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Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2013 Article ID 252140 9 pageshttpdxdoiorg1011552013252140
Research ArticleModeling of the ORNL PCA Benchmark Using SCALE60 HybridDeterministic-Stochastic Methodology
Mario MatijeviT Dubravko Pevec and Krešimir Trontl
University of Zagreb Faculty of Electrical Engineering and Computing Department of Applied Physics Unska 3 10000 Zagreb Croatia
Correspondence should be addressed to Kresimir Trontl kresimirtrontlferhr
Received 30 May 2013 Accepted 29 August 2013
Academic Editor Valerio Giusti
Copyright copy 2013 Mario Matijevic et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Revised guidelines with the support of computational benchmarks are needed for the regulation of the allowed neutron irradiationto reactor structures during power plant lifetime Currently US NRC Regulatory Guide 1190 is the effective guideline forreactor dosimetry calculations A well known international shielding database SINBAD contains large selection of models forbenchmarking neutron transport methods In this paper a PCA benchmark has been chosen from SINBAD for qualificationof our methodology for pressure vessel neutron fluence calculations as required by the Regulatory Guide 1190 The SCALE60code package developed at Oak Ridge National Laboratory was used for modeling of the PCA benchmark The CSAS6 criticalitysequence of the SCALE60 code package which includesKENO-VIMonteCarlo code aswell asMAVRICMonaco hybrid shieldingsequence was utilized for calculation of equivalent fission fluxesThe shielding analysis was performed using multigroup shieldinglibrary v7 200n47g derived from general purpose ENDFB-VII0 library As a source of response functions for reaction ratecalculations with MAVRIC we used international reactor dosimetry libraries (IRDF-2002 and IRDF-90v2) and appropriate cross-sections from transport library v7 200n47gThe comparison of calculational results and benchmark data showed a good agreementof the calculated and measured equivalent fission fluxes
1 Introduction
Calculational methods for determining the neutron fluenceare necessary to estimate the fracture toughness of the reactorpressure vessel (RPV) materials which is one of the keyrequirements in determining operational limits and lifetimeof nuclear power plantsThis area of research is of a particularimportance in the era of plant lifetime extension demandsand possible financial savings which could be achieved byapproving the extensions Any developed or analyzed cal-culation methodology requires comprehensive verificationand validation against evaluated reference data A largedatabase of benchmarks aimed at validation of computercodes and nuclear data used for radiation transport andshielding problems is ldquoShielding Integral Benchmark Archiveand Database (SINBAD)rdquo [1] One of the most widely usedSINBAD benchmarks for qualification of radiation transportmethods and evaluation of appropriate nuclear data used fortransport as well as for dosimetry calculations in Light WaterReactors (LWR) is the ldquoPool Critical Assembly PressureVessel Facility Benchmarkrdquo (PCA benchmark) [2]
The purpose of the benchmark was to validate thecapabilities of the calculational methodology to predict thereaction rates in the region outside the reactor core whenthe neutron source material compositions and geometry arewell defined Over the years a number of PCA benchmarkstudies have been conducted Their classification is possiblebased on the type of neutron transport calculation (discreteordinates method orMonte Carlomethod) as well as nucleardata libraries used either for neutron transport or dosimetrycalculations
Benchmark original calculational results obtained by dis-crete ordinates synthesis transport method through DORTand DOTSYN codes and BUGLE-93 SAILOR-95 andBUGLE-96 nuclear data libraries for transport calculationand CROSS-95 library for dosimetry calculations wereimproved by Fero et al [3] using full 3D discrete ordi-nates transportmethod andBUGLE-96 library Improvementof calculated to measured ratio (CM) was observed andattributed to full 3D approach Lee [4] used 3D TRIPOLI-43 Monte Carlo code with continuous energy ENDFB-VI4
2 Science and Technology of Nuclear Installations
and JEF 22 nuclear data libraries for neutron transport andIRDF-90 IRDF-90v2 RRDF-98 and JENDLD-99 as well asENDFB-VI4 and JEF 22 nuclear data libraries for dosimetrycalculationsThe author finds the IRDF-90 file generally goodfor RPV dosimetry calculations but recommends 103Rh(nn1015840)103mRh and 237Np(n f)137Cs dosimetry cross-sectionsfrom RRDF-98 and JENDLD-99 libraries
An initial analysis of the applicability of SCALE60 [5]hybrid deterministic-stochastic methodology for the PCAbenchmark analysis was conducted by Vragolov et al [6]Only a preliminary averaged equivalent fission fluxes werecalculated and the results showed SCALE60 possibilitiesbut also raised issues that required further analysis Themain concern was the choice of nuclear data library used fordosimetry calculation
Recently Risner et al [7] used SCALE60 code packagefor validation of VITAMIN-B7 and BUGLE-B7 nucleardata libraries on a number of benchmarks including PCAbenchmark The overall results showed applicability of bothlibraries with SCALE60 sequences for PCA benchmarkanalysis with exception of 103Rh(n n1015840)103mRh and 115In(nn1015840)115mIn dosimetry cross-sectionsThe authors advice usageof IRDF-2002 library for named dosimeter reactions
We believe that additional investigation of SCALE60capabilities could be useful primarily in the context of directapplication of SCALE60 built-in fine-group data librariesfor neutron transport as well as for dosimetry calcula-tions Such an approach would speed up analysis and itwould avoid incorporation of external cross-section librariesinto SCALE60 sequences which is not a straight-forwardprocedure especially for inexperienced users Thereforewe conducted PCA benchmark analysis using SCALE60code package with built-in fine-group nuclear data librariesnamely v7 238 [5] for criticality calculation using CSAS6and v7 200n47g [5] for shielding calculations usingMAVRICsequence Dosimetry cross-section data were extractedfrom nuclear data library used for transport calculation(v7 200n47g) Sincewe faced similar problems as Risner et alwith data for 103Rh(n n1015840)103mRh and 115In(n n1015840)115mIn weused IRDF-2002 [8] and IRDF-90v2 [9] dosimetry librariesfor all dosimeters in order to examine the behavior of everyPCA benchmark dosimeter reaction with different library
The PCA benchmark is described in Section 2 Thedescription of the SCALE60 code package used formodelingof the PCA benchmark and calculational methodology aregiven in Section 3 The analysis of the PCA benchmarkincluding results of calculation and comparison of calculatedvalues with benchmark data is presented in Section 4 whilethe conclusions are given in Section 5 References are given atthe end of the paper
2 PCA Benchmark Facility Description
The main cause for limiting the PWR power plant lifetimeis the fast neutron fluence induced embrittlement of thereactor pressure vessel (RPV)With the advances of computercomputational power the reactor dosimetry calculations givebetter insight in radiation damage of RPV when exposed
to intense neutron flux Correlations can be made betweenneutron flux and irradiation of in-core and ex-core detectorstypically via displacements per atom (DPA)This is importantfor advanced nuclear material selection probing and scopingmaterial behavior in intense radiation environments forexample gas accumulations in reactor baffle plates by 58Ni(n120574)59Ni(n 120572) reaction sequence The current guideline forRPV dosimetry calculations is the USNRCRegulatory Guide1190 [10] which states that calculational methods used toestimate RPV fast fluence should use the latest version of theEvaluated Nuclear Data File (ENDFB) in fast energy range(01ndash15)MeV In accordance with this guideline we presentcalculational results for ORNL PCA Benchmark
The scope of PCA benchmark is to validate the capa-bilities of the calculational methodologies to predict thereaction rates in the region outside the core when theneutron source material compositions and relatively simplegeometry configuration are well defined and given The PCAbenchmark provides calculated and measured reaction rates(CM ratio) inside the simulated pressure vessel as well asin the water gap in front of the pressure vessel This allowsan assessment of the accuracy with which the calculationspredict the neutronflux attenuation inside the pressure vessel
The PCA benchmark facility consists of the reactor coreand the components that mock up the reactor-to-cavityregion in light water reactors These components are thethermal shield (TS) the reactor pressure vessel simulator(RPVS) and the void box (VB) which simulates the reactorcavity An overall view of the PCA benchmark facility isshown in Figure 1 An aluminum plate referred to in Figure 1as the reactor window simulator was added to the facilityfor operational reasons The thicknesses of the water gapsbetween the aluminum window and thermal shield andbetween the thermal shield and pressure vessel are approx-imately 12 cm and 13 cm respectively Such configuration isknown as 1213 configuration The materials used for thecomponents outside the core were aluminum for the reactorwindow simulator stainless steel for the thermal shield andcarbon steel for the pressure vessel The facility is located ina large pool of water which serves as reactor core coolantand moderator and provides shielding The PCA benchmarkfacility core is a light water moderated enriched uraniumfueled critical assembly It consists of 25 material test reactor(MTR) plate type elements The standard MTR fuel elementand control element are depicted in Figure 2 The eight ver-tical experimental access tubes in which the measurementswere done were filled with appropriate material (steel inthe pressure vessel locations and Plexiglas in the in-waterlocations) in order to minimize the perturbations of theneutron field
Measured quantities used in PCA benchmark are givenin terms of the equivalent 235U fission fluxes which were cal-culated by dividing the reaction rates with the cross-sectionsaveraged over the 235U fission spectrum [2] All measuredquantities provided for comparisonwith calculated values aregiven per unit PCA benchmark facility core neutron sourceTherefore the calculated results need to be normalized tothe source strength of one fission neutron per second being
Science and Technology of Nuclear Installations 3
Void box(VB)
Thermalshield(TS)
Reactorwindow
simulator
PCAcore with
control rods
Reactor pressurevessel simulator
(RPVS)
A1A2A3
A4A5A6A7
Figure 1 SCALE60 model of PCA benchmark facility (water removed)
Figure 2 PCA standard MTR fuel and control element (waterincluded)
born in the whole PCA core The ratios of the calculated-to-measured (CM) equivalent fission fluxes for DORT librariesBUGLE-93 SAILOR-95 and BUGLE-96 are given in PCAbenchmark reference [2] Measurements were performed atcore midplane (119911 = 0) at several locations labeled in Figure 1as A1 to A7 To complete the PCA benchmark analysis theanalyst must determine the calculated-to-measured (CM)ratios of the equivalent 235U fission fluxes for all the locationsand all the dosimeters for which the measured values areprovided
The significance of the PCA Benchmark are experimentaldata measurements inside thick steel RPV in locations A4to A6 that is neutron flux gradient inside the pressurevessel which provides themeans for verification of calculatedneutron flux attenuation This is in contrast to availabledata from operating reactors which are typically addressingneutron flux for downcomer region internal to RPV andreactor cavity external to RPV wall [11]
3 SCALE60 Code Package
The SCALE60 [5] code system was developed for the USNRC to satisfy a need for a standardized method of analysisfor the evaluation of nuclear facilities and package designsIn its present form the system has the capability to performcriticality shielding radiation source term spent fuel deple-tiondecay reactor physics and sensitivity analyses usingwell established functionalmodules tailored to the SCALE60system
31 The CSAS6 Sequence The CSAS6 criticality sequence isdeveloped to provide automated problem-dependent cross-section processing followed by calculation of the neu-tron multiplication factor 119896eff The cross-section process-ing code BONAMI is used for the unresolved reso-nance range (Bondarenko factors) and either NITAWL orWORKERCENTRMPMC for the resolved resonance rangeKENO-VI a 3D multigroup Monte Carlo code is its func-tional module
32 The MAVRIC Sequence The MAVRIC shielding se-quence uses automated hybrid deterministic-stochasticmethodology to generate variance reduction (VR) param-eters forMonte Carlo calculationsMAVRIC uses 3Dneutrontransport code Monaco with integrated 119878
119873code Denovo
and it is based on CADIS (Consistent Adjoint DrivenImportance Sampling) [12] and FW-CADIS methodology[13] Denovo is used in forward and adjoint mode toapproximate space-energy flux and adjoint functionrespectively These solutions are utilized to calculate spaceand energy dependent biasing parameters that is biased
4 Science and Technology of Nuclear Installations
source and transport importance map to be used as a VRin Monaco CADIS is used to optimize results in localizedregions of phase-space while FW-CADIS tends to obtainglobal uniform statistical uncertainty by weighting of theadjoint source with expected detector response approximatedwith forward Denovo solution CADIS and FW-CADIS arebased on the adjoint function [14] (ie solution of the adjointBoltzmann equation) which has long been recognized as theimportance function for some objective function of interestDetector response is found by integrating the product ofthe detector cross-section 120590
119889( 119903 119864) and flux over detector
volume
119877 = int119881119863
int119864
120590119889( 119903 119864) 120601 ( 119903 119864) 119889119881119889119864 (1)
Alternatively if we approximate adjoint scalar flux with quickDenovo solution where the adjoint source is set as 119902dagger( 119903 119864) =120590119889( 119903 119864) then the detector response is found by integrating
over source volume
119877 = int119881119878
int119864
119902 ( 119903 119864) 120601dagger( 119903 119864) 119889119881119889119864 (2)
The biased source distribution [15] which minimizes thevariance of user-desired response is given as
119902 ( 119903 119864) =120601dagger( 119903 119864) 119902 ( 119903 119864)
119877 (3)
where 120601dagger( 119903 119864) 119902( 119903 119864) and 119877 are the scalar adjoint functionthe source emission probability (forward source) and totaldetector response from (2) respectively For transport biasingthe weight window technique is employed that is space-energy dependent geometric splittingroulette Biased sourceand weight-window lower bounds are consistent so thesource particles are created with statistical weight withinweight windows
119908 ( 119903 119864) =119902 ( 119903 119864)
119902 ( 119903 119864)=
119877
120601dagger ( 119903 119864) (4)
Inverse relationship between particle statistical weight andadjoint functionmust be emphasized Since PCA Benchmarkinvolves calculation of near and far detector reaction ratesthis FW-CADIS methodology is highly desirable choice
33 Cross-Section Libraries There are several multigroupcross-section libraries distributed within SCALE60 for criti-cality safety analyses and shielding calculations For criticalitysafety analyses the v7-238 library [5] was used while for theshielding calculations v7-200n47g library [5] was used Theyare based on ENDFB-VII0 data [16] For shielding part ofcalculations it was imperative to use fine structure libraryv7 200n47g because high-energy threshold for all reactionscould not be correctly accounted for if broad shieldingv7 27n19g library was used
4 Analysis of the PCA Benchmark
The calculational models of the PCA benchmark withinCSAS6 and MAVRIC sequences of SCALE60 code package
have been determined The results of the calculations that isequivalent fission fluxes using the established models havebeen compared with the PCA benchmark data
41 CSAS6 Results The initial CSAS6KENO-VI criticalityeigenvalue calculation of the PCA benchmark facility wasperformed using 550 batches and 2000 neutrons per batchwith first 50 batches skipped in order for the fission sourcedistribution to converge to eigenmode Critical control rodpositions were validated and obtained effective multiplica-tion factor of the system was 119896eff = (099856 plusmn 000071)This result was tested with MCNP5 code [17] Shannonentropy check for source stationarity was successful andsimilar 119896eff was obtained 119896eff = (099911 plusmn 000051) ThisCSAS6KENO-VI calculation was then rerun with betterstatistics (2150 batches10000 neutrons per batch) for thegeneration of mesh-based fission source distribution (ldquoCDS= YESrdquo option) to be used as a criticality source in the subse-quent MAVRIC calculations This approach in SCALE60 isknown as CAAS (Criticality Accident Alarm Systems)
42 MAVRICMonaco Results The MAVRIC shielding se-quence was run with the mesh-based source from criticalityeigenvalue run FW-CADIS methodology provides consis-tentweightwindows (ie importancemap) and biased sourcedistributions for transport of the PCA core neutrons to thelocations of interest detectors in experimental access tubesA1ndashA7
The equivalent fission fluxes in PCA report were cal-culated by dividing the reaction rates by the cross-sectionsaveraged over the 235U fission spectrum That fast neutronfluence calculation was reasonable approach in the time ofPCA Benchmark calculation with DORT but full spectrumcalculation nowadays with modern Monte Carlo code is notprohibitive So our calculations were conducted with fullneutron spectrum in accordance with SCALE60 multigroupweighting function (spectrum) [2] defined as
(1) Maxwellian spectrum (peak at 300K) from 10minus5 to0125 eV
(2) a 1119864 spectrum from 0125 eV to 674 keV(3) a fission spectrum (effective temperature at 1273
MeV) from 674 keV to 10MeV(4) a 1119864 spectrum from 10 to 20MeV
Equivalent fission fluxes thus are defined as
120601eq =int119864120590119894(119864) 120601 (119864) 119889119864
int119864120590119894(119864) 120593 (119864) 119889119864 int
119864120593 (119864) 119889119864
=reaction rates
120590119894
(5)
where 120590119894(119864) 120601(119864) and 120593(119864) are the dosimetry cross-sections
for the reactions being considered the Monte Carlo flux atthe dosimetry location and weighting spectrum functionrespectively The spectrum averaged cross-sections (120590
119894) were
taken from Table 16 from PCA report [2] for consistencysince they are in very good agreement with calculated valuesfrom our libraries
Science and Technology of Nuclear Installations 5
For seven detector locations (A1ndashA7) we used twodosimetry libraries as a source of a response functionsfor reaction rate calculations Reaction rate calculationswere done with IRDF-2002 and IRDF-90v2 (older version)libraries for the total of six PCA benchmark reactions237Np(n f)137Cs 238U(n f)137Cs 103Rh(n n1015840)103mRh 115In(nn1015840)115mIn 58Ni(n p)58Co and 27Al(n120572)24NaThese reactionswere defined as a response functions for FW-CADISmethod-ology
The threshold energies for the 27Al(n 120572)24Na 58Ni(np)58Co 238U(n f)137Cs 237Np(n f)137Cs 115In(n n1015840)115mInand 103Rh(n n1015840)103mRh reactions are 50 205 145 06903 and 01MeV respectively This is in fast neutron rangebut still calculations were performed for full neutron spec-trum (10minus5 eV to 20MeV) with fine-group shielding libraryv7 200n47g
Also we investigated SCALE60 capabilities in genera-tionmixing of multigroup cross-sections from v7 200n47glibrary for reactions 237Np(n f)137Cs 238U(n f)137Cs 58Ni(np)58Co and 27Al(n 120572)24Na using AJAX and PALEALEutility modules of AMPX working library Reaction 115In(nn1015840)115mIn was derived from ENDFB-VI8 while reaction103Rh(n n1015840)103mRh was not derived because there is no singleor combination of reaction type numbers [18] (MT numbersin ENDFB) for computation of production rate ofmetastableisomer of rhodium (first excited state resulting from inelasticscattering) The obtained multigroup cross-sections withoutrhodium are Doppler and resonances corrected and haveMAVRIC shielding structure of 200n47g These reactionswere also defined as a response functions for FW-CADISmethodology
Two different approaches for the MAVRIC source distri-bution were
(1) fission distribution in space and energy determinedby KENO-VI calculation (transferred as a sourceinput into MAVRIC)mdashCAAS case
(2) Watt spectrum [5] for source energy distribution119901(119864) = 119862119890
minus119864119886 sinh(radic119887119864) (we used thermal fissionof 235U with 119886 = 1028MeV and 119887 = 2249MeV)with uniform space sampling restricted to the reactorcoremdashWatt spectrum case
The total number of neutron batches was 2000 with 2000neutrons per batch for MAVRIC sequence The Denovo 119878
119873
mesh had approximately 20000 cells over PCA facility modelthat is 48 times 23 times 18 cells in 119909119910119911 direction with average cellside of 32 cm while Monaco Monte Carlo mesh had 36000cells (60 times 30 times 20) with average cell side of 26 cm We used1198788as quadrature order and119875
3for Legendre order of scattering
cross-section expansion (upscatteringwas deactivated) Sincethe axial flux gradients inside tubes are confirmed to besufficiently small the user-selected height of plusmn15 cm forvolumetric cylindrical tally regions in MAVRIC calculationrepresents a good compromise between Monte Carlo relativeerror and spatial description of PCA benchmark facilityDifferential small void cylinders were also placed in themidplane (119911 = 0) of the access tubes Point detectors andregion track length estimators were used to find multigroup
1E16
1E15
1E14
1E13
1E12
1E11
1E10
1E09
minus50
minus100
50
x axis (cm) 0
Neu
tron
forw
ard
flux
(nc
m3 s
)
Figure 3 Denovo forward neutron flux axial distribution (front halfremoved)
1E minus 02
1E minus 03
1E minus 04
1E minus 05
1E minus 06
1E minus 07
1E minus 08
1E minus 09
1E minus 10
minus50
minus100
50
0x axis (cm)
Neu
tron
adjo
int fl
ux (n
cm
2s
)
Figure 4 Denovo adjoint neutron flux axial distribution (front halfremoved)
neutron fluxes reaction rates and finally equivalent fissionfluxes
The elements of the FW-CADIS methodology aredepicted next Forward and adjoint neutron flux axial dis-tribution from Denovo code for CAAS case are shown inFigures 3 and 4 respectively Biased source distribution andmesh-based importance map are shown in Figures 5 and 6respectively Total Monte Carlo neutron flux in form of meshtally is depicted in Figures 7 and 8
The calculated equivalent fission fluxes with Monte Carlorelative error (1 sigma level) for PCA Benchmark are givenin Table 1 for MAVRIC CAAS case Only the reactions forwhich the measurements were done are listed AveragedCM ratios for detectors A1ndashA7 are shown in Figure 9 forCAAS case and in Figure 10 for Watt spectrum case Theseresults are compared to the referencedDORT results [2] Onecan notice high similarity between Monaco results for twodifferent source distribution approaches The Watt spectrumcase results aremore conservative and they are 10ndash15 higherthan CAAS case results
6 Science and Technology of Nuclear Installations
127E14 minus 264E14
613E13 minus 127E14
295E13 minus 613E13
142E13 minus 295E13
685E12 minus 142E13
330E12 minus 685E12
159E12 minus 330E12
765E11 minus 159E12
369E11 minus 765E11
178E11 minus 369E11
856E10 minus 178E11
412E10 minus 856E10
199E10 minus 412E10
956E09 minus 199E10
461E09 minus 956E09
Sampled neutronsTotal sampled neutronsValues
Figure 5 Biased source distribution (front half removed)
Values252E-02 minus 717E-02886E-03 minus 252E-02311E-03 minus 886E-03110E-03 minus 311E-03385E-04 minus 110E-031355E-04 minus 385E-04476E-05 minus 135E-04167E-05 minus 476E-05588E-06 minus 167E-05207E-06 minus 588E-06
256E-07 minus 727E-07727E-07 minus 207E-06
899E-08 minus 256E-07316E-08 minus 899E-08111E-08 minus 316E-08
Group 1Neutron target
Figure 6 Mesh-based importance map (front quarter removed)
Values136E15 minus 576E153233E14 minus 136E15764E13 minus 323E14181E13 minus 764E13
240E11 minus 101E12101E12 minus 428E12428E12 minus 181E13
568E10 minus 240E11134E10 minus 568E10318E09 minus 134E10753E08 minus 318E09178E08 minus 753E08
236E06 minus 998E06
422E07 minus 178E08998E06 minus 422E07
Neutron fluxTotal neutron flux
Figure 7 Neutron flux mesh tally (front quarter removed)
5 Discussion of Results
All obtained results are in accordance with calculationaluncertainty criterion from US NRC Regulatory Guide 1190the calculated reaction rates agree with the measurementsto within 20 for out-of-core dosimetry locations Under
prediction in CM ratio can be observed for 238U(n f)137Cs(145MeV threshold) through the thick RPV simulator (fromlocations A4 to A6) with 08 on average High attenuationof neutron flux in that area (around 700 for IRDF-2002) willcause softening of neutron spectrum inRPV simulator whichshifts neutrons in resonance regions for inelastic scattering
Science and Technology of Nuclear Installations 7
000076
000001
14ndash7
19ndash7
26ndash11
Figure 8 Neutron flux mesh tally in axial midplane (MCNP5 criti-cality results)
08
085
09
095
1
10511
Detector position (cm)
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE6 IRDF-2002
SCALE6 IRDF-90v2DORT BUGLE-93
DORT SAILOR-95DORT BUGLE-96
10 15 20 25 30 35 40 45 5550 60
Figure 9 Average DORT [2] and SCALE60 (CAAS case) CMratios for detectors
on iron Microscopic cross-section for neutron inelasticscattering on iron is shown in Figure 11 Results for 238U(nf)137Cs indicate self-shielding effects that is sensitivity ofmultigroup shielding library v7 200n47g on the iron cross-sections
Overprediction in results is highest for detector A2immediately after stainless steel thermal shield which haslarge amount of iron Again self-shielding effects of ironcross-sections are pronounced especially for 27Al(n 120572)24Na(IRDF-90v2) with CM of 117 The IRDF-90v2 library gen-erally gives the highest values while SCALE60 v7 200n47glibrary gives the lowest values of calculated fluxesThe IRDF-2002 results are right in the middle so this library wouldbe favorable for RPV dosimetry calculations The obtainedcalculational results show overall a good agreement withexperimental results however for distant detectors fromPCA core there is under prediction less than 10 on averageexcept excellent result for 27Al(n 120572)24Na
An important issue that has to be addressed whendiscussing Monte Carlo method is a burden the appliedcalculational model will place on memory resources andCPU time requirements For that purpose the figure-of-merit (FOM) factor [17] is defined to account for the time it
08085
09095
1105
11115
12
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE IRDF-2002SCALE IRDF-90v2DORT BUGLE-93DORT SAILOR-95
DORT BUGLE-96
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
Figure 10 Average DORT [2] and SCALE60 (Watt spectrum case)CM ratios for detectors
11
1
1
102
102
10minus4
10minus4
10minus2
10minus2
10minus10
10minus10
10minus5
10minus5
Cros
s sec
tion
(bar
ns)
Incident energy (MeV)
Figure 11 Inelastic scattering on iron [19]
takes to achieve a given level of uncertainty in Monte Carlocalculation
FOM =1
1198771198642sdot 119879
(6)
where 119877119864 and 119879 are Monte Carlo relative error (on 1 sigmalevel) and Monte Carlo CPU run time (in min) respectivelyMAVRIC run time for highest energy threshold reaction(5MeV for 27Al(n 120572)24Na) was 7 h while for the lowest(01MeV for 103Rh(n n1015840)103mRh) was 10 h In this paper allcalculations have been performed on QuadCore Q6600 with8GB of RAM FOM factors for IRDF-2002 and CAAS caseare shown in Figure 12 Application of automated variancereduction technique based on adjoint fluxes removes theburden of manually tuning VR parameters and significantlyimproves the quality of Monte Carlo calculations
6 Conclusion
The analysis of the PCA benchmark has been performedusing the SCALE60 code package The calculational mod-els of the PCA benchmark within CSAS6 and MAVRICsequences of SCALE60 have been determined The results
8 Science and Technology of Nuclear Installations
Table1Eq
uivalent
fissio
nflu
xes(per1
PCAcore
fissio
nneutronpersecon
d(cmminus2 ))
Detector
locatio
nRe
spon
sefunctio
ndata
237 N
p(n
f)137 C
sCM
238 U
(nf)1
37Cs
CM
103 R
h(n
n1015840)103119898Rh
CM
115 In(n
n1015840)115119898Inloz
CM
58Ni(n
p)5
8 Co
CM
27Al(n
120572)2
4 Na
CM
A1
ENDFB-VII0
664sdot10minus6plusmn113
099
544sdot10minus6plusmn071
lowast507sdot10minus6plusmn068
090
554sdot10minus6plusmn059
095
857sdot10minus6plusmn042
109
IRDF-2002
683sdot10minus6plusmn139
103
552sdot10minus6plusmn068
lowast554sdot10minus6plusmn099
099
534sdot10minus6plusmn072
095
565sdot10minus6plusmn061
097
859sdot10minus6plusmn049
109
IRDF-90v2
653sdot10minus6plusmn115
098
558sdot10minus6plusmn068
lowast549sdot10minus6plusmn078
099
534sdot10minus6plusmn061
095
572sdot10minus6plusmn066
098
895sdot10minus6plusmn061
113
A2
ENDFB-VII0
837sdot10minus7plusmn277
lowast620sdot10minus7plusmn069
lowast573sdot10minus7plusmn062
095
616sdot10minus7plusmn060
099
115sdot10minus6plusmn078
113
IRDF-2002
795sdot10minus7plusmn099
lowast627sdot10minus7plusmn073
lowast646sdot10minus7plusmn079
lowast613sdot10minus7plusmn076
101
639sdot10minus7plusmn065
103
116sdot10minus6plusmn071
113
IRDF-90v2
786sdot10minus7plusmn151
lowast631sdot10minus7plusmn066
lowast653sdot10minus7plusmn079
lowast614sdot10minus7plusmn061
101
635sdot10minus7plusmn062
103
120sdot10minus6plusmn074
117
A3
ENDFB-VII0
211sdot10minus7plusmn102
093
181sdot10minus7plusmn062
lowast162sdot10minus7plusmn059
081
199sdot10minus7plusmn068
086
437sdot10minus7plusmn055
097
IRDF-2002
218sdot10minus7plusmn111
096
181sdot10minus7plusmn059
lowast176sdot10minus7plusmn072
lowast172sdot10minus7plusmn062
087
204sdot10minus7plusmn060
088
440sdot10minus7plusmn056
098
IRDF-90v2
204sdot10minus7plusmn078
090
184sdot10minus7plusmn061
lowast176sdot10minus7plusmn067
lowast172sdot10minus7plusmn061
087
204sdot10minus7plusmn059
088
455sdot10minus7plusmn059
101
A4
ENDFB-VII0
907sdot10minus8plusmn056
098
533sdot10minus8plusmn065
087
531sdot10minus8plusmn067
090
482sdot10minus8plusmn084
091
107sdot10minus7plusmn115
105
IRDF-2002
916sdot10minus8plusmn054
099
542sdot10minus8plusmn069
089
750sdot10minus8plusmn055
097
563sdot10minus8plusmn063
096
487sdot10minus8plusmn085
092
107sdot10minus7plusmn117
105
IRDF-90v2
900sdot10minus8plusmn053
097
561sdot10minus8plusmn079
092
751sdot10minus8plusmn052
097
575sdot10minus8plusmn061
098
497sdot10minus8plusmn079
094
111sdot10minus7plusmn129
108
A5
ENDFB-VII0
495sdot10minus8plusmn049
095
223sdot10minus8plusmn063
081
236sdot10minus7plusmn058
086
182sdot10minus8plusmn073
087
417sdot10minus8plusmn115
102
IRDF-2002
495sdot10minus8plusmn048
096
226sdot10minus8plusmn073
082
393sdot10minus8plusmn048
090
252sdot10minus8plusmn058
091
182sdot10minus8plusmn068
087
413sdot10minus8plusmn098
101
IRDF-90v2
496sdot10minus8plusmn047
096
233sdot10minus8plusmn062
085
401sdot10minus8plusmn047
092
257sdot10minus8plusmn055
093
189sdot10minus8plusmn067
090
428sdot10minus8plusmn102
104
A6
ENDFB-VII0
247sdot10minus8plusmn051
091
867sdot10minus9plusmn059
077
986sdot10minus9plusmn054
084
652sdot10minus9plusmn065
088
155sdot10minus8plusmn089
101
IRDF-2002
249sdot10minus8plusmn049
092
873sdot10minus9plusmn060
078
195sdot10minus8plusmn056
089
105sdot10minus8plusmn053
089
665sdot10minus9plusmn083
090
155sdot10minus8plusmn091
101
IRDF-90v2
250sdot10minus8plusmn047
092
916sdot10minus9plusmn059
082
199sdot10minus8plusmn048
091
109sdot10minus8plusmn054
093
691sdot10minus9plusmn067
093
160sdot10minus8plusmn089
103
A7
ENDFB-VII0
630sdot10minus9plusmn077
087
189sdot10minus9plusmn103
lowast223sdot10minus9plusmn093
lowast140sdot10minus9plusmn106
lowast358sdot10minus9plusmn107
lowast
IRDF-2002
634sdot10minus9plusmn086
087
186sdot10minus9plusmn073
lowast487sdot10minus9plusmn062
lowast237sdot10minus9plusmn071
lowast137sdot10minus9plusmn093
lowast350sdot10minus9plusmn089
lowast
IRDF-90v2
640sdot10minus9plusmn074
088
198sdot10minus9plusmn101
lowast507sdot10minus9plusmn081
lowast250sdot10minus9plusmn079
lowast143sdot10minus9plusmn083
lowast368sdot10minus9plusmn100
lowast
lozEN
DFB-VI8
datawas
used
fore
xtractionof
crosssectio
nldquoin
elastic
tometastablerdquoiso
mer
115 In(n
n1015840)115119898In
lowastEx
perim
entald
atan
otprovided
inPC
Abenchm
ark
Science and Technology of Nuclear Installations 9
0
20
40
60
80
100
FOM
fact
or
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
27Al(n 120572)103Rh(n n998400)
238U(n f)
115In(n n998400)58Ni(n p)
237Np(n f)
Figure 12 FOM factors for IRDF-2002 (CAAS case)
of calculations using the established models have been com-pared with PCA benchmark data A good agreement of thecalculated and measured equivalent fission fluxes has beenobtained No systematic decrease of agreements betweencalculations and measurements with increasing distance ofdetector from the PCA benchmark facility core was observedfor any of the applied approaches This indicates that theshapes of calculated neutron spectra in the energy rangeweredosimeters are sensitive are properly determined SCALE60capabilities in generationmixing cross-sections from work-ing library v7 200n47g to be used as a response functions inMAVRIC proved to be very useful
References
[1] ldquoShielding Integral Benchmark Archive and Databaserdquo SINBADReactor Shielding Benchmark Experiments OECDNEA 2011
[2] I Remec and F B Kam ldquoPool Critical Assembly Pressure Ves-sel Facility Benchmarkrdquo NUREGCR-6454 (ORNLTM-13205)prepared for the USNRC by Oak Ridge National LaboratoryAugust 1997
[3] A H Fero S L Anderson and G K Roberts ldquoAnalysis ofthe ORNL PCA benchmark using TORT and BUGLE-96rdquoin Reactor Dosimetry Radiation Metrology and Assessment JG Williams D W Vehar F H Ruddy and D M GilliamEds pp 360ndash366 American Society for Testing and MaterialsPhiladelphia Pa USA 2001
[4] Y K Lee ldquoAnalysis of the NRC PCA pressure vessel dosimetrybenchmark using TRIPOLI-43 Monte Carlo code and ENDFB-VI4 JEF22 and IRDF-90 librariesrdquo Nuclear Mathematical andComputational Science ACentury in Review ACenturyAnewGatlinburg Tenn USA April 2003
[5] ldquoSCALE A Modular Code System for Performing Standard-ized Computer Analyses for Licensing Evaluationrdquo ORNLTM-200539 Version 6 Radiation Safety Information Computa-tional Center at Oak Ridge National Laboratory 2009
[6] D VragolovMMatijevic andD Pevec ldquoModeling of pool crit-ical assembly pressure vessel facility benchmarkrdquo in Proceedingsof the International Conference Nuclear Energy for New EuropeLjubljana Slovenia 2010
[7] J M Risner D Wiarda M E Dunn T M Miller D E Peplowand B W Patton ldquoProduction and Testing of the VITAMIN-B7 Fine-Group and BUGLE-B7 Broad-Group Coupled Neu-tronGamma Cross-Section Libraries Derived from ENDFB-VII0 Nuclear Datardquo USNRC NUREGCR-7045 2011
[8] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File 2002 (IRDF-2002) 2006
[9] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File (IRDF-90 Version 2) 1993
[10] USNRCCalculational andDosimetryMethods forDeterminingPressure Vessel Neutron Fluence Regulatory Guide 1190 2001
[11] I Remec and F B K Kam ldquoHB Robinson-2 Pressure VesselBenchmarkrdquo NUREGCR-6453 (ORNLTM-13204) preparedfor the USNRC by Oak Ridge National Laboratory October1997
[12] J C Wagner and A Haghighat ldquoAutomated variance reductionof Monte Carlo shielding calculations using the discrete ordi-nates adjoint functionrdquo Nuclear Science and Engineering vol128 no 2 pp 186ndash208 1998
[13] J C Wagner E D Blakeman and D E Peplow ldquoForward-weighted CADIS method for global variance reductionrdquo Trans-actions of the American Nuclear Society vol 97 pp 630ndash6332007
[14] G I Bell and S Glasstone Nuclear Reactor Theory VanNostrand Reinhold Company Litton Educational Publishing1970
[15] J C Wagner Acceleration of Monte Carlo shielding calculationswith an automated variance reduction technique and parallel pro-cessing [PhD thesis] Pennsylvania State University UniversityPark Pa USA 1997
[16] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technologyrdquoNuclear Data Sheets vol 107 no 12 pp2931ndash3060 2006
[17] X-5 Monte Carlo Team MCNPmdashA General N-Particle Trans-port Code Version 5 vol 1 of Overview andTheory LA-UR-03-1987 Los Alamos National Laboratory 2003
[18] A Trkov M Herman and D A Brown ldquoENDF-6 FormatsManualrdquo Data Formats and Procedures for the EvaluatedNuclear Data Files ENDFB-VI and ENDFB-VII NationalNuclear Data Center Brookhaven National Laboratory 2011
[19] IAEA Nuclear Data Services httpwww-ndsiaeaorg
TribologyAdvances in
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International Journal of
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FuelsJournal of
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
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Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
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Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
2 Science and Technology of Nuclear Installations
and JEF 22 nuclear data libraries for neutron transport andIRDF-90 IRDF-90v2 RRDF-98 and JENDLD-99 as well asENDFB-VI4 and JEF 22 nuclear data libraries for dosimetrycalculationsThe author finds the IRDF-90 file generally goodfor RPV dosimetry calculations but recommends 103Rh(nn1015840)103mRh and 237Np(n f)137Cs dosimetry cross-sectionsfrom RRDF-98 and JENDLD-99 libraries
An initial analysis of the applicability of SCALE60 [5]hybrid deterministic-stochastic methodology for the PCAbenchmark analysis was conducted by Vragolov et al [6]Only a preliminary averaged equivalent fission fluxes werecalculated and the results showed SCALE60 possibilitiesbut also raised issues that required further analysis Themain concern was the choice of nuclear data library used fordosimetry calculation
Recently Risner et al [7] used SCALE60 code packagefor validation of VITAMIN-B7 and BUGLE-B7 nucleardata libraries on a number of benchmarks including PCAbenchmark The overall results showed applicability of bothlibraries with SCALE60 sequences for PCA benchmarkanalysis with exception of 103Rh(n n1015840)103mRh and 115In(nn1015840)115mIn dosimetry cross-sectionsThe authors advice usageof IRDF-2002 library for named dosimeter reactions
We believe that additional investigation of SCALE60capabilities could be useful primarily in the context of directapplication of SCALE60 built-in fine-group data librariesfor neutron transport as well as for dosimetry calcula-tions Such an approach would speed up analysis and itwould avoid incorporation of external cross-section librariesinto SCALE60 sequences which is not a straight-forwardprocedure especially for inexperienced users Thereforewe conducted PCA benchmark analysis using SCALE60code package with built-in fine-group nuclear data librariesnamely v7 238 [5] for criticality calculation using CSAS6and v7 200n47g [5] for shielding calculations usingMAVRICsequence Dosimetry cross-section data were extractedfrom nuclear data library used for transport calculation(v7 200n47g) Sincewe faced similar problems as Risner et alwith data for 103Rh(n n1015840)103mRh and 115In(n n1015840)115mIn weused IRDF-2002 [8] and IRDF-90v2 [9] dosimetry librariesfor all dosimeters in order to examine the behavior of everyPCA benchmark dosimeter reaction with different library
The PCA benchmark is described in Section 2 Thedescription of the SCALE60 code package used formodelingof the PCA benchmark and calculational methodology aregiven in Section 3 The analysis of the PCA benchmarkincluding results of calculation and comparison of calculatedvalues with benchmark data is presented in Section 4 whilethe conclusions are given in Section 5 References are given atthe end of the paper
2 PCA Benchmark Facility Description
The main cause for limiting the PWR power plant lifetimeis the fast neutron fluence induced embrittlement of thereactor pressure vessel (RPV)With the advances of computercomputational power the reactor dosimetry calculations givebetter insight in radiation damage of RPV when exposed
to intense neutron flux Correlations can be made betweenneutron flux and irradiation of in-core and ex-core detectorstypically via displacements per atom (DPA)This is importantfor advanced nuclear material selection probing and scopingmaterial behavior in intense radiation environments forexample gas accumulations in reactor baffle plates by 58Ni(n120574)59Ni(n 120572) reaction sequence The current guideline forRPV dosimetry calculations is the USNRCRegulatory Guide1190 [10] which states that calculational methods used toestimate RPV fast fluence should use the latest version of theEvaluated Nuclear Data File (ENDFB) in fast energy range(01ndash15)MeV In accordance with this guideline we presentcalculational results for ORNL PCA Benchmark
The scope of PCA benchmark is to validate the capa-bilities of the calculational methodologies to predict thereaction rates in the region outside the core when theneutron source material compositions and relatively simplegeometry configuration are well defined and given The PCAbenchmark provides calculated and measured reaction rates(CM ratio) inside the simulated pressure vessel as well asin the water gap in front of the pressure vessel This allowsan assessment of the accuracy with which the calculationspredict the neutronflux attenuation inside the pressure vessel
The PCA benchmark facility consists of the reactor coreand the components that mock up the reactor-to-cavityregion in light water reactors These components are thethermal shield (TS) the reactor pressure vessel simulator(RPVS) and the void box (VB) which simulates the reactorcavity An overall view of the PCA benchmark facility isshown in Figure 1 An aluminum plate referred to in Figure 1as the reactor window simulator was added to the facilityfor operational reasons The thicknesses of the water gapsbetween the aluminum window and thermal shield andbetween the thermal shield and pressure vessel are approx-imately 12 cm and 13 cm respectively Such configuration isknown as 1213 configuration The materials used for thecomponents outside the core were aluminum for the reactorwindow simulator stainless steel for the thermal shield andcarbon steel for the pressure vessel The facility is located ina large pool of water which serves as reactor core coolantand moderator and provides shielding The PCA benchmarkfacility core is a light water moderated enriched uraniumfueled critical assembly It consists of 25 material test reactor(MTR) plate type elements The standard MTR fuel elementand control element are depicted in Figure 2 The eight ver-tical experimental access tubes in which the measurementswere done were filled with appropriate material (steel inthe pressure vessel locations and Plexiglas in the in-waterlocations) in order to minimize the perturbations of theneutron field
Measured quantities used in PCA benchmark are givenin terms of the equivalent 235U fission fluxes which were cal-culated by dividing the reaction rates with the cross-sectionsaveraged over the 235U fission spectrum [2] All measuredquantities provided for comparisonwith calculated values aregiven per unit PCA benchmark facility core neutron sourceTherefore the calculated results need to be normalized tothe source strength of one fission neutron per second being
Science and Technology of Nuclear Installations 3
Void box(VB)
Thermalshield(TS)
Reactorwindow
simulator
PCAcore with
control rods
Reactor pressurevessel simulator
(RPVS)
A1A2A3
A4A5A6A7
Figure 1 SCALE60 model of PCA benchmark facility (water removed)
Figure 2 PCA standard MTR fuel and control element (waterincluded)
born in the whole PCA core The ratios of the calculated-to-measured (CM) equivalent fission fluxes for DORT librariesBUGLE-93 SAILOR-95 and BUGLE-96 are given in PCAbenchmark reference [2] Measurements were performed atcore midplane (119911 = 0) at several locations labeled in Figure 1as A1 to A7 To complete the PCA benchmark analysis theanalyst must determine the calculated-to-measured (CM)ratios of the equivalent 235U fission fluxes for all the locationsand all the dosimeters for which the measured values areprovided
The significance of the PCA Benchmark are experimentaldata measurements inside thick steel RPV in locations A4to A6 that is neutron flux gradient inside the pressurevessel which provides themeans for verification of calculatedneutron flux attenuation This is in contrast to availabledata from operating reactors which are typically addressingneutron flux for downcomer region internal to RPV andreactor cavity external to RPV wall [11]
3 SCALE60 Code Package
The SCALE60 [5] code system was developed for the USNRC to satisfy a need for a standardized method of analysisfor the evaluation of nuclear facilities and package designsIn its present form the system has the capability to performcriticality shielding radiation source term spent fuel deple-tiondecay reactor physics and sensitivity analyses usingwell established functionalmodules tailored to the SCALE60system
31 The CSAS6 Sequence The CSAS6 criticality sequence isdeveloped to provide automated problem-dependent cross-section processing followed by calculation of the neu-tron multiplication factor 119896eff The cross-section process-ing code BONAMI is used for the unresolved reso-nance range (Bondarenko factors) and either NITAWL orWORKERCENTRMPMC for the resolved resonance rangeKENO-VI a 3D multigroup Monte Carlo code is its func-tional module
32 The MAVRIC Sequence The MAVRIC shielding se-quence uses automated hybrid deterministic-stochasticmethodology to generate variance reduction (VR) param-eters forMonte Carlo calculationsMAVRIC uses 3Dneutrontransport code Monaco with integrated 119878
119873code Denovo
and it is based on CADIS (Consistent Adjoint DrivenImportance Sampling) [12] and FW-CADIS methodology[13] Denovo is used in forward and adjoint mode toapproximate space-energy flux and adjoint functionrespectively These solutions are utilized to calculate spaceand energy dependent biasing parameters that is biased
4 Science and Technology of Nuclear Installations
source and transport importance map to be used as a VRin Monaco CADIS is used to optimize results in localizedregions of phase-space while FW-CADIS tends to obtainglobal uniform statistical uncertainty by weighting of theadjoint source with expected detector response approximatedwith forward Denovo solution CADIS and FW-CADIS arebased on the adjoint function [14] (ie solution of the adjointBoltzmann equation) which has long been recognized as theimportance function for some objective function of interestDetector response is found by integrating the product ofthe detector cross-section 120590
119889( 119903 119864) and flux over detector
volume
119877 = int119881119863
int119864
120590119889( 119903 119864) 120601 ( 119903 119864) 119889119881119889119864 (1)
Alternatively if we approximate adjoint scalar flux with quickDenovo solution where the adjoint source is set as 119902dagger( 119903 119864) =120590119889( 119903 119864) then the detector response is found by integrating
over source volume
119877 = int119881119878
int119864
119902 ( 119903 119864) 120601dagger( 119903 119864) 119889119881119889119864 (2)
The biased source distribution [15] which minimizes thevariance of user-desired response is given as
119902 ( 119903 119864) =120601dagger( 119903 119864) 119902 ( 119903 119864)
119877 (3)
where 120601dagger( 119903 119864) 119902( 119903 119864) and 119877 are the scalar adjoint functionthe source emission probability (forward source) and totaldetector response from (2) respectively For transport biasingthe weight window technique is employed that is space-energy dependent geometric splittingroulette Biased sourceand weight-window lower bounds are consistent so thesource particles are created with statistical weight withinweight windows
119908 ( 119903 119864) =119902 ( 119903 119864)
119902 ( 119903 119864)=
119877
120601dagger ( 119903 119864) (4)
Inverse relationship between particle statistical weight andadjoint functionmust be emphasized Since PCA Benchmarkinvolves calculation of near and far detector reaction ratesthis FW-CADIS methodology is highly desirable choice
33 Cross-Section Libraries There are several multigroupcross-section libraries distributed within SCALE60 for criti-cality safety analyses and shielding calculations For criticalitysafety analyses the v7-238 library [5] was used while for theshielding calculations v7-200n47g library [5] was used Theyare based on ENDFB-VII0 data [16] For shielding part ofcalculations it was imperative to use fine structure libraryv7 200n47g because high-energy threshold for all reactionscould not be correctly accounted for if broad shieldingv7 27n19g library was used
4 Analysis of the PCA Benchmark
The calculational models of the PCA benchmark withinCSAS6 and MAVRIC sequences of SCALE60 code package
have been determined The results of the calculations that isequivalent fission fluxes using the established models havebeen compared with the PCA benchmark data
41 CSAS6 Results The initial CSAS6KENO-VI criticalityeigenvalue calculation of the PCA benchmark facility wasperformed using 550 batches and 2000 neutrons per batchwith first 50 batches skipped in order for the fission sourcedistribution to converge to eigenmode Critical control rodpositions were validated and obtained effective multiplica-tion factor of the system was 119896eff = (099856 plusmn 000071)This result was tested with MCNP5 code [17] Shannonentropy check for source stationarity was successful andsimilar 119896eff was obtained 119896eff = (099911 plusmn 000051) ThisCSAS6KENO-VI calculation was then rerun with betterstatistics (2150 batches10000 neutrons per batch) for thegeneration of mesh-based fission source distribution (ldquoCDS= YESrdquo option) to be used as a criticality source in the subse-quent MAVRIC calculations This approach in SCALE60 isknown as CAAS (Criticality Accident Alarm Systems)
42 MAVRICMonaco Results The MAVRIC shielding se-quence was run with the mesh-based source from criticalityeigenvalue run FW-CADIS methodology provides consis-tentweightwindows (ie importancemap) and biased sourcedistributions for transport of the PCA core neutrons to thelocations of interest detectors in experimental access tubesA1ndashA7
The equivalent fission fluxes in PCA report were cal-culated by dividing the reaction rates by the cross-sectionsaveraged over the 235U fission spectrum That fast neutronfluence calculation was reasonable approach in the time ofPCA Benchmark calculation with DORT but full spectrumcalculation nowadays with modern Monte Carlo code is notprohibitive So our calculations were conducted with fullneutron spectrum in accordance with SCALE60 multigroupweighting function (spectrum) [2] defined as
(1) Maxwellian spectrum (peak at 300K) from 10minus5 to0125 eV
(2) a 1119864 spectrum from 0125 eV to 674 keV(3) a fission spectrum (effective temperature at 1273
MeV) from 674 keV to 10MeV(4) a 1119864 spectrum from 10 to 20MeV
Equivalent fission fluxes thus are defined as
120601eq =int119864120590119894(119864) 120601 (119864) 119889119864
int119864120590119894(119864) 120593 (119864) 119889119864 int
119864120593 (119864) 119889119864
=reaction rates
120590119894
(5)
where 120590119894(119864) 120601(119864) and 120593(119864) are the dosimetry cross-sections
for the reactions being considered the Monte Carlo flux atthe dosimetry location and weighting spectrum functionrespectively The spectrum averaged cross-sections (120590
119894) were
taken from Table 16 from PCA report [2] for consistencysince they are in very good agreement with calculated valuesfrom our libraries
Science and Technology of Nuclear Installations 5
For seven detector locations (A1ndashA7) we used twodosimetry libraries as a source of a response functionsfor reaction rate calculations Reaction rate calculationswere done with IRDF-2002 and IRDF-90v2 (older version)libraries for the total of six PCA benchmark reactions237Np(n f)137Cs 238U(n f)137Cs 103Rh(n n1015840)103mRh 115In(nn1015840)115mIn 58Ni(n p)58Co and 27Al(n120572)24NaThese reactionswere defined as a response functions for FW-CADISmethod-ology
The threshold energies for the 27Al(n 120572)24Na 58Ni(np)58Co 238U(n f)137Cs 237Np(n f)137Cs 115In(n n1015840)115mInand 103Rh(n n1015840)103mRh reactions are 50 205 145 06903 and 01MeV respectively This is in fast neutron rangebut still calculations were performed for full neutron spec-trum (10minus5 eV to 20MeV) with fine-group shielding libraryv7 200n47g
Also we investigated SCALE60 capabilities in genera-tionmixing of multigroup cross-sections from v7 200n47glibrary for reactions 237Np(n f)137Cs 238U(n f)137Cs 58Ni(np)58Co and 27Al(n 120572)24Na using AJAX and PALEALEutility modules of AMPX working library Reaction 115In(nn1015840)115mIn was derived from ENDFB-VI8 while reaction103Rh(n n1015840)103mRh was not derived because there is no singleor combination of reaction type numbers [18] (MT numbersin ENDFB) for computation of production rate ofmetastableisomer of rhodium (first excited state resulting from inelasticscattering) The obtained multigroup cross-sections withoutrhodium are Doppler and resonances corrected and haveMAVRIC shielding structure of 200n47g These reactionswere also defined as a response functions for FW-CADISmethodology
Two different approaches for the MAVRIC source distri-bution were
(1) fission distribution in space and energy determinedby KENO-VI calculation (transferred as a sourceinput into MAVRIC)mdashCAAS case
(2) Watt spectrum [5] for source energy distribution119901(119864) = 119862119890
minus119864119886 sinh(radic119887119864) (we used thermal fissionof 235U with 119886 = 1028MeV and 119887 = 2249MeV)with uniform space sampling restricted to the reactorcoremdashWatt spectrum case
The total number of neutron batches was 2000 with 2000neutrons per batch for MAVRIC sequence The Denovo 119878
119873
mesh had approximately 20000 cells over PCA facility modelthat is 48 times 23 times 18 cells in 119909119910119911 direction with average cellside of 32 cm while Monaco Monte Carlo mesh had 36000cells (60 times 30 times 20) with average cell side of 26 cm We used1198788as quadrature order and119875
3for Legendre order of scattering
cross-section expansion (upscatteringwas deactivated) Sincethe axial flux gradients inside tubes are confirmed to besufficiently small the user-selected height of plusmn15 cm forvolumetric cylindrical tally regions in MAVRIC calculationrepresents a good compromise between Monte Carlo relativeerror and spatial description of PCA benchmark facilityDifferential small void cylinders were also placed in themidplane (119911 = 0) of the access tubes Point detectors andregion track length estimators were used to find multigroup
1E16
1E15
1E14
1E13
1E12
1E11
1E10
1E09
minus50
minus100
50
x axis (cm) 0
Neu
tron
forw
ard
flux
(nc
m3 s
)
Figure 3 Denovo forward neutron flux axial distribution (front halfremoved)
1E minus 02
1E minus 03
1E minus 04
1E minus 05
1E minus 06
1E minus 07
1E minus 08
1E minus 09
1E minus 10
minus50
minus100
50
0x axis (cm)
Neu
tron
adjo
int fl
ux (n
cm
2s
)
Figure 4 Denovo adjoint neutron flux axial distribution (front halfremoved)
neutron fluxes reaction rates and finally equivalent fissionfluxes
The elements of the FW-CADIS methodology aredepicted next Forward and adjoint neutron flux axial dis-tribution from Denovo code for CAAS case are shown inFigures 3 and 4 respectively Biased source distribution andmesh-based importance map are shown in Figures 5 and 6respectively Total Monte Carlo neutron flux in form of meshtally is depicted in Figures 7 and 8
The calculated equivalent fission fluxes with Monte Carlorelative error (1 sigma level) for PCA Benchmark are givenin Table 1 for MAVRIC CAAS case Only the reactions forwhich the measurements were done are listed AveragedCM ratios for detectors A1ndashA7 are shown in Figure 9 forCAAS case and in Figure 10 for Watt spectrum case Theseresults are compared to the referencedDORT results [2] Onecan notice high similarity between Monaco results for twodifferent source distribution approaches The Watt spectrumcase results aremore conservative and they are 10ndash15 higherthan CAAS case results
6 Science and Technology of Nuclear Installations
127E14 minus 264E14
613E13 minus 127E14
295E13 minus 613E13
142E13 minus 295E13
685E12 minus 142E13
330E12 minus 685E12
159E12 minus 330E12
765E11 minus 159E12
369E11 minus 765E11
178E11 minus 369E11
856E10 minus 178E11
412E10 minus 856E10
199E10 minus 412E10
956E09 minus 199E10
461E09 minus 956E09
Sampled neutronsTotal sampled neutronsValues
Figure 5 Biased source distribution (front half removed)
Values252E-02 minus 717E-02886E-03 minus 252E-02311E-03 minus 886E-03110E-03 minus 311E-03385E-04 minus 110E-031355E-04 minus 385E-04476E-05 minus 135E-04167E-05 minus 476E-05588E-06 minus 167E-05207E-06 minus 588E-06
256E-07 minus 727E-07727E-07 minus 207E-06
899E-08 minus 256E-07316E-08 minus 899E-08111E-08 minus 316E-08
Group 1Neutron target
Figure 6 Mesh-based importance map (front quarter removed)
Values136E15 minus 576E153233E14 minus 136E15764E13 minus 323E14181E13 minus 764E13
240E11 minus 101E12101E12 minus 428E12428E12 minus 181E13
568E10 minus 240E11134E10 minus 568E10318E09 minus 134E10753E08 minus 318E09178E08 minus 753E08
236E06 minus 998E06
422E07 minus 178E08998E06 minus 422E07
Neutron fluxTotal neutron flux
Figure 7 Neutron flux mesh tally (front quarter removed)
5 Discussion of Results
All obtained results are in accordance with calculationaluncertainty criterion from US NRC Regulatory Guide 1190the calculated reaction rates agree with the measurementsto within 20 for out-of-core dosimetry locations Under
prediction in CM ratio can be observed for 238U(n f)137Cs(145MeV threshold) through the thick RPV simulator (fromlocations A4 to A6) with 08 on average High attenuationof neutron flux in that area (around 700 for IRDF-2002) willcause softening of neutron spectrum inRPV simulator whichshifts neutrons in resonance regions for inelastic scattering
Science and Technology of Nuclear Installations 7
000076
000001
14ndash7
19ndash7
26ndash11
Figure 8 Neutron flux mesh tally in axial midplane (MCNP5 criti-cality results)
08
085
09
095
1
10511
Detector position (cm)
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE6 IRDF-2002
SCALE6 IRDF-90v2DORT BUGLE-93
DORT SAILOR-95DORT BUGLE-96
10 15 20 25 30 35 40 45 5550 60
Figure 9 Average DORT [2] and SCALE60 (CAAS case) CMratios for detectors
on iron Microscopic cross-section for neutron inelasticscattering on iron is shown in Figure 11 Results for 238U(nf)137Cs indicate self-shielding effects that is sensitivity ofmultigroup shielding library v7 200n47g on the iron cross-sections
Overprediction in results is highest for detector A2immediately after stainless steel thermal shield which haslarge amount of iron Again self-shielding effects of ironcross-sections are pronounced especially for 27Al(n 120572)24Na(IRDF-90v2) with CM of 117 The IRDF-90v2 library gen-erally gives the highest values while SCALE60 v7 200n47glibrary gives the lowest values of calculated fluxesThe IRDF-2002 results are right in the middle so this library wouldbe favorable for RPV dosimetry calculations The obtainedcalculational results show overall a good agreement withexperimental results however for distant detectors fromPCA core there is under prediction less than 10 on averageexcept excellent result for 27Al(n 120572)24Na
An important issue that has to be addressed whendiscussing Monte Carlo method is a burden the appliedcalculational model will place on memory resources andCPU time requirements For that purpose the figure-of-merit (FOM) factor [17] is defined to account for the time it
08085
09095
1105
11115
12
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE IRDF-2002SCALE IRDF-90v2DORT BUGLE-93DORT SAILOR-95
DORT BUGLE-96
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
Figure 10 Average DORT [2] and SCALE60 (Watt spectrum case)CM ratios for detectors
11
1
1
102
102
10minus4
10minus4
10minus2
10minus2
10minus10
10minus10
10minus5
10minus5
Cros
s sec
tion
(bar
ns)
Incident energy (MeV)
Figure 11 Inelastic scattering on iron [19]
takes to achieve a given level of uncertainty in Monte Carlocalculation
FOM =1
1198771198642sdot 119879
(6)
where 119877119864 and 119879 are Monte Carlo relative error (on 1 sigmalevel) and Monte Carlo CPU run time (in min) respectivelyMAVRIC run time for highest energy threshold reaction(5MeV for 27Al(n 120572)24Na) was 7 h while for the lowest(01MeV for 103Rh(n n1015840)103mRh) was 10 h In this paper allcalculations have been performed on QuadCore Q6600 with8GB of RAM FOM factors for IRDF-2002 and CAAS caseare shown in Figure 12 Application of automated variancereduction technique based on adjoint fluxes removes theburden of manually tuning VR parameters and significantlyimproves the quality of Monte Carlo calculations
6 Conclusion
The analysis of the PCA benchmark has been performedusing the SCALE60 code package The calculational mod-els of the PCA benchmark within CSAS6 and MAVRICsequences of SCALE60 have been determined The results
8 Science and Technology of Nuclear Installations
Table1Eq
uivalent
fissio
nflu
xes(per1
PCAcore
fissio
nneutronpersecon
d(cmminus2 ))
Detector
locatio
nRe
spon
sefunctio
ndata
237 N
p(n
f)137 C
sCM
238 U
(nf)1
37Cs
CM
103 R
h(n
n1015840)103119898Rh
CM
115 In(n
n1015840)115119898Inloz
CM
58Ni(n
p)5
8 Co
CM
27Al(n
120572)2
4 Na
CM
A1
ENDFB-VII0
664sdot10minus6plusmn113
099
544sdot10minus6plusmn071
lowast507sdot10minus6plusmn068
090
554sdot10minus6plusmn059
095
857sdot10minus6plusmn042
109
IRDF-2002
683sdot10minus6plusmn139
103
552sdot10minus6plusmn068
lowast554sdot10minus6plusmn099
099
534sdot10minus6plusmn072
095
565sdot10minus6plusmn061
097
859sdot10minus6plusmn049
109
IRDF-90v2
653sdot10minus6plusmn115
098
558sdot10minus6plusmn068
lowast549sdot10minus6plusmn078
099
534sdot10minus6plusmn061
095
572sdot10minus6plusmn066
098
895sdot10minus6plusmn061
113
A2
ENDFB-VII0
837sdot10minus7plusmn277
lowast620sdot10minus7plusmn069
lowast573sdot10minus7plusmn062
095
616sdot10minus7plusmn060
099
115sdot10minus6plusmn078
113
IRDF-2002
795sdot10minus7plusmn099
lowast627sdot10minus7plusmn073
lowast646sdot10minus7plusmn079
lowast613sdot10minus7plusmn076
101
639sdot10minus7plusmn065
103
116sdot10minus6plusmn071
113
IRDF-90v2
786sdot10minus7plusmn151
lowast631sdot10minus7plusmn066
lowast653sdot10minus7plusmn079
lowast614sdot10minus7plusmn061
101
635sdot10minus7plusmn062
103
120sdot10minus6plusmn074
117
A3
ENDFB-VII0
211sdot10minus7plusmn102
093
181sdot10minus7plusmn062
lowast162sdot10minus7plusmn059
081
199sdot10minus7plusmn068
086
437sdot10minus7plusmn055
097
IRDF-2002
218sdot10minus7plusmn111
096
181sdot10minus7plusmn059
lowast176sdot10minus7plusmn072
lowast172sdot10minus7plusmn062
087
204sdot10minus7plusmn060
088
440sdot10minus7plusmn056
098
IRDF-90v2
204sdot10minus7plusmn078
090
184sdot10minus7plusmn061
lowast176sdot10minus7plusmn067
lowast172sdot10minus7plusmn061
087
204sdot10minus7plusmn059
088
455sdot10minus7plusmn059
101
A4
ENDFB-VII0
907sdot10minus8plusmn056
098
533sdot10minus8plusmn065
087
531sdot10minus8plusmn067
090
482sdot10minus8plusmn084
091
107sdot10minus7plusmn115
105
IRDF-2002
916sdot10minus8plusmn054
099
542sdot10minus8plusmn069
089
750sdot10minus8plusmn055
097
563sdot10minus8plusmn063
096
487sdot10minus8plusmn085
092
107sdot10minus7plusmn117
105
IRDF-90v2
900sdot10minus8plusmn053
097
561sdot10minus8plusmn079
092
751sdot10minus8plusmn052
097
575sdot10minus8plusmn061
098
497sdot10minus8plusmn079
094
111sdot10minus7plusmn129
108
A5
ENDFB-VII0
495sdot10minus8plusmn049
095
223sdot10minus8plusmn063
081
236sdot10minus7plusmn058
086
182sdot10minus8plusmn073
087
417sdot10minus8plusmn115
102
IRDF-2002
495sdot10minus8plusmn048
096
226sdot10minus8plusmn073
082
393sdot10minus8plusmn048
090
252sdot10minus8plusmn058
091
182sdot10minus8plusmn068
087
413sdot10minus8plusmn098
101
IRDF-90v2
496sdot10minus8plusmn047
096
233sdot10minus8plusmn062
085
401sdot10minus8plusmn047
092
257sdot10minus8plusmn055
093
189sdot10minus8plusmn067
090
428sdot10minus8plusmn102
104
A6
ENDFB-VII0
247sdot10minus8plusmn051
091
867sdot10minus9plusmn059
077
986sdot10minus9plusmn054
084
652sdot10minus9plusmn065
088
155sdot10minus8plusmn089
101
IRDF-2002
249sdot10minus8plusmn049
092
873sdot10minus9plusmn060
078
195sdot10minus8plusmn056
089
105sdot10minus8plusmn053
089
665sdot10minus9plusmn083
090
155sdot10minus8plusmn091
101
IRDF-90v2
250sdot10minus8plusmn047
092
916sdot10minus9plusmn059
082
199sdot10minus8plusmn048
091
109sdot10minus8plusmn054
093
691sdot10minus9plusmn067
093
160sdot10minus8plusmn089
103
A7
ENDFB-VII0
630sdot10minus9plusmn077
087
189sdot10minus9plusmn103
lowast223sdot10minus9plusmn093
lowast140sdot10minus9plusmn106
lowast358sdot10minus9plusmn107
lowast
IRDF-2002
634sdot10minus9plusmn086
087
186sdot10minus9plusmn073
lowast487sdot10minus9plusmn062
lowast237sdot10minus9plusmn071
lowast137sdot10minus9plusmn093
lowast350sdot10minus9plusmn089
lowast
IRDF-90v2
640sdot10minus9plusmn074
088
198sdot10minus9plusmn101
lowast507sdot10minus9plusmn081
lowast250sdot10minus9plusmn079
lowast143sdot10minus9plusmn083
lowast368sdot10minus9plusmn100
lowast
lozEN
DFB-VI8
datawas
used
fore
xtractionof
crosssectio
nldquoin
elastic
tometastablerdquoiso
mer
115 In(n
n1015840)115119898In
lowastEx
perim
entald
atan
otprovided
inPC
Abenchm
ark
Science and Technology of Nuclear Installations 9
0
20
40
60
80
100
FOM
fact
or
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
27Al(n 120572)103Rh(n n998400)
238U(n f)
115In(n n998400)58Ni(n p)
237Np(n f)
Figure 12 FOM factors for IRDF-2002 (CAAS case)
of calculations using the established models have been com-pared with PCA benchmark data A good agreement of thecalculated and measured equivalent fission fluxes has beenobtained No systematic decrease of agreements betweencalculations and measurements with increasing distance ofdetector from the PCA benchmark facility core was observedfor any of the applied approaches This indicates that theshapes of calculated neutron spectra in the energy rangeweredosimeters are sensitive are properly determined SCALE60capabilities in generationmixing cross-sections from work-ing library v7 200n47g to be used as a response functions inMAVRIC proved to be very useful
References
[1] ldquoShielding Integral Benchmark Archive and Databaserdquo SINBADReactor Shielding Benchmark Experiments OECDNEA 2011
[2] I Remec and F B Kam ldquoPool Critical Assembly Pressure Ves-sel Facility Benchmarkrdquo NUREGCR-6454 (ORNLTM-13205)prepared for the USNRC by Oak Ridge National LaboratoryAugust 1997
[3] A H Fero S L Anderson and G K Roberts ldquoAnalysis ofthe ORNL PCA benchmark using TORT and BUGLE-96rdquoin Reactor Dosimetry Radiation Metrology and Assessment JG Williams D W Vehar F H Ruddy and D M GilliamEds pp 360ndash366 American Society for Testing and MaterialsPhiladelphia Pa USA 2001
[4] Y K Lee ldquoAnalysis of the NRC PCA pressure vessel dosimetrybenchmark using TRIPOLI-43 Monte Carlo code and ENDFB-VI4 JEF22 and IRDF-90 librariesrdquo Nuclear Mathematical andComputational Science ACentury in Review ACenturyAnewGatlinburg Tenn USA April 2003
[5] ldquoSCALE A Modular Code System for Performing Standard-ized Computer Analyses for Licensing Evaluationrdquo ORNLTM-200539 Version 6 Radiation Safety Information Computa-tional Center at Oak Ridge National Laboratory 2009
[6] D VragolovMMatijevic andD Pevec ldquoModeling of pool crit-ical assembly pressure vessel facility benchmarkrdquo in Proceedingsof the International Conference Nuclear Energy for New EuropeLjubljana Slovenia 2010
[7] J M Risner D Wiarda M E Dunn T M Miller D E Peplowand B W Patton ldquoProduction and Testing of the VITAMIN-B7 Fine-Group and BUGLE-B7 Broad-Group Coupled Neu-tronGamma Cross-Section Libraries Derived from ENDFB-VII0 Nuclear Datardquo USNRC NUREGCR-7045 2011
[8] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File 2002 (IRDF-2002) 2006
[9] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File (IRDF-90 Version 2) 1993
[10] USNRCCalculational andDosimetryMethods forDeterminingPressure Vessel Neutron Fluence Regulatory Guide 1190 2001
[11] I Remec and F B K Kam ldquoHB Robinson-2 Pressure VesselBenchmarkrdquo NUREGCR-6453 (ORNLTM-13204) preparedfor the USNRC by Oak Ridge National Laboratory October1997
[12] J C Wagner and A Haghighat ldquoAutomated variance reductionof Monte Carlo shielding calculations using the discrete ordi-nates adjoint functionrdquo Nuclear Science and Engineering vol128 no 2 pp 186ndash208 1998
[13] J C Wagner E D Blakeman and D E Peplow ldquoForward-weighted CADIS method for global variance reductionrdquo Trans-actions of the American Nuclear Society vol 97 pp 630ndash6332007
[14] G I Bell and S Glasstone Nuclear Reactor Theory VanNostrand Reinhold Company Litton Educational Publishing1970
[15] J C Wagner Acceleration of Monte Carlo shielding calculationswith an automated variance reduction technique and parallel pro-cessing [PhD thesis] Pennsylvania State University UniversityPark Pa USA 1997
[16] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technologyrdquoNuclear Data Sheets vol 107 no 12 pp2931ndash3060 2006
[17] X-5 Monte Carlo Team MCNPmdashA General N-Particle Trans-port Code Version 5 vol 1 of Overview andTheory LA-UR-03-1987 Los Alamos National Laboratory 2003
[18] A Trkov M Herman and D A Brown ldquoENDF-6 FormatsManualrdquo Data Formats and Procedures for the EvaluatedNuclear Data Files ENDFB-VI and ENDFB-VII NationalNuclear Data Center Brookhaven National Laboratory 2011
[19] IAEA Nuclear Data Services httpwww-ndsiaeaorg
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Science and Technology of Nuclear Installations 3
Void box(VB)
Thermalshield(TS)
Reactorwindow
simulator
PCAcore with
control rods
Reactor pressurevessel simulator
(RPVS)
A1A2A3
A4A5A6A7
Figure 1 SCALE60 model of PCA benchmark facility (water removed)
Figure 2 PCA standard MTR fuel and control element (waterincluded)
born in the whole PCA core The ratios of the calculated-to-measured (CM) equivalent fission fluxes for DORT librariesBUGLE-93 SAILOR-95 and BUGLE-96 are given in PCAbenchmark reference [2] Measurements were performed atcore midplane (119911 = 0) at several locations labeled in Figure 1as A1 to A7 To complete the PCA benchmark analysis theanalyst must determine the calculated-to-measured (CM)ratios of the equivalent 235U fission fluxes for all the locationsand all the dosimeters for which the measured values areprovided
The significance of the PCA Benchmark are experimentaldata measurements inside thick steel RPV in locations A4to A6 that is neutron flux gradient inside the pressurevessel which provides themeans for verification of calculatedneutron flux attenuation This is in contrast to availabledata from operating reactors which are typically addressingneutron flux for downcomer region internal to RPV andreactor cavity external to RPV wall [11]
3 SCALE60 Code Package
The SCALE60 [5] code system was developed for the USNRC to satisfy a need for a standardized method of analysisfor the evaluation of nuclear facilities and package designsIn its present form the system has the capability to performcriticality shielding radiation source term spent fuel deple-tiondecay reactor physics and sensitivity analyses usingwell established functionalmodules tailored to the SCALE60system
31 The CSAS6 Sequence The CSAS6 criticality sequence isdeveloped to provide automated problem-dependent cross-section processing followed by calculation of the neu-tron multiplication factor 119896eff The cross-section process-ing code BONAMI is used for the unresolved reso-nance range (Bondarenko factors) and either NITAWL orWORKERCENTRMPMC for the resolved resonance rangeKENO-VI a 3D multigroup Monte Carlo code is its func-tional module
32 The MAVRIC Sequence The MAVRIC shielding se-quence uses automated hybrid deterministic-stochasticmethodology to generate variance reduction (VR) param-eters forMonte Carlo calculationsMAVRIC uses 3Dneutrontransport code Monaco with integrated 119878
119873code Denovo
and it is based on CADIS (Consistent Adjoint DrivenImportance Sampling) [12] and FW-CADIS methodology[13] Denovo is used in forward and adjoint mode toapproximate space-energy flux and adjoint functionrespectively These solutions are utilized to calculate spaceand energy dependent biasing parameters that is biased
4 Science and Technology of Nuclear Installations
source and transport importance map to be used as a VRin Monaco CADIS is used to optimize results in localizedregions of phase-space while FW-CADIS tends to obtainglobal uniform statistical uncertainty by weighting of theadjoint source with expected detector response approximatedwith forward Denovo solution CADIS and FW-CADIS arebased on the adjoint function [14] (ie solution of the adjointBoltzmann equation) which has long been recognized as theimportance function for some objective function of interestDetector response is found by integrating the product ofthe detector cross-section 120590
119889( 119903 119864) and flux over detector
volume
119877 = int119881119863
int119864
120590119889( 119903 119864) 120601 ( 119903 119864) 119889119881119889119864 (1)
Alternatively if we approximate adjoint scalar flux with quickDenovo solution where the adjoint source is set as 119902dagger( 119903 119864) =120590119889( 119903 119864) then the detector response is found by integrating
over source volume
119877 = int119881119878
int119864
119902 ( 119903 119864) 120601dagger( 119903 119864) 119889119881119889119864 (2)
The biased source distribution [15] which minimizes thevariance of user-desired response is given as
119902 ( 119903 119864) =120601dagger( 119903 119864) 119902 ( 119903 119864)
119877 (3)
where 120601dagger( 119903 119864) 119902( 119903 119864) and 119877 are the scalar adjoint functionthe source emission probability (forward source) and totaldetector response from (2) respectively For transport biasingthe weight window technique is employed that is space-energy dependent geometric splittingroulette Biased sourceand weight-window lower bounds are consistent so thesource particles are created with statistical weight withinweight windows
119908 ( 119903 119864) =119902 ( 119903 119864)
119902 ( 119903 119864)=
119877
120601dagger ( 119903 119864) (4)
Inverse relationship between particle statistical weight andadjoint functionmust be emphasized Since PCA Benchmarkinvolves calculation of near and far detector reaction ratesthis FW-CADIS methodology is highly desirable choice
33 Cross-Section Libraries There are several multigroupcross-section libraries distributed within SCALE60 for criti-cality safety analyses and shielding calculations For criticalitysafety analyses the v7-238 library [5] was used while for theshielding calculations v7-200n47g library [5] was used Theyare based on ENDFB-VII0 data [16] For shielding part ofcalculations it was imperative to use fine structure libraryv7 200n47g because high-energy threshold for all reactionscould not be correctly accounted for if broad shieldingv7 27n19g library was used
4 Analysis of the PCA Benchmark
The calculational models of the PCA benchmark withinCSAS6 and MAVRIC sequences of SCALE60 code package
have been determined The results of the calculations that isequivalent fission fluxes using the established models havebeen compared with the PCA benchmark data
41 CSAS6 Results The initial CSAS6KENO-VI criticalityeigenvalue calculation of the PCA benchmark facility wasperformed using 550 batches and 2000 neutrons per batchwith first 50 batches skipped in order for the fission sourcedistribution to converge to eigenmode Critical control rodpositions were validated and obtained effective multiplica-tion factor of the system was 119896eff = (099856 plusmn 000071)This result was tested with MCNP5 code [17] Shannonentropy check for source stationarity was successful andsimilar 119896eff was obtained 119896eff = (099911 plusmn 000051) ThisCSAS6KENO-VI calculation was then rerun with betterstatistics (2150 batches10000 neutrons per batch) for thegeneration of mesh-based fission source distribution (ldquoCDS= YESrdquo option) to be used as a criticality source in the subse-quent MAVRIC calculations This approach in SCALE60 isknown as CAAS (Criticality Accident Alarm Systems)
42 MAVRICMonaco Results The MAVRIC shielding se-quence was run with the mesh-based source from criticalityeigenvalue run FW-CADIS methodology provides consis-tentweightwindows (ie importancemap) and biased sourcedistributions for transport of the PCA core neutrons to thelocations of interest detectors in experimental access tubesA1ndashA7
The equivalent fission fluxes in PCA report were cal-culated by dividing the reaction rates by the cross-sectionsaveraged over the 235U fission spectrum That fast neutronfluence calculation was reasonable approach in the time ofPCA Benchmark calculation with DORT but full spectrumcalculation nowadays with modern Monte Carlo code is notprohibitive So our calculations were conducted with fullneutron spectrum in accordance with SCALE60 multigroupweighting function (spectrum) [2] defined as
(1) Maxwellian spectrum (peak at 300K) from 10minus5 to0125 eV
(2) a 1119864 spectrum from 0125 eV to 674 keV(3) a fission spectrum (effective temperature at 1273
MeV) from 674 keV to 10MeV(4) a 1119864 spectrum from 10 to 20MeV
Equivalent fission fluxes thus are defined as
120601eq =int119864120590119894(119864) 120601 (119864) 119889119864
int119864120590119894(119864) 120593 (119864) 119889119864 int
119864120593 (119864) 119889119864
=reaction rates
120590119894
(5)
where 120590119894(119864) 120601(119864) and 120593(119864) are the dosimetry cross-sections
for the reactions being considered the Monte Carlo flux atthe dosimetry location and weighting spectrum functionrespectively The spectrum averaged cross-sections (120590
119894) were
taken from Table 16 from PCA report [2] for consistencysince they are in very good agreement with calculated valuesfrom our libraries
Science and Technology of Nuclear Installations 5
For seven detector locations (A1ndashA7) we used twodosimetry libraries as a source of a response functionsfor reaction rate calculations Reaction rate calculationswere done with IRDF-2002 and IRDF-90v2 (older version)libraries for the total of six PCA benchmark reactions237Np(n f)137Cs 238U(n f)137Cs 103Rh(n n1015840)103mRh 115In(nn1015840)115mIn 58Ni(n p)58Co and 27Al(n120572)24NaThese reactionswere defined as a response functions for FW-CADISmethod-ology
The threshold energies for the 27Al(n 120572)24Na 58Ni(np)58Co 238U(n f)137Cs 237Np(n f)137Cs 115In(n n1015840)115mInand 103Rh(n n1015840)103mRh reactions are 50 205 145 06903 and 01MeV respectively This is in fast neutron rangebut still calculations were performed for full neutron spec-trum (10minus5 eV to 20MeV) with fine-group shielding libraryv7 200n47g
Also we investigated SCALE60 capabilities in genera-tionmixing of multigroup cross-sections from v7 200n47glibrary for reactions 237Np(n f)137Cs 238U(n f)137Cs 58Ni(np)58Co and 27Al(n 120572)24Na using AJAX and PALEALEutility modules of AMPX working library Reaction 115In(nn1015840)115mIn was derived from ENDFB-VI8 while reaction103Rh(n n1015840)103mRh was not derived because there is no singleor combination of reaction type numbers [18] (MT numbersin ENDFB) for computation of production rate ofmetastableisomer of rhodium (first excited state resulting from inelasticscattering) The obtained multigroup cross-sections withoutrhodium are Doppler and resonances corrected and haveMAVRIC shielding structure of 200n47g These reactionswere also defined as a response functions for FW-CADISmethodology
Two different approaches for the MAVRIC source distri-bution were
(1) fission distribution in space and energy determinedby KENO-VI calculation (transferred as a sourceinput into MAVRIC)mdashCAAS case
(2) Watt spectrum [5] for source energy distribution119901(119864) = 119862119890
minus119864119886 sinh(radic119887119864) (we used thermal fissionof 235U with 119886 = 1028MeV and 119887 = 2249MeV)with uniform space sampling restricted to the reactorcoremdashWatt spectrum case
The total number of neutron batches was 2000 with 2000neutrons per batch for MAVRIC sequence The Denovo 119878
119873
mesh had approximately 20000 cells over PCA facility modelthat is 48 times 23 times 18 cells in 119909119910119911 direction with average cellside of 32 cm while Monaco Monte Carlo mesh had 36000cells (60 times 30 times 20) with average cell side of 26 cm We used1198788as quadrature order and119875
3for Legendre order of scattering
cross-section expansion (upscatteringwas deactivated) Sincethe axial flux gradients inside tubes are confirmed to besufficiently small the user-selected height of plusmn15 cm forvolumetric cylindrical tally regions in MAVRIC calculationrepresents a good compromise between Monte Carlo relativeerror and spatial description of PCA benchmark facilityDifferential small void cylinders were also placed in themidplane (119911 = 0) of the access tubes Point detectors andregion track length estimators were used to find multigroup
1E16
1E15
1E14
1E13
1E12
1E11
1E10
1E09
minus50
minus100
50
x axis (cm) 0
Neu
tron
forw
ard
flux
(nc
m3 s
)
Figure 3 Denovo forward neutron flux axial distribution (front halfremoved)
1E minus 02
1E minus 03
1E minus 04
1E minus 05
1E minus 06
1E minus 07
1E minus 08
1E minus 09
1E minus 10
minus50
minus100
50
0x axis (cm)
Neu
tron
adjo
int fl
ux (n
cm
2s
)
Figure 4 Denovo adjoint neutron flux axial distribution (front halfremoved)
neutron fluxes reaction rates and finally equivalent fissionfluxes
The elements of the FW-CADIS methodology aredepicted next Forward and adjoint neutron flux axial dis-tribution from Denovo code for CAAS case are shown inFigures 3 and 4 respectively Biased source distribution andmesh-based importance map are shown in Figures 5 and 6respectively Total Monte Carlo neutron flux in form of meshtally is depicted in Figures 7 and 8
The calculated equivalent fission fluxes with Monte Carlorelative error (1 sigma level) for PCA Benchmark are givenin Table 1 for MAVRIC CAAS case Only the reactions forwhich the measurements were done are listed AveragedCM ratios for detectors A1ndashA7 are shown in Figure 9 forCAAS case and in Figure 10 for Watt spectrum case Theseresults are compared to the referencedDORT results [2] Onecan notice high similarity between Monaco results for twodifferent source distribution approaches The Watt spectrumcase results aremore conservative and they are 10ndash15 higherthan CAAS case results
6 Science and Technology of Nuclear Installations
127E14 minus 264E14
613E13 minus 127E14
295E13 minus 613E13
142E13 minus 295E13
685E12 minus 142E13
330E12 minus 685E12
159E12 minus 330E12
765E11 minus 159E12
369E11 minus 765E11
178E11 minus 369E11
856E10 minus 178E11
412E10 minus 856E10
199E10 minus 412E10
956E09 minus 199E10
461E09 minus 956E09
Sampled neutronsTotal sampled neutronsValues
Figure 5 Biased source distribution (front half removed)
Values252E-02 minus 717E-02886E-03 minus 252E-02311E-03 minus 886E-03110E-03 minus 311E-03385E-04 minus 110E-031355E-04 minus 385E-04476E-05 minus 135E-04167E-05 minus 476E-05588E-06 minus 167E-05207E-06 minus 588E-06
256E-07 minus 727E-07727E-07 minus 207E-06
899E-08 minus 256E-07316E-08 minus 899E-08111E-08 minus 316E-08
Group 1Neutron target
Figure 6 Mesh-based importance map (front quarter removed)
Values136E15 minus 576E153233E14 minus 136E15764E13 minus 323E14181E13 minus 764E13
240E11 minus 101E12101E12 minus 428E12428E12 minus 181E13
568E10 minus 240E11134E10 minus 568E10318E09 minus 134E10753E08 minus 318E09178E08 minus 753E08
236E06 minus 998E06
422E07 minus 178E08998E06 minus 422E07
Neutron fluxTotal neutron flux
Figure 7 Neutron flux mesh tally (front quarter removed)
5 Discussion of Results
All obtained results are in accordance with calculationaluncertainty criterion from US NRC Regulatory Guide 1190the calculated reaction rates agree with the measurementsto within 20 for out-of-core dosimetry locations Under
prediction in CM ratio can be observed for 238U(n f)137Cs(145MeV threshold) through the thick RPV simulator (fromlocations A4 to A6) with 08 on average High attenuationof neutron flux in that area (around 700 for IRDF-2002) willcause softening of neutron spectrum inRPV simulator whichshifts neutrons in resonance regions for inelastic scattering
Science and Technology of Nuclear Installations 7
000076
000001
14ndash7
19ndash7
26ndash11
Figure 8 Neutron flux mesh tally in axial midplane (MCNP5 criti-cality results)
08
085
09
095
1
10511
Detector position (cm)
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE6 IRDF-2002
SCALE6 IRDF-90v2DORT BUGLE-93
DORT SAILOR-95DORT BUGLE-96
10 15 20 25 30 35 40 45 5550 60
Figure 9 Average DORT [2] and SCALE60 (CAAS case) CMratios for detectors
on iron Microscopic cross-section for neutron inelasticscattering on iron is shown in Figure 11 Results for 238U(nf)137Cs indicate self-shielding effects that is sensitivity ofmultigroup shielding library v7 200n47g on the iron cross-sections
Overprediction in results is highest for detector A2immediately after stainless steel thermal shield which haslarge amount of iron Again self-shielding effects of ironcross-sections are pronounced especially for 27Al(n 120572)24Na(IRDF-90v2) with CM of 117 The IRDF-90v2 library gen-erally gives the highest values while SCALE60 v7 200n47glibrary gives the lowest values of calculated fluxesThe IRDF-2002 results are right in the middle so this library wouldbe favorable for RPV dosimetry calculations The obtainedcalculational results show overall a good agreement withexperimental results however for distant detectors fromPCA core there is under prediction less than 10 on averageexcept excellent result for 27Al(n 120572)24Na
An important issue that has to be addressed whendiscussing Monte Carlo method is a burden the appliedcalculational model will place on memory resources andCPU time requirements For that purpose the figure-of-merit (FOM) factor [17] is defined to account for the time it
08085
09095
1105
11115
12
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE IRDF-2002SCALE IRDF-90v2DORT BUGLE-93DORT SAILOR-95
DORT BUGLE-96
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
Figure 10 Average DORT [2] and SCALE60 (Watt spectrum case)CM ratios for detectors
11
1
1
102
102
10minus4
10minus4
10minus2
10minus2
10minus10
10minus10
10minus5
10minus5
Cros
s sec
tion
(bar
ns)
Incident energy (MeV)
Figure 11 Inelastic scattering on iron [19]
takes to achieve a given level of uncertainty in Monte Carlocalculation
FOM =1
1198771198642sdot 119879
(6)
where 119877119864 and 119879 are Monte Carlo relative error (on 1 sigmalevel) and Monte Carlo CPU run time (in min) respectivelyMAVRIC run time for highest energy threshold reaction(5MeV for 27Al(n 120572)24Na) was 7 h while for the lowest(01MeV for 103Rh(n n1015840)103mRh) was 10 h In this paper allcalculations have been performed on QuadCore Q6600 with8GB of RAM FOM factors for IRDF-2002 and CAAS caseare shown in Figure 12 Application of automated variancereduction technique based on adjoint fluxes removes theburden of manually tuning VR parameters and significantlyimproves the quality of Monte Carlo calculations
6 Conclusion
The analysis of the PCA benchmark has been performedusing the SCALE60 code package The calculational mod-els of the PCA benchmark within CSAS6 and MAVRICsequences of SCALE60 have been determined The results
8 Science and Technology of Nuclear Installations
Table1Eq
uivalent
fissio
nflu
xes(per1
PCAcore
fissio
nneutronpersecon
d(cmminus2 ))
Detector
locatio
nRe
spon
sefunctio
ndata
237 N
p(n
f)137 C
sCM
238 U
(nf)1
37Cs
CM
103 R
h(n
n1015840)103119898Rh
CM
115 In(n
n1015840)115119898Inloz
CM
58Ni(n
p)5
8 Co
CM
27Al(n
120572)2
4 Na
CM
A1
ENDFB-VII0
664sdot10minus6plusmn113
099
544sdot10minus6plusmn071
lowast507sdot10minus6plusmn068
090
554sdot10minus6plusmn059
095
857sdot10minus6plusmn042
109
IRDF-2002
683sdot10minus6plusmn139
103
552sdot10minus6plusmn068
lowast554sdot10minus6plusmn099
099
534sdot10minus6plusmn072
095
565sdot10minus6plusmn061
097
859sdot10minus6plusmn049
109
IRDF-90v2
653sdot10minus6plusmn115
098
558sdot10minus6plusmn068
lowast549sdot10minus6plusmn078
099
534sdot10minus6plusmn061
095
572sdot10minus6plusmn066
098
895sdot10minus6plusmn061
113
A2
ENDFB-VII0
837sdot10minus7plusmn277
lowast620sdot10minus7plusmn069
lowast573sdot10minus7plusmn062
095
616sdot10minus7plusmn060
099
115sdot10minus6plusmn078
113
IRDF-2002
795sdot10minus7plusmn099
lowast627sdot10minus7plusmn073
lowast646sdot10minus7plusmn079
lowast613sdot10minus7plusmn076
101
639sdot10minus7plusmn065
103
116sdot10minus6plusmn071
113
IRDF-90v2
786sdot10minus7plusmn151
lowast631sdot10minus7plusmn066
lowast653sdot10minus7plusmn079
lowast614sdot10minus7plusmn061
101
635sdot10minus7plusmn062
103
120sdot10minus6plusmn074
117
A3
ENDFB-VII0
211sdot10minus7plusmn102
093
181sdot10minus7plusmn062
lowast162sdot10minus7plusmn059
081
199sdot10minus7plusmn068
086
437sdot10minus7plusmn055
097
IRDF-2002
218sdot10minus7plusmn111
096
181sdot10minus7plusmn059
lowast176sdot10minus7plusmn072
lowast172sdot10minus7plusmn062
087
204sdot10minus7plusmn060
088
440sdot10minus7plusmn056
098
IRDF-90v2
204sdot10minus7plusmn078
090
184sdot10minus7plusmn061
lowast176sdot10minus7plusmn067
lowast172sdot10minus7plusmn061
087
204sdot10minus7plusmn059
088
455sdot10minus7plusmn059
101
A4
ENDFB-VII0
907sdot10minus8plusmn056
098
533sdot10minus8plusmn065
087
531sdot10minus8plusmn067
090
482sdot10minus8plusmn084
091
107sdot10minus7plusmn115
105
IRDF-2002
916sdot10minus8plusmn054
099
542sdot10minus8plusmn069
089
750sdot10minus8plusmn055
097
563sdot10minus8plusmn063
096
487sdot10minus8plusmn085
092
107sdot10minus7plusmn117
105
IRDF-90v2
900sdot10minus8plusmn053
097
561sdot10minus8plusmn079
092
751sdot10minus8plusmn052
097
575sdot10minus8plusmn061
098
497sdot10minus8plusmn079
094
111sdot10minus7plusmn129
108
A5
ENDFB-VII0
495sdot10minus8plusmn049
095
223sdot10minus8plusmn063
081
236sdot10minus7plusmn058
086
182sdot10minus8plusmn073
087
417sdot10minus8plusmn115
102
IRDF-2002
495sdot10minus8plusmn048
096
226sdot10minus8plusmn073
082
393sdot10minus8plusmn048
090
252sdot10minus8plusmn058
091
182sdot10minus8plusmn068
087
413sdot10minus8plusmn098
101
IRDF-90v2
496sdot10minus8plusmn047
096
233sdot10minus8plusmn062
085
401sdot10minus8plusmn047
092
257sdot10minus8plusmn055
093
189sdot10minus8plusmn067
090
428sdot10minus8plusmn102
104
A6
ENDFB-VII0
247sdot10minus8plusmn051
091
867sdot10minus9plusmn059
077
986sdot10minus9plusmn054
084
652sdot10minus9plusmn065
088
155sdot10minus8plusmn089
101
IRDF-2002
249sdot10minus8plusmn049
092
873sdot10minus9plusmn060
078
195sdot10minus8plusmn056
089
105sdot10minus8plusmn053
089
665sdot10minus9plusmn083
090
155sdot10minus8plusmn091
101
IRDF-90v2
250sdot10minus8plusmn047
092
916sdot10minus9plusmn059
082
199sdot10minus8plusmn048
091
109sdot10minus8plusmn054
093
691sdot10minus9plusmn067
093
160sdot10minus8plusmn089
103
A7
ENDFB-VII0
630sdot10minus9plusmn077
087
189sdot10minus9plusmn103
lowast223sdot10minus9plusmn093
lowast140sdot10minus9plusmn106
lowast358sdot10minus9plusmn107
lowast
IRDF-2002
634sdot10minus9plusmn086
087
186sdot10minus9plusmn073
lowast487sdot10minus9plusmn062
lowast237sdot10minus9plusmn071
lowast137sdot10minus9plusmn093
lowast350sdot10minus9plusmn089
lowast
IRDF-90v2
640sdot10minus9plusmn074
088
198sdot10minus9plusmn101
lowast507sdot10minus9plusmn081
lowast250sdot10minus9plusmn079
lowast143sdot10minus9plusmn083
lowast368sdot10minus9plusmn100
lowast
lozEN
DFB-VI8
datawas
used
fore
xtractionof
crosssectio
nldquoin
elastic
tometastablerdquoiso
mer
115 In(n
n1015840)115119898In
lowastEx
perim
entald
atan
otprovided
inPC
Abenchm
ark
Science and Technology of Nuclear Installations 9
0
20
40
60
80
100
FOM
fact
or
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
27Al(n 120572)103Rh(n n998400)
238U(n f)
115In(n n998400)58Ni(n p)
237Np(n f)
Figure 12 FOM factors for IRDF-2002 (CAAS case)
of calculations using the established models have been com-pared with PCA benchmark data A good agreement of thecalculated and measured equivalent fission fluxes has beenobtained No systematic decrease of agreements betweencalculations and measurements with increasing distance ofdetector from the PCA benchmark facility core was observedfor any of the applied approaches This indicates that theshapes of calculated neutron spectra in the energy rangeweredosimeters are sensitive are properly determined SCALE60capabilities in generationmixing cross-sections from work-ing library v7 200n47g to be used as a response functions inMAVRIC proved to be very useful
References
[1] ldquoShielding Integral Benchmark Archive and Databaserdquo SINBADReactor Shielding Benchmark Experiments OECDNEA 2011
[2] I Remec and F B Kam ldquoPool Critical Assembly Pressure Ves-sel Facility Benchmarkrdquo NUREGCR-6454 (ORNLTM-13205)prepared for the USNRC by Oak Ridge National LaboratoryAugust 1997
[3] A H Fero S L Anderson and G K Roberts ldquoAnalysis ofthe ORNL PCA benchmark using TORT and BUGLE-96rdquoin Reactor Dosimetry Radiation Metrology and Assessment JG Williams D W Vehar F H Ruddy and D M GilliamEds pp 360ndash366 American Society for Testing and MaterialsPhiladelphia Pa USA 2001
[4] Y K Lee ldquoAnalysis of the NRC PCA pressure vessel dosimetrybenchmark using TRIPOLI-43 Monte Carlo code and ENDFB-VI4 JEF22 and IRDF-90 librariesrdquo Nuclear Mathematical andComputational Science ACentury in Review ACenturyAnewGatlinburg Tenn USA April 2003
[5] ldquoSCALE A Modular Code System for Performing Standard-ized Computer Analyses for Licensing Evaluationrdquo ORNLTM-200539 Version 6 Radiation Safety Information Computa-tional Center at Oak Ridge National Laboratory 2009
[6] D VragolovMMatijevic andD Pevec ldquoModeling of pool crit-ical assembly pressure vessel facility benchmarkrdquo in Proceedingsof the International Conference Nuclear Energy for New EuropeLjubljana Slovenia 2010
[7] J M Risner D Wiarda M E Dunn T M Miller D E Peplowand B W Patton ldquoProduction and Testing of the VITAMIN-B7 Fine-Group and BUGLE-B7 Broad-Group Coupled Neu-tronGamma Cross-Section Libraries Derived from ENDFB-VII0 Nuclear Datardquo USNRC NUREGCR-7045 2011
[8] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File 2002 (IRDF-2002) 2006
[9] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File (IRDF-90 Version 2) 1993
[10] USNRCCalculational andDosimetryMethods forDeterminingPressure Vessel Neutron Fluence Regulatory Guide 1190 2001
[11] I Remec and F B K Kam ldquoHB Robinson-2 Pressure VesselBenchmarkrdquo NUREGCR-6453 (ORNLTM-13204) preparedfor the USNRC by Oak Ridge National Laboratory October1997
[12] J C Wagner and A Haghighat ldquoAutomated variance reductionof Monte Carlo shielding calculations using the discrete ordi-nates adjoint functionrdquo Nuclear Science and Engineering vol128 no 2 pp 186ndash208 1998
[13] J C Wagner E D Blakeman and D E Peplow ldquoForward-weighted CADIS method for global variance reductionrdquo Trans-actions of the American Nuclear Society vol 97 pp 630ndash6332007
[14] G I Bell and S Glasstone Nuclear Reactor Theory VanNostrand Reinhold Company Litton Educational Publishing1970
[15] J C Wagner Acceleration of Monte Carlo shielding calculationswith an automated variance reduction technique and parallel pro-cessing [PhD thesis] Pennsylvania State University UniversityPark Pa USA 1997
[16] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technologyrdquoNuclear Data Sheets vol 107 no 12 pp2931ndash3060 2006
[17] X-5 Monte Carlo Team MCNPmdashA General N-Particle Trans-port Code Version 5 vol 1 of Overview andTheory LA-UR-03-1987 Los Alamos National Laboratory 2003
[18] A Trkov M Herman and D A Brown ldquoENDF-6 FormatsManualrdquo Data Formats and Procedures for the EvaluatedNuclear Data Files ENDFB-VI and ENDFB-VII NationalNuclear Data Center Brookhaven National Laboratory 2011
[19] IAEA Nuclear Data Services httpwww-ndsiaeaorg
TribologyAdvances in
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Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal of
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Submit your manuscripts athttpwwwhindawicom
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International Journal of
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
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Wind EnergyJournal of
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Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
4 Science and Technology of Nuclear Installations
source and transport importance map to be used as a VRin Monaco CADIS is used to optimize results in localizedregions of phase-space while FW-CADIS tends to obtainglobal uniform statistical uncertainty by weighting of theadjoint source with expected detector response approximatedwith forward Denovo solution CADIS and FW-CADIS arebased on the adjoint function [14] (ie solution of the adjointBoltzmann equation) which has long been recognized as theimportance function for some objective function of interestDetector response is found by integrating the product ofthe detector cross-section 120590
119889( 119903 119864) and flux over detector
volume
119877 = int119881119863
int119864
120590119889( 119903 119864) 120601 ( 119903 119864) 119889119881119889119864 (1)
Alternatively if we approximate adjoint scalar flux with quickDenovo solution where the adjoint source is set as 119902dagger( 119903 119864) =120590119889( 119903 119864) then the detector response is found by integrating
over source volume
119877 = int119881119878
int119864
119902 ( 119903 119864) 120601dagger( 119903 119864) 119889119881119889119864 (2)
The biased source distribution [15] which minimizes thevariance of user-desired response is given as
119902 ( 119903 119864) =120601dagger( 119903 119864) 119902 ( 119903 119864)
119877 (3)
where 120601dagger( 119903 119864) 119902( 119903 119864) and 119877 are the scalar adjoint functionthe source emission probability (forward source) and totaldetector response from (2) respectively For transport biasingthe weight window technique is employed that is space-energy dependent geometric splittingroulette Biased sourceand weight-window lower bounds are consistent so thesource particles are created with statistical weight withinweight windows
119908 ( 119903 119864) =119902 ( 119903 119864)
119902 ( 119903 119864)=
119877
120601dagger ( 119903 119864) (4)
Inverse relationship between particle statistical weight andadjoint functionmust be emphasized Since PCA Benchmarkinvolves calculation of near and far detector reaction ratesthis FW-CADIS methodology is highly desirable choice
33 Cross-Section Libraries There are several multigroupcross-section libraries distributed within SCALE60 for criti-cality safety analyses and shielding calculations For criticalitysafety analyses the v7-238 library [5] was used while for theshielding calculations v7-200n47g library [5] was used Theyare based on ENDFB-VII0 data [16] For shielding part ofcalculations it was imperative to use fine structure libraryv7 200n47g because high-energy threshold for all reactionscould not be correctly accounted for if broad shieldingv7 27n19g library was used
4 Analysis of the PCA Benchmark
The calculational models of the PCA benchmark withinCSAS6 and MAVRIC sequences of SCALE60 code package
have been determined The results of the calculations that isequivalent fission fluxes using the established models havebeen compared with the PCA benchmark data
41 CSAS6 Results The initial CSAS6KENO-VI criticalityeigenvalue calculation of the PCA benchmark facility wasperformed using 550 batches and 2000 neutrons per batchwith first 50 batches skipped in order for the fission sourcedistribution to converge to eigenmode Critical control rodpositions were validated and obtained effective multiplica-tion factor of the system was 119896eff = (099856 plusmn 000071)This result was tested with MCNP5 code [17] Shannonentropy check for source stationarity was successful andsimilar 119896eff was obtained 119896eff = (099911 plusmn 000051) ThisCSAS6KENO-VI calculation was then rerun with betterstatistics (2150 batches10000 neutrons per batch) for thegeneration of mesh-based fission source distribution (ldquoCDS= YESrdquo option) to be used as a criticality source in the subse-quent MAVRIC calculations This approach in SCALE60 isknown as CAAS (Criticality Accident Alarm Systems)
42 MAVRICMonaco Results The MAVRIC shielding se-quence was run with the mesh-based source from criticalityeigenvalue run FW-CADIS methodology provides consis-tentweightwindows (ie importancemap) and biased sourcedistributions for transport of the PCA core neutrons to thelocations of interest detectors in experimental access tubesA1ndashA7
The equivalent fission fluxes in PCA report were cal-culated by dividing the reaction rates by the cross-sectionsaveraged over the 235U fission spectrum That fast neutronfluence calculation was reasonable approach in the time ofPCA Benchmark calculation with DORT but full spectrumcalculation nowadays with modern Monte Carlo code is notprohibitive So our calculations were conducted with fullneutron spectrum in accordance with SCALE60 multigroupweighting function (spectrum) [2] defined as
(1) Maxwellian spectrum (peak at 300K) from 10minus5 to0125 eV
(2) a 1119864 spectrum from 0125 eV to 674 keV(3) a fission spectrum (effective temperature at 1273
MeV) from 674 keV to 10MeV(4) a 1119864 spectrum from 10 to 20MeV
Equivalent fission fluxes thus are defined as
120601eq =int119864120590119894(119864) 120601 (119864) 119889119864
int119864120590119894(119864) 120593 (119864) 119889119864 int
119864120593 (119864) 119889119864
=reaction rates
120590119894
(5)
where 120590119894(119864) 120601(119864) and 120593(119864) are the dosimetry cross-sections
for the reactions being considered the Monte Carlo flux atthe dosimetry location and weighting spectrum functionrespectively The spectrum averaged cross-sections (120590
119894) were
taken from Table 16 from PCA report [2] for consistencysince they are in very good agreement with calculated valuesfrom our libraries
Science and Technology of Nuclear Installations 5
For seven detector locations (A1ndashA7) we used twodosimetry libraries as a source of a response functionsfor reaction rate calculations Reaction rate calculationswere done with IRDF-2002 and IRDF-90v2 (older version)libraries for the total of six PCA benchmark reactions237Np(n f)137Cs 238U(n f)137Cs 103Rh(n n1015840)103mRh 115In(nn1015840)115mIn 58Ni(n p)58Co and 27Al(n120572)24NaThese reactionswere defined as a response functions for FW-CADISmethod-ology
The threshold energies for the 27Al(n 120572)24Na 58Ni(np)58Co 238U(n f)137Cs 237Np(n f)137Cs 115In(n n1015840)115mInand 103Rh(n n1015840)103mRh reactions are 50 205 145 06903 and 01MeV respectively This is in fast neutron rangebut still calculations were performed for full neutron spec-trum (10minus5 eV to 20MeV) with fine-group shielding libraryv7 200n47g
Also we investigated SCALE60 capabilities in genera-tionmixing of multigroup cross-sections from v7 200n47glibrary for reactions 237Np(n f)137Cs 238U(n f)137Cs 58Ni(np)58Co and 27Al(n 120572)24Na using AJAX and PALEALEutility modules of AMPX working library Reaction 115In(nn1015840)115mIn was derived from ENDFB-VI8 while reaction103Rh(n n1015840)103mRh was not derived because there is no singleor combination of reaction type numbers [18] (MT numbersin ENDFB) for computation of production rate ofmetastableisomer of rhodium (first excited state resulting from inelasticscattering) The obtained multigroup cross-sections withoutrhodium are Doppler and resonances corrected and haveMAVRIC shielding structure of 200n47g These reactionswere also defined as a response functions for FW-CADISmethodology
Two different approaches for the MAVRIC source distri-bution were
(1) fission distribution in space and energy determinedby KENO-VI calculation (transferred as a sourceinput into MAVRIC)mdashCAAS case
(2) Watt spectrum [5] for source energy distribution119901(119864) = 119862119890
minus119864119886 sinh(radic119887119864) (we used thermal fissionof 235U with 119886 = 1028MeV and 119887 = 2249MeV)with uniform space sampling restricted to the reactorcoremdashWatt spectrum case
The total number of neutron batches was 2000 with 2000neutrons per batch for MAVRIC sequence The Denovo 119878
119873
mesh had approximately 20000 cells over PCA facility modelthat is 48 times 23 times 18 cells in 119909119910119911 direction with average cellside of 32 cm while Monaco Monte Carlo mesh had 36000cells (60 times 30 times 20) with average cell side of 26 cm We used1198788as quadrature order and119875
3for Legendre order of scattering
cross-section expansion (upscatteringwas deactivated) Sincethe axial flux gradients inside tubes are confirmed to besufficiently small the user-selected height of plusmn15 cm forvolumetric cylindrical tally regions in MAVRIC calculationrepresents a good compromise between Monte Carlo relativeerror and spatial description of PCA benchmark facilityDifferential small void cylinders were also placed in themidplane (119911 = 0) of the access tubes Point detectors andregion track length estimators were used to find multigroup
1E16
1E15
1E14
1E13
1E12
1E11
1E10
1E09
minus50
minus100
50
x axis (cm) 0
Neu
tron
forw
ard
flux
(nc
m3 s
)
Figure 3 Denovo forward neutron flux axial distribution (front halfremoved)
1E minus 02
1E minus 03
1E minus 04
1E minus 05
1E minus 06
1E minus 07
1E minus 08
1E minus 09
1E minus 10
minus50
minus100
50
0x axis (cm)
Neu
tron
adjo
int fl
ux (n
cm
2s
)
Figure 4 Denovo adjoint neutron flux axial distribution (front halfremoved)
neutron fluxes reaction rates and finally equivalent fissionfluxes
The elements of the FW-CADIS methodology aredepicted next Forward and adjoint neutron flux axial dis-tribution from Denovo code for CAAS case are shown inFigures 3 and 4 respectively Biased source distribution andmesh-based importance map are shown in Figures 5 and 6respectively Total Monte Carlo neutron flux in form of meshtally is depicted in Figures 7 and 8
The calculated equivalent fission fluxes with Monte Carlorelative error (1 sigma level) for PCA Benchmark are givenin Table 1 for MAVRIC CAAS case Only the reactions forwhich the measurements were done are listed AveragedCM ratios for detectors A1ndashA7 are shown in Figure 9 forCAAS case and in Figure 10 for Watt spectrum case Theseresults are compared to the referencedDORT results [2] Onecan notice high similarity between Monaco results for twodifferent source distribution approaches The Watt spectrumcase results aremore conservative and they are 10ndash15 higherthan CAAS case results
6 Science and Technology of Nuclear Installations
127E14 minus 264E14
613E13 minus 127E14
295E13 minus 613E13
142E13 minus 295E13
685E12 minus 142E13
330E12 minus 685E12
159E12 minus 330E12
765E11 minus 159E12
369E11 minus 765E11
178E11 minus 369E11
856E10 minus 178E11
412E10 minus 856E10
199E10 minus 412E10
956E09 minus 199E10
461E09 minus 956E09
Sampled neutronsTotal sampled neutronsValues
Figure 5 Biased source distribution (front half removed)
Values252E-02 minus 717E-02886E-03 minus 252E-02311E-03 minus 886E-03110E-03 minus 311E-03385E-04 minus 110E-031355E-04 minus 385E-04476E-05 minus 135E-04167E-05 minus 476E-05588E-06 minus 167E-05207E-06 minus 588E-06
256E-07 minus 727E-07727E-07 minus 207E-06
899E-08 minus 256E-07316E-08 minus 899E-08111E-08 minus 316E-08
Group 1Neutron target
Figure 6 Mesh-based importance map (front quarter removed)
Values136E15 minus 576E153233E14 minus 136E15764E13 minus 323E14181E13 minus 764E13
240E11 minus 101E12101E12 minus 428E12428E12 minus 181E13
568E10 minus 240E11134E10 minus 568E10318E09 minus 134E10753E08 minus 318E09178E08 minus 753E08
236E06 minus 998E06
422E07 minus 178E08998E06 minus 422E07
Neutron fluxTotal neutron flux
Figure 7 Neutron flux mesh tally (front quarter removed)
5 Discussion of Results
All obtained results are in accordance with calculationaluncertainty criterion from US NRC Regulatory Guide 1190the calculated reaction rates agree with the measurementsto within 20 for out-of-core dosimetry locations Under
prediction in CM ratio can be observed for 238U(n f)137Cs(145MeV threshold) through the thick RPV simulator (fromlocations A4 to A6) with 08 on average High attenuationof neutron flux in that area (around 700 for IRDF-2002) willcause softening of neutron spectrum inRPV simulator whichshifts neutrons in resonance regions for inelastic scattering
Science and Technology of Nuclear Installations 7
000076
000001
14ndash7
19ndash7
26ndash11
Figure 8 Neutron flux mesh tally in axial midplane (MCNP5 criti-cality results)
08
085
09
095
1
10511
Detector position (cm)
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE6 IRDF-2002
SCALE6 IRDF-90v2DORT BUGLE-93
DORT SAILOR-95DORT BUGLE-96
10 15 20 25 30 35 40 45 5550 60
Figure 9 Average DORT [2] and SCALE60 (CAAS case) CMratios for detectors
on iron Microscopic cross-section for neutron inelasticscattering on iron is shown in Figure 11 Results for 238U(nf)137Cs indicate self-shielding effects that is sensitivity ofmultigroup shielding library v7 200n47g on the iron cross-sections
Overprediction in results is highest for detector A2immediately after stainless steel thermal shield which haslarge amount of iron Again self-shielding effects of ironcross-sections are pronounced especially for 27Al(n 120572)24Na(IRDF-90v2) with CM of 117 The IRDF-90v2 library gen-erally gives the highest values while SCALE60 v7 200n47glibrary gives the lowest values of calculated fluxesThe IRDF-2002 results are right in the middle so this library wouldbe favorable for RPV dosimetry calculations The obtainedcalculational results show overall a good agreement withexperimental results however for distant detectors fromPCA core there is under prediction less than 10 on averageexcept excellent result for 27Al(n 120572)24Na
An important issue that has to be addressed whendiscussing Monte Carlo method is a burden the appliedcalculational model will place on memory resources andCPU time requirements For that purpose the figure-of-merit (FOM) factor [17] is defined to account for the time it
08085
09095
1105
11115
12
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE IRDF-2002SCALE IRDF-90v2DORT BUGLE-93DORT SAILOR-95
DORT BUGLE-96
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
Figure 10 Average DORT [2] and SCALE60 (Watt spectrum case)CM ratios for detectors
11
1
1
102
102
10minus4
10minus4
10minus2
10minus2
10minus10
10minus10
10minus5
10minus5
Cros
s sec
tion
(bar
ns)
Incident energy (MeV)
Figure 11 Inelastic scattering on iron [19]
takes to achieve a given level of uncertainty in Monte Carlocalculation
FOM =1
1198771198642sdot 119879
(6)
where 119877119864 and 119879 are Monte Carlo relative error (on 1 sigmalevel) and Monte Carlo CPU run time (in min) respectivelyMAVRIC run time for highest energy threshold reaction(5MeV for 27Al(n 120572)24Na) was 7 h while for the lowest(01MeV for 103Rh(n n1015840)103mRh) was 10 h In this paper allcalculations have been performed on QuadCore Q6600 with8GB of RAM FOM factors for IRDF-2002 and CAAS caseare shown in Figure 12 Application of automated variancereduction technique based on adjoint fluxes removes theburden of manually tuning VR parameters and significantlyimproves the quality of Monte Carlo calculations
6 Conclusion
The analysis of the PCA benchmark has been performedusing the SCALE60 code package The calculational mod-els of the PCA benchmark within CSAS6 and MAVRICsequences of SCALE60 have been determined The results
8 Science and Technology of Nuclear Installations
Table1Eq
uivalent
fissio
nflu
xes(per1
PCAcore
fissio
nneutronpersecon
d(cmminus2 ))
Detector
locatio
nRe
spon
sefunctio
ndata
237 N
p(n
f)137 C
sCM
238 U
(nf)1
37Cs
CM
103 R
h(n
n1015840)103119898Rh
CM
115 In(n
n1015840)115119898Inloz
CM
58Ni(n
p)5
8 Co
CM
27Al(n
120572)2
4 Na
CM
A1
ENDFB-VII0
664sdot10minus6plusmn113
099
544sdot10minus6plusmn071
lowast507sdot10minus6plusmn068
090
554sdot10minus6plusmn059
095
857sdot10minus6plusmn042
109
IRDF-2002
683sdot10minus6plusmn139
103
552sdot10minus6plusmn068
lowast554sdot10minus6plusmn099
099
534sdot10minus6plusmn072
095
565sdot10minus6plusmn061
097
859sdot10minus6plusmn049
109
IRDF-90v2
653sdot10minus6plusmn115
098
558sdot10minus6plusmn068
lowast549sdot10minus6plusmn078
099
534sdot10minus6plusmn061
095
572sdot10minus6plusmn066
098
895sdot10minus6plusmn061
113
A2
ENDFB-VII0
837sdot10minus7plusmn277
lowast620sdot10minus7plusmn069
lowast573sdot10minus7plusmn062
095
616sdot10minus7plusmn060
099
115sdot10minus6plusmn078
113
IRDF-2002
795sdot10minus7plusmn099
lowast627sdot10minus7plusmn073
lowast646sdot10minus7plusmn079
lowast613sdot10minus7plusmn076
101
639sdot10minus7plusmn065
103
116sdot10minus6plusmn071
113
IRDF-90v2
786sdot10minus7plusmn151
lowast631sdot10minus7plusmn066
lowast653sdot10minus7plusmn079
lowast614sdot10minus7plusmn061
101
635sdot10minus7plusmn062
103
120sdot10minus6plusmn074
117
A3
ENDFB-VII0
211sdot10minus7plusmn102
093
181sdot10minus7plusmn062
lowast162sdot10minus7plusmn059
081
199sdot10minus7plusmn068
086
437sdot10minus7plusmn055
097
IRDF-2002
218sdot10minus7plusmn111
096
181sdot10minus7plusmn059
lowast176sdot10minus7plusmn072
lowast172sdot10minus7plusmn062
087
204sdot10minus7plusmn060
088
440sdot10minus7plusmn056
098
IRDF-90v2
204sdot10minus7plusmn078
090
184sdot10minus7plusmn061
lowast176sdot10minus7plusmn067
lowast172sdot10minus7plusmn061
087
204sdot10minus7plusmn059
088
455sdot10minus7plusmn059
101
A4
ENDFB-VII0
907sdot10minus8plusmn056
098
533sdot10minus8plusmn065
087
531sdot10minus8plusmn067
090
482sdot10minus8plusmn084
091
107sdot10minus7plusmn115
105
IRDF-2002
916sdot10minus8plusmn054
099
542sdot10minus8plusmn069
089
750sdot10minus8plusmn055
097
563sdot10minus8plusmn063
096
487sdot10minus8plusmn085
092
107sdot10minus7plusmn117
105
IRDF-90v2
900sdot10minus8plusmn053
097
561sdot10minus8plusmn079
092
751sdot10minus8plusmn052
097
575sdot10minus8plusmn061
098
497sdot10minus8plusmn079
094
111sdot10minus7plusmn129
108
A5
ENDFB-VII0
495sdot10minus8plusmn049
095
223sdot10minus8plusmn063
081
236sdot10minus7plusmn058
086
182sdot10minus8plusmn073
087
417sdot10minus8plusmn115
102
IRDF-2002
495sdot10minus8plusmn048
096
226sdot10minus8plusmn073
082
393sdot10minus8plusmn048
090
252sdot10minus8plusmn058
091
182sdot10minus8plusmn068
087
413sdot10minus8plusmn098
101
IRDF-90v2
496sdot10minus8plusmn047
096
233sdot10minus8plusmn062
085
401sdot10minus8plusmn047
092
257sdot10minus8plusmn055
093
189sdot10minus8plusmn067
090
428sdot10minus8plusmn102
104
A6
ENDFB-VII0
247sdot10minus8plusmn051
091
867sdot10minus9plusmn059
077
986sdot10minus9plusmn054
084
652sdot10minus9plusmn065
088
155sdot10minus8plusmn089
101
IRDF-2002
249sdot10minus8plusmn049
092
873sdot10minus9plusmn060
078
195sdot10minus8plusmn056
089
105sdot10minus8plusmn053
089
665sdot10minus9plusmn083
090
155sdot10minus8plusmn091
101
IRDF-90v2
250sdot10minus8plusmn047
092
916sdot10minus9plusmn059
082
199sdot10minus8plusmn048
091
109sdot10minus8plusmn054
093
691sdot10minus9plusmn067
093
160sdot10minus8plusmn089
103
A7
ENDFB-VII0
630sdot10minus9plusmn077
087
189sdot10minus9plusmn103
lowast223sdot10minus9plusmn093
lowast140sdot10minus9plusmn106
lowast358sdot10minus9plusmn107
lowast
IRDF-2002
634sdot10minus9plusmn086
087
186sdot10minus9plusmn073
lowast487sdot10minus9plusmn062
lowast237sdot10minus9plusmn071
lowast137sdot10minus9plusmn093
lowast350sdot10minus9plusmn089
lowast
IRDF-90v2
640sdot10minus9plusmn074
088
198sdot10minus9plusmn101
lowast507sdot10minus9plusmn081
lowast250sdot10minus9plusmn079
lowast143sdot10minus9plusmn083
lowast368sdot10minus9plusmn100
lowast
lozEN
DFB-VI8
datawas
used
fore
xtractionof
crosssectio
nldquoin
elastic
tometastablerdquoiso
mer
115 In(n
n1015840)115119898In
lowastEx
perim
entald
atan
otprovided
inPC
Abenchm
ark
Science and Technology of Nuclear Installations 9
0
20
40
60
80
100
FOM
fact
or
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
27Al(n 120572)103Rh(n n998400)
238U(n f)
115In(n n998400)58Ni(n p)
237Np(n f)
Figure 12 FOM factors for IRDF-2002 (CAAS case)
of calculations using the established models have been com-pared with PCA benchmark data A good agreement of thecalculated and measured equivalent fission fluxes has beenobtained No systematic decrease of agreements betweencalculations and measurements with increasing distance ofdetector from the PCA benchmark facility core was observedfor any of the applied approaches This indicates that theshapes of calculated neutron spectra in the energy rangeweredosimeters are sensitive are properly determined SCALE60capabilities in generationmixing cross-sections from work-ing library v7 200n47g to be used as a response functions inMAVRIC proved to be very useful
References
[1] ldquoShielding Integral Benchmark Archive and Databaserdquo SINBADReactor Shielding Benchmark Experiments OECDNEA 2011
[2] I Remec and F B Kam ldquoPool Critical Assembly Pressure Ves-sel Facility Benchmarkrdquo NUREGCR-6454 (ORNLTM-13205)prepared for the USNRC by Oak Ridge National LaboratoryAugust 1997
[3] A H Fero S L Anderson and G K Roberts ldquoAnalysis ofthe ORNL PCA benchmark using TORT and BUGLE-96rdquoin Reactor Dosimetry Radiation Metrology and Assessment JG Williams D W Vehar F H Ruddy and D M GilliamEds pp 360ndash366 American Society for Testing and MaterialsPhiladelphia Pa USA 2001
[4] Y K Lee ldquoAnalysis of the NRC PCA pressure vessel dosimetrybenchmark using TRIPOLI-43 Monte Carlo code and ENDFB-VI4 JEF22 and IRDF-90 librariesrdquo Nuclear Mathematical andComputational Science ACentury in Review ACenturyAnewGatlinburg Tenn USA April 2003
[5] ldquoSCALE A Modular Code System for Performing Standard-ized Computer Analyses for Licensing Evaluationrdquo ORNLTM-200539 Version 6 Radiation Safety Information Computa-tional Center at Oak Ridge National Laboratory 2009
[6] D VragolovMMatijevic andD Pevec ldquoModeling of pool crit-ical assembly pressure vessel facility benchmarkrdquo in Proceedingsof the International Conference Nuclear Energy for New EuropeLjubljana Slovenia 2010
[7] J M Risner D Wiarda M E Dunn T M Miller D E Peplowand B W Patton ldquoProduction and Testing of the VITAMIN-B7 Fine-Group and BUGLE-B7 Broad-Group Coupled Neu-tronGamma Cross-Section Libraries Derived from ENDFB-VII0 Nuclear Datardquo USNRC NUREGCR-7045 2011
[8] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File 2002 (IRDF-2002) 2006
[9] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File (IRDF-90 Version 2) 1993
[10] USNRCCalculational andDosimetryMethods forDeterminingPressure Vessel Neutron Fluence Regulatory Guide 1190 2001
[11] I Remec and F B K Kam ldquoHB Robinson-2 Pressure VesselBenchmarkrdquo NUREGCR-6453 (ORNLTM-13204) preparedfor the USNRC by Oak Ridge National Laboratory October1997
[12] J C Wagner and A Haghighat ldquoAutomated variance reductionof Monte Carlo shielding calculations using the discrete ordi-nates adjoint functionrdquo Nuclear Science and Engineering vol128 no 2 pp 186ndash208 1998
[13] J C Wagner E D Blakeman and D E Peplow ldquoForward-weighted CADIS method for global variance reductionrdquo Trans-actions of the American Nuclear Society vol 97 pp 630ndash6332007
[14] G I Bell and S Glasstone Nuclear Reactor Theory VanNostrand Reinhold Company Litton Educational Publishing1970
[15] J C Wagner Acceleration of Monte Carlo shielding calculationswith an automated variance reduction technique and parallel pro-cessing [PhD thesis] Pennsylvania State University UniversityPark Pa USA 1997
[16] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technologyrdquoNuclear Data Sheets vol 107 no 12 pp2931ndash3060 2006
[17] X-5 Monte Carlo Team MCNPmdashA General N-Particle Trans-port Code Version 5 vol 1 of Overview andTheory LA-UR-03-1987 Los Alamos National Laboratory 2003
[18] A Trkov M Herman and D A Brown ldquoENDF-6 FormatsManualrdquo Data Formats and Procedures for the EvaluatedNuclear Data Files ENDFB-VI and ENDFB-VII NationalNuclear Data Center Brookhaven National Laboratory 2011
[19] IAEA Nuclear Data Services httpwww-ndsiaeaorg
TribologyAdvances in
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Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Submit your manuscripts athttpwwwhindawicom
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International Journal of
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Journal ofEngineeringVolume 2014
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Nuclear InstallationsScience and Technology of
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Solar EnergyJournal of
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Wind EnergyJournal of
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Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Science and Technology of Nuclear Installations 5
For seven detector locations (A1ndashA7) we used twodosimetry libraries as a source of a response functionsfor reaction rate calculations Reaction rate calculationswere done with IRDF-2002 and IRDF-90v2 (older version)libraries for the total of six PCA benchmark reactions237Np(n f)137Cs 238U(n f)137Cs 103Rh(n n1015840)103mRh 115In(nn1015840)115mIn 58Ni(n p)58Co and 27Al(n120572)24NaThese reactionswere defined as a response functions for FW-CADISmethod-ology
The threshold energies for the 27Al(n 120572)24Na 58Ni(np)58Co 238U(n f)137Cs 237Np(n f)137Cs 115In(n n1015840)115mInand 103Rh(n n1015840)103mRh reactions are 50 205 145 06903 and 01MeV respectively This is in fast neutron rangebut still calculations were performed for full neutron spec-trum (10minus5 eV to 20MeV) with fine-group shielding libraryv7 200n47g
Also we investigated SCALE60 capabilities in genera-tionmixing of multigroup cross-sections from v7 200n47glibrary for reactions 237Np(n f)137Cs 238U(n f)137Cs 58Ni(np)58Co and 27Al(n 120572)24Na using AJAX and PALEALEutility modules of AMPX working library Reaction 115In(nn1015840)115mIn was derived from ENDFB-VI8 while reaction103Rh(n n1015840)103mRh was not derived because there is no singleor combination of reaction type numbers [18] (MT numbersin ENDFB) for computation of production rate ofmetastableisomer of rhodium (first excited state resulting from inelasticscattering) The obtained multigroup cross-sections withoutrhodium are Doppler and resonances corrected and haveMAVRIC shielding structure of 200n47g These reactionswere also defined as a response functions for FW-CADISmethodology
Two different approaches for the MAVRIC source distri-bution were
(1) fission distribution in space and energy determinedby KENO-VI calculation (transferred as a sourceinput into MAVRIC)mdashCAAS case
(2) Watt spectrum [5] for source energy distribution119901(119864) = 119862119890
minus119864119886 sinh(radic119887119864) (we used thermal fissionof 235U with 119886 = 1028MeV and 119887 = 2249MeV)with uniform space sampling restricted to the reactorcoremdashWatt spectrum case
The total number of neutron batches was 2000 with 2000neutrons per batch for MAVRIC sequence The Denovo 119878
119873
mesh had approximately 20000 cells over PCA facility modelthat is 48 times 23 times 18 cells in 119909119910119911 direction with average cellside of 32 cm while Monaco Monte Carlo mesh had 36000cells (60 times 30 times 20) with average cell side of 26 cm We used1198788as quadrature order and119875
3for Legendre order of scattering
cross-section expansion (upscatteringwas deactivated) Sincethe axial flux gradients inside tubes are confirmed to besufficiently small the user-selected height of plusmn15 cm forvolumetric cylindrical tally regions in MAVRIC calculationrepresents a good compromise between Monte Carlo relativeerror and spatial description of PCA benchmark facilityDifferential small void cylinders were also placed in themidplane (119911 = 0) of the access tubes Point detectors andregion track length estimators were used to find multigroup
1E16
1E15
1E14
1E13
1E12
1E11
1E10
1E09
minus50
minus100
50
x axis (cm) 0
Neu
tron
forw
ard
flux
(nc
m3 s
)
Figure 3 Denovo forward neutron flux axial distribution (front halfremoved)
1E minus 02
1E minus 03
1E minus 04
1E minus 05
1E minus 06
1E minus 07
1E minus 08
1E minus 09
1E minus 10
minus50
minus100
50
0x axis (cm)
Neu
tron
adjo
int fl
ux (n
cm
2s
)
Figure 4 Denovo adjoint neutron flux axial distribution (front halfremoved)
neutron fluxes reaction rates and finally equivalent fissionfluxes
The elements of the FW-CADIS methodology aredepicted next Forward and adjoint neutron flux axial dis-tribution from Denovo code for CAAS case are shown inFigures 3 and 4 respectively Biased source distribution andmesh-based importance map are shown in Figures 5 and 6respectively Total Monte Carlo neutron flux in form of meshtally is depicted in Figures 7 and 8
The calculated equivalent fission fluxes with Monte Carlorelative error (1 sigma level) for PCA Benchmark are givenin Table 1 for MAVRIC CAAS case Only the reactions forwhich the measurements were done are listed AveragedCM ratios for detectors A1ndashA7 are shown in Figure 9 forCAAS case and in Figure 10 for Watt spectrum case Theseresults are compared to the referencedDORT results [2] Onecan notice high similarity between Monaco results for twodifferent source distribution approaches The Watt spectrumcase results aremore conservative and they are 10ndash15 higherthan CAAS case results
6 Science and Technology of Nuclear Installations
127E14 minus 264E14
613E13 minus 127E14
295E13 minus 613E13
142E13 minus 295E13
685E12 minus 142E13
330E12 minus 685E12
159E12 minus 330E12
765E11 minus 159E12
369E11 minus 765E11
178E11 minus 369E11
856E10 minus 178E11
412E10 minus 856E10
199E10 minus 412E10
956E09 minus 199E10
461E09 minus 956E09
Sampled neutronsTotal sampled neutronsValues
Figure 5 Biased source distribution (front half removed)
Values252E-02 minus 717E-02886E-03 minus 252E-02311E-03 minus 886E-03110E-03 minus 311E-03385E-04 minus 110E-031355E-04 minus 385E-04476E-05 minus 135E-04167E-05 minus 476E-05588E-06 minus 167E-05207E-06 minus 588E-06
256E-07 minus 727E-07727E-07 minus 207E-06
899E-08 minus 256E-07316E-08 minus 899E-08111E-08 minus 316E-08
Group 1Neutron target
Figure 6 Mesh-based importance map (front quarter removed)
Values136E15 minus 576E153233E14 minus 136E15764E13 minus 323E14181E13 minus 764E13
240E11 minus 101E12101E12 minus 428E12428E12 minus 181E13
568E10 minus 240E11134E10 minus 568E10318E09 minus 134E10753E08 minus 318E09178E08 minus 753E08
236E06 minus 998E06
422E07 minus 178E08998E06 minus 422E07
Neutron fluxTotal neutron flux
Figure 7 Neutron flux mesh tally (front quarter removed)
5 Discussion of Results
All obtained results are in accordance with calculationaluncertainty criterion from US NRC Regulatory Guide 1190the calculated reaction rates agree with the measurementsto within 20 for out-of-core dosimetry locations Under
prediction in CM ratio can be observed for 238U(n f)137Cs(145MeV threshold) through the thick RPV simulator (fromlocations A4 to A6) with 08 on average High attenuationof neutron flux in that area (around 700 for IRDF-2002) willcause softening of neutron spectrum inRPV simulator whichshifts neutrons in resonance regions for inelastic scattering
Science and Technology of Nuclear Installations 7
000076
000001
14ndash7
19ndash7
26ndash11
Figure 8 Neutron flux mesh tally in axial midplane (MCNP5 criti-cality results)
08
085
09
095
1
10511
Detector position (cm)
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE6 IRDF-2002
SCALE6 IRDF-90v2DORT BUGLE-93
DORT SAILOR-95DORT BUGLE-96
10 15 20 25 30 35 40 45 5550 60
Figure 9 Average DORT [2] and SCALE60 (CAAS case) CMratios for detectors
on iron Microscopic cross-section for neutron inelasticscattering on iron is shown in Figure 11 Results for 238U(nf)137Cs indicate self-shielding effects that is sensitivity ofmultigroup shielding library v7 200n47g on the iron cross-sections
Overprediction in results is highest for detector A2immediately after stainless steel thermal shield which haslarge amount of iron Again self-shielding effects of ironcross-sections are pronounced especially for 27Al(n 120572)24Na(IRDF-90v2) with CM of 117 The IRDF-90v2 library gen-erally gives the highest values while SCALE60 v7 200n47glibrary gives the lowest values of calculated fluxesThe IRDF-2002 results are right in the middle so this library wouldbe favorable for RPV dosimetry calculations The obtainedcalculational results show overall a good agreement withexperimental results however for distant detectors fromPCA core there is under prediction less than 10 on averageexcept excellent result for 27Al(n 120572)24Na
An important issue that has to be addressed whendiscussing Monte Carlo method is a burden the appliedcalculational model will place on memory resources andCPU time requirements For that purpose the figure-of-merit (FOM) factor [17] is defined to account for the time it
08085
09095
1105
11115
12
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE IRDF-2002SCALE IRDF-90v2DORT BUGLE-93DORT SAILOR-95
DORT BUGLE-96
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
Figure 10 Average DORT [2] and SCALE60 (Watt spectrum case)CM ratios for detectors
11
1
1
102
102
10minus4
10minus4
10minus2
10minus2
10minus10
10minus10
10minus5
10minus5
Cros
s sec
tion
(bar
ns)
Incident energy (MeV)
Figure 11 Inelastic scattering on iron [19]
takes to achieve a given level of uncertainty in Monte Carlocalculation
FOM =1
1198771198642sdot 119879
(6)
where 119877119864 and 119879 are Monte Carlo relative error (on 1 sigmalevel) and Monte Carlo CPU run time (in min) respectivelyMAVRIC run time for highest energy threshold reaction(5MeV for 27Al(n 120572)24Na) was 7 h while for the lowest(01MeV for 103Rh(n n1015840)103mRh) was 10 h In this paper allcalculations have been performed on QuadCore Q6600 with8GB of RAM FOM factors for IRDF-2002 and CAAS caseare shown in Figure 12 Application of automated variancereduction technique based on adjoint fluxes removes theburden of manually tuning VR parameters and significantlyimproves the quality of Monte Carlo calculations
6 Conclusion
The analysis of the PCA benchmark has been performedusing the SCALE60 code package The calculational mod-els of the PCA benchmark within CSAS6 and MAVRICsequences of SCALE60 have been determined The results
8 Science and Technology of Nuclear Installations
Table1Eq
uivalent
fissio
nflu
xes(per1
PCAcore
fissio
nneutronpersecon
d(cmminus2 ))
Detector
locatio
nRe
spon
sefunctio
ndata
237 N
p(n
f)137 C
sCM
238 U
(nf)1
37Cs
CM
103 R
h(n
n1015840)103119898Rh
CM
115 In(n
n1015840)115119898Inloz
CM
58Ni(n
p)5
8 Co
CM
27Al(n
120572)2
4 Na
CM
A1
ENDFB-VII0
664sdot10minus6plusmn113
099
544sdot10minus6plusmn071
lowast507sdot10minus6plusmn068
090
554sdot10minus6plusmn059
095
857sdot10minus6plusmn042
109
IRDF-2002
683sdot10minus6plusmn139
103
552sdot10minus6plusmn068
lowast554sdot10minus6plusmn099
099
534sdot10minus6plusmn072
095
565sdot10minus6plusmn061
097
859sdot10minus6plusmn049
109
IRDF-90v2
653sdot10minus6plusmn115
098
558sdot10minus6plusmn068
lowast549sdot10minus6plusmn078
099
534sdot10minus6plusmn061
095
572sdot10minus6plusmn066
098
895sdot10minus6plusmn061
113
A2
ENDFB-VII0
837sdot10minus7plusmn277
lowast620sdot10minus7plusmn069
lowast573sdot10minus7plusmn062
095
616sdot10minus7plusmn060
099
115sdot10minus6plusmn078
113
IRDF-2002
795sdot10minus7plusmn099
lowast627sdot10minus7plusmn073
lowast646sdot10minus7plusmn079
lowast613sdot10minus7plusmn076
101
639sdot10minus7plusmn065
103
116sdot10minus6plusmn071
113
IRDF-90v2
786sdot10minus7plusmn151
lowast631sdot10minus7plusmn066
lowast653sdot10minus7plusmn079
lowast614sdot10minus7plusmn061
101
635sdot10minus7plusmn062
103
120sdot10minus6plusmn074
117
A3
ENDFB-VII0
211sdot10minus7plusmn102
093
181sdot10minus7plusmn062
lowast162sdot10minus7plusmn059
081
199sdot10minus7plusmn068
086
437sdot10minus7plusmn055
097
IRDF-2002
218sdot10minus7plusmn111
096
181sdot10minus7plusmn059
lowast176sdot10minus7plusmn072
lowast172sdot10minus7plusmn062
087
204sdot10minus7plusmn060
088
440sdot10minus7plusmn056
098
IRDF-90v2
204sdot10minus7plusmn078
090
184sdot10minus7plusmn061
lowast176sdot10minus7plusmn067
lowast172sdot10minus7plusmn061
087
204sdot10minus7plusmn059
088
455sdot10minus7plusmn059
101
A4
ENDFB-VII0
907sdot10minus8plusmn056
098
533sdot10minus8plusmn065
087
531sdot10minus8plusmn067
090
482sdot10minus8plusmn084
091
107sdot10minus7plusmn115
105
IRDF-2002
916sdot10minus8plusmn054
099
542sdot10minus8plusmn069
089
750sdot10minus8plusmn055
097
563sdot10minus8plusmn063
096
487sdot10minus8plusmn085
092
107sdot10minus7plusmn117
105
IRDF-90v2
900sdot10minus8plusmn053
097
561sdot10minus8plusmn079
092
751sdot10minus8plusmn052
097
575sdot10minus8plusmn061
098
497sdot10minus8plusmn079
094
111sdot10minus7plusmn129
108
A5
ENDFB-VII0
495sdot10minus8plusmn049
095
223sdot10minus8plusmn063
081
236sdot10minus7plusmn058
086
182sdot10minus8plusmn073
087
417sdot10minus8plusmn115
102
IRDF-2002
495sdot10minus8plusmn048
096
226sdot10minus8plusmn073
082
393sdot10minus8plusmn048
090
252sdot10minus8plusmn058
091
182sdot10minus8plusmn068
087
413sdot10minus8plusmn098
101
IRDF-90v2
496sdot10minus8plusmn047
096
233sdot10minus8plusmn062
085
401sdot10minus8plusmn047
092
257sdot10minus8plusmn055
093
189sdot10minus8plusmn067
090
428sdot10minus8plusmn102
104
A6
ENDFB-VII0
247sdot10minus8plusmn051
091
867sdot10minus9plusmn059
077
986sdot10minus9plusmn054
084
652sdot10minus9plusmn065
088
155sdot10minus8plusmn089
101
IRDF-2002
249sdot10minus8plusmn049
092
873sdot10minus9plusmn060
078
195sdot10minus8plusmn056
089
105sdot10minus8plusmn053
089
665sdot10minus9plusmn083
090
155sdot10minus8plusmn091
101
IRDF-90v2
250sdot10minus8plusmn047
092
916sdot10minus9plusmn059
082
199sdot10minus8plusmn048
091
109sdot10minus8plusmn054
093
691sdot10minus9plusmn067
093
160sdot10minus8plusmn089
103
A7
ENDFB-VII0
630sdot10minus9plusmn077
087
189sdot10minus9plusmn103
lowast223sdot10minus9plusmn093
lowast140sdot10minus9plusmn106
lowast358sdot10minus9plusmn107
lowast
IRDF-2002
634sdot10minus9plusmn086
087
186sdot10minus9plusmn073
lowast487sdot10minus9plusmn062
lowast237sdot10minus9plusmn071
lowast137sdot10minus9plusmn093
lowast350sdot10minus9plusmn089
lowast
IRDF-90v2
640sdot10minus9plusmn074
088
198sdot10minus9plusmn101
lowast507sdot10minus9plusmn081
lowast250sdot10minus9plusmn079
lowast143sdot10minus9plusmn083
lowast368sdot10minus9plusmn100
lowast
lozEN
DFB-VI8
datawas
used
fore
xtractionof
crosssectio
nldquoin
elastic
tometastablerdquoiso
mer
115 In(n
n1015840)115119898In
lowastEx
perim
entald
atan
otprovided
inPC
Abenchm
ark
Science and Technology of Nuclear Installations 9
0
20
40
60
80
100
FOM
fact
or
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
27Al(n 120572)103Rh(n n998400)
238U(n f)
115In(n n998400)58Ni(n p)
237Np(n f)
Figure 12 FOM factors for IRDF-2002 (CAAS case)
of calculations using the established models have been com-pared with PCA benchmark data A good agreement of thecalculated and measured equivalent fission fluxes has beenobtained No systematic decrease of agreements betweencalculations and measurements with increasing distance ofdetector from the PCA benchmark facility core was observedfor any of the applied approaches This indicates that theshapes of calculated neutron spectra in the energy rangeweredosimeters are sensitive are properly determined SCALE60capabilities in generationmixing cross-sections from work-ing library v7 200n47g to be used as a response functions inMAVRIC proved to be very useful
References
[1] ldquoShielding Integral Benchmark Archive and Databaserdquo SINBADReactor Shielding Benchmark Experiments OECDNEA 2011
[2] I Remec and F B Kam ldquoPool Critical Assembly Pressure Ves-sel Facility Benchmarkrdquo NUREGCR-6454 (ORNLTM-13205)prepared for the USNRC by Oak Ridge National LaboratoryAugust 1997
[3] A H Fero S L Anderson and G K Roberts ldquoAnalysis ofthe ORNL PCA benchmark using TORT and BUGLE-96rdquoin Reactor Dosimetry Radiation Metrology and Assessment JG Williams D W Vehar F H Ruddy and D M GilliamEds pp 360ndash366 American Society for Testing and MaterialsPhiladelphia Pa USA 2001
[4] Y K Lee ldquoAnalysis of the NRC PCA pressure vessel dosimetrybenchmark using TRIPOLI-43 Monte Carlo code and ENDFB-VI4 JEF22 and IRDF-90 librariesrdquo Nuclear Mathematical andComputational Science ACentury in Review ACenturyAnewGatlinburg Tenn USA April 2003
[5] ldquoSCALE A Modular Code System for Performing Standard-ized Computer Analyses for Licensing Evaluationrdquo ORNLTM-200539 Version 6 Radiation Safety Information Computa-tional Center at Oak Ridge National Laboratory 2009
[6] D VragolovMMatijevic andD Pevec ldquoModeling of pool crit-ical assembly pressure vessel facility benchmarkrdquo in Proceedingsof the International Conference Nuclear Energy for New EuropeLjubljana Slovenia 2010
[7] J M Risner D Wiarda M E Dunn T M Miller D E Peplowand B W Patton ldquoProduction and Testing of the VITAMIN-B7 Fine-Group and BUGLE-B7 Broad-Group Coupled Neu-tronGamma Cross-Section Libraries Derived from ENDFB-VII0 Nuclear Datardquo USNRC NUREGCR-7045 2011
[8] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File 2002 (IRDF-2002) 2006
[9] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File (IRDF-90 Version 2) 1993
[10] USNRCCalculational andDosimetryMethods forDeterminingPressure Vessel Neutron Fluence Regulatory Guide 1190 2001
[11] I Remec and F B K Kam ldquoHB Robinson-2 Pressure VesselBenchmarkrdquo NUREGCR-6453 (ORNLTM-13204) preparedfor the USNRC by Oak Ridge National Laboratory October1997
[12] J C Wagner and A Haghighat ldquoAutomated variance reductionof Monte Carlo shielding calculations using the discrete ordi-nates adjoint functionrdquo Nuclear Science and Engineering vol128 no 2 pp 186ndash208 1998
[13] J C Wagner E D Blakeman and D E Peplow ldquoForward-weighted CADIS method for global variance reductionrdquo Trans-actions of the American Nuclear Society vol 97 pp 630ndash6332007
[14] G I Bell and S Glasstone Nuclear Reactor Theory VanNostrand Reinhold Company Litton Educational Publishing1970
[15] J C Wagner Acceleration of Monte Carlo shielding calculationswith an automated variance reduction technique and parallel pro-cessing [PhD thesis] Pennsylvania State University UniversityPark Pa USA 1997
[16] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technologyrdquoNuclear Data Sheets vol 107 no 12 pp2931ndash3060 2006
[17] X-5 Monte Carlo Team MCNPmdashA General N-Particle Trans-port Code Version 5 vol 1 of Overview andTheory LA-UR-03-1987 Los Alamos National Laboratory 2003
[18] A Trkov M Herman and D A Brown ldquoENDF-6 FormatsManualrdquo Data Formats and Procedures for the EvaluatedNuclear Data Files ENDFB-VI and ENDFB-VII NationalNuclear Data Center Brookhaven National Laboratory 2011
[19] IAEA Nuclear Data Services httpwww-ndsiaeaorg
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
6 Science and Technology of Nuclear Installations
127E14 minus 264E14
613E13 minus 127E14
295E13 minus 613E13
142E13 minus 295E13
685E12 minus 142E13
330E12 minus 685E12
159E12 minus 330E12
765E11 minus 159E12
369E11 minus 765E11
178E11 minus 369E11
856E10 minus 178E11
412E10 minus 856E10
199E10 minus 412E10
956E09 minus 199E10
461E09 minus 956E09
Sampled neutronsTotal sampled neutronsValues
Figure 5 Biased source distribution (front half removed)
Values252E-02 minus 717E-02886E-03 minus 252E-02311E-03 minus 886E-03110E-03 minus 311E-03385E-04 minus 110E-031355E-04 minus 385E-04476E-05 minus 135E-04167E-05 minus 476E-05588E-06 minus 167E-05207E-06 minus 588E-06
256E-07 minus 727E-07727E-07 minus 207E-06
899E-08 minus 256E-07316E-08 minus 899E-08111E-08 minus 316E-08
Group 1Neutron target
Figure 6 Mesh-based importance map (front quarter removed)
Values136E15 minus 576E153233E14 minus 136E15764E13 minus 323E14181E13 minus 764E13
240E11 minus 101E12101E12 minus 428E12428E12 minus 181E13
568E10 minus 240E11134E10 minus 568E10318E09 minus 134E10753E08 minus 318E09178E08 minus 753E08
236E06 minus 998E06
422E07 minus 178E08998E06 minus 422E07
Neutron fluxTotal neutron flux
Figure 7 Neutron flux mesh tally (front quarter removed)
5 Discussion of Results
All obtained results are in accordance with calculationaluncertainty criterion from US NRC Regulatory Guide 1190the calculated reaction rates agree with the measurementsto within 20 for out-of-core dosimetry locations Under
prediction in CM ratio can be observed for 238U(n f)137Cs(145MeV threshold) through the thick RPV simulator (fromlocations A4 to A6) with 08 on average High attenuationof neutron flux in that area (around 700 for IRDF-2002) willcause softening of neutron spectrum inRPV simulator whichshifts neutrons in resonance regions for inelastic scattering
Science and Technology of Nuclear Installations 7
000076
000001
14ndash7
19ndash7
26ndash11
Figure 8 Neutron flux mesh tally in axial midplane (MCNP5 criti-cality results)
08
085
09
095
1
10511
Detector position (cm)
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE6 IRDF-2002
SCALE6 IRDF-90v2DORT BUGLE-93
DORT SAILOR-95DORT BUGLE-96
10 15 20 25 30 35 40 45 5550 60
Figure 9 Average DORT [2] and SCALE60 (CAAS case) CMratios for detectors
on iron Microscopic cross-section for neutron inelasticscattering on iron is shown in Figure 11 Results for 238U(nf)137Cs indicate self-shielding effects that is sensitivity ofmultigroup shielding library v7 200n47g on the iron cross-sections
Overprediction in results is highest for detector A2immediately after stainless steel thermal shield which haslarge amount of iron Again self-shielding effects of ironcross-sections are pronounced especially for 27Al(n 120572)24Na(IRDF-90v2) with CM of 117 The IRDF-90v2 library gen-erally gives the highest values while SCALE60 v7 200n47glibrary gives the lowest values of calculated fluxesThe IRDF-2002 results are right in the middle so this library wouldbe favorable for RPV dosimetry calculations The obtainedcalculational results show overall a good agreement withexperimental results however for distant detectors fromPCA core there is under prediction less than 10 on averageexcept excellent result for 27Al(n 120572)24Na
An important issue that has to be addressed whendiscussing Monte Carlo method is a burden the appliedcalculational model will place on memory resources andCPU time requirements For that purpose the figure-of-merit (FOM) factor [17] is defined to account for the time it
08085
09095
1105
11115
12
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE IRDF-2002SCALE IRDF-90v2DORT BUGLE-93DORT SAILOR-95
DORT BUGLE-96
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
Figure 10 Average DORT [2] and SCALE60 (Watt spectrum case)CM ratios for detectors
11
1
1
102
102
10minus4
10minus4
10minus2
10minus2
10minus10
10minus10
10minus5
10minus5
Cros
s sec
tion
(bar
ns)
Incident energy (MeV)
Figure 11 Inelastic scattering on iron [19]
takes to achieve a given level of uncertainty in Monte Carlocalculation
FOM =1
1198771198642sdot 119879
(6)
where 119877119864 and 119879 are Monte Carlo relative error (on 1 sigmalevel) and Monte Carlo CPU run time (in min) respectivelyMAVRIC run time for highest energy threshold reaction(5MeV for 27Al(n 120572)24Na) was 7 h while for the lowest(01MeV for 103Rh(n n1015840)103mRh) was 10 h In this paper allcalculations have been performed on QuadCore Q6600 with8GB of RAM FOM factors for IRDF-2002 and CAAS caseare shown in Figure 12 Application of automated variancereduction technique based on adjoint fluxes removes theburden of manually tuning VR parameters and significantlyimproves the quality of Monte Carlo calculations
6 Conclusion
The analysis of the PCA benchmark has been performedusing the SCALE60 code package The calculational mod-els of the PCA benchmark within CSAS6 and MAVRICsequences of SCALE60 have been determined The results
8 Science and Technology of Nuclear Installations
Table1Eq
uivalent
fissio
nflu
xes(per1
PCAcore
fissio
nneutronpersecon
d(cmminus2 ))
Detector
locatio
nRe
spon
sefunctio
ndata
237 N
p(n
f)137 C
sCM
238 U
(nf)1
37Cs
CM
103 R
h(n
n1015840)103119898Rh
CM
115 In(n
n1015840)115119898Inloz
CM
58Ni(n
p)5
8 Co
CM
27Al(n
120572)2
4 Na
CM
A1
ENDFB-VII0
664sdot10minus6plusmn113
099
544sdot10minus6plusmn071
lowast507sdot10minus6plusmn068
090
554sdot10minus6plusmn059
095
857sdot10minus6plusmn042
109
IRDF-2002
683sdot10minus6plusmn139
103
552sdot10minus6plusmn068
lowast554sdot10minus6plusmn099
099
534sdot10minus6plusmn072
095
565sdot10minus6plusmn061
097
859sdot10minus6plusmn049
109
IRDF-90v2
653sdot10minus6plusmn115
098
558sdot10minus6plusmn068
lowast549sdot10minus6plusmn078
099
534sdot10minus6plusmn061
095
572sdot10minus6plusmn066
098
895sdot10minus6plusmn061
113
A2
ENDFB-VII0
837sdot10minus7plusmn277
lowast620sdot10minus7plusmn069
lowast573sdot10minus7plusmn062
095
616sdot10minus7plusmn060
099
115sdot10minus6plusmn078
113
IRDF-2002
795sdot10minus7plusmn099
lowast627sdot10minus7plusmn073
lowast646sdot10minus7plusmn079
lowast613sdot10minus7plusmn076
101
639sdot10minus7plusmn065
103
116sdot10minus6plusmn071
113
IRDF-90v2
786sdot10minus7plusmn151
lowast631sdot10minus7plusmn066
lowast653sdot10minus7plusmn079
lowast614sdot10minus7plusmn061
101
635sdot10minus7plusmn062
103
120sdot10minus6plusmn074
117
A3
ENDFB-VII0
211sdot10minus7plusmn102
093
181sdot10minus7plusmn062
lowast162sdot10minus7plusmn059
081
199sdot10minus7plusmn068
086
437sdot10minus7plusmn055
097
IRDF-2002
218sdot10minus7plusmn111
096
181sdot10minus7plusmn059
lowast176sdot10minus7plusmn072
lowast172sdot10minus7plusmn062
087
204sdot10minus7plusmn060
088
440sdot10minus7plusmn056
098
IRDF-90v2
204sdot10minus7plusmn078
090
184sdot10minus7plusmn061
lowast176sdot10minus7plusmn067
lowast172sdot10minus7plusmn061
087
204sdot10minus7plusmn059
088
455sdot10minus7plusmn059
101
A4
ENDFB-VII0
907sdot10minus8plusmn056
098
533sdot10minus8plusmn065
087
531sdot10minus8plusmn067
090
482sdot10minus8plusmn084
091
107sdot10minus7plusmn115
105
IRDF-2002
916sdot10minus8plusmn054
099
542sdot10minus8plusmn069
089
750sdot10minus8plusmn055
097
563sdot10minus8plusmn063
096
487sdot10minus8plusmn085
092
107sdot10minus7plusmn117
105
IRDF-90v2
900sdot10minus8plusmn053
097
561sdot10minus8plusmn079
092
751sdot10minus8plusmn052
097
575sdot10minus8plusmn061
098
497sdot10minus8plusmn079
094
111sdot10minus7plusmn129
108
A5
ENDFB-VII0
495sdot10minus8plusmn049
095
223sdot10minus8plusmn063
081
236sdot10minus7plusmn058
086
182sdot10minus8plusmn073
087
417sdot10minus8plusmn115
102
IRDF-2002
495sdot10minus8plusmn048
096
226sdot10minus8plusmn073
082
393sdot10minus8plusmn048
090
252sdot10minus8plusmn058
091
182sdot10minus8plusmn068
087
413sdot10minus8plusmn098
101
IRDF-90v2
496sdot10minus8plusmn047
096
233sdot10minus8plusmn062
085
401sdot10minus8plusmn047
092
257sdot10minus8plusmn055
093
189sdot10minus8plusmn067
090
428sdot10minus8plusmn102
104
A6
ENDFB-VII0
247sdot10minus8plusmn051
091
867sdot10minus9plusmn059
077
986sdot10minus9plusmn054
084
652sdot10minus9plusmn065
088
155sdot10minus8plusmn089
101
IRDF-2002
249sdot10minus8plusmn049
092
873sdot10minus9plusmn060
078
195sdot10minus8plusmn056
089
105sdot10minus8plusmn053
089
665sdot10minus9plusmn083
090
155sdot10minus8plusmn091
101
IRDF-90v2
250sdot10minus8plusmn047
092
916sdot10minus9plusmn059
082
199sdot10minus8plusmn048
091
109sdot10minus8plusmn054
093
691sdot10minus9plusmn067
093
160sdot10minus8plusmn089
103
A7
ENDFB-VII0
630sdot10minus9plusmn077
087
189sdot10minus9plusmn103
lowast223sdot10minus9plusmn093
lowast140sdot10minus9plusmn106
lowast358sdot10minus9plusmn107
lowast
IRDF-2002
634sdot10minus9plusmn086
087
186sdot10minus9plusmn073
lowast487sdot10minus9plusmn062
lowast237sdot10minus9plusmn071
lowast137sdot10minus9plusmn093
lowast350sdot10minus9plusmn089
lowast
IRDF-90v2
640sdot10minus9plusmn074
088
198sdot10minus9plusmn101
lowast507sdot10minus9plusmn081
lowast250sdot10minus9plusmn079
lowast143sdot10minus9plusmn083
lowast368sdot10minus9plusmn100
lowast
lozEN
DFB-VI8
datawas
used
fore
xtractionof
crosssectio
nldquoin
elastic
tometastablerdquoiso
mer
115 In(n
n1015840)115119898In
lowastEx
perim
entald
atan
otprovided
inPC
Abenchm
ark
Science and Technology of Nuclear Installations 9
0
20
40
60
80
100
FOM
fact
or
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
27Al(n 120572)103Rh(n n998400)
238U(n f)
115In(n n998400)58Ni(n p)
237Np(n f)
Figure 12 FOM factors for IRDF-2002 (CAAS case)
of calculations using the established models have been com-pared with PCA benchmark data A good agreement of thecalculated and measured equivalent fission fluxes has beenobtained No systematic decrease of agreements betweencalculations and measurements with increasing distance ofdetector from the PCA benchmark facility core was observedfor any of the applied approaches This indicates that theshapes of calculated neutron spectra in the energy rangeweredosimeters are sensitive are properly determined SCALE60capabilities in generationmixing cross-sections from work-ing library v7 200n47g to be used as a response functions inMAVRIC proved to be very useful
References
[1] ldquoShielding Integral Benchmark Archive and Databaserdquo SINBADReactor Shielding Benchmark Experiments OECDNEA 2011
[2] I Remec and F B Kam ldquoPool Critical Assembly Pressure Ves-sel Facility Benchmarkrdquo NUREGCR-6454 (ORNLTM-13205)prepared for the USNRC by Oak Ridge National LaboratoryAugust 1997
[3] A H Fero S L Anderson and G K Roberts ldquoAnalysis ofthe ORNL PCA benchmark using TORT and BUGLE-96rdquoin Reactor Dosimetry Radiation Metrology and Assessment JG Williams D W Vehar F H Ruddy and D M GilliamEds pp 360ndash366 American Society for Testing and MaterialsPhiladelphia Pa USA 2001
[4] Y K Lee ldquoAnalysis of the NRC PCA pressure vessel dosimetrybenchmark using TRIPOLI-43 Monte Carlo code and ENDFB-VI4 JEF22 and IRDF-90 librariesrdquo Nuclear Mathematical andComputational Science ACentury in Review ACenturyAnewGatlinburg Tenn USA April 2003
[5] ldquoSCALE A Modular Code System for Performing Standard-ized Computer Analyses for Licensing Evaluationrdquo ORNLTM-200539 Version 6 Radiation Safety Information Computa-tional Center at Oak Ridge National Laboratory 2009
[6] D VragolovMMatijevic andD Pevec ldquoModeling of pool crit-ical assembly pressure vessel facility benchmarkrdquo in Proceedingsof the International Conference Nuclear Energy for New EuropeLjubljana Slovenia 2010
[7] J M Risner D Wiarda M E Dunn T M Miller D E Peplowand B W Patton ldquoProduction and Testing of the VITAMIN-B7 Fine-Group and BUGLE-B7 Broad-Group Coupled Neu-tronGamma Cross-Section Libraries Derived from ENDFB-VII0 Nuclear Datardquo USNRC NUREGCR-7045 2011
[8] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File 2002 (IRDF-2002) 2006
[9] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File (IRDF-90 Version 2) 1993
[10] USNRCCalculational andDosimetryMethods forDeterminingPressure Vessel Neutron Fluence Regulatory Guide 1190 2001
[11] I Remec and F B K Kam ldquoHB Robinson-2 Pressure VesselBenchmarkrdquo NUREGCR-6453 (ORNLTM-13204) preparedfor the USNRC by Oak Ridge National Laboratory October1997
[12] J C Wagner and A Haghighat ldquoAutomated variance reductionof Monte Carlo shielding calculations using the discrete ordi-nates adjoint functionrdquo Nuclear Science and Engineering vol128 no 2 pp 186ndash208 1998
[13] J C Wagner E D Blakeman and D E Peplow ldquoForward-weighted CADIS method for global variance reductionrdquo Trans-actions of the American Nuclear Society vol 97 pp 630ndash6332007
[14] G I Bell and S Glasstone Nuclear Reactor Theory VanNostrand Reinhold Company Litton Educational Publishing1970
[15] J C Wagner Acceleration of Monte Carlo shielding calculationswith an automated variance reduction technique and parallel pro-cessing [PhD thesis] Pennsylvania State University UniversityPark Pa USA 1997
[16] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technologyrdquoNuclear Data Sheets vol 107 no 12 pp2931ndash3060 2006
[17] X-5 Monte Carlo Team MCNPmdashA General N-Particle Trans-port Code Version 5 vol 1 of Overview andTheory LA-UR-03-1987 Los Alamos National Laboratory 2003
[18] A Trkov M Herman and D A Brown ldquoENDF-6 FormatsManualrdquo Data Formats and Procedures for the EvaluatedNuclear Data Files ENDFB-VI and ENDFB-VII NationalNuclear Data Center Brookhaven National Laboratory 2011
[19] IAEA Nuclear Data Services httpwww-ndsiaeaorg
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Science and Technology of Nuclear Installations 7
000076
000001
14ndash7
19ndash7
26ndash11
Figure 8 Neutron flux mesh tally in axial midplane (MCNP5 criti-cality results)
08
085
09
095
1
10511
Detector position (cm)
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE6 IRDF-2002
SCALE6 IRDF-90v2DORT BUGLE-93
DORT SAILOR-95DORT BUGLE-96
10 15 20 25 30 35 40 45 5550 60
Figure 9 Average DORT [2] and SCALE60 (CAAS case) CMratios for detectors
on iron Microscopic cross-section for neutron inelasticscattering on iron is shown in Figure 11 Results for 238U(nf)137Cs indicate self-shielding effects that is sensitivity ofmultigroup shielding library v7 200n47g on the iron cross-sections
Overprediction in results is highest for detector A2immediately after stainless steel thermal shield which haslarge amount of iron Again self-shielding effects of ironcross-sections are pronounced especially for 27Al(n 120572)24Na(IRDF-90v2) with CM of 117 The IRDF-90v2 library gen-erally gives the highest values while SCALE60 v7 200n47glibrary gives the lowest values of calculated fluxesThe IRDF-2002 results are right in the middle so this library wouldbe favorable for RPV dosimetry calculations The obtainedcalculational results show overall a good agreement withexperimental results however for distant detectors fromPCA core there is under prediction less than 10 on averageexcept excellent result for 27Al(n 120572)24Na
An important issue that has to be addressed whendiscussing Monte Carlo method is a burden the appliedcalculational model will place on memory resources andCPU time requirements For that purpose the figure-of-merit (FOM) factor [17] is defined to account for the time it
08085
09095
1105
11115
12
Aver
age C
M ra
tio
SCALE6 ENDFB-VII0
SCALE IRDF-2002SCALE IRDF-90v2DORT BUGLE-93DORT SAILOR-95
DORT BUGLE-96
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
Figure 10 Average DORT [2] and SCALE60 (Watt spectrum case)CM ratios for detectors
11
1
1
102
102
10minus4
10minus4
10minus2
10minus2
10minus10
10minus10
10minus5
10minus5
Cros
s sec
tion
(bar
ns)
Incident energy (MeV)
Figure 11 Inelastic scattering on iron [19]
takes to achieve a given level of uncertainty in Monte Carlocalculation
FOM =1
1198771198642sdot 119879
(6)
where 119877119864 and 119879 are Monte Carlo relative error (on 1 sigmalevel) and Monte Carlo CPU run time (in min) respectivelyMAVRIC run time for highest energy threshold reaction(5MeV for 27Al(n 120572)24Na) was 7 h while for the lowest(01MeV for 103Rh(n n1015840)103mRh) was 10 h In this paper allcalculations have been performed on QuadCore Q6600 with8GB of RAM FOM factors for IRDF-2002 and CAAS caseare shown in Figure 12 Application of automated variancereduction technique based on adjoint fluxes removes theburden of manually tuning VR parameters and significantlyimproves the quality of Monte Carlo calculations
6 Conclusion
The analysis of the PCA benchmark has been performedusing the SCALE60 code package The calculational mod-els of the PCA benchmark within CSAS6 and MAVRICsequences of SCALE60 have been determined The results
8 Science and Technology of Nuclear Installations
Table1Eq
uivalent
fissio
nflu
xes(per1
PCAcore
fissio
nneutronpersecon
d(cmminus2 ))
Detector
locatio
nRe
spon
sefunctio
ndata
237 N
p(n
f)137 C
sCM
238 U
(nf)1
37Cs
CM
103 R
h(n
n1015840)103119898Rh
CM
115 In(n
n1015840)115119898Inloz
CM
58Ni(n
p)5
8 Co
CM
27Al(n
120572)2
4 Na
CM
A1
ENDFB-VII0
664sdot10minus6plusmn113
099
544sdot10minus6plusmn071
lowast507sdot10minus6plusmn068
090
554sdot10minus6plusmn059
095
857sdot10minus6plusmn042
109
IRDF-2002
683sdot10minus6plusmn139
103
552sdot10minus6plusmn068
lowast554sdot10minus6plusmn099
099
534sdot10minus6plusmn072
095
565sdot10minus6plusmn061
097
859sdot10minus6plusmn049
109
IRDF-90v2
653sdot10minus6plusmn115
098
558sdot10minus6plusmn068
lowast549sdot10minus6plusmn078
099
534sdot10minus6plusmn061
095
572sdot10minus6plusmn066
098
895sdot10minus6plusmn061
113
A2
ENDFB-VII0
837sdot10minus7plusmn277
lowast620sdot10minus7plusmn069
lowast573sdot10minus7plusmn062
095
616sdot10minus7plusmn060
099
115sdot10minus6plusmn078
113
IRDF-2002
795sdot10minus7plusmn099
lowast627sdot10minus7plusmn073
lowast646sdot10minus7plusmn079
lowast613sdot10minus7plusmn076
101
639sdot10minus7plusmn065
103
116sdot10minus6plusmn071
113
IRDF-90v2
786sdot10minus7plusmn151
lowast631sdot10minus7plusmn066
lowast653sdot10minus7plusmn079
lowast614sdot10minus7plusmn061
101
635sdot10minus7plusmn062
103
120sdot10minus6plusmn074
117
A3
ENDFB-VII0
211sdot10minus7plusmn102
093
181sdot10minus7plusmn062
lowast162sdot10minus7plusmn059
081
199sdot10minus7plusmn068
086
437sdot10minus7plusmn055
097
IRDF-2002
218sdot10minus7plusmn111
096
181sdot10minus7plusmn059
lowast176sdot10minus7plusmn072
lowast172sdot10minus7plusmn062
087
204sdot10minus7plusmn060
088
440sdot10minus7plusmn056
098
IRDF-90v2
204sdot10minus7plusmn078
090
184sdot10minus7plusmn061
lowast176sdot10minus7plusmn067
lowast172sdot10minus7plusmn061
087
204sdot10minus7plusmn059
088
455sdot10minus7plusmn059
101
A4
ENDFB-VII0
907sdot10minus8plusmn056
098
533sdot10minus8plusmn065
087
531sdot10minus8plusmn067
090
482sdot10minus8plusmn084
091
107sdot10minus7plusmn115
105
IRDF-2002
916sdot10minus8plusmn054
099
542sdot10minus8plusmn069
089
750sdot10minus8plusmn055
097
563sdot10minus8plusmn063
096
487sdot10minus8plusmn085
092
107sdot10minus7plusmn117
105
IRDF-90v2
900sdot10minus8plusmn053
097
561sdot10minus8plusmn079
092
751sdot10minus8plusmn052
097
575sdot10minus8plusmn061
098
497sdot10minus8plusmn079
094
111sdot10minus7plusmn129
108
A5
ENDFB-VII0
495sdot10minus8plusmn049
095
223sdot10minus8plusmn063
081
236sdot10minus7plusmn058
086
182sdot10minus8plusmn073
087
417sdot10minus8plusmn115
102
IRDF-2002
495sdot10minus8plusmn048
096
226sdot10minus8plusmn073
082
393sdot10minus8plusmn048
090
252sdot10minus8plusmn058
091
182sdot10minus8plusmn068
087
413sdot10minus8plusmn098
101
IRDF-90v2
496sdot10minus8plusmn047
096
233sdot10minus8plusmn062
085
401sdot10minus8plusmn047
092
257sdot10minus8plusmn055
093
189sdot10minus8plusmn067
090
428sdot10minus8plusmn102
104
A6
ENDFB-VII0
247sdot10minus8plusmn051
091
867sdot10minus9plusmn059
077
986sdot10minus9plusmn054
084
652sdot10minus9plusmn065
088
155sdot10minus8plusmn089
101
IRDF-2002
249sdot10minus8plusmn049
092
873sdot10minus9plusmn060
078
195sdot10minus8plusmn056
089
105sdot10minus8plusmn053
089
665sdot10minus9plusmn083
090
155sdot10minus8plusmn091
101
IRDF-90v2
250sdot10minus8plusmn047
092
916sdot10minus9plusmn059
082
199sdot10minus8plusmn048
091
109sdot10minus8plusmn054
093
691sdot10minus9plusmn067
093
160sdot10minus8plusmn089
103
A7
ENDFB-VII0
630sdot10minus9plusmn077
087
189sdot10minus9plusmn103
lowast223sdot10minus9plusmn093
lowast140sdot10minus9plusmn106
lowast358sdot10minus9plusmn107
lowast
IRDF-2002
634sdot10minus9plusmn086
087
186sdot10minus9plusmn073
lowast487sdot10minus9plusmn062
lowast237sdot10minus9plusmn071
lowast137sdot10minus9plusmn093
lowast350sdot10minus9plusmn089
lowast
IRDF-90v2
640sdot10minus9plusmn074
088
198sdot10minus9plusmn101
lowast507sdot10minus9plusmn081
lowast250sdot10minus9plusmn079
lowast143sdot10minus9plusmn083
lowast368sdot10minus9plusmn100
lowast
lozEN
DFB-VI8
datawas
used
fore
xtractionof
crosssectio
nldquoin
elastic
tometastablerdquoiso
mer
115 In(n
n1015840)115119898In
lowastEx
perim
entald
atan
otprovided
inPC
Abenchm
ark
Science and Technology of Nuclear Installations 9
0
20
40
60
80
100
FOM
fact
or
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
27Al(n 120572)103Rh(n n998400)
238U(n f)
115In(n n998400)58Ni(n p)
237Np(n f)
Figure 12 FOM factors for IRDF-2002 (CAAS case)
of calculations using the established models have been com-pared with PCA benchmark data A good agreement of thecalculated and measured equivalent fission fluxes has beenobtained No systematic decrease of agreements betweencalculations and measurements with increasing distance ofdetector from the PCA benchmark facility core was observedfor any of the applied approaches This indicates that theshapes of calculated neutron spectra in the energy rangeweredosimeters are sensitive are properly determined SCALE60capabilities in generationmixing cross-sections from work-ing library v7 200n47g to be used as a response functions inMAVRIC proved to be very useful
References
[1] ldquoShielding Integral Benchmark Archive and Databaserdquo SINBADReactor Shielding Benchmark Experiments OECDNEA 2011
[2] I Remec and F B Kam ldquoPool Critical Assembly Pressure Ves-sel Facility Benchmarkrdquo NUREGCR-6454 (ORNLTM-13205)prepared for the USNRC by Oak Ridge National LaboratoryAugust 1997
[3] A H Fero S L Anderson and G K Roberts ldquoAnalysis ofthe ORNL PCA benchmark using TORT and BUGLE-96rdquoin Reactor Dosimetry Radiation Metrology and Assessment JG Williams D W Vehar F H Ruddy and D M GilliamEds pp 360ndash366 American Society for Testing and MaterialsPhiladelphia Pa USA 2001
[4] Y K Lee ldquoAnalysis of the NRC PCA pressure vessel dosimetrybenchmark using TRIPOLI-43 Monte Carlo code and ENDFB-VI4 JEF22 and IRDF-90 librariesrdquo Nuclear Mathematical andComputational Science ACentury in Review ACenturyAnewGatlinburg Tenn USA April 2003
[5] ldquoSCALE A Modular Code System for Performing Standard-ized Computer Analyses for Licensing Evaluationrdquo ORNLTM-200539 Version 6 Radiation Safety Information Computa-tional Center at Oak Ridge National Laboratory 2009
[6] D VragolovMMatijevic andD Pevec ldquoModeling of pool crit-ical assembly pressure vessel facility benchmarkrdquo in Proceedingsof the International Conference Nuclear Energy for New EuropeLjubljana Slovenia 2010
[7] J M Risner D Wiarda M E Dunn T M Miller D E Peplowand B W Patton ldquoProduction and Testing of the VITAMIN-B7 Fine-Group and BUGLE-B7 Broad-Group Coupled Neu-tronGamma Cross-Section Libraries Derived from ENDFB-VII0 Nuclear Datardquo USNRC NUREGCR-7045 2011
[8] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File 2002 (IRDF-2002) 2006
[9] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File (IRDF-90 Version 2) 1993
[10] USNRCCalculational andDosimetryMethods forDeterminingPressure Vessel Neutron Fluence Regulatory Guide 1190 2001
[11] I Remec and F B K Kam ldquoHB Robinson-2 Pressure VesselBenchmarkrdquo NUREGCR-6453 (ORNLTM-13204) preparedfor the USNRC by Oak Ridge National Laboratory October1997
[12] J C Wagner and A Haghighat ldquoAutomated variance reductionof Monte Carlo shielding calculations using the discrete ordi-nates adjoint functionrdquo Nuclear Science and Engineering vol128 no 2 pp 186ndash208 1998
[13] J C Wagner E D Blakeman and D E Peplow ldquoForward-weighted CADIS method for global variance reductionrdquo Trans-actions of the American Nuclear Society vol 97 pp 630ndash6332007
[14] G I Bell and S Glasstone Nuclear Reactor Theory VanNostrand Reinhold Company Litton Educational Publishing1970
[15] J C Wagner Acceleration of Monte Carlo shielding calculationswith an automated variance reduction technique and parallel pro-cessing [PhD thesis] Pennsylvania State University UniversityPark Pa USA 1997
[16] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technologyrdquoNuclear Data Sheets vol 107 no 12 pp2931ndash3060 2006
[17] X-5 Monte Carlo Team MCNPmdashA General N-Particle Trans-port Code Version 5 vol 1 of Overview andTheory LA-UR-03-1987 Los Alamos National Laboratory 2003
[18] A Trkov M Herman and D A Brown ldquoENDF-6 FormatsManualrdquo Data Formats and Procedures for the EvaluatedNuclear Data Files ENDFB-VI and ENDFB-VII NationalNuclear Data Center Brookhaven National Laboratory 2011
[19] IAEA Nuclear Data Services httpwww-ndsiaeaorg
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
8 Science and Technology of Nuclear Installations
Table1Eq
uivalent
fissio
nflu
xes(per1
PCAcore
fissio
nneutronpersecon
d(cmminus2 ))
Detector
locatio
nRe
spon
sefunctio
ndata
237 N
p(n
f)137 C
sCM
238 U
(nf)1
37Cs
CM
103 R
h(n
n1015840)103119898Rh
CM
115 In(n
n1015840)115119898Inloz
CM
58Ni(n
p)5
8 Co
CM
27Al(n
120572)2
4 Na
CM
A1
ENDFB-VII0
664sdot10minus6plusmn113
099
544sdot10minus6plusmn071
lowast507sdot10minus6plusmn068
090
554sdot10minus6plusmn059
095
857sdot10minus6plusmn042
109
IRDF-2002
683sdot10minus6plusmn139
103
552sdot10minus6plusmn068
lowast554sdot10minus6plusmn099
099
534sdot10minus6plusmn072
095
565sdot10minus6plusmn061
097
859sdot10minus6plusmn049
109
IRDF-90v2
653sdot10minus6plusmn115
098
558sdot10minus6plusmn068
lowast549sdot10minus6plusmn078
099
534sdot10minus6plusmn061
095
572sdot10minus6plusmn066
098
895sdot10minus6plusmn061
113
A2
ENDFB-VII0
837sdot10minus7plusmn277
lowast620sdot10minus7plusmn069
lowast573sdot10minus7plusmn062
095
616sdot10minus7plusmn060
099
115sdot10minus6plusmn078
113
IRDF-2002
795sdot10minus7plusmn099
lowast627sdot10minus7plusmn073
lowast646sdot10minus7plusmn079
lowast613sdot10minus7plusmn076
101
639sdot10minus7plusmn065
103
116sdot10minus6plusmn071
113
IRDF-90v2
786sdot10minus7plusmn151
lowast631sdot10minus7plusmn066
lowast653sdot10minus7plusmn079
lowast614sdot10minus7plusmn061
101
635sdot10minus7plusmn062
103
120sdot10minus6plusmn074
117
A3
ENDFB-VII0
211sdot10minus7plusmn102
093
181sdot10minus7plusmn062
lowast162sdot10minus7plusmn059
081
199sdot10minus7plusmn068
086
437sdot10minus7plusmn055
097
IRDF-2002
218sdot10minus7plusmn111
096
181sdot10minus7plusmn059
lowast176sdot10minus7plusmn072
lowast172sdot10minus7plusmn062
087
204sdot10minus7plusmn060
088
440sdot10minus7plusmn056
098
IRDF-90v2
204sdot10minus7plusmn078
090
184sdot10minus7plusmn061
lowast176sdot10minus7plusmn067
lowast172sdot10minus7plusmn061
087
204sdot10minus7plusmn059
088
455sdot10minus7plusmn059
101
A4
ENDFB-VII0
907sdot10minus8plusmn056
098
533sdot10minus8plusmn065
087
531sdot10minus8plusmn067
090
482sdot10minus8plusmn084
091
107sdot10minus7plusmn115
105
IRDF-2002
916sdot10minus8plusmn054
099
542sdot10minus8plusmn069
089
750sdot10minus8plusmn055
097
563sdot10minus8plusmn063
096
487sdot10minus8plusmn085
092
107sdot10minus7plusmn117
105
IRDF-90v2
900sdot10minus8plusmn053
097
561sdot10minus8plusmn079
092
751sdot10minus8plusmn052
097
575sdot10minus8plusmn061
098
497sdot10minus8plusmn079
094
111sdot10minus7plusmn129
108
A5
ENDFB-VII0
495sdot10minus8plusmn049
095
223sdot10minus8plusmn063
081
236sdot10minus7plusmn058
086
182sdot10minus8plusmn073
087
417sdot10minus8plusmn115
102
IRDF-2002
495sdot10minus8plusmn048
096
226sdot10minus8plusmn073
082
393sdot10minus8plusmn048
090
252sdot10minus8plusmn058
091
182sdot10minus8plusmn068
087
413sdot10minus8plusmn098
101
IRDF-90v2
496sdot10minus8plusmn047
096
233sdot10minus8plusmn062
085
401sdot10minus8plusmn047
092
257sdot10minus8plusmn055
093
189sdot10minus8plusmn067
090
428sdot10minus8plusmn102
104
A6
ENDFB-VII0
247sdot10minus8plusmn051
091
867sdot10minus9plusmn059
077
986sdot10minus9plusmn054
084
652sdot10minus9plusmn065
088
155sdot10minus8plusmn089
101
IRDF-2002
249sdot10minus8plusmn049
092
873sdot10minus9plusmn060
078
195sdot10minus8plusmn056
089
105sdot10minus8plusmn053
089
665sdot10minus9plusmn083
090
155sdot10minus8plusmn091
101
IRDF-90v2
250sdot10minus8plusmn047
092
916sdot10minus9plusmn059
082
199sdot10minus8plusmn048
091
109sdot10minus8plusmn054
093
691sdot10minus9plusmn067
093
160sdot10minus8plusmn089
103
A7
ENDFB-VII0
630sdot10minus9plusmn077
087
189sdot10minus9plusmn103
lowast223sdot10minus9plusmn093
lowast140sdot10minus9plusmn106
lowast358sdot10minus9plusmn107
lowast
IRDF-2002
634sdot10minus9plusmn086
087
186sdot10minus9plusmn073
lowast487sdot10minus9plusmn062
lowast237sdot10minus9plusmn071
lowast137sdot10minus9plusmn093
lowast350sdot10minus9plusmn089
lowast
IRDF-90v2
640sdot10minus9plusmn074
088
198sdot10minus9plusmn101
lowast507sdot10minus9plusmn081
lowast250sdot10minus9plusmn079
lowast143sdot10minus9plusmn083
lowast368sdot10minus9plusmn100
lowast
lozEN
DFB-VI8
datawas
used
fore
xtractionof
crosssectio
nldquoin
elastic
tometastablerdquoiso
mer
115 In(n
n1015840)115119898In
lowastEx
perim
entald
atan
otprovided
inPC
Abenchm
ark
Science and Technology of Nuclear Installations 9
0
20
40
60
80
100
FOM
fact
or
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
27Al(n 120572)103Rh(n n998400)
238U(n f)
115In(n n998400)58Ni(n p)
237Np(n f)
Figure 12 FOM factors for IRDF-2002 (CAAS case)
of calculations using the established models have been com-pared with PCA benchmark data A good agreement of thecalculated and measured equivalent fission fluxes has beenobtained No systematic decrease of agreements betweencalculations and measurements with increasing distance ofdetector from the PCA benchmark facility core was observedfor any of the applied approaches This indicates that theshapes of calculated neutron spectra in the energy rangeweredosimeters are sensitive are properly determined SCALE60capabilities in generationmixing cross-sections from work-ing library v7 200n47g to be used as a response functions inMAVRIC proved to be very useful
References
[1] ldquoShielding Integral Benchmark Archive and Databaserdquo SINBADReactor Shielding Benchmark Experiments OECDNEA 2011
[2] I Remec and F B Kam ldquoPool Critical Assembly Pressure Ves-sel Facility Benchmarkrdquo NUREGCR-6454 (ORNLTM-13205)prepared for the USNRC by Oak Ridge National LaboratoryAugust 1997
[3] A H Fero S L Anderson and G K Roberts ldquoAnalysis ofthe ORNL PCA benchmark using TORT and BUGLE-96rdquoin Reactor Dosimetry Radiation Metrology and Assessment JG Williams D W Vehar F H Ruddy and D M GilliamEds pp 360ndash366 American Society for Testing and MaterialsPhiladelphia Pa USA 2001
[4] Y K Lee ldquoAnalysis of the NRC PCA pressure vessel dosimetrybenchmark using TRIPOLI-43 Monte Carlo code and ENDFB-VI4 JEF22 and IRDF-90 librariesrdquo Nuclear Mathematical andComputational Science ACentury in Review ACenturyAnewGatlinburg Tenn USA April 2003
[5] ldquoSCALE A Modular Code System for Performing Standard-ized Computer Analyses for Licensing Evaluationrdquo ORNLTM-200539 Version 6 Radiation Safety Information Computa-tional Center at Oak Ridge National Laboratory 2009
[6] D VragolovMMatijevic andD Pevec ldquoModeling of pool crit-ical assembly pressure vessel facility benchmarkrdquo in Proceedingsof the International Conference Nuclear Energy for New EuropeLjubljana Slovenia 2010
[7] J M Risner D Wiarda M E Dunn T M Miller D E Peplowand B W Patton ldquoProduction and Testing of the VITAMIN-B7 Fine-Group and BUGLE-B7 Broad-Group Coupled Neu-tronGamma Cross-Section Libraries Derived from ENDFB-VII0 Nuclear Datardquo USNRC NUREGCR-7045 2011
[8] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File 2002 (IRDF-2002) 2006
[9] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File (IRDF-90 Version 2) 1993
[10] USNRCCalculational andDosimetryMethods forDeterminingPressure Vessel Neutron Fluence Regulatory Guide 1190 2001
[11] I Remec and F B K Kam ldquoHB Robinson-2 Pressure VesselBenchmarkrdquo NUREGCR-6453 (ORNLTM-13204) preparedfor the USNRC by Oak Ridge National Laboratory October1997
[12] J C Wagner and A Haghighat ldquoAutomated variance reductionof Monte Carlo shielding calculations using the discrete ordi-nates adjoint functionrdquo Nuclear Science and Engineering vol128 no 2 pp 186ndash208 1998
[13] J C Wagner E D Blakeman and D E Peplow ldquoForward-weighted CADIS method for global variance reductionrdquo Trans-actions of the American Nuclear Society vol 97 pp 630ndash6332007
[14] G I Bell and S Glasstone Nuclear Reactor Theory VanNostrand Reinhold Company Litton Educational Publishing1970
[15] J C Wagner Acceleration of Monte Carlo shielding calculationswith an automated variance reduction technique and parallel pro-cessing [PhD thesis] Pennsylvania State University UniversityPark Pa USA 1997
[16] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technologyrdquoNuclear Data Sheets vol 107 no 12 pp2931ndash3060 2006
[17] X-5 Monte Carlo Team MCNPmdashA General N-Particle Trans-port Code Version 5 vol 1 of Overview andTheory LA-UR-03-1987 Los Alamos National Laboratory 2003
[18] A Trkov M Herman and D A Brown ldquoENDF-6 FormatsManualrdquo Data Formats and Procedures for the EvaluatedNuclear Data Files ENDFB-VI and ENDFB-VII NationalNuclear Data Center Brookhaven National Laboratory 2011
[19] IAEA Nuclear Data Services httpwww-ndsiaeaorg
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Science and Technology of Nuclear Installations 9
0
20
40
60
80
100
FOM
fact
or
Detector position (cm)10 15 20 25 30 35 40 45 5550 60
27Al(n 120572)103Rh(n n998400)
238U(n f)
115In(n n998400)58Ni(n p)
237Np(n f)
Figure 12 FOM factors for IRDF-2002 (CAAS case)
of calculations using the established models have been com-pared with PCA benchmark data A good agreement of thecalculated and measured equivalent fission fluxes has beenobtained No systematic decrease of agreements betweencalculations and measurements with increasing distance ofdetector from the PCA benchmark facility core was observedfor any of the applied approaches This indicates that theshapes of calculated neutron spectra in the energy rangeweredosimeters are sensitive are properly determined SCALE60capabilities in generationmixing cross-sections from work-ing library v7 200n47g to be used as a response functions inMAVRIC proved to be very useful
References
[1] ldquoShielding Integral Benchmark Archive and Databaserdquo SINBADReactor Shielding Benchmark Experiments OECDNEA 2011
[2] I Remec and F B Kam ldquoPool Critical Assembly Pressure Ves-sel Facility Benchmarkrdquo NUREGCR-6454 (ORNLTM-13205)prepared for the USNRC by Oak Ridge National LaboratoryAugust 1997
[3] A H Fero S L Anderson and G K Roberts ldquoAnalysis ofthe ORNL PCA benchmark using TORT and BUGLE-96rdquoin Reactor Dosimetry Radiation Metrology and Assessment JG Williams D W Vehar F H Ruddy and D M GilliamEds pp 360ndash366 American Society for Testing and MaterialsPhiladelphia Pa USA 2001
[4] Y K Lee ldquoAnalysis of the NRC PCA pressure vessel dosimetrybenchmark using TRIPOLI-43 Monte Carlo code and ENDFB-VI4 JEF22 and IRDF-90 librariesrdquo Nuclear Mathematical andComputational Science ACentury in Review ACenturyAnewGatlinburg Tenn USA April 2003
[5] ldquoSCALE A Modular Code System for Performing Standard-ized Computer Analyses for Licensing Evaluationrdquo ORNLTM-200539 Version 6 Radiation Safety Information Computa-tional Center at Oak Ridge National Laboratory 2009
[6] D VragolovMMatijevic andD Pevec ldquoModeling of pool crit-ical assembly pressure vessel facility benchmarkrdquo in Proceedingsof the International Conference Nuclear Energy for New EuropeLjubljana Slovenia 2010
[7] J M Risner D Wiarda M E Dunn T M Miller D E Peplowand B W Patton ldquoProduction and Testing of the VITAMIN-B7 Fine-Group and BUGLE-B7 Broad-Group Coupled Neu-tronGamma Cross-Section Libraries Derived from ENDFB-VII0 Nuclear Datardquo USNRC NUREGCR-7045 2011
[8] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File 2002 (IRDF-2002) 2006
[9] International Atomic Energy Agency Vienna Austria Interna-tional Reactor Dosimetry File (IRDF-90 Version 2) 1993
[10] USNRCCalculational andDosimetryMethods forDeterminingPressure Vessel Neutron Fluence Regulatory Guide 1190 2001
[11] I Remec and F B K Kam ldquoHB Robinson-2 Pressure VesselBenchmarkrdquo NUREGCR-6453 (ORNLTM-13204) preparedfor the USNRC by Oak Ridge National Laboratory October1997
[12] J C Wagner and A Haghighat ldquoAutomated variance reductionof Monte Carlo shielding calculations using the discrete ordi-nates adjoint functionrdquo Nuclear Science and Engineering vol128 no 2 pp 186ndash208 1998
[13] J C Wagner E D Blakeman and D E Peplow ldquoForward-weighted CADIS method for global variance reductionrdquo Trans-actions of the American Nuclear Society vol 97 pp 630ndash6332007
[14] G I Bell and S Glasstone Nuclear Reactor Theory VanNostrand Reinhold Company Litton Educational Publishing1970
[15] J C Wagner Acceleration of Monte Carlo shielding calculationswith an automated variance reduction technique and parallel pro-cessing [PhD thesis] Pennsylvania State University UniversityPark Pa USA 1997
[16] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technologyrdquoNuclear Data Sheets vol 107 no 12 pp2931ndash3060 2006
[17] X-5 Monte Carlo Team MCNPmdashA General N-Particle Trans-port Code Version 5 vol 1 of Overview andTheory LA-UR-03-1987 Los Alamos National Laboratory 2003
[18] A Trkov M Herman and D A Brown ldquoENDF-6 FormatsManualrdquo Data Formats and Procedures for the EvaluatedNuclear Data Files ENDFB-VI and ENDFB-VII NationalNuclear Data Center Brookhaven National Laboratory 2011
[19] IAEA Nuclear Data Services httpwww-ndsiaeaorg
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
TribologyAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FuelsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofPetroleum Engineering
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in
CombustionJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Renewable Energy
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
StructuresJournal of
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
International Journal ofPhotoenergy
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear InstallationsScience and Technology of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solar EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Wind EnergyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nuclear EnergyInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014