Research ArticleComparative Analysis of the Dalat Nuclear Research Reactorwith HEU Fuel Using SRAC and MCNP5

Giang Phan1 Hoai-Nam Tran2 Kien-Cuong Nguyen3 Viet-Phu Tran4 Van-Khanh Hoang4

PhamNhu Viet Ha4 and Hoang Anh Tuan Kiet25

1Faculty of Applied Sciences Ton Duc Thang University Ho Chi Minh City 700000 Vietnam2Institute of Fundamental and Applied Sciences Duy Tan University 3 Quang Trung Da Nang 550000 Vietnam3Nuclear Research Institute VINATOM 01 Nguyen Tu Luc Dalat Lamdong 670000 Vietnam4Institute for Nuclear Science and Technology VINATOM 179 Hoang Quoc Viet Hanoi 100000 Vietnam5Western University Hanoi Yen Nghia Ward Ha Dong District Hanoi 100000 Vietnam

Correspondence should be addressed to Giang Phan phangiangtdteduvn and Hoai-Nam Tran tranhoainam4dtueduvn

Received 7 June 2017 Revised 25 August 2017 Accepted 24 September 2017 Published 27 December 2017

Academic Editor Arkady Serikov

Copyright copy 2017 Giang Phan et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Neutronics analysis has been performed for the 500 kWDalat Nuclear Research Reactor loaded with highly enriched uranium fuelusing the SRAC code systemThe effective multiplication factors keff were analyzed for the core at criticality conditions and in twocases corresponding to the complete withdrawal and the full insertion of control rods MCNP5 calculations were also conductedand compared to that obtained with the SRAC code The results show that the difference of the keff values between the codes iswithin 55 pcm Compared to the criticality conditions established in the experiments the maximum differences of the keff valuesobtained from the SRAC andMCNP5 calculations are 119 pcm and 64 pcm respectivelyThe radial and axial power peaking factorsare 1334 and 1710 respectively in the case of no control rod insertion At the criticality condition these values become 1445 and1832 when the control rods are partially inserted Compared toMCNP5 calculations the deviation of the relative power densities isless than 4 at the fuel bundles in the middle of the core while the maximum deviation is about 7 appearing at some peripheralbundles This agreement indicates the verification of the analysis models

1 Introduction

The TRIGA reactor designed and manufactured by GeneralAtomics (California USA) is the most common researchreactor with 66 facilities in 24 countries [1] The TRIGAMark II reactor is a pool-type multipurpose research reactorwith the power range of 20 kW to 16MW In 1960s the250 kW TRIGA Mark II reactor was installed in NuclearResearch Institute located in Dalat Vietnam It is also theunique reactor of the country until present In early 1980sthe reactor was upgraded to a 500 kW pool-type researchreactor named the Dalat Nuclear Research Reactor (DNRR)The feature of the DNRR is that the main structures of theTRIGA Mark II reactor were kept except the active corezone The core is loaded with the Russian VVR-M2 fueltype and cooled by natural convection The first criticality

of the DNRR was achieved on November 1 1983 and theoperation with full power was achieved in March 1984During the period from 1984 to 2007 the corewas loadedwithhighly enriched uranium (HEU) fuel with 235U enrichmentof 36 [2 3]Then the DNRR core was partly converted intolow enriched uranium (LEU) fuel with 235U enrichment of1975 in September 2007 The full-core conversion to LEUfuel was performed during the period from November 242011 to January 13 2012 At present the operation of DNRRis mainly for radioisotope production neutron activationanalysis education and researches The DNRR is operatedin a continuous mode of about 100ndash130 hrs in a period of3-4 weeks Then the reactor is shut down for maintenanceactivities During the maintenance experimental physicsresearches are conducted The yearly average operation timeof the DNRR is about 1300 hrs [3]

HindawiScience and Technology of Nuclear InstallationsVolume 2017 Article ID 2615409 10 pageshttpsdoiorg10115520172615409

2 Science and Technology of Nuclear Installations

Similar to the TRIGA Mark II reactor the DNRR con-sists of many components such as a neutron trap watergaps irradiation channels horizontal beam ports berylliumblocks control rods rotary specimen rack and graphitereflector These components make the core geometry com-plicated Such a complicated geometry is only possible tobe simulated using a Monte Carlo code However even inMonte Carlo simulation possible modifications are usuallymade to simplify the core geometry [4] Simplification andhomogenization of complicated material regions outside theactive core could usually be applied if the neutronic character-istics of the core are not affected significantly Alternatively adeterministic simulation model of the DNRR core is usefulwhen the advantage in computational time is consideredIn this respect the WIMSDCITATION codes were used tosimulate the DNRR core and applied to the problem of in-core fuel management [5]

In the present work analysis models of the DNRR reactorhave been developed using the SRAC deterministic codesystem [6] Taking into account the advantage of the deter-ministic method the SRAC code system allows simulatingthe DNRR core with small mesh sizes within reasonablecomputational timeThePIJ code of the SRAC system and theENDFB-VII0 data library were used for lattice calculationsto generate themacroscopic cross sections of fuel and nonfuellattice cells The full core was modelled using the COREBNcodewith hexagonal lattice cells Numerical calculations havebeen conducted based on the core configuration loaded with88HEU fresh fuel bundles During the startup period of theDNRR core configuration of 88HEU fuel bundles severalcriticality conditions were established with the control rodpositions determined experimentally and reported in thestartup report of the DNRR [7] Therefore in this work thecriticality calculations were analyzed and compared againstthe experimentally established conditions to verify the mod-els The effective multiplication factors 119896eff were analyzedfor two cases corresponding to the complete withdrawaland the full insertion of control rods (four shim rods andone automatic regulating rod) Criticality calculations ofthe DNRR were carried out with four different control rodbanks determined during the experiments Thermal neutronflux and power distributions have also been investigatedthroughout the radial core and along axial channels In orderto verify the analysis models the results obtained with theMCNP5 code were compared to that obtained with the SRACcode system Excess reactivity and the 119896eff values of thecriticality calculations obtained using the codes are thencompared to that reported in the startup report of the DNRR

2 Description of DNRR

Figure 1 and Table 1 show the horizontal view and thespecifications of the DNRR reactor [2] The core consistsof 121 hexagonal cells including fuel bundles control rodsirradiation channels and beryllium blocks The VVR-M2fuel bundle is made of aluminum-uranium alloy cladded inaluminumThe total 235Umass in a HEU fuel bundle is about402 g distributed in three coaxial fuel tubes The outer tubehas a hexagonal sharp appearance and the two inner tubes

are cylindricalThe reactor core is controlled by seven controlrods two safety rods (SR) four shim rods (ShR) and oneautomatic regulating rod (AR) The safety and shim rods aremade of boron carbide (B

4C) while the automatic regulating

rod is made of stainless steel The absorption length of thecontrol rods is 65 cm which ensures completely covering theactive core (60 cm) Dry channel and wet channel are coveredby aluminum cylinders with the thickness of 05mm Theneutron trap at the center of the core is a water cylinder with65 cm in diameter and 60 cm in length surrounded by sixberyllium blocks The beryllium block has the same outershape and dimension as the fuel bundle At several peripheralcells if no fuel bundle is loaded the beryllium blocksare loaded for providing supplementary neutron reflectionA beryllium ring of serrated beryllium blocks is locatedbetween the active core and the graphite reflector and servesas an additional reflector This beryllium ring and the coreare placed in a cylindrical aluminum shell the lower sectionof the supporting structure The thickness of the graphitereflector is 305 cm The core and the graphite reflector areplaced into the reactor pool In the present work neutronicscalculations have been performed based on the core configu-ration of 88HEU fuel bundles as illustrated in Figure 2

3 Calculation Models

31 Description of the SRAC Code System SRAC is a deter-ministic code system developed by Japan Atomic EnergyAgency for neutronics calculations of both lattice physicsand core physics of various reactor types [6] The SRACcode system integrates three transport codes (PIJ ANISNand TWOTRAN) and two diffusion codes (TUD andCITATION) for neutron flux calculations The PIJ codeis based on the collision probability method which couldsimulate 16 different lattice geometries An auxiliary codeCOREBN is also integrated for core burnup calculationsThe COREBN consists of the CITATION and a function tointerpolate macroscopic cross sections provided by latticecell calculationsThis interpolation function allowsCOREBNperforming burnup calculations for various thermal reactorswith strong heterogeneity which cannot be conducted usingthe original CITATION In the present work the PIJ andCOREBN have been used for the lattice physics and corephysics analyses of the DNRR respectively The cell averagedmacroscopic cross sections of all material types are preparedin the lattice physics calculations using the PIJ code Themacroscopic cross sections are then calculated for corephysics calculations using COREBN

32 Lattice Calculations Using PIJ The macroscopic crosssections of fuel cell neutron trap control rods and othernonfuel lattice cells were prepared via lattice cell calculationsusing the PIJ code and ENDFB-VII0 data library [6 8]For fuel cell the hexagonal fuel bundle was modelled witha small geometrical modification of the outer hexagonal fueltube of the VVR-M2 fuel bundle Figure 3 shows the cross-sectional views of the VVR-M2 fuel bundle and the fuellattice cell model in the PIJ code along with the detaileddimensional parameters The fuel bundle consists of three

Science and Technology of Nuclear Installations 3

7-1 drychannel

13-2 drychannel

1-4 wetchannelermalizing

column ermal column

Graphitereector

reectorBeryllium

Neutrontrap

Safetyshimrod

rodRegulating

BT number 1

BT number 4 BT number 3

BT number 2

Figure 1 Horizontal view of the DNRR

1-1

2-1

3-1

4-1

5-1

6-1

1-2

2-2

3-2

4-2

5-2

6-2 6-3 6-4 6-5 6-8 6-9 6-10

7-107-97-8

8-8

9-89-79-69-59-49-39-29-1

10-1 10-2 10-4 10-5 10-6 10-7 10-9

11-911-811-711-611-311-2

12-1

11-1

12-2 12-3 12-4 12-7 12-8

13-513-413-2 13-313-1

12-5 12-6

11-4

10-10

8-1 8-2 8-3 8-4 8-5

7-47-37-2

8-9

9-9

8-10

9-10

8-11 8-12

9-11

6-11 6-12

1-3

2-3

3-3

5-3

1-4 1-5

2-4

3-4

4-4

5-4

2-5

4-5

5-5

2-6

3-6

4-6

5-6

2-7

3-7

4-7

5-7

2-8

3-8

5-8

3-9

4-9

5-9

4-10

5-10 5-11

SR

ShR4ShR3

ShR1

SR

ShR2

AR

Figure 2 Configuration of the DNRR core with 88HEU fuel bundles SR safety rod ShR shim rod and AR automatic regulating rod

4 Science and Technology of Nuclear Installations

U-Al alloy (36 U 64 Al)Aluminum (100)

(a)

11 6

325

09

0909

0909

0907

07

07

2525

22 32

Unit in mm

U-Al alloy (36 U 64 Al)Aluminum (100)

(b)

Figure 3 Horizontal cross sections of (a) the VVR-M2 fuel bundle and (b) the fuel lattice cell model in the PIJ code

Table 1 Specifications of the DNRR

Reactor type Pool typeNominal thermal power 500 kWCoolant and moderator WaterCore cooling mechanism Natural convectionReflector Graphite beryllium waterActive core height 60 cmCore equivalent diameter 442 cmFuel pitch 35 cmFuel type VVR-M2 typeFuel meat U-Al alloyFuel cladding Aluminum alloy235U enrichment 36wtNumber of control rods 7 (2 safety rods 4 shim rods 1 regulating rod)Material of safety and shim rods B

4C

Material of automatic regulating rod Stainless steelNeutron measuring channels 9 (6 CFC 3 CIC)Vertical irradiation channels 4 (1 neutron trap 1 wet channel 2 dry channels)Horizontal beam ports 4 (1 tangential 3 radials)

fuel tubes cladded by aluminum The two inner tubes havecylindrical shapes while the outer tube is hexagonal with sixcircular corners However since the PIJ code is not able tosimulate exactly the circular corners of the outer hexagonalfuel tube of the VVR-M2 fuel bundle a sharp hexagonaltube was assumed in the simulation model by preserving thetotal fuel mass In the lattice calculations of the PIJ code 107energy groupsrsquo structure was used Then the cross sectionswere collapsed into seven energy groups (4 fast groups and 3thermal groups) for full-core calculations

The neutron trap consists of a cylindrical water holesurrounded by six beryllium blocks Since SRAC does not

allow simulating exactly the geometry of the neutron trapin the full-core model the neutron trap is modelled asa hexagonal water cell at the center surrounded by sixhexagonal blocks of homogeneous beryllium and waterTherefore in the lattice calculation the homogenizationof beryllium and water at the six surrounding cells hasbeen conducted while preserving the volume fractions ofthe beryllium and water Calculating the cross sections ofthe safety and shim rods is more complicated due to thestrong absorption of the control rods Since the control rodsare considered as black absorber materials the extrapolatedboundary constants corresponding to each neutron energy

Science and Technology of Nuclear Installations 5

X

Y

Figure 4 Full-core model with hexagonal grid

group should be taken into account Therefore once themacroscopic cross sections of the control rods were obtainedusing PIJ the ANISN code based on the Sn theory was usedto determine the extrapolated length in each energy groupOther nonfuel lattice cells such as aluminum rod berylliumrod and regulating rod were also simulated using the PIJcode The cross sections of materials in the active core weretaken from the previous lattice cell calculations and inputtedexactly at the same positions in the core model using PIJ(supercell calculation) Other lattice cells at the positions ofthe horizontal beam tubes rotary specimen rack and theinterface regions were not calculated using the PIJ code butthe compositions (air water aluminum and graphite) werehomogenized and inputted in the full-core model

33 Full-CoreModel TheCOREBNof the SRAC code systemwas used for the full-core calculation with hexagonal latticecells [6] The full-core model was described by hexagonalgrids of 37 times 37 in the X-Y plane as shown in Figure 4The total height of the model (1845 cm) was axially dividedinto a number of layers so that each axial layer has the samematerial For instance the active core is axially divided into60 layers with the mesh size about 1 cm However the actualmesh size of each layer in the full-core models could beslightly changed depending on the position of control rodsThe upper part of the beryllium blocks is water and the lowerpart is the homogenization of aluminum and water

34 Monte Carlo Model Monte Carlo calculations of theDNRR have been performed using the MCNP5 code andENDFB-VII0 data library to verify the analysis models andthe results obtained with the SRAC code system MCNP5 isa general Monte Carlo N-Particle transport code developedat Los Alamos National Laboratory [9] MCNP5 has anability to describe precisely the complex geometry of theDNRR including the fuel bundles horizontal beam tubesreflector and thermal column and thermalizing column Tosimplify the simulation model but not affecting significantlythe neutronic characteristics of the DNRR core the upperand lower parts of the fuel bundle aluminum rod berylliumrod and dry and wet irradiation channels were described asthe homogeneous mixtures of aluminum and water Figure 5displays the vertical and horizontal cross-sectional views of

theDNRR core in theMCNP5modelThemodel is expandedfrom the active core to reactor tank following the radialdirection with 198 cm in diameter and the axial directionwith 1845 cm in height The history number of 210 times 106 waschosen so that the statistic error of 119896eff would be less than0006 Tallies 4 and 7 were used to calculate the neutronflux and power distributions

Since the simulation requires a high computationalresource in the present work the criticality calculationswere performed on a Windows server with 80 CPUs Thecomputational time of each run for the mentioned historynumber is about 156 minutes When the computational timeof the codes is compared the SRAC code is advantageoussince it can run fast on a personal computerwith Intel Core i5-4460 of CPU 33GHz Once the macroscopic cross sectionsof all materials are prepared using the PIJ code the full-corecalculation takes about half a minute

4 Numerical Calculations andComparison with MCNP5

41 Lattice Calculations The infinite multiplication factor119896infin of the fuel bundle obtained from the PIJ code is 164463

greater than that obtained fromMCNP5 (164034 plusmn 000004)by about 261 pcm If the MCNP5 model uses the modifiedgeometry of the outer fuel tube as in the PIJ model thedeviation of 119896

infinis about 139 pcm This indicates that the

lattice calculation results of the codes have a good agreement

42 Criticality Calculations The 119896eff values obtained areshown in Table 2 It can be seen that in the case of con-trol rod withdrawal the 119896eff values of 108633 and 108632were obtained from the SRAC and MCNP5 calculationsrespectively The calculated values are well consistent witheach other Taking into account the fact that the effectivedelayed neutron fraction 120573eff of the core is 00081 the 119896effvalues correspond to the excess reactivity of about 981$Thisvalue is comparable with that (985$) reported in the startupreport of the DNRR [7] The leakage reactivity penalty isminus001940 and that associated with absorption is minus090114In the case of full insertion of the four shim rods and theautomatic regulating rod the difference of the 119896eff valuesis about 242 pcm This agreement between the SRAC and

6 Science and Technology of Nuclear Installations

(a) Vertical (b) Horizontal

Figure 5 Vertical and horizontal cross sections of the DNRR in the MCNP5 model

Table 2 The 119896eff in the cases of complete withdrawal and full insertion of control rods

Code 119896eff (A) 119896eff (B) Reactivity worth (Δ1198961198961198961015840)SRAC 108633 098029 996MCNP5 108632 plusmn 000006 097787 plusmn 000005 1021(A) All control rods are completely withdrawn (B) Two safety rods are withdrawn four shim rods and the automatic regulating rod are fully inserted

MCNP5 calculations gives a certain confidence for furtheranalysis of the DNRR core The total worth values of the fourshim rods and the automatic regulating rod of 123$ and 126$obtained from SRAC andMCNP5 respectively are sufficientto shut down the reactor

Criticality calculations of the core with four control rodbanks have been carried out To do this the four shim rodswere inserted into the core Then the position of the AR wasadjusted to obtain the criticality of the core These criticalityconditions were achieved during the startup of the DNRRcore with HEU fuel [7] Since the two safety rods are usedonly for emergency shutdown in all cases they were assumedto be completely withdrawn

Table 3 shows the results of the criticality calculations cor-responding to the four control rod banks The 119896eff values areclosed to unity with the deviation within 119 pcm In all casesthe 119896eff values obtained for SRAC are in good agreementwith that obtained from MCNP5 calculations The greatestdifference is about 55 pcm corresponding to the case withthe insertions of ShRs = 45 cm and AR = 65 cm Comparedto unity that is the criticality conditions established in theexperiments [7] the maximum difference of the 119896eff valuesobtained from the SRAC calculations is 119 pcm while thisvalue is 64 pcm for the MCNP5 calculations This agreementcompared to the experiments indicates the verification of themodels

43 Power andThermal Neutron Flux Distributions Thermalneutron flux and power distributions of the DNRR corehave been analyzed in detail for two cases corresponding tothe complete withdrawal and the partial insertion (ShR =457 cm and AR = 40 cm) of control rods in comparison with

MCNP5 calculations Figure 6 shows the radial relative powerdistribution at the initial critical condition correspondingto the control rod insertions of ShR = 457 cm and AR =40 cmThe radial power peaking factor is 1445which appearsat the fuel bundle 9-6 This value is obtained as 1486 inthe MCNP5 calculation The deviation of the relative powerdensities between the codes is less than 4 at most of fuelbundles except some bundles located at periphery wherethe maximum deviation is about 7 Figure 7 is similar toFigure 6 but for the case of complete withdrawal of all controlrodsThe radial power peaking factor is about 1334 at the fuelcell 9-6 obtained with SRAC smaller than that obtained withMCNP5 (1385) by about 37

Figures 8 and 9 depict the axial power distributions at thefuel cells 9-6 and 7-10 in the cases of control rod insertion andcontrol rod withdrawal respectively The fuel cell 9-6 corre-sponds to the highest power ratingThe fuel cell 7-10 is locatedclose to the AR and therefore its power profile and fluxdistribution show clearly the effect of control rod insertionWhen the control rod is partially inserted the power profileis shifted to the lower half of the core and the power peakingfactor increasesThe axial power peaking factor is about 1710in the case of control rod withdrawal while it is about 1832in the case of control rod insertion Furthermore axial powerprofile results of the codes are in good agreementThe largestdifference is found at the boundary interfaces between theactive fuel and the upper and lower reflectors

Figures 10 and 11 show the axial thermal neutron fluxdistribution in the fuel cells 9-6 and 7-10 for the two casescorresponding to the control rod insertion and withdrawalrespectively Figure 12 shows the axial distribution of thethermal neutron flux along the height of neutron trap in

Science and Technology of Nuclear Installations 7

Table 3 Criticality calculations of the DNRR with four control rod banks

Position of control rods (cm) 119896eff Dev(pcm)ShR1 ShR2 ShR3 ShR4 AR SRAC MCNP545 45 45 45 65 100119 100064 plusmn 000006 55472 472 472 472 0 099960 099969 plusmn 000006 9457 457 457 457 40 100086 100051 plusmn 000006 35467 467 467 467 20 100009 099998 plusmn 000006 11

09200968

09791021

10601131 1130

1059 09771023

09180977

07770798

08470887

08410854

08960912

09450931

09650925

09750936

09110963

08830843

08290776

08350808

07730759

10010977

09360915

08030825

09050944

09960991

10611121

10091000

111811230950

0928

08330838

098510371004

0931

08260790

07920778 ShR3

SR08690935

09150872

08930894

08760886

10701099

10471079

10641098

097310060883

0864

07690771

079707810850

0879

08560870

09480978

10581044

09960972

10761047

10551062 0998

0981

09611012

08890875

10070978

10631132

11101121

07190757

ShR4

08220868

10261083

10001054

14551429

08400869

09560997

09160944

082208260995

1002

11201115

128612811486

1444

11181122

100509970829

0825

09480922

12911292

14391481

13221324

14391483

12931293 1481

1445 12871274

09970947

14521429

12921309

10341083

08030859

AR

09420905

08370863

07570761

SR

ShR2 ShR1

Figure 6 Relative power distribution in the core at the initial critical condition corresponding to the control rod insertion ShR = 457 cmAR = 40 cm The upper and lower values were obtained with SRAC and MCNP5 respectively

comparison with the results obtained from the MCNP5calculations It can be seen that the maximum thermalneutron flux is about 217 times 1013 ncm2sdots in the case of controlrod withdrawal The axial flux distribution is also shifted tothe lower part of the core when the control rods are insertedIn this case the peak value of thermal flux is about 238 times1013 ncm2sdots shifted to about 10 cm from the central point ofthe neutron trap to the core bottom as shown in Figure 12noting that there is a good agreement between the two codesThis indicates the validity of the analysis models and thepotential use for further applications

Since theDNRR core containsmany complicated compo-nents it is a challenge to model the core using a deterministiccode Homogenization of materials especially in particularregions where control rods are withdrawn could affect theaccuracy of the results However in the present work theanalysis results show an acceptable agreement between thecodes as well as the startup report The current models ofthe DNRR core in the SRAC code could handle flexible axialmesh sizes along the core height depending on the actualcontrol rod positions A possible improvement of the modelsto handle finer radial meshes such as triangular meshes could

8 Science and Technology of Nuclear Installations

0922 0954 10221064 1066

1023 09570991 0979

09160930

08400846

08870907

09720983

084108630970

0949

10361005

10471071

10131034

093609460990

0978

10821062

12171228

1329

1385

1063

1230

10141033 1082

097809900944

0931091209170872

08900878

08320837

08620848

09700956

08850908

09740962 0916

10371017

13301384

10511072

13311384

10381023

099209850962

09700977

0922

08960938 0863

09730966 1061 1232

1218 13341381

12171219

13291369

12081211

09890952

09810966

09680956

08750839

08280775

085508260890

0912

08470889

08100859

089209321035

0998

092909681071

1034

10330998

10821055

09900969

09450916

0971105810641025

09970990

09800992

106310191035

094409240871

090008960846

0877 ShR3

0920

1083

09460948

0931 0959 1024 0956 09240940

10730867

0936

097212101227

0934

0854

1217 1333

137309330906

08820893

09000866

09280958 0985

SR

ShR4

AR

ShR2

SR

ShR1

Figure 7 Relative power distribution in the case of complete withdrawal of the control rods The upper and lower values were obtained withSRAC and MCNP5 respectively

Cell 7-10

SRACMCNP5

Cell 9-6

ShR = 457cm AR = 40 cm

04

06

08

10

12

14

16

18

20

Relat

ive p

ower

den

sity

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Figure 8 Axial power distribution along the fuel bundles 7-10 and 9-6 at the critical core condition corresponding to the insertion of controlrods ShR = 457 cm and AR = 40 cm

Science and Technology of Nuclear Installations 9

04

06

08

10

12

14

16

18

Relat

ive p

ower

den

sity

20

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

Figure 9 Axial power distribution along the fuel bundles 7-10 and9-6 in the case of complete withdrawal of control rods

Cell 7-10

SRACMCNP5

Cell 9-6

0

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

9 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

ShR = 457cm AR = 40 cm

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

Figure 10Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 at the critical core condition corresponding to theinsertion of control rods ShR = 457 cm and AR = 40 cm

be useful to improve the accuracy of the calculation resultsFurther analyses are necessary to verify themodels using bothSRAC andMCNP5 codes for burnup and rod worth analysesof the DNRR core in comparison with themeasurement dataEvaluation of the effect of the cross section data libraries onthe neutronic properties of the DNRR core is being investi-gated Application in analyzing the current working configu-rations of the DNRR with low enriched uranium (LEU) fuelbundles is also being planned

5 Conclusions

Neutronics model of the DNRR was developed using theSRAC code system The PIJ and COREBN codes of the

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 11 Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 in the case of complete withdrawal of control rods

Rods in SRACRods in MCNP5

Rods out SRACRods out MCNP5

100 20 30minus20 minus10minus30Core height (top to bottom) (cm)

40 times 1012

60 times 1012

80 times 1012

10 times 1013

12 times 1013

14 times 1013

16 times 1013

18 times 1013

20 times 1013

22 times 1013

24 times 1013

26 times 1013

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 12Thermal neutron flux distribution along the neutron trapRods in ShR = 457 cm and AR = 40 cm Rods out ShR = 0 cm andAR = 0 cm

SRAC code system were used for lattice physics and full-coreanalyses In order to handle the complicated geometries ofthe DNRR such as the neutron trap neutron channels andupper and lower parts of the active core homogenizationhas been conducted Numerical calculations were performedto analyze the effective multiplication factors 119896eff for twocases corresponding to the complete withdrawal and thefull insertion of control rods Criticality analyses were thenconducted with the four different control rod banks Theradial and axial power peaking factors of the DNRR core arecalculated to be 1334 and 1710 respectively in the case of nocontrol rod insertion These values are 1445 and 1832 at thecriticality condition with the partial insertion of control rodsComparing to the MCNP5 calculations the results show that

10 Science and Technology of Nuclear Installations

the difference between the 119896eff values of the codes is less than55 pcm The maximum deviations of the 119896eff values obtainedfrom SRAC and MCNP5 compared to the experiments are119 pcm and 64 pcm respectivelyThedeviation of the relativepower distributions between the codes is less than 4 formost of the fuel bundles in the middle of the core while themaximum deviation is about 7 which appears at peripheralbundles In addition thermal neutron flux distributions inthe neutron trap are in good agreement This agreementindicates the verification of the models and the possibility forfurther analysis

Conflicts of Interest

The authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

This research is funded by Foundation for Science andTechnology Development of Ton Duc Thang University(FOSTECT) website httpfostecttdteduvn under GrantFOSTECT2016BR13

References

[1] TRIGA History URL httpwwwgacomtriga-history[2] N D Nguyen Ed Safety Analysis Report for the Dalat Nuclear

Research Reactor Nuclear Research Institute Vietnam AtomicEnergy Commission 2009

[3] N D Nguyen B V Luong V V Le et al ldquoResults of Operationand Utilization of the Dalat Nuclear Research ReactorrdquoNuclearScience and Technology vol 4 no 1 pp 1ndash9 2014

[4] M Turkmen and U Colak ldquoAnalysis of ITU TRIGA MarkII research reactor using Monte Carlo methodrdquo Progress inNuclear Energy vol 77 pp 152ndash159 2014

[5] B Q Do and L P Nguyen ldquoApplication of a genetic algorithmto the fuel reload optimization for a research reactorrdquo AppliedMathematics andComputation vol 187 no 2 pp 977ndash988 2007

[6] K Okumura T Kugo K Kaneko and K TsuchihashiSRAC2006 A Comprehensive Neutronics Calculation Code Sys-tem JAEA-DataCode 2007-004 2007

[7] D H Pham Q H Ngo H L Vu and KM Tran Report startupof nuclear research reactor Part 2 - Physics startup for coreconfiguration with a neutron trap Nuclear Research Institute1984

[8] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technology Nucl Data Sheetsrdquo Special Issue onEvaluated Nuclear Data File ENDFB-VII0 2006

[9] X-5 Monte Carlo Team 2005 MCNP - A General Monte CarloN-Particle Transport Code Version 5 LA-UR-03-1987 April 242003

Science and Technology of Nuclear Installations 3

7-1 drychannel

13-2 drychannel

1-4 wetchannelermalizing

column ermal column

Graphitereector

reectorBeryllium

Neutrontrap

Safetyshimrod

rodRegulating

BT number 1

BT number 4 BT number 3

BT number 2

Figure 1 Horizontal view of the DNRR

1-1

2-1

3-1

4-1

5-1

6-1

1-2

2-2

3-2

4-2

5-2

6-2 6-3 6-4 6-5 6-8 6-9 6-10

7-107-97-8

8-8

9-89-79-69-59-49-39-29-1

10-1 10-2 10-4 10-5 10-6 10-7 10-9

11-911-811-711-611-311-2

12-1

11-1

12-2 12-3 12-4 12-7 12-8

13-513-413-2 13-313-1

12-5 12-6

11-4

10-10

8-1 8-2 8-3 8-4 8-5

7-47-37-2

8-9

9-9

8-10

9-10

8-11 8-12

9-11

6-11 6-12

1-3

2-3

3-3

5-3

1-4 1-5

2-4

3-4

4-4

5-4

2-5

4-5

5-5

2-6

3-6

4-6

5-6

2-7

3-7

4-7

5-7

2-8

3-8

5-8

3-9

4-9

5-9

4-10

5-10 5-11

SR

ShR4ShR3

ShR1

SR

ShR2

AR

Figure 2 Configuration of the DNRR core with 88HEU fuel bundles SR safety rod ShR shim rod and AR automatic regulating rod

4 Science and Technology of Nuclear Installations

U-Al alloy (36 U 64 Al)Aluminum (100)

(a)

11 6

325

09

0909

0909

0907

07

07

2525

22 32

Unit in mm

U-Al alloy (36 U 64 Al)Aluminum (100)

(b)

Figure 3 Horizontal cross sections of (a) the VVR-M2 fuel bundle and (b) the fuel lattice cell model in the PIJ code

Table 1 Specifications of the DNRR

Reactor type Pool typeNominal thermal power 500 kWCoolant and moderator WaterCore cooling mechanism Natural convectionReflector Graphite beryllium waterActive core height 60 cmCore equivalent diameter 442 cmFuel pitch 35 cmFuel type VVR-M2 typeFuel meat U-Al alloyFuel cladding Aluminum alloy235U enrichment 36wtNumber of control rods 7 (2 safety rods 4 shim rods 1 regulating rod)Material of safety and shim rods B

4C

Material of automatic regulating rod Stainless steelNeutron measuring channels 9 (6 CFC 3 CIC)Vertical irradiation channels 4 (1 neutron trap 1 wet channel 2 dry channels)Horizontal beam ports 4 (1 tangential 3 radials)

fuel tubes cladded by aluminum The two inner tubes havecylindrical shapes while the outer tube is hexagonal with sixcircular corners However since the PIJ code is not able tosimulate exactly the circular corners of the outer hexagonalfuel tube of the VVR-M2 fuel bundle a sharp hexagonaltube was assumed in the simulation model by preserving thetotal fuel mass In the lattice calculations of the PIJ code 107energy groupsrsquo structure was used Then the cross sectionswere collapsed into seven energy groups (4 fast groups and 3thermal groups) for full-core calculations

The neutron trap consists of a cylindrical water holesurrounded by six beryllium blocks Since SRAC does not

allow simulating exactly the geometry of the neutron trapin the full-core model the neutron trap is modelled asa hexagonal water cell at the center surrounded by sixhexagonal blocks of homogeneous beryllium and waterTherefore in the lattice calculation the homogenizationof beryllium and water at the six surrounding cells hasbeen conducted while preserving the volume fractions ofthe beryllium and water Calculating the cross sections ofthe safety and shim rods is more complicated due to thestrong absorption of the control rods Since the control rodsare considered as black absorber materials the extrapolatedboundary constants corresponding to each neutron energy

Science and Technology of Nuclear Installations 5

X

Y

Figure 4 Full-core model with hexagonal grid

group should be taken into account Therefore once themacroscopic cross sections of the control rods were obtainedusing PIJ the ANISN code based on the Sn theory was usedto determine the extrapolated length in each energy groupOther nonfuel lattice cells such as aluminum rod berylliumrod and regulating rod were also simulated using the PIJcode The cross sections of materials in the active core weretaken from the previous lattice cell calculations and inputtedexactly at the same positions in the core model using PIJ(supercell calculation) Other lattice cells at the positions ofthe horizontal beam tubes rotary specimen rack and theinterface regions were not calculated using the PIJ code butthe compositions (air water aluminum and graphite) werehomogenized and inputted in the full-core model

33 Full-CoreModel TheCOREBNof the SRAC code systemwas used for the full-core calculation with hexagonal latticecells [6] The full-core model was described by hexagonalgrids of 37 times 37 in the X-Y plane as shown in Figure 4The total height of the model (1845 cm) was axially dividedinto a number of layers so that each axial layer has the samematerial For instance the active core is axially divided into60 layers with the mesh size about 1 cm However the actualmesh size of each layer in the full-core models could beslightly changed depending on the position of control rodsThe upper part of the beryllium blocks is water and the lowerpart is the homogenization of aluminum and water

34 Monte Carlo Model Monte Carlo calculations of theDNRR have been performed using the MCNP5 code andENDFB-VII0 data library to verify the analysis models andthe results obtained with the SRAC code system MCNP5 isa general Monte Carlo N-Particle transport code developedat Los Alamos National Laboratory [9] MCNP5 has anability to describe precisely the complex geometry of theDNRR including the fuel bundles horizontal beam tubesreflector and thermal column and thermalizing column Tosimplify the simulation model but not affecting significantlythe neutronic characteristics of the DNRR core the upperand lower parts of the fuel bundle aluminum rod berylliumrod and dry and wet irradiation channels were described asthe homogeneous mixtures of aluminum and water Figure 5displays the vertical and horizontal cross-sectional views of

theDNRR core in theMCNP5modelThemodel is expandedfrom the active core to reactor tank following the radialdirection with 198 cm in diameter and the axial directionwith 1845 cm in height The history number of 210 times 106 waschosen so that the statistic error of 119896eff would be less than0006 Tallies 4 and 7 were used to calculate the neutronflux and power distributions

Since the simulation requires a high computationalresource in the present work the criticality calculationswere performed on a Windows server with 80 CPUs Thecomputational time of each run for the mentioned historynumber is about 156 minutes When the computational timeof the codes is compared the SRAC code is advantageoussince it can run fast on a personal computerwith Intel Core i5-4460 of CPU 33GHz Once the macroscopic cross sectionsof all materials are prepared using the PIJ code the full-corecalculation takes about half a minute

4 Numerical Calculations andComparison with MCNP5

41 Lattice Calculations The infinite multiplication factor119896infin of the fuel bundle obtained from the PIJ code is 164463

greater than that obtained fromMCNP5 (164034 plusmn 000004)by about 261 pcm If the MCNP5 model uses the modifiedgeometry of the outer fuel tube as in the PIJ model thedeviation of 119896

infinis about 139 pcm This indicates that the

lattice calculation results of the codes have a good agreement

42 Criticality Calculations The 119896eff values obtained areshown in Table 2 It can be seen that in the case of con-trol rod withdrawal the 119896eff values of 108633 and 108632were obtained from the SRAC and MCNP5 calculationsrespectively The calculated values are well consistent witheach other Taking into account the fact that the effectivedelayed neutron fraction 120573eff of the core is 00081 the 119896effvalues correspond to the excess reactivity of about 981$Thisvalue is comparable with that (985$) reported in the startupreport of the DNRR [7] The leakage reactivity penalty isminus001940 and that associated with absorption is minus090114In the case of full insertion of the four shim rods and theautomatic regulating rod the difference of the 119896eff valuesis about 242 pcm This agreement between the SRAC and

6 Science and Technology of Nuclear Installations

(a) Vertical (b) Horizontal

Figure 5 Vertical and horizontal cross sections of the DNRR in the MCNP5 model

Table 2 The 119896eff in the cases of complete withdrawal and full insertion of control rods

Code 119896eff (A) 119896eff (B) Reactivity worth (Δ1198961198961198961015840)SRAC 108633 098029 996MCNP5 108632 plusmn 000006 097787 plusmn 000005 1021(A) All control rods are completely withdrawn (B) Two safety rods are withdrawn four shim rods and the automatic regulating rod are fully inserted

MCNP5 calculations gives a certain confidence for furtheranalysis of the DNRR core The total worth values of the fourshim rods and the automatic regulating rod of 123$ and 126$obtained from SRAC andMCNP5 respectively are sufficientto shut down the reactor

Criticality calculations of the core with four control rodbanks have been carried out To do this the four shim rodswere inserted into the core Then the position of the AR wasadjusted to obtain the criticality of the core These criticalityconditions were achieved during the startup of the DNRRcore with HEU fuel [7] Since the two safety rods are usedonly for emergency shutdown in all cases they were assumedto be completely withdrawn

Table 3 shows the results of the criticality calculations cor-responding to the four control rod banks The 119896eff values areclosed to unity with the deviation within 119 pcm In all casesthe 119896eff values obtained for SRAC are in good agreementwith that obtained from MCNP5 calculations The greatestdifference is about 55 pcm corresponding to the case withthe insertions of ShRs = 45 cm and AR = 65 cm Comparedto unity that is the criticality conditions established in theexperiments [7] the maximum difference of the 119896eff valuesobtained from the SRAC calculations is 119 pcm while thisvalue is 64 pcm for the MCNP5 calculations This agreementcompared to the experiments indicates the verification of themodels

43 Power andThermal Neutron Flux Distributions Thermalneutron flux and power distributions of the DNRR corehave been analyzed in detail for two cases corresponding tothe complete withdrawal and the partial insertion (ShR =457 cm and AR = 40 cm) of control rods in comparison with

MCNP5 calculations Figure 6 shows the radial relative powerdistribution at the initial critical condition correspondingto the control rod insertions of ShR = 457 cm and AR =40 cmThe radial power peaking factor is 1445which appearsat the fuel bundle 9-6 This value is obtained as 1486 inthe MCNP5 calculation The deviation of the relative powerdensities between the codes is less than 4 at most of fuelbundles except some bundles located at periphery wherethe maximum deviation is about 7 Figure 7 is similar toFigure 6 but for the case of complete withdrawal of all controlrodsThe radial power peaking factor is about 1334 at the fuelcell 9-6 obtained with SRAC smaller than that obtained withMCNP5 (1385) by about 37

Figures 8 and 9 depict the axial power distributions at thefuel cells 9-6 and 7-10 in the cases of control rod insertion andcontrol rod withdrawal respectively The fuel cell 9-6 corre-sponds to the highest power ratingThe fuel cell 7-10 is locatedclose to the AR and therefore its power profile and fluxdistribution show clearly the effect of control rod insertionWhen the control rod is partially inserted the power profileis shifted to the lower half of the core and the power peakingfactor increasesThe axial power peaking factor is about 1710in the case of control rod withdrawal while it is about 1832in the case of control rod insertion Furthermore axial powerprofile results of the codes are in good agreementThe largestdifference is found at the boundary interfaces between theactive fuel and the upper and lower reflectors

Figures 10 and 11 show the axial thermal neutron fluxdistribution in the fuel cells 9-6 and 7-10 for the two casescorresponding to the control rod insertion and withdrawalrespectively Figure 12 shows the axial distribution of thethermal neutron flux along the height of neutron trap in

Science and Technology of Nuclear Installations 7

Table 3 Criticality calculations of the DNRR with four control rod banks

Position of control rods (cm) 119896eff Dev(pcm)ShR1 ShR2 ShR3 ShR4 AR SRAC MCNP545 45 45 45 65 100119 100064 plusmn 000006 55472 472 472 472 0 099960 099969 plusmn 000006 9457 457 457 457 40 100086 100051 plusmn 000006 35467 467 467 467 20 100009 099998 plusmn 000006 11

09200968

09791021

10601131 1130

1059 09771023

09180977

07770798

08470887

08410854

08960912

09450931

09650925

09750936

09110963

08830843

08290776

08350808

07730759

10010977

09360915

08030825

09050944

09960991

10611121

10091000

111811230950

0928

08330838

098510371004

0931

08260790

07920778 ShR3

SR08690935

09150872

08930894

08760886

10701099

10471079

10641098

097310060883

0864

07690771

079707810850

0879

08560870

09480978

10581044

09960972

10761047

10551062 0998

0981

09611012

08890875

10070978

10631132

11101121

07190757

ShR4

08220868

10261083

10001054

14551429

08400869

09560997

09160944

082208260995

1002

11201115

128612811486

1444

11181122

100509970829

0825

09480922

12911292

14391481

13221324

14391483

12931293 1481

1445 12871274

09970947

14521429

12921309

10341083

08030859

AR

09420905

08370863

07570761

SR

ShR2 ShR1

Figure 6 Relative power distribution in the core at the initial critical condition corresponding to the control rod insertion ShR = 457 cmAR = 40 cm The upper and lower values were obtained with SRAC and MCNP5 respectively

comparison with the results obtained from the MCNP5calculations It can be seen that the maximum thermalneutron flux is about 217 times 1013 ncm2sdots in the case of controlrod withdrawal The axial flux distribution is also shifted tothe lower part of the core when the control rods are insertedIn this case the peak value of thermal flux is about 238 times1013 ncm2sdots shifted to about 10 cm from the central point ofthe neutron trap to the core bottom as shown in Figure 12noting that there is a good agreement between the two codesThis indicates the validity of the analysis models and thepotential use for further applications

Since theDNRR core containsmany complicated compo-nents it is a challenge to model the core using a deterministiccode Homogenization of materials especially in particularregions where control rods are withdrawn could affect theaccuracy of the results However in the present work theanalysis results show an acceptable agreement between thecodes as well as the startup report The current models ofthe DNRR core in the SRAC code could handle flexible axialmesh sizes along the core height depending on the actualcontrol rod positions A possible improvement of the modelsto handle finer radial meshes such as triangular meshes could

8 Science and Technology of Nuclear Installations

0922 0954 10221064 1066

1023 09570991 0979

09160930

08400846

08870907

09720983

084108630970

0949

10361005

10471071

10131034

093609460990

0978

10821062

12171228

1329

1385

1063

1230

10141033 1082

097809900944

0931091209170872

08900878

08320837

08620848

09700956

08850908

09740962 0916

10371017

13301384

10511072

13311384

10381023

099209850962

09700977

0922

08960938 0863

09730966 1061 1232

1218 13341381

12171219

13291369

12081211

09890952

09810966

09680956

08750839

08280775

085508260890

0912

08470889

08100859

089209321035

0998

092909681071

1034

10330998

10821055

09900969

09450916

0971105810641025

09970990

09800992

106310191035

094409240871

090008960846

0877 ShR3

0920

1083

09460948

0931 0959 1024 0956 09240940

10730867

0936

097212101227

0934

0854

1217 1333

137309330906

08820893

09000866

09280958 0985

SR

ShR4

AR

ShR2

SR

ShR1

Figure 7 Relative power distribution in the case of complete withdrawal of the control rods The upper and lower values were obtained withSRAC and MCNP5 respectively

Cell 7-10

SRACMCNP5

Cell 9-6

ShR = 457cm AR = 40 cm

04

06

08

10

12

14

16

18

20

Relat

ive p

ower

den

sity

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Figure 8 Axial power distribution along the fuel bundles 7-10 and 9-6 at the critical core condition corresponding to the insertion of controlrods ShR = 457 cm and AR = 40 cm

Science and Technology of Nuclear Installations 9

04

06

08

10

12

14

16

18

Relat

ive p

ower

den

sity

20

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

Figure 9 Axial power distribution along the fuel bundles 7-10 and9-6 in the case of complete withdrawal of control rods

Cell 7-10

SRACMCNP5

Cell 9-6

0

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

9 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

ShR = 457cm AR = 40 cm

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

Figure 10Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 at the critical core condition corresponding to theinsertion of control rods ShR = 457 cm and AR = 40 cm

be useful to improve the accuracy of the calculation resultsFurther analyses are necessary to verify themodels using bothSRAC andMCNP5 codes for burnup and rod worth analysesof the DNRR core in comparison with themeasurement dataEvaluation of the effect of the cross section data libraries onthe neutronic properties of the DNRR core is being investi-gated Application in analyzing the current working configu-rations of the DNRR with low enriched uranium (LEU) fuelbundles is also being planned

5 Conclusions

Neutronics model of the DNRR was developed using theSRAC code system The PIJ and COREBN codes of the

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 11 Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 in the case of complete withdrawal of control rods

Rods in SRACRods in MCNP5

Rods out SRACRods out MCNP5

100 20 30minus20 minus10minus30Core height (top to bottom) (cm)

40 times 1012

60 times 1012

80 times 1012

10 times 1013

12 times 1013

14 times 1013

16 times 1013

18 times 1013

20 times 1013

22 times 1013

24 times 1013

26 times 1013

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 12Thermal neutron flux distribution along the neutron trapRods in ShR = 457 cm and AR = 40 cm Rods out ShR = 0 cm andAR = 0 cm

SRAC code system were used for lattice physics and full-coreanalyses In order to handle the complicated geometries ofthe DNRR such as the neutron trap neutron channels andupper and lower parts of the active core homogenizationhas been conducted Numerical calculations were performedto analyze the effective multiplication factors 119896eff for twocases corresponding to the complete withdrawal and thefull insertion of control rods Criticality analyses were thenconducted with the four different control rod banks Theradial and axial power peaking factors of the DNRR core arecalculated to be 1334 and 1710 respectively in the case of nocontrol rod insertion These values are 1445 and 1832 at thecriticality condition with the partial insertion of control rodsComparing to the MCNP5 calculations the results show that

10 Science and Technology of Nuclear Installations

the difference between the 119896eff values of the codes is less than55 pcm The maximum deviations of the 119896eff values obtainedfrom SRAC and MCNP5 compared to the experiments are119 pcm and 64 pcm respectivelyThedeviation of the relativepower distributions between the codes is less than 4 formost of the fuel bundles in the middle of the core while themaximum deviation is about 7 which appears at peripheralbundles In addition thermal neutron flux distributions inthe neutron trap are in good agreement This agreementindicates the verification of the models and the possibility forfurther analysis

Conflicts of Interest

The authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

This research is funded by Foundation for Science andTechnology Development of Ton Duc Thang University(FOSTECT) website httpfostecttdteduvn under GrantFOSTECT2016BR13

References

[1] TRIGA History URL httpwwwgacomtriga-history[2] N D Nguyen Ed Safety Analysis Report for the Dalat Nuclear

Research Reactor Nuclear Research Institute Vietnam AtomicEnergy Commission 2009

[3] N D Nguyen B V Luong V V Le et al ldquoResults of Operationand Utilization of the Dalat Nuclear Research ReactorrdquoNuclearScience and Technology vol 4 no 1 pp 1ndash9 2014

[4] M Turkmen and U Colak ldquoAnalysis of ITU TRIGA MarkII research reactor using Monte Carlo methodrdquo Progress inNuclear Energy vol 77 pp 152ndash159 2014

[5] B Q Do and L P Nguyen ldquoApplication of a genetic algorithmto the fuel reload optimization for a research reactorrdquo AppliedMathematics andComputation vol 187 no 2 pp 977ndash988 2007

[6] K Okumura T Kugo K Kaneko and K TsuchihashiSRAC2006 A Comprehensive Neutronics Calculation Code Sys-tem JAEA-DataCode 2007-004 2007

[7] D H Pham Q H Ngo H L Vu and KM Tran Report startupof nuclear research reactor Part 2 - Physics startup for coreconfiguration with a neutron trap Nuclear Research Institute1984

[8] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technology Nucl Data Sheetsrdquo Special Issue onEvaluated Nuclear Data File ENDFB-VII0 2006

[9] X-5 Monte Carlo Team 2005 MCNP - A General Monte CarloN-Particle Transport Code Version 5 LA-UR-03-1987 April 242003

4 Science and Technology of Nuclear Installations

U-Al alloy (36 U 64 Al)Aluminum (100)

(a)

11 6

325

09

0909

0909

0907

07

07

2525

22 32

Unit in mm

U-Al alloy (36 U 64 Al)Aluminum (100)

(b)

Figure 3 Horizontal cross sections of (a) the VVR-M2 fuel bundle and (b) the fuel lattice cell model in the PIJ code

Table 1 Specifications of the DNRR

Reactor type Pool typeNominal thermal power 500 kWCoolant and moderator WaterCore cooling mechanism Natural convectionReflector Graphite beryllium waterActive core height 60 cmCore equivalent diameter 442 cmFuel pitch 35 cmFuel type VVR-M2 typeFuel meat U-Al alloyFuel cladding Aluminum alloy235U enrichment 36wtNumber of control rods 7 (2 safety rods 4 shim rods 1 regulating rod)Material of safety and shim rods B

4C

Material of automatic regulating rod Stainless steelNeutron measuring channels 9 (6 CFC 3 CIC)Vertical irradiation channels 4 (1 neutron trap 1 wet channel 2 dry channels)Horizontal beam ports 4 (1 tangential 3 radials)

fuel tubes cladded by aluminum The two inner tubes havecylindrical shapes while the outer tube is hexagonal with sixcircular corners However since the PIJ code is not able tosimulate exactly the circular corners of the outer hexagonalfuel tube of the VVR-M2 fuel bundle a sharp hexagonaltube was assumed in the simulation model by preserving thetotal fuel mass In the lattice calculations of the PIJ code 107energy groupsrsquo structure was used Then the cross sectionswere collapsed into seven energy groups (4 fast groups and 3thermal groups) for full-core calculations

The neutron trap consists of a cylindrical water holesurrounded by six beryllium blocks Since SRAC does not

allow simulating exactly the geometry of the neutron trapin the full-core model the neutron trap is modelled asa hexagonal water cell at the center surrounded by sixhexagonal blocks of homogeneous beryllium and waterTherefore in the lattice calculation the homogenizationof beryllium and water at the six surrounding cells hasbeen conducted while preserving the volume fractions ofthe beryllium and water Calculating the cross sections ofthe safety and shim rods is more complicated due to thestrong absorption of the control rods Since the control rodsare considered as black absorber materials the extrapolatedboundary constants corresponding to each neutron energy

Science and Technology of Nuclear Installations 5

X

Y

Figure 4 Full-core model with hexagonal grid

group should be taken into account Therefore once themacroscopic cross sections of the control rods were obtainedusing PIJ the ANISN code based on the Sn theory was usedto determine the extrapolated length in each energy groupOther nonfuel lattice cells such as aluminum rod berylliumrod and regulating rod were also simulated using the PIJcode The cross sections of materials in the active core weretaken from the previous lattice cell calculations and inputtedexactly at the same positions in the core model using PIJ(supercell calculation) Other lattice cells at the positions ofthe horizontal beam tubes rotary specimen rack and theinterface regions were not calculated using the PIJ code butthe compositions (air water aluminum and graphite) werehomogenized and inputted in the full-core model

33 Full-CoreModel TheCOREBNof the SRAC code systemwas used for the full-core calculation with hexagonal latticecells [6] The full-core model was described by hexagonalgrids of 37 times 37 in the X-Y plane as shown in Figure 4The total height of the model (1845 cm) was axially dividedinto a number of layers so that each axial layer has the samematerial For instance the active core is axially divided into60 layers with the mesh size about 1 cm However the actualmesh size of each layer in the full-core models could beslightly changed depending on the position of control rodsThe upper part of the beryllium blocks is water and the lowerpart is the homogenization of aluminum and water

34 Monte Carlo Model Monte Carlo calculations of theDNRR have been performed using the MCNP5 code andENDFB-VII0 data library to verify the analysis models andthe results obtained with the SRAC code system MCNP5 isa general Monte Carlo N-Particle transport code developedat Los Alamos National Laboratory [9] MCNP5 has anability to describe precisely the complex geometry of theDNRR including the fuel bundles horizontal beam tubesreflector and thermal column and thermalizing column Tosimplify the simulation model but not affecting significantlythe neutronic characteristics of the DNRR core the upperand lower parts of the fuel bundle aluminum rod berylliumrod and dry and wet irradiation channels were described asthe homogeneous mixtures of aluminum and water Figure 5displays the vertical and horizontal cross-sectional views of

theDNRR core in theMCNP5modelThemodel is expandedfrom the active core to reactor tank following the radialdirection with 198 cm in diameter and the axial directionwith 1845 cm in height The history number of 210 times 106 waschosen so that the statistic error of 119896eff would be less than0006 Tallies 4 and 7 were used to calculate the neutronflux and power distributions

Since the simulation requires a high computationalresource in the present work the criticality calculationswere performed on a Windows server with 80 CPUs Thecomputational time of each run for the mentioned historynumber is about 156 minutes When the computational timeof the codes is compared the SRAC code is advantageoussince it can run fast on a personal computerwith Intel Core i5-4460 of CPU 33GHz Once the macroscopic cross sectionsof all materials are prepared using the PIJ code the full-corecalculation takes about half a minute

4 Numerical Calculations andComparison with MCNP5

41 Lattice Calculations The infinite multiplication factor119896infin of the fuel bundle obtained from the PIJ code is 164463

greater than that obtained fromMCNP5 (164034 plusmn 000004)by about 261 pcm If the MCNP5 model uses the modifiedgeometry of the outer fuel tube as in the PIJ model thedeviation of 119896

infinis about 139 pcm This indicates that the

lattice calculation results of the codes have a good agreement

42 Criticality Calculations The 119896eff values obtained areshown in Table 2 It can be seen that in the case of con-trol rod withdrawal the 119896eff values of 108633 and 108632were obtained from the SRAC and MCNP5 calculationsrespectively The calculated values are well consistent witheach other Taking into account the fact that the effectivedelayed neutron fraction 120573eff of the core is 00081 the 119896effvalues correspond to the excess reactivity of about 981$Thisvalue is comparable with that (985$) reported in the startupreport of the DNRR [7] The leakage reactivity penalty isminus001940 and that associated with absorption is minus090114In the case of full insertion of the four shim rods and theautomatic regulating rod the difference of the 119896eff valuesis about 242 pcm This agreement between the SRAC and

6 Science and Technology of Nuclear Installations

(a) Vertical (b) Horizontal

Figure 5 Vertical and horizontal cross sections of the DNRR in the MCNP5 model

Table 2 The 119896eff in the cases of complete withdrawal and full insertion of control rods

Code 119896eff (A) 119896eff (B) Reactivity worth (Δ1198961198961198961015840)SRAC 108633 098029 996MCNP5 108632 plusmn 000006 097787 plusmn 000005 1021(A) All control rods are completely withdrawn (B) Two safety rods are withdrawn four shim rods and the automatic regulating rod are fully inserted

MCNP5 calculations gives a certain confidence for furtheranalysis of the DNRR core The total worth values of the fourshim rods and the automatic regulating rod of 123$ and 126$obtained from SRAC andMCNP5 respectively are sufficientto shut down the reactor

Criticality calculations of the core with four control rodbanks have been carried out To do this the four shim rodswere inserted into the core Then the position of the AR wasadjusted to obtain the criticality of the core These criticalityconditions were achieved during the startup of the DNRRcore with HEU fuel [7] Since the two safety rods are usedonly for emergency shutdown in all cases they were assumedto be completely withdrawn

Table 3 shows the results of the criticality calculations cor-responding to the four control rod banks The 119896eff values areclosed to unity with the deviation within 119 pcm In all casesthe 119896eff values obtained for SRAC are in good agreementwith that obtained from MCNP5 calculations The greatestdifference is about 55 pcm corresponding to the case withthe insertions of ShRs = 45 cm and AR = 65 cm Comparedto unity that is the criticality conditions established in theexperiments [7] the maximum difference of the 119896eff valuesobtained from the SRAC calculations is 119 pcm while thisvalue is 64 pcm for the MCNP5 calculations This agreementcompared to the experiments indicates the verification of themodels

43 Power andThermal Neutron Flux Distributions Thermalneutron flux and power distributions of the DNRR corehave been analyzed in detail for two cases corresponding tothe complete withdrawal and the partial insertion (ShR =457 cm and AR = 40 cm) of control rods in comparison with

MCNP5 calculations Figure 6 shows the radial relative powerdistribution at the initial critical condition correspondingto the control rod insertions of ShR = 457 cm and AR =40 cmThe radial power peaking factor is 1445which appearsat the fuel bundle 9-6 This value is obtained as 1486 inthe MCNP5 calculation The deviation of the relative powerdensities between the codes is less than 4 at most of fuelbundles except some bundles located at periphery wherethe maximum deviation is about 7 Figure 7 is similar toFigure 6 but for the case of complete withdrawal of all controlrodsThe radial power peaking factor is about 1334 at the fuelcell 9-6 obtained with SRAC smaller than that obtained withMCNP5 (1385) by about 37

Figures 8 and 9 depict the axial power distributions at thefuel cells 9-6 and 7-10 in the cases of control rod insertion andcontrol rod withdrawal respectively The fuel cell 9-6 corre-sponds to the highest power ratingThe fuel cell 7-10 is locatedclose to the AR and therefore its power profile and fluxdistribution show clearly the effect of control rod insertionWhen the control rod is partially inserted the power profileis shifted to the lower half of the core and the power peakingfactor increasesThe axial power peaking factor is about 1710in the case of control rod withdrawal while it is about 1832in the case of control rod insertion Furthermore axial powerprofile results of the codes are in good agreementThe largestdifference is found at the boundary interfaces between theactive fuel and the upper and lower reflectors

Figures 10 and 11 show the axial thermal neutron fluxdistribution in the fuel cells 9-6 and 7-10 for the two casescorresponding to the control rod insertion and withdrawalrespectively Figure 12 shows the axial distribution of thethermal neutron flux along the height of neutron trap in

Science and Technology of Nuclear Installations 7

Table 3 Criticality calculations of the DNRR with four control rod banks

Position of control rods (cm) 119896eff Dev(pcm)ShR1 ShR2 ShR3 ShR4 AR SRAC MCNP545 45 45 45 65 100119 100064 plusmn 000006 55472 472 472 472 0 099960 099969 plusmn 000006 9457 457 457 457 40 100086 100051 plusmn 000006 35467 467 467 467 20 100009 099998 plusmn 000006 11

09200968

09791021

10601131 1130

1059 09771023

09180977

07770798

08470887

08410854

08960912

09450931

09650925

09750936

09110963

08830843

08290776

08350808

07730759

10010977

09360915

08030825

09050944

09960991

10611121

10091000

111811230950

0928

08330838

098510371004

0931

08260790

07920778 ShR3

SR08690935

09150872

08930894

08760886

10701099

10471079

10641098

097310060883

0864

07690771

079707810850

0879

08560870

09480978

10581044

09960972

10761047

10551062 0998

0981

09611012

08890875

10070978

10631132

11101121

07190757

ShR4

08220868

10261083

10001054

14551429

08400869

09560997

09160944

082208260995

1002

11201115

128612811486

1444

11181122

100509970829

0825

09480922

12911292

14391481

13221324

14391483

12931293 1481

1445 12871274

09970947

14521429

12921309

10341083

08030859

AR

09420905

08370863

07570761

SR

ShR2 ShR1

Figure 6 Relative power distribution in the core at the initial critical condition corresponding to the control rod insertion ShR = 457 cmAR = 40 cm The upper and lower values were obtained with SRAC and MCNP5 respectively

comparison with the results obtained from the MCNP5calculations It can be seen that the maximum thermalneutron flux is about 217 times 1013 ncm2sdots in the case of controlrod withdrawal The axial flux distribution is also shifted tothe lower part of the core when the control rods are insertedIn this case the peak value of thermal flux is about 238 times1013 ncm2sdots shifted to about 10 cm from the central point ofthe neutron trap to the core bottom as shown in Figure 12noting that there is a good agreement between the two codesThis indicates the validity of the analysis models and thepotential use for further applications

Since theDNRR core containsmany complicated compo-nents it is a challenge to model the core using a deterministiccode Homogenization of materials especially in particularregions where control rods are withdrawn could affect theaccuracy of the results However in the present work theanalysis results show an acceptable agreement between thecodes as well as the startup report The current models ofthe DNRR core in the SRAC code could handle flexible axialmesh sizes along the core height depending on the actualcontrol rod positions A possible improvement of the modelsto handle finer radial meshes such as triangular meshes could

8 Science and Technology of Nuclear Installations

0922 0954 10221064 1066

1023 09570991 0979

09160930

08400846

08870907

09720983

084108630970

0949

10361005

10471071

10131034

093609460990

0978

10821062

12171228

1329

1385

1063

1230

10141033 1082

097809900944

0931091209170872

08900878

08320837

08620848

09700956

08850908

09740962 0916

10371017

13301384

10511072

13311384

10381023

099209850962

09700977

0922

08960938 0863

09730966 1061 1232

1218 13341381

12171219

13291369

12081211

09890952

09810966

09680956

08750839

08280775

085508260890

0912

08470889

08100859

089209321035

0998

092909681071

1034

10330998

10821055

09900969

09450916

0971105810641025

09970990

09800992

106310191035

094409240871

090008960846

0877 ShR3

0920

1083

09460948

0931 0959 1024 0956 09240940

10730867

0936

097212101227

0934

0854

1217 1333

137309330906

08820893

09000866

09280958 0985

SR

ShR4

AR

ShR2

SR

ShR1

Figure 7 Relative power distribution in the case of complete withdrawal of the control rods The upper and lower values were obtained withSRAC and MCNP5 respectively

Cell 7-10

SRACMCNP5

Cell 9-6

ShR = 457cm AR = 40 cm

04

06

08

10

12

14

16

18

20

Relat

ive p

ower

den

sity

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Figure 8 Axial power distribution along the fuel bundles 7-10 and 9-6 at the critical core condition corresponding to the insertion of controlrods ShR = 457 cm and AR = 40 cm

Science and Technology of Nuclear Installations 9

04

06

08

10

12

14

16

18

Relat

ive p

ower

den

sity

20

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

Figure 9 Axial power distribution along the fuel bundles 7-10 and9-6 in the case of complete withdrawal of control rods

Cell 7-10

SRACMCNP5

Cell 9-6

0

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

9 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

ShR = 457cm AR = 40 cm

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

Figure 10Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 at the critical core condition corresponding to theinsertion of control rods ShR = 457 cm and AR = 40 cm

be useful to improve the accuracy of the calculation resultsFurther analyses are necessary to verify themodels using bothSRAC andMCNP5 codes for burnup and rod worth analysesof the DNRR core in comparison with themeasurement dataEvaluation of the effect of the cross section data libraries onthe neutronic properties of the DNRR core is being investi-gated Application in analyzing the current working configu-rations of the DNRR with low enriched uranium (LEU) fuelbundles is also being planned

5 Conclusions

Neutronics model of the DNRR was developed using theSRAC code system The PIJ and COREBN codes of the

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 11 Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 in the case of complete withdrawal of control rods

Rods in SRACRods in MCNP5

Rods out SRACRods out MCNP5

100 20 30minus20 minus10minus30Core height (top to bottom) (cm)

40 times 1012

60 times 1012

80 times 1012

10 times 1013

12 times 1013

14 times 1013

16 times 1013

18 times 1013

20 times 1013

22 times 1013

24 times 1013

26 times 1013

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 12Thermal neutron flux distribution along the neutron trapRods in ShR = 457 cm and AR = 40 cm Rods out ShR = 0 cm andAR = 0 cm

SRAC code system were used for lattice physics and full-coreanalyses In order to handle the complicated geometries ofthe DNRR such as the neutron trap neutron channels andupper and lower parts of the active core homogenizationhas been conducted Numerical calculations were performedto analyze the effective multiplication factors 119896eff for twocases corresponding to the complete withdrawal and thefull insertion of control rods Criticality analyses were thenconducted with the four different control rod banks Theradial and axial power peaking factors of the DNRR core arecalculated to be 1334 and 1710 respectively in the case of nocontrol rod insertion These values are 1445 and 1832 at thecriticality condition with the partial insertion of control rodsComparing to the MCNP5 calculations the results show that

10 Science and Technology of Nuclear Installations

the difference between the 119896eff values of the codes is less than55 pcm The maximum deviations of the 119896eff values obtainedfrom SRAC and MCNP5 compared to the experiments are119 pcm and 64 pcm respectivelyThedeviation of the relativepower distributions between the codes is less than 4 formost of the fuel bundles in the middle of the core while themaximum deviation is about 7 which appears at peripheralbundles In addition thermal neutron flux distributions inthe neutron trap are in good agreement This agreementindicates the verification of the models and the possibility forfurther analysis

Conflicts of Interest

The authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

This research is funded by Foundation for Science andTechnology Development of Ton Duc Thang University(FOSTECT) website httpfostecttdteduvn under GrantFOSTECT2016BR13

References

[1] TRIGA History URL httpwwwgacomtriga-history[2] N D Nguyen Ed Safety Analysis Report for the Dalat Nuclear

Research Reactor Nuclear Research Institute Vietnam AtomicEnergy Commission 2009

[3] N D Nguyen B V Luong V V Le et al ldquoResults of Operationand Utilization of the Dalat Nuclear Research ReactorrdquoNuclearScience and Technology vol 4 no 1 pp 1ndash9 2014

[4] M Turkmen and U Colak ldquoAnalysis of ITU TRIGA MarkII research reactor using Monte Carlo methodrdquo Progress inNuclear Energy vol 77 pp 152ndash159 2014

[5] B Q Do and L P Nguyen ldquoApplication of a genetic algorithmto the fuel reload optimization for a research reactorrdquo AppliedMathematics andComputation vol 187 no 2 pp 977ndash988 2007

[6] K Okumura T Kugo K Kaneko and K TsuchihashiSRAC2006 A Comprehensive Neutronics Calculation Code Sys-tem JAEA-DataCode 2007-004 2007

[7] D H Pham Q H Ngo H L Vu and KM Tran Report startupof nuclear research reactor Part 2 - Physics startup for coreconfiguration with a neutron trap Nuclear Research Institute1984

[8] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technology Nucl Data Sheetsrdquo Special Issue onEvaluated Nuclear Data File ENDFB-VII0 2006

[9] X-5 Monte Carlo Team 2005 MCNP - A General Monte CarloN-Particle Transport Code Version 5 LA-UR-03-1987 April 242003

Science and Technology of Nuclear Installations 5

X

Y

Figure 4 Full-core model with hexagonal grid

group should be taken into account Therefore once themacroscopic cross sections of the control rods were obtainedusing PIJ the ANISN code based on the Sn theory was usedto determine the extrapolated length in each energy groupOther nonfuel lattice cells such as aluminum rod berylliumrod and regulating rod were also simulated using the PIJcode The cross sections of materials in the active core weretaken from the previous lattice cell calculations and inputtedexactly at the same positions in the core model using PIJ(supercell calculation) Other lattice cells at the positions ofthe horizontal beam tubes rotary specimen rack and theinterface regions were not calculated using the PIJ code butthe compositions (air water aluminum and graphite) werehomogenized and inputted in the full-core model

33 Full-CoreModel TheCOREBNof the SRAC code systemwas used for the full-core calculation with hexagonal latticecells [6] The full-core model was described by hexagonalgrids of 37 times 37 in the X-Y plane as shown in Figure 4The total height of the model (1845 cm) was axially dividedinto a number of layers so that each axial layer has the samematerial For instance the active core is axially divided into60 layers with the mesh size about 1 cm However the actualmesh size of each layer in the full-core models could beslightly changed depending on the position of control rodsThe upper part of the beryllium blocks is water and the lowerpart is the homogenization of aluminum and water

34 Monte Carlo Model Monte Carlo calculations of theDNRR have been performed using the MCNP5 code andENDFB-VII0 data library to verify the analysis models andthe results obtained with the SRAC code system MCNP5 isa general Monte Carlo N-Particle transport code developedat Los Alamos National Laboratory [9] MCNP5 has anability to describe precisely the complex geometry of theDNRR including the fuel bundles horizontal beam tubesreflector and thermal column and thermalizing column Tosimplify the simulation model but not affecting significantlythe neutronic characteristics of the DNRR core the upperand lower parts of the fuel bundle aluminum rod berylliumrod and dry and wet irradiation channels were described asthe homogeneous mixtures of aluminum and water Figure 5displays the vertical and horizontal cross-sectional views of

theDNRR core in theMCNP5modelThemodel is expandedfrom the active core to reactor tank following the radialdirection with 198 cm in diameter and the axial directionwith 1845 cm in height The history number of 210 times 106 waschosen so that the statistic error of 119896eff would be less than0006 Tallies 4 and 7 were used to calculate the neutronflux and power distributions

Since the simulation requires a high computationalresource in the present work the criticality calculationswere performed on a Windows server with 80 CPUs Thecomputational time of each run for the mentioned historynumber is about 156 minutes When the computational timeof the codes is compared the SRAC code is advantageoussince it can run fast on a personal computerwith Intel Core i5-4460 of CPU 33GHz Once the macroscopic cross sectionsof all materials are prepared using the PIJ code the full-corecalculation takes about half a minute

4 Numerical Calculations andComparison with MCNP5

41 Lattice Calculations The infinite multiplication factor119896infin of the fuel bundle obtained from the PIJ code is 164463

greater than that obtained fromMCNP5 (164034 plusmn 000004)by about 261 pcm If the MCNP5 model uses the modifiedgeometry of the outer fuel tube as in the PIJ model thedeviation of 119896

infinis about 139 pcm This indicates that the

lattice calculation results of the codes have a good agreement

42 Criticality Calculations The 119896eff values obtained areshown in Table 2 It can be seen that in the case of con-trol rod withdrawal the 119896eff values of 108633 and 108632were obtained from the SRAC and MCNP5 calculationsrespectively The calculated values are well consistent witheach other Taking into account the fact that the effectivedelayed neutron fraction 120573eff of the core is 00081 the 119896effvalues correspond to the excess reactivity of about 981$Thisvalue is comparable with that (985$) reported in the startupreport of the DNRR [7] The leakage reactivity penalty isminus001940 and that associated with absorption is minus090114In the case of full insertion of the four shim rods and theautomatic regulating rod the difference of the 119896eff valuesis about 242 pcm This agreement between the SRAC and

6 Science and Technology of Nuclear Installations

(a) Vertical (b) Horizontal

Figure 5 Vertical and horizontal cross sections of the DNRR in the MCNP5 model

Table 2 The 119896eff in the cases of complete withdrawal and full insertion of control rods

Code 119896eff (A) 119896eff (B) Reactivity worth (Δ1198961198961198961015840)SRAC 108633 098029 996MCNP5 108632 plusmn 000006 097787 plusmn 000005 1021(A) All control rods are completely withdrawn (B) Two safety rods are withdrawn four shim rods and the automatic regulating rod are fully inserted

MCNP5 calculations gives a certain confidence for furtheranalysis of the DNRR core The total worth values of the fourshim rods and the automatic regulating rod of 123$ and 126$obtained from SRAC andMCNP5 respectively are sufficientto shut down the reactor

Criticality calculations of the core with four control rodbanks have been carried out To do this the four shim rodswere inserted into the core Then the position of the AR wasadjusted to obtain the criticality of the core These criticalityconditions were achieved during the startup of the DNRRcore with HEU fuel [7] Since the two safety rods are usedonly for emergency shutdown in all cases they were assumedto be completely withdrawn

Table 3 shows the results of the criticality calculations cor-responding to the four control rod banks The 119896eff values areclosed to unity with the deviation within 119 pcm In all casesthe 119896eff values obtained for SRAC are in good agreementwith that obtained from MCNP5 calculations The greatestdifference is about 55 pcm corresponding to the case withthe insertions of ShRs = 45 cm and AR = 65 cm Comparedto unity that is the criticality conditions established in theexperiments [7] the maximum difference of the 119896eff valuesobtained from the SRAC calculations is 119 pcm while thisvalue is 64 pcm for the MCNP5 calculations This agreementcompared to the experiments indicates the verification of themodels

43 Power andThermal Neutron Flux Distributions Thermalneutron flux and power distributions of the DNRR corehave been analyzed in detail for two cases corresponding tothe complete withdrawal and the partial insertion (ShR =457 cm and AR = 40 cm) of control rods in comparison with

MCNP5 calculations Figure 6 shows the radial relative powerdistribution at the initial critical condition correspondingto the control rod insertions of ShR = 457 cm and AR =40 cmThe radial power peaking factor is 1445which appearsat the fuel bundle 9-6 This value is obtained as 1486 inthe MCNP5 calculation The deviation of the relative powerdensities between the codes is less than 4 at most of fuelbundles except some bundles located at periphery wherethe maximum deviation is about 7 Figure 7 is similar toFigure 6 but for the case of complete withdrawal of all controlrodsThe radial power peaking factor is about 1334 at the fuelcell 9-6 obtained with SRAC smaller than that obtained withMCNP5 (1385) by about 37

Figures 8 and 9 depict the axial power distributions at thefuel cells 9-6 and 7-10 in the cases of control rod insertion andcontrol rod withdrawal respectively The fuel cell 9-6 corre-sponds to the highest power ratingThe fuel cell 7-10 is locatedclose to the AR and therefore its power profile and fluxdistribution show clearly the effect of control rod insertionWhen the control rod is partially inserted the power profileis shifted to the lower half of the core and the power peakingfactor increasesThe axial power peaking factor is about 1710in the case of control rod withdrawal while it is about 1832in the case of control rod insertion Furthermore axial powerprofile results of the codes are in good agreementThe largestdifference is found at the boundary interfaces between theactive fuel and the upper and lower reflectors

Figures 10 and 11 show the axial thermal neutron fluxdistribution in the fuel cells 9-6 and 7-10 for the two casescorresponding to the control rod insertion and withdrawalrespectively Figure 12 shows the axial distribution of thethermal neutron flux along the height of neutron trap in

Science and Technology of Nuclear Installations 7

Table 3 Criticality calculations of the DNRR with four control rod banks

Position of control rods (cm) 119896eff Dev(pcm)ShR1 ShR2 ShR3 ShR4 AR SRAC MCNP545 45 45 45 65 100119 100064 plusmn 000006 55472 472 472 472 0 099960 099969 plusmn 000006 9457 457 457 457 40 100086 100051 plusmn 000006 35467 467 467 467 20 100009 099998 plusmn 000006 11

09200968

09791021

10601131 1130

1059 09771023

09180977

07770798

08470887

08410854

08960912

09450931

09650925

09750936

09110963

08830843

08290776

08350808

07730759

10010977

09360915

08030825

09050944

09960991

10611121

10091000

111811230950

0928

08330838

098510371004

0931

08260790

07920778 ShR3

SR08690935

09150872

08930894

08760886

10701099

10471079

10641098

097310060883

0864

07690771

079707810850

0879

08560870

09480978

10581044

09960972

10761047

10551062 0998

0981

09611012

08890875

10070978

10631132

11101121

07190757

ShR4

08220868

10261083

10001054

14551429

08400869

09560997

09160944

082208260995

1002

11201115

128612811486

1444

11181122

100509970829

0825

09480922

12911292

14391481

13221324

14391483

12931293 1481

1445 12871274

09970947

14521429

12921309

10341083

08030859

AR

09420905

08370863

07570761

SR

ShR2 ShR1

Figure 6 Relative power distribution in the core at the initial critical condition corresponding to the control rod insertion ShR = 457 cmAR = 40 cm The upper and lower values were obtained with SRAC and MCNP5 respectively

comparison with the results obtained from the MCNP5calculations It can be seen that the maximum thermalneutron flux is about 217 times 1013 ncm2sdots in the case of controlrod withdrawal The axial flux distribution is also shifted tothe lower part of the core when the control rods are insertedIn this case the peak value of thermal flux is about 238 times1013 ncm2sdots shifted to about 10 cm from the central point ofthe neutron trap to the core bottom as shown in Figure 12noting that there is a good agreement between the two codesThis indicates the validity of the analysis models and thepotential use for further applications

Since theDNRR core containsmany complicated compo-nents it is a challenge to model the core using a deterministiccode Homogenization of materials especially in particularregions where control rods are withdrawn could affect theaccuracy of the results However in the present work theanalysis results show an acceptable agreement between thecodes as well as the startup report The current models ofthe DNRR core in the SRAC code could handle flexible axialmesh sizes along the core height depending on the actualcontrol rod positions A possible improvement of the modelsto handle finer radial meshes such as triangular meshes could

8 Science and Technology of Nuclear Installations

0922 0954 10221064 1066

1023 09570991 0979

09160930

08400846

08870907

09720983

084108630970

0949

10361005

10471071

10131034

093609460990

0978

10821062

12171228

1329

1385

1063

1230

10141033 1082

097809900944

0931091209170872

08900878

08320837

08620848

09700956

08850908

09740962 0916

10371017

13301384

10511072

13311384

10381023

099209850962

09700977

0922

08960938 0863

09730966 1061 1232

1218 13341381

12171219

13291369

12081211

09890952

09810966

09680956

08750839

08280775

085508260890

0912

08470889

08100859

089209321035

0998

092909681071

1034

10330998

10821055

09900969

09450916

0971105810641025

09970990

09800992

106310191035

094409240871

090008960846

0877 ShR3

0920

1083

09460948

0931 0959 1024 0956 09240940

10730867

0936

097212101227

0934

0854

1217 1333

137309330906

08820893

09000866

09280958 0985

SR

ShR4

AR

ShR2

SR

ShR1

Figure 7 Relative power distribution in the case of complete withdrawal of the control rods The upper and lower values were obtained withSRAC and MCNP5 respectively

Cell 7-10

SRACMCNP5

Cell 9-6

ShR = 457cm AR = 40 cm

04

06

08

10

12

14

16

18

20

Relat

ive p

ower

den

sity

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Figure 8 Axial power distribution along the fuel bundles 7-10 and 9-6 at the critical core condition corresponding to the insertion of controlrods ShR = 457 cm and AR = 40 cm

Science and Technology of Nuclear Installations 9

04

06

08

10

12

14

16

18

Relat

ive p

ower

den

sity

20

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

Figure 9 Axial power distribution along the fuel bundles 7-10 and9-6 in the case of complete withdrawal of control rods

Cell 7-10

SRACMCNP5

Cell 9-6

0

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

9 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

ShR = 457cm AR = 40 cm

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

Figure 10Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 at the critical core condition corresponding to theinsertion of control rods ShR = 457 cm and AR = 40 cm

be useful to improve the accuracy of the calculation resultsFurther analyses are necessary to verify themodels using bothSRAC andMCNP5 codes for burnup and rod worth analysesof the DNRR core in comparison with themeasurement dataEvaluation of the effect of the cross section data libraries onthe neutronic properties of the DNRR core is being investi-gated Application in analyzing the current working configu-rations of the DNRR with low enriched uranium (LEU) fuelbundles is also being planned

5 Conclusions

Neutronics model of the DNRR was developed using theSRAC code system The PIJ and COREBN codes of the

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 11 Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 in the case of complete withdrawal of control rods

Rods in SRACRods in MCNP5

Rods out SRACRods out MCNP5

100 20 30minus20 minus10minus30Core height (top to bottom) (cm)

40 times 1012

60 times 1012

80 times 1012

10 times 1013

12 times 1013

14 times 1013

16 times 1013

18 times 1013

20 times 1013

22 times 1013

24 times 1013

26 times 1013

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 12Thermal neutron flux distribution along the neutron trapRods in ShR = 457 cm and AR = 40 cm Rods out ShR = 0 cm andAR = 0 cm

SRAC code system were used for lattice physics and full-coreanalyses In order to handle the complicated geometries ofthe DNRR such as the neutron trap neutron channels andupper and lower parts of the active core homogenizationhas been conducted Numerical calculations were performedto analyze the effective multiplication factors 119896eff for twocases corresponding to the complete withdrawal and thefull insertion of control rods Criticality analyses were thenconducted with the four different control rod banks Theradial and axial power peaking factors of the DNRR core arecalculated to be 1334 and 1710 respectively in the case of nocontrol rod insertion These values are 1445 and 1832 at thecriticality condition with the partial insertion of control rodsComparing to the MCNP5 calculations the results show that

10 Science and Technology of Nuclear Installations

the difference between the 119896eff values of the codes is less than55 pcm The maximum deviations of the 119896eff values obtainedfrom SRAC and MCNP5 compared to the experiments are119 pcm and 64 pcm respectivelyThedeviation of the relativepower distributions between the codes is less than 4 formost of the fuel bundles in the middle of the core while themaximum deviation is about 7 which appears at peripheralbundles In addition thermal neutron flux distributions inthe neutron trap are in good agreement This agreementindicates the verification of the models and the possibility forfurther analysis

Conflicts of Interest

The authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

This research is funded by Foundation for Science andTechnology Development of Ton Duc Thang University(FOSTECT) website httpfostecttdteduvn under GrantFOSTECT2016BR13

References

[1] TRIGA History URL httpwwwgacomtriga-history[2] N D Nguyen Ed Safety Analysis Report for the Dalat Nuclear

Research Reactor Nuclear Research Institute Vietnam AtomicEnergy Commission 2009

[3] N D Nguyen B V Luong V V Le et al ldquoResults of Operationand Utilization of the Dalat Nuclear Research ReactorrdquoNuclearScience and Technology vol 4 no 1 pp 1ndash9 2014

[4] M Turkmen and U Colak ldquoAnalysis of ITU TRIGA MarkII research reactor using Monte Carlo methodrdquo Progress inNuclear Energy vol 77 pp 152ndash159 2014

[5] B Q Do and L P Nguyen ldquoApplication of a genetic algorithmto the fuel reload optimization for a research reactorrdquo AppliedMathematics andComputation vol 187 no 2 pp 977ndash988 2007

[6] K Okumura T Kugo K Kaneko and K TsuchihashiSRAC2006 A Comprehensive Neutronics Calculation Code Sys-tem JAEA-DataCode 2007-004 2007

[7] D H Pham Q H Ngo H L Vu and KM Tran Report startupof nuclear research reactor Part 2 - Physics startup for coreconfiguration with a neutron trap Nuclear Research Institute1984

[8] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technology Nucl Data Sheetsrdquo Special Issue onEvaluated Nuclear Data File ENDFB-VII0 2006

[9] X-5 Monte Carlo Team 2005 MCNP - A General Monte CarloN-Particle Transport Code Version 5 LA-UR-03-1987 April 242003

6 Science and Technology of Nuclear Installations

(a) Vertical (b) Horizontal

Figure 5 Vertical and horizontal cross sections of the DNRR in the MCNP5 model

Table 2 The 119896eff in the cases of complete withdrawal and full insertion of control rods

Code 119896eff (A) 119896eff (B) Reactivity worth (Δ1198961198961198961015840)SRAC 108633 098029 996MCNP5 108632 plusmn 000006 097787 plusmn 000005 1021(A) All control rods are completely withdrawn (B) Two safety rods are withdrawn four shim rods and the automatic regulating rod are fully inserted

MCNP5 calculations gives a certain confidence for furtheranalysis of the DNRR core The total worth values of the fourshim rods and the automatic regulating rod of 123$ and 126$obtained from SRAC andMCNP5 respectively are sufficientto shut down the reactor

Criticality calculations of the core with four control rodbanks have been carried out To do this the four shim rodswere inserted into the core Then the position of the AR wasadjusted to obtain the criticality of the core These criticalityconditions were achieved during the startup of the DNRRcore with HEU fuel [7] Since the two safety rods are usedonly for emergency shutdown in all cases they were assumedto be completely withdrawn

Table 3 shows the results of the criticality calculations cor-responding to the four control rod banks The 119896eff values areclosed to unity with the deviation within 119 pcm In all casesthe 119896eff values obtained for SRAC are in good agreementwith that obtained from MCNP5 calculations The greatestdifference is about 55 pcm corresponding to the case withthe insertions of ShRs = 45 cm and AR = 65 cm Comparedto unity that is the criticality conditions established in theexperiments [7] the maximum difference of the 119896eff valuesobtained from the SRAC calculations is 119 pcm while thisvalue is 64 pcm for the MCNP5 calculations This agreementcompared to the experiments indicates the verification of themodels

43 Power andThermal Neutron Flux Distributions Thermalneutron flux and power distributions of the DNRR corehave been analyzed in detail for two cases corresponding tothe complete withdrawal and the partial insertion (ShR =457 cm and AR = 40 cm) of control rods in comparison with

MCNP5 calculations Figure 6 shows the radial relative powerdistribution at the initial critical condition correspondingto the control rod insertions of ShR = 457 cm and AR =40 cmThe radial power peaking factor is 1445which appearsat the fuel bundle 9-6 This value is obtained as 1486 inthe MCNP5 calculation The deviation of the relative powerdensities between the codes is less than 4 at most of fuelbundles except some bundles located at periphery wherethe maximum deviation is about 7 Figure 7 is similar toFigure 6 but for the case of complete withdrawal of all controlrodsThe radial power peaking factor is about 1334 at the fuelcell 9-6 obtained with SRAC smaller than that obtained withMCNP5 (1385) by about 37

Figures 8 and 9 depict the axial power distributions at thefuel cells 9-6 and 7-10 in the cases of control rod insertion andcontrol rod withdrawal respectively The fuel cell 9-6 corre-sponds to the highest power ratingThe fuel cell 7-10 is locatedclose to the AR and therefore its power profile and fluxdistribution show clearly the effect of control rod insertionWhen the control rod is partially inserted the power profileis shifted to the lower half of the core and the power peakingfactor increasesThe axial power peaking factor is about 1710in the case of control rod withdrawal while it is about 1832in the case of control rod insertion Furthermore axial powerprofile results of the codes are in good agreementThe largestdifference is found at the boundary interfaces between theactive fuel and the upper and lower reflectors

Figures 10 and 11 show the axial thermal neutron fluxdistribution in the fuel cells 9-6 and 7-10 for the two casescorresponding to the control rod insertion and withdrawalrespectively Figure 12 shows the axial distribution of thethermal neutron flux along the height of neutron trap in

Science and Technology of Nuclear Installations 7

Table 3 Criticality calculations of the DNRR with four control rod banks

Position of control rods (cm) 119896eff Dev(pcm)ShR1 ShR2 ShR3 ShR4 AR SRAC MCNP545 45 45 45 65 100119 100064 plusmn 000006 55472 472 472 472 0 099960 099969 plusmn 000006 9457 457 457 457 40 100086 100051 plusmn 000006 35467 467 467 467 20 100009 099998 plusmn 000006 11

09200968

09791021

10601131 1130

1059 09771023

09180977

07770798

08470887

08410854

08960912

09450931

09650925

09750936

09110963

08830843

08290776

08350808

07730759

10010977

09360915

08030825

09050944

09960991

10611121

10091000

111811230950

0928

08330838

098510371004

0931

08260790

07920778 ShR3

SR08690935

09150872

08930894

08760886

10701099

10471079

10641098

097310060883

0864

07690771

079707810850

0879

08560870

09480978

10581044

09960972

10761047

10551062 0998

0981

09611012

08890875

10070978

10631132

11101121

07190757

ShR4

08220868

10261083

10001054

14551429

08400869

09560997

09160944

082208260995

1002

11201115

128612811486

1444

11181122

100509970829

0825

09480922

12911292

14391481

13221324

14391483

12931293 1481

1445 12871274

09970947

14521429

12921309

10341083

08030859

AR

09420905

08370863

07570761

SR

ShR2 ShR1

Figure 6 Relative power distribution in the core at the initial critical condition corresponding to the control rod insertion ShR = 457 cmAR = 40 cm The upper and lower values were obtained with SRAC and MCNP5 respectively

comparison with the results obtained from the MCNP5calculations It can be seen that the maximum thermalneutron flux is about 217 times 1013 ncm2sdots in the case of controlrod withdrawal The axial flux distribution is also shifted tothe lower part of the core when the control rods are insertedIn this case the peak value of thermal flux is about 238 times1013 ncm2sdots shifted to about 10 cm from the central point ofthe neutron trap to the core bottom as shown in Figure 12noting that there is a good agreement between the two codesThis indicates the validity of the analysis models and thepotential use for further applications

Since theDNRR core containsmany complicated compo-nents it is a challenge to model the core using a deterministiccode Homogenization of materials especially in particularregions where control rods are withdrawn could affect theaccuracy of the results However in the present work theanalysis results show an acceptable agreement between thecodes as well as the startup report The current models ofthe DNRR core in the SRAC code could handle flexible axialmesh sizes along the core height depending on the actualcontrol rod positions A possible improvement of the modelsto handle finer radial meshes such as triangular meshes could

8 Science and Technology of Nuclear Installations

0922 0954 10221064 1066

1023 09570991 0979

09160930

08400846

08870907

09720983

084108630970

0949

10361005

10471071

10131034

093609460990

0978

10821062

12171228

1329

1385

1063

1230

10141033 1082

097809900944

0931091209170872

08900878

08320837

08620848

09700956

08850908

09740962 0916

10371017

13301384

10511072

13311384

10381023

099209850962

09700977

0922

08960938 0863

09730966 1061 1232

1218 13341381

12171219

13291369

12081211

09890952

09810966

09680956

08750839

08280775

085508260890

0912

08470889

08100859

089209321035

0998

092909681071

1034

10330998

10821055

09900969

09450916

0971105810641025

09970990

09800992

106310191035

094409240871

090008960846

0877 ShR3

0920

1083

09460948

0931 0959 1024 0956 09240940

10730867

0936

097212101227

0934

0854

1217 1333

137309330906

08820893

09000866

09280958 0985

SR

ShR4

AR

ShR2

SR

ShR1

Figure 7 Relative power distribution in the case of complete withdrawal of the control rods The upper and lower values were obtained withSRAC and MCNP5 respectively

Cell 7-10

SRACMCNP5

Cell 9-6

ShR = 457cm AR = 40 cm

04

06

08

10

12

14

16

18

20

Relat

ive p

ower

den

sity

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Figure 8 Axial power distribution along the fuel bundles 7-10 and 9-6 at the critical core condition corresponding to the insertion of controlrods ShR = 457 cm and AR = 40 cm

Science and Technology of Nuclear Installations 9

04

06

08

10

12

14

16

18

Relat

ive p

ower

den

sity

20

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

Figure 9 Axial power distribution along the fuel bundles 7-10 and9-6 in the case of complete withdrawal of control rods

Cell 7-10

SRACMCNP5

Cell 9-6

0

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

9 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

ShR = 457cm AR = 40 cm

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

Figure 10Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 at the critical core condition corresponding to theinsertion of control rods ShR = 457 cm and AR = 40 cm

be useful to improve the accuracy of the calculation resultsFurther analyses are necessary to verify themodels using bothSRAC andMCNP5 codes for burnup and rod worth analysesof the DNRR core in comparison with themeasurement dataEvaluation of the effect of the cross section data libraries onthe neutronic properties of the DNRR core is being investi-gated Application in analyzing the current working configu-rations of the DNRR with low enriched uranium (LEU) fuelbundles is also being planned

5 Conclusions

Neutronics model of the DNRR was developed using theSRAC code system The PIJ and COREBN codes of the

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 11 Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 in the case of complete withdrawal of control rods

Rods in SRACRods in MCNP5

Rods out SRACRods out MCNP5

100 20 30minus20 minus10minus30Core height (top to bottom) (cm)

40 times 1012

60 times 1012

80 times 1012

10 times 1013

12 times 1013

14 times 1013

16 times 1013

18 times 1013

20 times 1013

22 times 1013

24 times 1013

26 times 1013

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 12Thermal neutron flux distribution along the neutron trapRods in ShR = 457 cm and AR = 40 cm Rods out ShR = 0 cm andAR = 0 cm

SRAC code system were used for lattice physics and full-coreanalyses In order to handle the complicated geometries ofthe DNRR such as the neutron trap neutron channels andupper and lower parts of the active core homogenizationhas been conducted Numerical calculations were performedto analyze the effective multiplication factors 119896eff for twocases corresponding to the complete withdrawal and thefull insertion of control rods Criticality analyses were thenconducted with the four different control rod banks Theradial and axial power peaking factors of the DNRR core arecalculated to be 1334 and 1710 respectively in the case of nocontrol rod insertion These values are 1445 and 1832 at thecriticality condition with the partial insertion of control rodsComparing to the MCNP5 calculations the results show that

10 Science and Technology of Nuclear Installations

the difference between the 119896eff values of the codes is less than55 pcm The maximum deviations of the 119896eff values obtainedfrom SRAC and MCNP5 compared to the experiments are119 pcm and 64 pcm respectivelyThedeviation of the relativepower distributions between the codes is less than 4 formost of the fuel bundles in the middle of the core while themaximum deviation is about 7 which appears at peripheralbundles In addition thermal neutron flux distributions inthe neutron trap are in good agreement This agreementindicates the verification of the models and the possibility forfurther analysis

Conflicts of Interest

The authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

This research is funded by Foundation for Science andTechnology Development of Ton Duc Thang University(FOSTECT) website httpfostecttdteduvn under GrantFOSTECT2016BR13

References

[1] TRIGA History URL httpwwwgacomtriga-history[2] N D Nguyen Ed Safety Analysis Report for the Dalat Nuclear

Research Reactor Nuclear Research Institute Vietnam AtomicEnergy Commission 2009

[3] N D Nguyen B V Luong V V Le et al ldquoResults of Operationand Utilization of the Dalat Nuclear Research ReactorrdquoNuclearScience and Technology vol 4 no 1 pp 1ndash9 2014

[4] M Turkmen and U Colak ldquoAnalysis of ITU TRIGA MarkII research reactor using Monte Carlo methodrdquo Progress inNuclear Energy vol 77 pp 152ndash159 2014

[5] B Q Do and L P Nguyen ldquoApplication of a genetic algorithmto the fuel reload optimization for a research reactorrdquo AppliedMathematics andComputation vol 187 no 2 pp 977ndash988 2007

[6] K Okumura T Kugo K Kaneko and K TsuchihashiSRAC2006 A Comprehensive Neutronics Calculation Code Sys-tem JAEA-DataCode 2007-004 2007

[7] D H Pham Q H Ngo H L Vu and KM Tran Report startupof nuclear research reactor Part 2 - Physics startup for coreconfiguration with a neutron trap Nuclear Research Institute1984

[8] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technology Nucl Data Sheetsrdquo Special Issue onEvaluated Nuclear Data File ENDFB-VII0 2006

[9] X-5 Monte Carlo Team 2005 MCNP - A General Monte CarloN-Particle Transport Code Version 5 LA-UR-03-1987 April 242003

Science and Technology of Nuclear Installations 7

Table 3 Criticality calculations of the DNRR with four control rod banks

Position of control rods (cm) 119896eff Dev(pcm)ShR1 ShR2 ShR3 ShR4 AR SRAC MCNP545 45 45 45 65 100119 100064 plusmn 000006 55472 472 472 472 0 099960 099969 plusmn 000006 9457 457 457 457 40 100086 100051 plusmn 000006 35467 467 467 467 20 100009 099998 plusmn 000006 11

09200968

09791021

10601131 1130

1059 09771023

09180977

07770798

08470887

08410854

08960912

09450931

09650925

09750936

09110963

08830843

08290776

08350808

07730759

10010977

09360915

08030825

09050944

09960991

10611121

10091000

111811230950

0928

08330838

098510371004

0931

08260790

07920778 ShR3

SR08690935

09150872

08930894

08760886

10701099

10471079

10641098

097310060883

0864

07690771

079707810850

0879

08560870

09480978

10581044

09960972

10761047

10551062 0998

0981

09611012

08890875

10070978

10631132

11101121

07190757

ShR4

08220868

10261083

10001054

14551429

08400869

09560997

09160944

082208260995

1002

11201115

128612811486

1444

11181122

100509970829

0825

09480922

12911292

14391481

13221324

14391483

12931293 1481

1445 12871274

09970947

14521429

12921309

10341083

08030859

AR

09420905

08370863

07570761

SR

ShR2 ShR1

Figure 6 Relative power distribution in the core at the initial critical condition corresponding to the control rod insertion ShR = 457 cmAR = 40 cm The upper and lower values were obtained with SRAC and MCNP5 respectively

comparison with the results obtained from the MCNP5calculations It can be seen that the maximum thermalneutron flux is about 217 times 1013 ncm2sdots in the case of controlrod withdrawal The axial flux distribution is also shifted tothe lower part of the core when the control rods are insertedIn this case the peak value of thermal flux is about 238 times1013 ncm2sdots shifted to about 10 cm from the central point ofthe neutron trap to the core bottom as shown in Figure 12noting that there is a good agreement between the two codesThis indicates the validity of the analysis models and thepotential use for further applications

Since theDNRR core containsmany complicated compo-nents it is a challenge to model the core using a deterministiccode Homogenization of materials especially in particularregions where control rods are withdrawn could affect theaccuracy of the results However in the present work theanalysis results show an acceptable agreement between thecodes as well as the startup report The current models ofthe DNRR core in the SRAC code could handle flexible axialmesh sizes along the core height depending on the actualcontrol rod positions A possible improvement of the modelsto handle finer radial meshes such as triangular meshes could

8 Science and Technology of Nuclear Installations

0922 0954 10221064 1066

1023 09570991 0979

09160930

08400846

08870907

09720983

084108630970

0949

10361005

10471071

10131034

093609460990

0978

10821062

12171228

1329

1385

1063

1230

10141033 1082

097809900944

0931091209170872

08900878

08320837

08620848

09700956

08850908

09740962 0916

10371017

13301384

10511072

13311384

10381023

099209850962

09700977

0922

08960938 0863

09730966 1061 1232

1218 13341381

12171219

13291369

12081211

09890952

09810966

09680956

08750839

08280775

085508260890

0912

08470889

08100859

089209321035

0998

092909681071

1034

10330998

10821055

09900969

09450916

0971105810641025

09970990

09800992

106310191035

094409240871

090008960846

0877 ShR3

0920

1083

09460948

0931 0959 1024 0956 09240940

10730867

0936

097212101227

0934

0854

1217 1333

137309330906

08820893

09000866

09280958 0985

SR

ShR4

AR

ShR2

SR

ShR1

Figure 7 Relative power distribution in the case of complete withdrawal of the control rods The upper and lower values were obtained withSRAC and MCNP5 respectively

Cell 7-10

SRACMCNP5

Cell 9-6

ShR = 457cm AR = 40 cm

04

06

08

10

12

14

16

18

20

Relat

ive p

ower

den

sity

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Figure 8 Axial power distribution along the fuel bundles 7-10 and 9-6 at the critical core condition corresponding to the insertion of controlrods ShR = 457 cm and AR = 40 cm

Science and Technology of Nuclear Installations 9

04

06

08

10

12

14

16

18

Relat

ive p

ower

den

sity

20

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

Figure 9 Axial power distribution along the fuel bundles 7-10 and9-6 in the case of complete withdrawal of control rods

Cell 7-10

SRACMCNP5

Cell 9-6

0

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

9 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

ShR = 457cm AR = 40 cm

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

Figure 10Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 at the critical core condition corresponding to theinsertion of control rods ShR = 457 cm and AR = 40 cm

be useful to improve the accuracy of the calculation resultsFurther analyses are necessary to verify themodels using bothSRAC andMCNP5 codes for burnup and rod worth analysesof the DNRR core in comparison with themeasurement dataEvaluation of the effect of the cross section data libraries onthe neutronic properties of the DNRR core is being investi-gated Application in analyzing the current working configu-rations of the DNRR with low enriched uranium (LEU) fuelbundles is also being planned

5 Conclusions

Neutronics model of the DNRR was developed using theSRAC code system The PIJ and COREBN codes of the

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 11 Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 in the case of complete withdrawal of control rods

Rods in SRACRods in MCNP5

Rods out SRACRods out MCNP5

100 20 30minus20 minus10minus30Core height (top to bottom) (cm)

40 times 1012

60 times 1012

80 times 1012

10 times 1013

12 times 1013

14 times 1013

16 times 1013

18 times 1013

20 times 1013

22 times 1013

24 times 1013

26 times 1013

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 12Thermal neutron flux distribution along the neutron trapRods in ShR = 457 cm and AR = 40 cm Rods out ShR = 0 cm andAR = 0 cm

SRAC code system were used for lattice physics and full-coreanalyses In order to handle the complicated geometries ofthe DNRR such as the neutron trap neutron channels andupper and lower parts of the active core homogenizationhas been conducted Numerical calculations were performedto analyze the effective multiplication factors 119896eff for twocases corresponding to the complete withdrawal and thefull insertion of control rods Criticality analyses were thenconducted with the four different control rod banks Theradial and axial power peaking factors of the DNRR core arecalculated to be 1334 and 1710 respectively in the case of nocontrol rod insertion These values are 1445 and 1832 at thecriticality condition with the partial insertion of control rodsComparing to the MCNP5 calculations the results show that

10 Science and Technology of Nuclear Installations

the difference between the 119896eff values of the codes is less than55 pcm The maximum deviations of the 119896eff values obtainedfrom SRAC and MCNP5 compared to the experiments are119 pcm and 64 pcm respectivelyThedeviation of the relativepower distributions between the codes is less than 4 formost of the fuel bundles in the middle of the core while themaximum deviation is about 7 which appears at peripheralbundles In addition thermal neutron flux distributions inthe neutron trap are in good agreement This agreementindicates the verification of the models and the possibility forfurther analysis

Conflicts of Interest

The authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

This research is funded by Foundation for Science andTechnology Development of Ton Duc Thang University(FOSTECT) website httpfostecttdteduvn under GrantFOSTECT2016BR13

References

[1] TRIGA History URL httpwwwgacomtriga-history[2] N D Nguyen Ed Safety Analysis Report for the Dalat Nuclear

Research Reactor Nuclear Research Institute Vietnam AtomicEnergy Commission 2009

[3] N D Nguyen B V Luong V V Le et al ldquoResults of Operationand Utilization of the Dalat Nuclear Research ReactorrdquoNuclearScience and Technology vol 4 no 1 pp 1ndash9 2014

[4] M Turkmen and U Colak ldquoAnalysis of ITU TRIGA MarkII research reactor using Monte Carlo methodrdquo Progress inNuclear Energy vol 77 pp 152ndash159 2014

[5] B Q Do and L P Nguyen ldquoApplication of a genetic algorithmto the fuel reload optimization for a research reactorrdquo AppliedMathematics andComputation vol 187 no 2 pp 977ndash988 2007

[6] K Okumura T Kugo K Kaneko and K TsuchihashiSRAC2006 A Comprehensive Neutronics Calculation Code Sys-tem JAEA-DataCode 2007-004 2007

[7] D H Pham Q H Ngo H L Vu and KM Tran Report startupof nuclear research reactor Part 2 - Physics startup for coreconfiguration with a neutron trap Nuclear Research Institute1984

[8] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technology Nucl Data Sheetsrdquo Special Issue onEvaluated Nuclear Data File ENDFB-VII0 2006

[9] X-5 Monte Carlo Team 2005 MCNP - A General Monte CarloN-Particle Transport Code Version 5 LA-UR-03-1987 April 242003

8 Science and Technology of Nuclear Installations

0922 0954 10221064 1066

1023 09570991 0979

09160930

08400846

08870907

09720983

084108630970

0949

10361005

10471071

10131034

093609460990

0978

10821062

12171228

1329

1385

1063

1230

10141033 1082

097809900944

0931091209170872

08900878

08320837

08620848

09700956

08850908

09740962 0916

10371017

13301384

10511072

13311384

10381023

099209850962

09700977

0922

08960938 0863

09730966 1061 1232

1218 13341381

12171219

13291369

12081211

09890952

09810966

09680956

08750839

08280775

085508260890

0912

08470889

08100859

089209321035

0998

092909681071

1034

10330998

10821055

09900969

09450916

0971105810641025

09970990

09800992

106310191035

094409240871

090008960846

0877 ShR3

0920

1083

09460948

0931 0959 1024 0956 09240940

10730867

0936

097212101227

0934

0854

1217 1333

137309330906

08820893

09000866

09280958 0985

SR

ShR4

AR

ShR2

SR

ShR1

Figure 7 Relative power distribution in the case of complete withdrawal of the control rods The upper and lower values were obtained withSRAC and MCNP5 respectively

Cell 7-10

SRACMCNP5

Cell 9-6

ShR = 457cm AR = 40 cm

04

06

08

10

12

14

16

18

20

Relat

ive p

ower

den

sity

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Figure 8 Axial power distribution along the fuel bundles 7-10 and 9-6 at the critical core condition corresponding to the insertion of controlrods ShR = 457 cm and AR = 40 cm

Science and Technology of Nuclear Installations 9

04

06

08

10

12

14

16

18

Relat

ive p

ower

den

sity

20

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

Figure 9 Axial power distribution along the fuel bundles 7-10 and9-6 in the case of complete withdrawal of control rods

Cell 7-10

SRACMCNP5

Cell 9-6

0

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

9 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

ShR = 457cm AR = 40 cm

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

Figure 10Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 at the critical core condition corresponding to theinsertion of control rods ShR = 457 cm and AR = 40 cm

be useful to improve the accuracy of the calculation resultsFurther analyses are necessary to verify themodels using bothSRAC andMCNP5 codes for burnup and rod worth analysesof the DNRR core in comparison with themeasurement dataEvaluation of the effect of the cross section data libraries onthe neutronic properties of the DNRR core is being investi-gated Application in analyzing the current working configu-rations of the DNRR with low enriched uranium (LEU) fuelbundles is also being planned

5 Conclusions

Neutronics model of the DNRR was developed using theSRAC code system The PIJ and COREBN codes of the

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 11 Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 in the case of complete withdrawal of control rods

Rods in SRACRods in MCNP5

Rods out SRACRods out MCNP5

100 20 30minus20 minus10minus30Core height (top to bottom) (cm)

40 times 1012

60 times 1012

80 times 1012

10 times 1013

12 times 1013

14 times 1013

16 times 1013

18 times 1013

20 times 1013

22 times 1013

24 times 1013

26 times 1013

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 12Thermal neutron flux distribution along the neutron trapRods in ShR = 457 cm and AR = 40 cm Rods out ShR = 0 cm andAR = 0 cm

SRAC code system were used for lattice physics and full-coreanalyses In order to handle the complicated geometries ofthe DNRR such as the neutron trap neutron channels andupper and lower parts of the active core homogenizationhas been conducted Numerical calculations were performedto analyze the effective multiplication factors 119896eff for twocases corresponding to the complete withdrawal and thefull insertion of control rods Criticality analyses were thenconducted with the four different control rod banks Theradial and axial power peaking factors of the DNRR core arecalculated to be 1334 and 1710 respectively in the case of nocontrol rod insertion These values are 1445 and 1832 at thecriticality condition with the partial insertion of control rodsComparing to the MCNP5 calculations the results show that

10 Science and Technology of Nuclear Installations

the difference between the 119896eff values of the codes is less than55 pcm The maximum deviations of the 119896eff values obtainedfrom SRAC and MCNP5 compared to the experiments are119 pcm and 64 pcm respectivelyThedeviation of the relativepower distributions between the codes is less than 4 formost of the fuel bundles in the middle of the core while themaximum deviation is about 7 which appears at peripheralbundles In addition thermal neutron flux distributions inthe neutron trap are in good agreement This agreementindicates the verification of the models and the possibility forfurther analysis

Conflicts of Interest

The authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

This research is funded by Foundation for Science andTechnology Development of Ton Duc Thang University(FOSTECT) website httpfostecttdteduvn under GrantFOSTECT2016BR13

References

[1] TRIGA History URL httpwwwgacomtriga-history[2] N D Nguyen Ed Safety Analysis Report for the Dalat Nuclear

Research Reactor Nuclear Research Institute Vietnam AtomicEnergy Commission 2009

[3] N D Nguyen B V Luong V V Le et al ldquoResults of Operationand Utilization of the Dalat Nuclear Research ReactorrdquoNuclearScience and Technology vol 4 no 1 pp 1ndash9 2014

[4] M Turkmen and U Colak ldquoAnalysis of ITU TRIGA MarkII research reactor using Monte Carlo methodrdquo Progress inNuclear Energy vol 77 pp 152ndash159 2014

[5] B Q Do and L P Nguyen ldquoApplication of a genetic algorithmto the fuel reload optimization for a research reactorrdquo AppliedMathematics andComputation vol 187 no 2 pp 977ndash988 2007

[6] K Okumura T Kugo K Kaneko and K TsuchihashiSRAC2006 A Comprehensive Neutronics Calculation Code Sys-tem JAEA-DataCode 2007-004 2007

[7] D H Pham Q H Ngo H L Vu and KM Tran Report startupof nuclear research reactor Part 2 - Physics startup for coreconfiguration with a neutron trap Nuclear Research Institute1984

[8] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technology Nucl Data Sheetsrdquo Special Issue onEvaluated Nuclear Data File ENDFB-VII0 2006

[9] X-5 Monte Carlo Team 2005 MCNP - A General Monte CarloN-Particle Transport Code Version 5 LA-UR-03-1987 April 242003

Science and Technology of Nuclear Installations 9

04

06

08

10

12

14

16

18

Relat

ive p

ower

den

sity

20

minus20 minus10 0 10 20 30minus30Core height (top to bottom) (cm)

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

Figure 9 Axial power distribution along the fuel bundles 7-10 and9-6 in the case of complete withdrawal of control rods

Cell 7-10

SRACMCNP5

Cell 9-6

0

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

9 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

ShR = 457cm AR = 40 cm

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

Figure 10Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 at the critical core condition corresponding to theinsertion of control rods ShR = 457 cm and AR = 40 cm

be useful to improve the accuracy of the calculation resultsFurther analyses are necessary to verify themodels using bothSRAC andMCNP5 codes for burnup and rod worth analysesof the DNRR core in comparison with themeasurement dataEvaluation of the effect of the cross section data libraries onthe neutronic properties of the DNRR core is being investi-gated Application in analyzing the current working configu-rations of the DNRR with low enriched uranium (LEU) fuelbundles is also being planned

5 Conclusions

Neutronics model of the DNRR was developed using theSRAC code system The PIJ and COREBN codes of the

Cell 7-10

SRACMCNP5

Cell 9-6

Control rods out

minus30 minus20 minus10 0 10 20 30 40minus40Core height (top to bottom) (cm)

1 times 1012

2 times 1012

3 times 1012

4 times 1012

5 times 1012

6 times 1012

7 times 1012

8 times 1012

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 11 Thermal neutron flux distribution along the fuel bundles7-10 and 9-6 in the case of complete withdrawal of control rods

Rods in SRACRods in MCNP5

Rods out SRACRods out MCNP5

100 20 30minus20 minus10minus30Core height (top to bottom) (cm)

40 times 1012

60 times 1012

80 times 1012

10 times 1013

12 times 1013

14 times 1013

16 times 1013

18 times 1013

20 times 1013

22 times 1013

24 times 1013

26 times 1013

er

mal

neu

tron

flux

(n＝Ｇ

2middots)

Figure 12Thermal neutron flux distribution along the neutron trapRods in ShR = 457 cm and AR = 40 cm Rods out ShR = 0 cm andAR = 0 cm

SRAC code system were used for lattice physics and full-coreanalyses In order to handle the complicated geometries ofthe DNRR such as the neutron trap neutron channels andupper and lower parts of the active core homogenizationhas been conducted Numerical calculations were performedto analyze the effective multiplication factors 119896eff for twocases corresponding to the complete withdrawal and thefull insertion of control rods Criticality analyses were thenconducted with the four different control rod banks Theradial and axial power peaking factors of the DNRR core arecalculated to be 1334 and 1710 respectively in the case of nocontrol rod insertion These values are 1445 and 1832 at thecriticality condition with the partial insertion of control rodsComparing to the MCNP5 calculations the results show that

10 Science and Technology of Nuclear Installations

the difference between the 119896eff values of the codes is less than55 pcm The maximum deviations of the 119896eff values obtainedfrom SRAC and MCNP5 compared to the experiments are119 pcm and 64 pcm respectivelyThedeviation of the relativepower distributions between the codes is less than 4 formost of the fuel bundles in the middle of the core while themaximum deviation is about 7 which appears at peripheralbundles In addition thermal neutron flux distributions inthe neutron trap are in good agreement This agreementindicates the verification of the models and the possibility forfurther analysis

Conflicts of Interest

The authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

This research is funded by Foundation for Science andTechnology Development of Ton Duc Thang University(FOSTECT) website httpfostecttdteduvn under GrantFOSTECT2016BR13

References

[1] TRIGA History URL httpwwwgacomtriga-history[2] N D Nguyen Ed Safety Analysis Report for the Dalat Nuclear

Research Reactor Nuclear Research Institute Vietnam AtomicEnergy Commission 2009

[3] N D Nguyen B V Luong V V Le et al ldquoResults of Operationand Utilization of the Dalat Nuclear Research ReactorrdquoNuclearScience and Technology vol 4 no 1 pp 1ndash9 2014

[4] M Turkmen and U Colak ldquoAnalysis of ITU TRIGA MarkII research reactor using Monte Carlo methodrdquo Progress inNuclear Energy vol 77 pp 152ndash159 2014

[5] B Q Do and L P Nguyen ldquoApplication of a genetic algorithmto the fuel reload optimization for a research reactorrdquo AppliedMathematics andComputation vol 187 no 2 pp 977ndash988 2007

[6] K Okumura T Kugo K Kaneko and K TsuchihashiSRAC2006 A Comprehensive Neutronics Calculation Code Sys-tem JAEA-DataCode 2007-004 2007

[7] D H Pham Q H Ngo H L Vu and KM Tran Report startupof nuclear research reactor Part 2 - Physics startup for coreconfiguration with a neutron trap Nuclear Research Institute1984

[8] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technology Nucl Data Sheetsrdquo Special Issue onEvaluated Nuclear Data File ENDFB-VII0 2006

[9] X-5 Monte Carlo Team 2005 MCNP - A General Monte CarloN-Particle Transport Code Version 5 LA-UR-03-1987 April 242003

10 Science and Technology of Nuclear Installations

the difference between the 119896eff values of the codes is less than55 pcm The maximum deviations of the 119896eff values obtainedfrom SRAC and MCNP5 compared to the experiments are119 pcm and 64 pcm respectivelyThedeviation of the relativepower distributions between the codes is less than 4 formost of the fuel bundles in the middle of the core while themaximum deviation is about 7 which appears at peripheralbundles In addition thermal neutron flux distributions inthe neutron trap are in good agreement This agreementindicates the verification of the models and the possibility forfurther analysis

Conflicts of Interest

The authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

This research is funded by Foundation for Science andTechnology Development of Ton Duc Thang University(FOSTECT) website httpfostecttdteduvn under GrantFOSTECT2016BR13

References

[1] TRIGA History URL httpwwwgacomtriga-history[2] N D Nguyen Ed Safety Analysis Report for the Dalat Nuclear

Research Reactor Nuclear Research Institute Vietnam AtomicEnergy Commission 2009

[3] N D Nguyen B V Luong V V Le et al ldquoResults of Operationand Utilization of the Dalat Nuclear Research ReactorrdquoNuclearScience and Technology vol 4 no 1 pp 1ndash9 2014

[4] M Turkmen and U Colak ldquoAnalysis of ITU TRIGA MarkII research reactor using Monte Carlo methodrdquo Progress inNuclear Energy vol 77 pp 152ndash159 2014

[5] B Q Do and L P Nguyen ldquoApplication of a genetic algorithmto the fuel reload optimization for a research reactorrdquo AppliedMathematics andComputation vol 187 no 2 pp 977ndash988 2007

[6] K Okumura T Kugo K Kaneko and K TsuchihashiSRAC2006 A Comprehensive Neutronics Calculation Code Sys-tem JAEA-DataCode 2007-004 2007

[7] D H Pham Q H Ngo H L Vu and KM Tran Report startupof nuclear research reactor Part 2 - Physics startup for coreconfiguration with a neutron trap Nuclear Research Institute1984

[8] M B Chadwick P Oblozinsky M Herman et al ldquoENDFB-VII0 next generation evaluated nuclear data library for nuclearscience and technology Nucl Data Sheetsrdquo Special Issue onEvaluated Nuclear Data File ENDFB-VII0 2006

[9] X-5 Monte Carlo Team 2005 MCNP - A General Monte CarloN-Particle Transport Code Version 5 LA-UR-03-1987 April 242003

TribologyAdvances in

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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

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Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpswwwhindawicom

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International Journal of

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EnergyJournal of

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Journal of

Volume 201Hindawi Publishing Corporation httpwwwhindawicom Volume 201

International Journal ofInternational Journal of

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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

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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014