ' 2.1681 1 0.2245 0.2806 0.2509 0.2536 0.3118 0.3096 0.3924 0.5918 0.9591 1.1203? 1.5349 2.2659 2.iS02:
-0.0054 -0.0045 -0.0057 -0.0071 -0.0103 -0.0088 -0.0074 -0.0050 -0.0056 0.0051 0.0224 0.045i 0.0179
,0.2432 0.3445 0.3487 0.2782 0.2952 0.0934 0.6702 0.8989 .1.5141- l'9778. 1.7383 '
O.2496 0.3507 0.3573- 0.2863: 0.3015 0.0950 0.6725 0.8958 1.4991" '1.9360 1.7133~
-0.0064 -0.0062 -0.0086 -0.0061 -0.0063 -0.0016 -0.0023 0.0031 0.0150 0.0418 0.0250 0.2710 I 0.3173 0.3182' 0.3'4'0' 4 0.6982 0.9933 1.0793
'O.2762 0.3238 0.3266 0.3476 0.6975 0.9834 1.0599-
-0.0052 .-0.0065 -0.0084.-0.0036 0.0007 - 0.0099 0.0194 Maximum Difference Standard - . Legend .ARROTTA Deviation - HERMITE
- Positive'O.0585 Difference
-Nega tive -0. 0 229 0.0173
' Figure 4-14. 'ARROTTA-HERMITE Comparison of Radial Power Distributions at 0.39s -
T T
, ~[,
_ s +m. .,b=. i giub. +g e -w-a+--tre-^'d
'-
- g h ** Vi- ' -' ' ' * - ' ' " ' ' "
"(W'-"4'97 d' ' ' " Y' # C'.
iY '
'T #
- Y* W ' "'
0 '
q ' . 3, O-se- _ i j-- ,
, .g g , . m,. m-
. u. m .
.y . g.
yn . -- g., zw g. - psy. g
" . lff
~
- i' y
~
~: ,
,- ..y'
~
[' ~ p x ? y&y n 9_ . s c ,3 ' w
~
s . s s-0.1201 0.0338 0.1486 ' O.1949 0.2640 0.2491' O.2793 ' O.2059 . T 0.6755 - 1.0761 1;8724 2;2065 3.1931) .3.6777. -4.5773.- - 0.1561 - - 0;2053 ' :0.2775 ? 022602' c 0 22894 ' 2 0 2117 I6.6919 - 1.0914' _1.8936 2.2173 3.1941.- '3.6500- "4.5226 ?
~
0.1247 0.0352
-0.0075 -0.0104 ~ -0.0135 -' -0.0111 -0. 0101 -0.0 0 58 -0.0164. -0.0153 -0.02121-0.0108 -0 ' 0010 : . 010i771 L 0.0547 ;
-0.0046 -0.0014 . ,
0.1757 0.1697 ?0.1636 0.2314 -0.2235J 0.2798';042934 0.4278.'O.6267 1.1261 115287 ' 3 2.4621.. 2.7798 ' .~ 4.3792 - 4;$844"- a r v
-0.1818 0.17621 0.1711 0.2431 0.2340 0.2920 O.3043- 6.4407 .016404 1.1446. 1.5420- 2.4781 -2.7731 4.3454 4.5236?
-0.0061 -0.0065 -0.0075 -0.0117.-0.0105 -0.0122 -0.0109 a -0.0129 -0.0137 : -0.0185 -0.0133 :-0.01(3 0.0067~ 0.0338 -'O.0,608' O.2200 0.1993 0.2185 0.2038 0.2465 ,0.1979 -0.3945' .0.4809 - 0.7087.- 0.6615 1.4954 ' ~ 1,8773 : 2.7979 ' 3.1576 . 3.8458-0;2259 'O.2056 0.2276 0.2122 0.2573' O.2061 .0.4089 'O.4941 :0.7227 0;6720: 1.5107 1.8780 2.7959 1 3.1262- 3.7930 7
-0.0 0 51 ~ -0. 006 3 -0.0091 -0.0084 -0.0108 -0.0082 -0.0144 -0.0132.-0.0140-0.0105 -0.0153; -0.0007 .. 0.0020 0.0314 020528-0.2191 0.2976 0.2194 0.2119 0,2233 10.3240 0.3899^ 0.6029 0;6630 ~ 0.9528 1$10741.1.6355 J 2.2316 3.5195 3 2.9293.
0.2227 0.3049- 0.2263 0.2199 0.2323 'O.3365 0.4019 0.6196 .0.6753 6.9643 1.1145 '1.6368 2.2144.-3.4723 1-2.8810-
-0.0036 -0.0073 -0.0069 -0.0000 -0.0090'-0.0125 -0.0120 -0.0167 -0.0123 -0.0115 -0.0071' -0.0013 0.0172 0.0472 ~0.0483'
O.3462 0.2625 0.1636 0.2599 0.3084' O.4487 10.5020 0.7758 0.8528 1.0743 .1.0132 '2.1408'.- '3.1924. 0.3515 0.2681 0.1690 0.2692 0.3186 0.4634- 0.5131 0.7890 0.8582 1.0740 1.0099 2.1111 3.1319
-0.0053 -0.0056. -0.0054 -0.0093 -0.0102 -0.0147 -0.0111. -0.0132 -0.0054 0.0003 0.0034 0.0297'. 0.0606 7 0.2780 0.3465 0.3014 0.2947 0.3494 0.3265- 0.4136_ 0.6142 0.9823 1.1421 1.5549 '2.2733 2.1157 4
_g 0.2845 0;3517' O.3081 '0.3031 0.3614 0.3365 0.4219 0.6198 0.9881. 1.1365^ 1.5314 ~2.2263 2.0955 .
-0.0065 -0.0052 -0.0067 -0.0084 '-0.0120 -0.0100~-0.0003 -0.0056 --0.0058 0.0056 0.0235-'O.0470- 0.0202 _
0.3033 -0.4226 0.4185- 0.3258 .0,3354 .0.1007 .0.7016 0.9290 1.5432 1.9862; 1.7269 0.3108 0.4297 0.4294- 0.3351- 0.3429 0.1025 0.7042 0.9258 1.5274 .1.9435 1.7012
-0.0075 -0.0071 -0.0099 -0.0093 -0.0075 -0.0018 -0.0026 0.0032 0.0158 0:0427- 0.0257 0.3241 0.3721 0 3619 0'3720
. 0.7333 1.0301 1.1070 0.3301 0.3794: 0.3713 0.3761 0.7328 1.0199 1.0876
-0.0060 -0.0074 -0.0094 -0.0041 0.0005_ 0.0102 0.0194~
.M6ximum Difference Standard Legend '. ARROTTA Deviation HERMITE-Positive 0.0608- Difference
- Negative -0.0212 0.0187
' Figure 4-15. ARR0TTA-HERMITE Comparison of Radial Power Distributions;at 0.50s:
T'
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SUMMARY
i y- 'yl _
" includes steady-state radial power distributions at hot zero power; conditions, ; with rods out, rods inserted and the ejected rod out.= The steady-states st s
_ , eigenvalues and'the ejected rod worth also show comparable agreement. The hot- , _ full power case demonstrates. acceptable. agreement in fuel temperature. ! [ The 3-D rod ejection _ transient at hot zero power conditions showed excellent' :f
. agreement between.ARROTTA~and HERMITE in the important parameters: total core power, peak assembly power, core ' average fuel temperature and maximum fuel e
- temperature. ,
J
-4.51 REFERENCES !
4.1 K. Ooran, B. lolotar,- "PWR- Rod Ejection Accident ARR0TTA Sensitivity'-
. Studies," Electric Power Research Institute (to be issued). ,
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h 1 . e Section 5 3 CONCLUSIONS The'following conclusions can be drawn from this study:
- l. The ARR0TTA code, using a lxl mesh, showed acceptable agreement with itself using a 2x2 mesh and with HERMITE using a 2x2 mesh. A 1x1 mesh is, therefore, adequate for ARR0TTA applications such-as the rod ejection accident and for both rodded and unrodded static l calculations, i
- 2. Twelve axial planes to model the active core is adequate based on the sensitivity studies using HERMITE and the ARR0TTA HERMITE q comparisons. j 1
- 3. The good agreement of key-parameters for the 3 0 rod ejection j transient initiated at hot zero power conditions served to verify i the transient neutronics, transient fuel temperature, transient j control rod motion and transient cross section treatments in ;
4
.ARR0TTA. The ARR0TTA. code can, therefore, be reliably used for any. l rod ejection type transient, including transients up to hot full power conditions, j
- 4. The analysis and sensitivity studies performed. for the rod ejection transient showed that the peak power, for both ARR0TTA and HERMITE, decreases as timesteps are made smaller. This means that results ,
can be biased in the conservative direction (higher peak power) by ! using-larger timesteps. j
- 5. The. ARR0TTA and HERMITE static fuel temperature calculations showed reasonable agreement. ;
.y, I 'I f
5-1
p .- _, _ h Appendix A
*! HERMITE SENSITIVITY STUDIES l
The objective of this study was to'model as closely as possible in HERMITE the l same problem that had been run in ARR0TTA. Further, it was necessary to assure J that the HERMITE case was converged and as accurate as possible. To do this a f number of sensitivity studies were run to select options for the 3-D rod ejection i analysis. These sensitivity studies are described in this appendix. i j i The first set of sensitivity studies examines the sensitivity to the radial mesh. ARR0TTA is typically run with one mesh interval in a fuel assembly (referred to as -!
-a lxl' mesh). HERMITE typically uses a 2x2 mesh in each fuel assembly. HERMITE j cases were run with both a lxl and 2x2 mesh structure and the results are shown in ~
Figure A-1. The assembly powers change by up to about 4% with a general shift in power towards the core periphery as the mesh becomes finer. ARR0TTA results for f lxl and 2x2 meshes were run as part of a separate study (Reference 4.1) and the i results are reproduced here as Figure A-2. In ARR0TTA, the assembly powers change j by less than 1% with a general shift in power towards the core center as the mesh j becomes finer. An examination of the pattern of the differences suggests that 'the I i two methods are converging to the same powers but from opposite directions--
'.HERMITE powers are higher in the center of the core but decrease with the finer f mesh, while the ARR0TTA power is lower in the center of the core but increases 1 with the finer mesh. Additional cases with a finer mesh would be required to
~
estimate the order of the two methods and to extrapolate the results to zero mesh spacing. This is beyond the scope of this study. For purposes of this study, it was decided to use the 1x1 mesh in ARR0TTA and the 2x2 mesh in HERMITE. !
' Sensitivity of results to the axial mesh structure was also addressed in this i study.with HERMITE. The HERMITE study employed a 3-0 model as well as a 1-0 axial model of the core with cross sections taken from a steady-state, hot zero power, all rods out volume-weighted edit. The purpose of this analysis was to look at s axial mesh spacing effects and no serious attempt was made to produce an axial f i
A-1
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r Heximum Difforence- Standard- "f Deviation' 4 4., k-effective 1x1 1.007677 ~ Positive -3.14% > k p,3 Lk-effective 2x2.- 1.008222 - Negative- -3.65% 1.62% , ,j i Difference -0.00054- -*'u
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. Figure A-1. HERMITE Comparison of.2x2 and'lxl Mesh Structures '
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> = . .
-0.64. -0.4% ' -0. 5C 0.0% -0.1% 0.4% 0.5% 0.8%
(l- . 0.7614 . ' O.9000 0.8222 1.0535. 1.4193 1.2787 1.4259 s' O.76371 0.9048 ~0.8232 1.0562 1.4159 1.2733 1.4141 y -0. 3% - .-0.5% ~ 1 - 0 .1 % , 0.3% 0 .' 2 % 0.4%- . 0.8% -
+
.-^"4 : 0.9367. 20.8549l 0.9983 <
1.0208: 1.2764 1.4128 1.0821
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,i r0.9855" 1.2195 ^ -0.9935- 1.2915 - - 1.4204 1.0012' _L I E <? s ' 0.98361 '-1.2219 0.9957, 1.2930J '1.4142 1.0841 /
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' ~1 24- 71 1855.- .F1'*21811 '1.1068 ' ' O.9469- Legend s
.ARROTTA 1x1 fjg 1".1806!-~ . s 1. 2181 i :1.1135- - 0 9475- .
' ARROTTA 2x2 ;
-NF , '0.4%s '0.0% ' .-0. 6% - 0 .14 - '%--difference ,
+
q yi 7 Maximum Difference. - standard Deviation v 7, Positive 0.83% q-jj Negative ' 0.71% - 0.40%
$ '^
,4 Figure-A-2. 'ARR0TTA Comparison of 2x2 and lxl Mesh Structures '
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k model which was fully consistent with the more detailed three dimensional model. The results are sumarized in Figure A 3. In all six cases were run: 12 and 24 [ ; planes in the core using the 3-D model,12 and 24 planes in the core using the 1-0 , model, and 100 planes in the core using the 1-D Nodal Expansion Method and the finite difference method (all.other cases used the' Nodal Expansion Method). All cases give essentially the same result. The two 100-plane 1-D cases are 3 essentially coincidental with each other. From this it is concluded that 12 axial mesh. intervals in the core for the three-dimensional calculation is adequate.
- Axial mesh . spacing was also studied separately for ARR0TTA. The results are presented in Reference 4.1.
A sensitivity study on timestep size for the transient was performed. Again the one-dimensional HERMITE model was used. The absorption cross section in HERMITE was arbitrarily adjusted to give a rod worth of about $1.16. Two effects contribute to the sensitivity of the results to timestep size--the neutronics
. equation solution algorithm and the fuel ter.iperature calculation. The first half of the _ transient .from t-0. to about t .25 s gives a good indication of the sensitivity of the neutronics algorithm because there is no heating of the fuel.
Figure A 4 is a plot of total core power as a function of time on a logarithmic scale for timesteps of 10 ms, 5 ms, and 1 ms. The early portion of the transient demonstrates that HERMITE neutronics are quite insensitive to the timestep_ size. This, therefore, suggests that the peak power level is most sensitive to the , timestep size in the fuel temperature calculation. Recall that in Section'2.4 two ' different approximations for the time dependence of the heat source in the pellet were presented. They were characterized by the parameter e. Figure A-5 shows the power for HERMITE cases using 10 ms and 1 ms timestep and e .5 -the default HERMITE option. As expected, the peak decreases with smaller timesteps. The cases'were repeated with a value of e l. These results, together with those for e .5 are shown on Figure A-6. Several conclusions can be drawn from this figure. - First, for small timesteps (1 ms) the results are not too sensitive to the value of e -Secondly, the results for 10 ms timesteps and e-1 agree well with the small . timestep' case. The 3 D transient was ran using both e .5 and e-l to further explore the sensitivity of the peak power to the fuel temperature calculation. These results are shown in Figure A-7. Based on these results, it was decided to use 10 ms timesteps and e-1 for the ARROTTA-HERMITE comparisons described in Section 4.3. Figures A-8 and A-9 show the core average and peak fuel temperature sensitivity to e for the 3-D transient. A-4 'r: >
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