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Research ArticleMethods and Models for the Coupled Neutronics andThermal-Hydraulics Analysis of the CROCUS Reactor at EFPL

A. Rais,1 D. Siefman,1 G. Girardin,1 M. Hursin,2 and A. Pautz1,2

1 Ecole Polytechnique Federale de Lausanne (EPFL), 1015 Lausanne, Switzerland2Paul Scherrer Institut (PSI), 5232 Villigen, Switzerland

Correspondence should be addressed to A. Rais; [email protected]

Received 6 March 2015; Accepted 30 May 2015

Academic Editor: Rafael Miro

Copyright © 2015 A. Rais et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In order to analyze the steady state and transient behavior of theCROCUS reactor, severalmethods andmodels need to be developedin the areas of reactor physics, thermal-hydraulics, and multiphysics coupling. The long-term objectives of this project are to worktowards the development of a modern method for the safety analysis of research reactors and to update the Final Safety AnalysisReport of the CROCUS reactor. A first part of the paper deals with generation of a core simulator nuclear data library for theCROCUS reactor using the Serpent 2 Monte Carlo code and also with reactor core modeling using the PARCS code. PARCSeigenvalue, radial power distribution, and control rod reactivity worth results were benchmarked against Serpent 2 full-core modelresults. Using the Serpent 2 model as reference, PARCS eigenvalue predictions were within 240 pcm, radial power was within 3% inthe central region of the core, and control rod reactivity worth was within 2%. A second part reviews the current methodology usedfor the safety analysis of the CROCUS reactor and presents the envisioned approach for the multiphysics modeling of the reactor.

1. Introduction

A large variety of research reactors have been designed andoperated during the last 50 years.These reactors are primarilydesigned for research purposes, yet they are widely appliedin education and training, materials testing, and isotopeproduction. Due to the diversity of research reactor designsand operating conditions, there is a wide variety of compu-tational tools used in their safety analysis and, nowadays, itis desired to adopt a standard approach for safety analysis ofthese research reactors [1]. The development of high powerresearch reactors and small modular reactors, together withthe extended and intensive utilization of research reactorsand the increased safety requirements of nuclear installationsafter the Fukushima accident [2], encourages the adoptionof nuclear power plant (NPP) tools and methods to researchreactor safety analysis. However, the use of NPP tools forresearch reactors is not straightforward as there are importantdifferences in operating pressure, coolant flow, size, andpower.

The coupling of thermal-hydraulic and neutronics codesbecomes a fundamental tool for an accurate reactor behavior

prediction under transient and accident conditions. Alongthose lines, a project financed by swissnuclear was startedwith the objective of developing methods and models for thecoupled neutronics and thermal-hydraulics analysis of theCROCUS reactor at EFPL using advanced and state-of-the-art NPP computational tools. The present work representsthe first stage of the project and focuses on the neutronicsmodeling.

This paper is divided into four sections. The first partbriefly reviews the design of the CROCUS reactor. Thesecond describes the methodology applied for the neutronicsmodeling of the reactor and the third section summarizesthe process by which the model was benchmarked against aMonte Carlo solution.The fourth section reviews the currentthermal-hydraulic modeling of the CROCUS reactor anddescribes the proposed model.

2. The CROCUS Reactor

The CROCUS reactor, operated by the Ecole PolytechniqueFederale de Lausanne (EPFL), Switzerland, is a two-zoneuranium-fuelled, H

2O-moderated critical research facility. It

Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2015, Article ID 237646, 9 pageshttp://dx.doi.org/10.1155/2015/237646

2 Science and Technology of Nuclear Installations

Figure 1: CROCUS core fuel lattices: UO2fuel (orange), U-metal

fuel (red), and control rods (white).

can be classified as a zero-power reactor, with a nominalpower of 100W.Thecore is approximately cylindrical in shapewith a diameter of about 58 cm and a height of 100 cm. Thereactivity in the CROCUS reactor is controlled by the waterlevel, which can be adjusted with an accuracy of ±0.1mm [3].

There are two different kinds of fuel rods within the CRO-CUS reactor core (see Figure 1). The central zone is fuelledwith 336UO

2fuel rods (1.806wt%-enriched), which are

thinner rods with a square lattice pitch of 1.8370 ± 0.0002 cm.The peripheral zone is loaded with 176 thicker, U-metal fuelrods (0.947wt%-enriched)with a pitch of 2.9170± 0.0002 cm.All fuel rods have an aluminum cladding and are maintainedin a vertical position by the upper grid and lower grid platesspaced 100 cm apart (see Figure 2). Because of the differentpitches used, the two fuel zones are separated by a water gap,as shown in Figure 1. The core is located in an aluminumwater tank of 130 cm diameter and 1.2 cm thickness. Lightwater (H

2O) is used as moderator and reflector. With the

current fuel loading, the critical water level is 95.22 ± 0.01 cm.Therefore, when the reactor becomes critical, a small axialsection of the active core is exposed to air at atmospheric con-ditions as shown in Figure 2. There are two shutdown safetysystems: (1) expansion tanks that allow fast reduction of thewater level and (2) two cruciform control blades insertedfrom top to bottom. Figure 2 also provides a view of the reac-tor structure, the water tank, support plates, and fuel rods.

3. Neutronics Modeling

Although direct full-core transport calculations for transientanalysis (such as DeCART [4], nTRACER [5], and MPACT[6]) are becoming possiblewith the increase of computationalpower, they remain very expensive and the full analysis ofa nuclear reactor core currently relies on the traditionalmultistep methodology [7].This approach begins with latticephysics to condense and homogenize spatially and spectrally

Lower grid

Upper gridUO2 fuel

U-metal fuelWater

Vessel

Figure 2: CROCUS reactor supporting structure and core internals.

the microscopic cross-section data into the structure neededfor coarser-level codes (i.e., few-group parameters genera-tion) and concludes with the core physics calculations to per-form steady-state and transient full-core reactor calculations.

3.1. Cross-Section Generation. Traditionally, few-group param-eters generation for full-core reactor simulators (such asPARCS) has been done using deterministic lattice physicscodes. However, the use of continuous-energy Monte Carlocodes to generate few-group parameters can become aninteresting option when dealing with reactor types that liebeyond the capabilities of conventional deterministic latticephysics codes [8]. CROCUS reactor characteristics make thismethodology interesting as its core presents two incongruentfuel lattices with a water gap in-between, with no possiblesubdivision of the core in simple repeatable subsections (suchas fuel assemblies).

Serpent 2.1.21, a Monte Carlo code developed at VTT [9],has been specifically designed for lattice physics applications.Serpent represents the state of the art for Monte Carlo latticephysics and has been chosen to provide the code PARCS withthe homogenized cross sections.The use of Serpent code as across-section generator for PARCS code has been investigatedby different research groups [10, 11].

In a previous work [12] the cross-section generation ofthe CROCUS reactor core was performed using Serpentcode version 1.1.19. The SerpentXS python script [13] wasused along with Serpent 1.1.19 to perform branch calculationsand print cross sections into a PARCS compatible format.However, results from the previousworkwere not satisfactorysince diffusion coefficients computed by Serpent 1 carriedimportant errors of up to 30% [14]. The second release of

Science and Technology of Nuclear Installations 3

the code, Serpent 2, implemented an updated approach fordiffusion coefficient generation with improved accuracy [14].

Serpent 2 has the ability to generate diffusion coefficientsusing the classical definition based on the 𝑃

1theory but it

has also implemented 𝐵1fundamental mode methodology

to correct diffusion coefficients based on an approximateleakage spectrum [8]. In this paper, both diffusion coefficientsdefinitionswere used and tested.Thefirst definition, based onthe traditional 𝑃

1approximation, is computed as

𝐷𝑔=

13Σtr,𝑔=

13 (Σ𝑡,𝑔− 𝜇0,𝑔Σ𝑠0,𝑔)

, (1)

where 𝐷𝑔is the microgroup diffusion coefficient, Σtr,𝑔 the

macroscopic transport corrected cross section, Σ𝑡,𝑔

the totalmacroscopic cross section, 𝜇0,𝑔 the average cosine of thescattering collision angle, and Σ

𝑠0,𝑔 the zeroth moment of thescattering cross section.Then, the energy condensation (frommicro- to coarse-group structure) of the diffusion coefficientis done as follows:

𝐷𝐺=

∑𝑔∈𝐺𝐷𝑔𝜙𝑔

∑𝑔∈𝐺𝜙𝑔

, (2)

where 𝐺 is the group index in the coarse-group structure.On the other hand, when the 𝐵

1leakage mode is invoked

in Serpent 2, the code solves the 𝐵1equations [15] where

𝑘eff is iterated to unity to get a better approximation of theneutron energy spectrum, resulting in the leakage-correctedflux spectrum (𝜑

𝑔) and current spectrum (𝐽

𝑔). Then, the

microgroup diffusion coefficient is computed as

𝐷𝑔=

𝐽𝑔

|𝐵| 𝜑𝑔

, (3)

where 𝐵 is the energy independent buckling and 𝑔 is thegroup index in themicrogroup structure.The energy conden-sation into a coarse-group structure is done with the leakage-corrected flux using (2).

Serpent 2 can solve the 𝐵1equations not only to provide

an alternative definition of diffusion coefficient but also togenerate leakage-corrected cross sections, that is, to use thecritical flux spectrum (𝜑

𝑔) for spectral collapsing of cross

sections.Since Serpent 2 uses different output variables names than

Serpent 1 (the first release of the code), one of the tasks per-formed in thisworkwas to update the SerpentXS scripts to (1)become compatible with Serpent 2 output and (2) to handleleakage corrected cross sections (𝐵

1mode corrected). This

updated script will be hereafter referred to as SerpentXS2.Given that the CROCUS reactor core presents a peculiar

geometry with two incongruent fuel lattices, the subdivisionof the core in the form of fuel assemblies is not possible. Forthat reason, the most natural subdivision of the core is at apin-cell level. This geometry was used to generate the fuelcross sections. Figure 3 illustrates the 2D geometry used tomodel the U-metal fuel (corresponding to the outer lattice)and also the one for the UO

2fuel (corresponding to the inner

lattice). These heterogeneous pin-cell models use reflective

fuel cellHomogenized U-metal

fuel cell

Refl. BCRefl. BC

Refl. BC Refl. BC

Refl.

BC

Refl.

BC

Refl.

BC

Refl.

BC

Fuel

Moderator

Homogenized UO2

Figure 3: Fuel cross-sections generation.

Homogenized control rod cell

Refl. BC

Refl. BC

Refl.

BC

Refl.

BC

Fuel

Control rod

Moderator

Figure 4: Control rods cross-sections generation.

boundary conditions in all three directions. Figure 3 alsoshows the difference in pin-cell sizes.

In order to generate the cross sections for control rods, a2-D geometry of eight U-metal fuel rods with a control rodin the center was used as illustrated in Figure 4. Reflectiveboundary conditions were also used in all three directions. Asshown in Figure 4, only the area surrounded by the dashedline was homogenized. The eight peripheral fuel pins wereused to provide the heterogeneous problem with neutrons.

The water reflector region was modeled using a 2Dgeometry representing the radial boundary between coreand reflector as illustrated in Figure 5. Reflective boundaryconditions were used in the all directions with exception ofthe side of the reflector facing the vessel, which uses vacuumboundary conditions. Since in the bottom of the core thereis a 47 cm layer of water, this heterogeneous model was alsoused to generate bottom reflector cross sections.

The top reflector region has been modeled with a geome-try that included all structures on top of the core as shown inFigure 6.

Special treatment was taken over the water gap betweenfuel lattices to include it in either the UO

2or U-metal fuel

lattices. For the case in which the water gap is contained inthe outer lattice, the water gap volume was smeared across


Homogenized reflector region

Refl. BC

Refl. BC

Refl.

BC

Vacu

um B

C

Fuel Moderator

Figure 5: Water reflector cross-sections generation.

Homogenized top reflector

AirAluminum FuelSide view of the CROCUS reactor core

Figure 6: Top reflector cross-sections generation.

all U-metal nodes by increasing the fuel pitch from 2.917 to3.023 cm. In a similar way, when the water gap is containedin the inner lattice, the UO

2pitch is increased from 1.837 to

1.909 cm.For the cross-section generation of fuelled regions (i.e.,

UO2and U-metal pin cells), two different diffusion coef-

ficients definitions were used: a first one based on the 𝑃1

approximation (1) and a second one based on the 𝐵1leakage

model (3). Also, the cross-section spectral homogenization ofall fuelled regions was computed in two different ways: oneusing the infinite flux spectrum (resulting from the infinitearray of fuel pins) and a second one using the leakage-corrected flux spectrum (from the 𝐵

1leakage correction

model). Since the 𝐵1model is only applicable to regions

where fission is taking place, reflector regions and controlrods cross-section generation were limited only to 𝑃

1-based

diffusion coefficients and infinite flux spectrum for the cross-section collapsing.

Since the cross sections are generated at a pin-cell level,standard deterministic codes like CASMO [16], HELIOS [17],or TRITON [18] could have been used. Serpent 2 is choseninstead to take advantage of being able to model the full-scaleheterogeneous problem, which represents the best available

reference solution for the calculation scheme. A full-scalehomogenization scheme is currently under development,which will provide an alternative to the presently used pin-cell level scheme.

Serpent 2.1.21 and the ENDF/B-VII nuclear data librarywere used for allMonte Carlo simulations (cross-section gen-eration and full-core calculations). The full-core calculationswere run using 900 cycles of 106 neutrons each, returning afinal statistical uncertainty below 8 pcm for eigenvalue calcu-lations and 0.1% for radial power distribution. For the pin-celland other cross-section models, 1100 cycles of 105 neutronseach were used, returning a final statistical uncertainty below0.01% for two-group parameters generation. The initial 100cycles were skipped in all simulations.

3.2. Reactor Core Modeling. The first task of the reactorcore modeling consisted of building a full-core model of thereactor using the Monte Carlo code Serpent 2. Since thismodel is used as reference for the comparison against thePARCS models, it was built including as many details aspossible. In a previous work, the full-core Serpent model hasbeen verified against a previously built MCNP model [19]. Avalidation work will be carried out in the near future.

Nodal methods are widely used for full-core reactorphysics calculations. Each node normally corresponds to asmall portion of the reactor core (e.g., to an axial slice of a fuelassembly) for which homogenized cross sections have firstbeen obtained. PARCS [20] is a multigroup nodal diffusioncode developed by the US NRC for 3D steady-state andtransient analyses. However, PARCS also includes a finitedifference kernel, which can be used for finer mesh solutions.

Due to the geometric characteristics of the CROCUSreactor core, subdivision of the core in fuel assemblies isnot possible. Hence, two pin-by-pin full-core models weredeveloped and run using the code PARCS v3.00. A firstmodeluses a fine Cartesian mesh with a size equivalent to a UO

2

fuel cell (1.837 cm) as illustrated in Figure 7. Since this finermesh model cannot be used to predict power distribution inthe outer lattice due to the mesh-fuel pin incongruences, asecond model was required. The second PARCS model usesa coarser Cartesian mesh with a size equivalent to a U-metalfuel cell (2.197 cm) as illustrated in Figure 8. The latter canbe used to predict the outer lattice radial power distribution;however, it fails to predict the inner lattice power distributiondue to similar mesh-fuel pin incongruences.

PARCS calculations were run using two-group diffusiontheory and a finite difference kernel.The two-group homoge-nized cross sections were generated using the Serpent 2 codeas presented in the previous section. No correction factorssuch as interface discontinuity factors were used.

Axially, the active region of the core was subdivided into25 nodes of 3.808 cm each, matching the 95.22 cm of waterlevel asmodeled in Serpent 2. Six nodes of 3.808 cm eachwereused to represent the region on top of the core.

Figure 9 shows the differences between the full-coreMonte Carlo model and the two different PARCS nodal-izations. The colors in the PARCS nodalization representdifferent cross-section sets: red for inner lattice, orange forouter lattice, green for control rods, and blue for reflector.


Figure 7: UO2fuel cell-size meshing.

Figure 8: U-metal fuel cell-size meshing.

Although it is difficult to visualize, the UO2cell-size mesh

model (Figure 9(b)) includes the water gap in the outerlattice cross-section set. Contrarily, the U-metal cell-sizemesh model (Figure 9(c)) includes the water gap in the innerlattice cross-section set.Themethod used to include thewatergap in one cross-section set or the other is described inSection 3.1.

4. Benchmark Results

This section is focused on the steady-state analysis and veri-fication of PARCS results against a Serpent 2 full-core model.Threemain steady-state parameters have been benchmarked:(1) effective multiplication factor, (2) control rods’ reactivity

worth, and (3) radial power distribution. The multiplicationfactor difference was computed as follows:

Δ𝑘eff = 𝑘𝑖

eff − 𝑘Serpent 2eff , (4)

where 𝑖 denotes each PARCS model.The control rod reactivity worthwas computed in Serpent

2 as the 𝑘eff difference between amodel containing the controlrods fully withdrawn and the one with control rods fullyinserted. In PARCS, the control rod worth was computed in asimilar way, using a card that allows inserting or withdrawingthe control rods. Finally, the percent difference reported inTable 1 was computed from the following expression:

Δ𝜌CR% =𝜌𝑖

CR − 𝜌Serpent 2CR

𝜌Serpent 2CR

⋅ 100, (5)

where 𝑖 denotes each PARCSmodel andCR stands for controlrods.

The results shown in Table 1 suggest that PARCS modelsusing 𝐵

1-based diffusion coefficients and leakage-corrected

cross sections are in good agreement with the Serpent 2reference. The use of 𝑃

1-based diffusion coefficients along

with non-leakage-corrected cross sections results in eigen-value underestimation. As for control rod reactivity worth,differences between the two PARCS models are related to thefact that control rods are being represented by threeUO

2cells

in theUO2cell-sizemodel and by only oneU-metal cell in the

other model (see Figures 9(b) and 9(c)). As a consequence,the UO

2cell-sizemodel contains an 18% excess of control rod

material.Since a 𝑘eff comparison does not return enough infor-

mation on the overall accuracy of the PARCS model, anadditional comparison exercise was performed focusing onradial power distribution. For this comparison, only𝐵

1-based

models have been used.The two PARCSmodels, respectively,using the UO

2and U-metal cell-size mesh are used to predict

the inner and outer lattice radial power distribution, sinceeach one has a node-to-fuel pin matching in their respectiveregions as previously shown in Figures 7 and 8.

Figure 10 shows the steady-state radial power distributionpredicted by Serpent 2 Monte Carlo code. The Serpent 2radial power distribution was compared against the twoPARCS models using the following expression:

Δ𝑃𝑖,% =𝑃𝑖,Serpent 2 − 𝑃𝑖,PARCS

𝑃𝑖,Serpent 2

⋅ 100, (6)

where the subindex 𝑖 denotes each node. Figure 11 illustratesthe results of the radial power distribution comparisonbetween Serpent 2 and PARCS. Note that the PARCS radialpower distribution has been calculated using two differentmodels: one for the inner lattice and another one for the outerlattice.Themaximum nodal differences are of about 20% andare located in the inner lattice nodes adjacent to the watergap. Such differences could be related to the fact that bothPARCS models smear the water gap, in the outer lattice forthe UO

2cell-size mesh and in the inner lattice for U-metal

cell-size mesh. PARCS power prediction in the central region


Table 1: 𝑘eff and control rod reactivity worth benchmark results.

Model Eigenvalue Control rod worth𝑘eff Δ𝑘eff (pcm) 𝜌CR (pcm) Δ𝜌CR%

Serpent 2 1.00184 ± 8 pcm — 358 —PARCS𝐵1UO2 cell-size mesh 0.99944 −240 365.1 2%𝐵1U-metal cell-size mesh 1.00136 −48 317 −12%𝑃1UO2 cell-size mesh 0.99369 −815 365 2%𝑃1U-metal cell-size mesh 0.99545 −639 317 −12%

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Figure 9: (a) Serpent 2 full-core model. (b) PARCS UO2cell-size mesh model. (c) PARCS U-metal cell-size mesh model.


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1.146130549 1.274881929 1.327077456 1.377663314 1.468913433 1.549358649 1.606053201 1.680079862 1.729876982 1.765241409 1.796022302 1.783199277 1.757698098 1.725120411 1.693035685 1.632526218 1.549493459 1.465458681 1.396232857 1.325978857 1.289656678 1.154810688

1.121723944 1.201668151 1.299853931 1.404130295 1.490782797 1.582205956 1.63570129 1.709951293 1.763977818 1.786736525 1.806448933 1.82973883 1.786311975 1.775251537 1.725838726 1.665514371 1.56403883 1.47823744 1.401574946 1.315071338 1.221809133 1.127909097

1.109160478 1.20832212 1.310544144 1.39545418 1.505571631 1.601322786 1.673244806 1.728043972 1.779726417 1.800249695 1.827972218 1.834010489 1.802736634 1.773963802 1.720496637 1.676120077 1.591896163 1.506563589 1.414800388 1.304326798 1.210159154 1.123045884

1.134341736 1.210545475 1.301485732 1.4066615 1.50775072 1.590598367 1.664313155 1.741877064 1.79357963 1.815217604 1.837422987 1.82964225 1.805364418 1.794696338 1.736444432 1.64895289 1.594582298 1.507054538 1.412963353 1.310095449 1.209980079 1.117655506

1.1301405 1.203400557 1.314399301 1.395538687 1.4828089 1.575888005 1.653596784 1.706015653 1.756197081 1.80913708 1.816593871 1.817855449 1.788750623 1.777722379 1.712778274 1.639258658 1.571431234 1.500829143 1.396723806 1.312004919 1.22463209 1.119285295

1.149414273 1.286032911 1.345063494 1.404363697 1.464108571 1.542253973 1.612445598 1.679731771 1.758861083 1.77087525 1.782736498 1.792291895 1.761967744 1.744160782 1.668431896 1.628916536 1.553839565 1.463327882 1.391965222 1.327043251 1.284892058 1.138961486

1.415070008 1.383711645 1.455434468 1.512634053 1.575461443 1.631542308 1.690528626 1.722265261 1.732388066 1.731001739 1.708796356 1.672228702 1.638610767 1.578960461 1.504941848 1.449995799 1.379437974 1.384818292

1.41081847 1.375564708 1.420214912 1.460446574 1.538867632 1.577733088 1.613876192 1.660719569 1.666522426 1.674130124 1.648387493 1.637023231 1.574340711 1.523682418 1.452575293 1.426876929 1.372413781 1.392872673

1.404331504 1.40308401 1.469118666 1.458865075 1.474130772 1.507316109 1.555674588 1.573564046 1.595200008 1.59240522 1.574177732 1.553539764 1.519465085 1.479981919 1.447921338 1.461508956 1.418313491 1.406341578

1.467643807 1.413585088 1.440860928 1.471987901 1.492708364 1.496332131 1.491561475 1.496006173 1.450611497 1.440164746 1.411742017 1.472997968

1.402281188 1.369816178 1.39573386 1.393876704 1.410389895 1.41532353 1.423146521 1.396848555 1.392083935 1.385307229 1.374138139 1.410746034

1.398061843 1.403804337 1.379546627 1.331934632 1.309986796 1.319035148 1.31535303 1.317723268 1.340091629 1.384289114 1.399130261 1.385433991

1.28845345 1.229006365 1.197197295 1.212034418 1.220839307 1.269658554

1.151074244 1.130919177 1.121683702 1.122166603 1.13228136 1.150398183

0.59 0.57 0.58 0.58 0.57 0.60 1.84 1.80.63 0.62 0.61 0.63 0.65 0.65 0.63 0.61 0.62 0.57 0.55 1.74

0.56 0.59 0.62 0.69 0.76 0.83 0.85 0.85 0.83 0.77 0.70 0.61 0.55 0.57 1.64

0.57 0.55 0.64 0.77 0.94 1.06 1.06 0.95 0.80 0.73 0.59 0.57 1.55

0.59 0.64 0.77 0.98 1.06 0.00 0.72 0.56 0.56 1.45

0.63 0.62 0.77 0.98 1.20 1.22 1.06 0.80 0.62 0.55 1.35

0.62 0.70 0.94 0.96 0.70 0.56 0.55 1.26

0.60 0.61 0.77 1.06 1.06 0.77 0.60 0.54 1.16

0.57 0.63 0.83 0.83 0.63 0.57 1.06

0.59 0.65 0.85 0.85 0.66 0.59 0.97 1.00.59 0.66 0.86 0.85 0.65 0.59 0.87

0.57 0.64 0.83 0.83 0.63 0.57 0.77

0.54 0.60 0.77 1.07 1.06 0.77 0.60 0.60 0.68

0.55 0.56 0.70 0.96 0.94 0.69 0.62 0.58

0.56 0.62 0.80 1.06 1.22 1.20 0.98 0.77 0.62 0.63 0.48

0.56 0.55 0.73 0.00 1.06 0.98 0.77 0.64 0.59 0.39

0.57 0.59 0.72 0.80 0.95 1.06 1.06 0.94 0.77 0.64 0.54 0.56 0.29

0.57 0.55 0.62 0.70 0.77 0.83 0.85 0.85 0.83 0.76 0.69 0.62 0.59 0.56 0.19

0.55 0.57 0.62 0.61 0.63 0.65 0.65 0.63 0.60 0.62 0.63 0.10

0.60 0.57 0.58 0.58 0.57 0.59 0.00 0.0

Figure 10: Serpent 2 radial power distribution (reference).

10% 8% 8% 8% 8% 11% 20% 2010% 6% 3% 2% 1% 1% 1% 3% 6% 8% 10% 19%

10% 6% 3% 2% 2% 2% 1% 1% 2% 2% 2% 1% 2% 8% 18%

10% 3% 1% 4% 10% 10% 10% 9% 5% 3% 4% 9% 17%

6% 2% 2% 8% 9% 3% 3% 11% 15%

10% 3% 4% 8% 10% 11% 9% 4% 1% 6% 14%

6% 2% 9% 10% 2% 3% 10% 13%

11% 3% 3% 10% 9% 2% 1% 8% 12%

8% 1% 3% 2% 1% 9% 10%

9% 1% 1% 1% 2% 9% 9% 99% 1% 1% 1% 1% 8% 8%

9% 1% 2% 3% 2% 8% 7%

9% 2% 2% 10% 10% 2% 2% 10% 5%

11% 3% 2% 10% 9% 2% 6% 4%

6% 2% 4% 9% 11% 10% 8% 3% 3% 10% 3%

11% 2% 3% 9% 8% 1% 1% 6% 2%

9% 4% 3% 5% 9% 10% 10% 10% 4% 1% 3% 10% 0%

9% 3% 2% 2% 2% 2% 1% 1% 2% 2% 2% 3% 6% 10% −1%

10% 8% 6% 3% 2% 1% 1% 2% 3% 6% 10% −2%

10% 8% 8% 8% 8% 10% −3%

0.101230694 0.059128798 0.041028597 0.042591815 0.062817275 0.093733448

0.097802374 0.033599427 0.018487784 0.016381914 0.027796572 0.097161902

0.193421449 0.156576013 0.122287949 0.053245906 0.006419807 0.00277798 0.001221311 0.01387293 0.051421478 0.114938918 0.157640118 0.197111519

0.139679237 0.062904624 0.032066197 −0.008211308 0.00164669 −0.014051975 −0.012184233 −0.008806055 0.001516244 0.038299338 0.065768664 0.141351265

0.099063107 0.032030056 −0.00502018 −0.008547831 −0.016173686 −0.012958208 −0.012763659 −0.008451473 −0.009434603 −0.006163952 0.021944407 0.116397212

0.193319044 0.130856014 0.097219624 0.040347941 −0.000670733 −0.01423138 −0.01940889 −0.025344706 −0.017734087 −0.021551204 −0.027919095 −0.014101351 −0.013793548 0.008898812 0.037597467 0.098610884 0.147326668 0.193690543

0.159342865 0.062578494 0.027764649 0.016751771 −0.018659396 −0.020138479 −0.012363714 −0.024943597 −0.027848723 −0.018851627 −0.018650528 −0.014421395 −0.010384124 −0.005325055 0.006843218 0.030707931 0.066364165 0.153264978

0.113486479 0.035901894 −0.003661841 −0.011455946 −0.012258338 −0.031103837 −0.026078665 −0.023612578−0.019806225 −0.022142212 −0.032323391 −0.029053369 −0.011002553 −0.007551447 −0.011120173 0.005511158 0.03582901 0.117018897

0.093733257 0.092857171 0.043235951 −0.001768709 −0.009862097 −0.017388712 −0.031410416 −0.025189361 −0.024812757 −0.023542724−0.015577589 −0.022824551 −0.027764667 −0.027348578 −0.016989787 −0.014256299 −0.016912973 −0.012038087 0.011411318 0.041689094 0.10162137 0.097687603

0.054758521 0.019612861 0.002503305 −0.004251532 −0.016311701 −0.016871409 −0.03307371 −0.027046798 −0.024389298 −0.030538064−0.028869384 −0.01571873 −0.030671028 −0.017714933 −0.017418357 −0.014401334 −0.028491089 −0.024801536 −0.00615383 0.013589634 0.034710113 0.05816878

0.03233119 0.014087402 −0.000347837 −0.021531212 −0.016955932 −0.015035828 −0.019934438 −0.026189165 −0.024989 −0.032467887−0.026273803 −0.022894913 −0.030988091 −0.028262244 −0.030632645 −0.018125147 −0.020983679 −0.016286343 −0.00756263 −0.00526954 0.015253493 0.043761243

0.053283534 0.015567754 −0.007463983 −0.013392348 −0.015419844 −0.021816716 −0.025347901 −0.017924879 −0.017016457 −0.023899281 −0.020995173 −0.025337057 −0.029542834 −0.016439362 −0.021224732 −0.034959829 −0.019326505 −0.01595527 −0.008872591 −0.000690447 0.015438336 0.039686205

0.060028377 0.019943947 0.013085294 −0.010505845 −0.021642101 −0.020757817 −0.021651721 −0.029240264 −0.028756977 −0.017667495 −0.023068518 −0.022413526 −0.029377699 −0.016469175 −0.025351633 −0.030831828 −0.023907356 −0.009508648 −0.009576835 0.01174151 0.037996791 0.052609728

0.093538314 0.099167688 0.055286233 0.017134947 −0.012971325 −0.021686459 −0.026887358 −0.025044611 −0.007640692 −0.02011703 −0.023090065 −0.017691373 −0.025444425 −0.016420056 −0.032346603 −0.016933627 −0.014454797 −0.013785098 0.00852408 0.04321129 0.099924392 0.087941065

0.127180992 0.033758222 0.012872079 −0.009761744 −0.019510828 −0.024429457 −0.018320526 −0.019239045 −0.023211851 −0.024089093 −0.027506873 −0.029823252 −0.020559631 −0.017948226 −0.015520967 0.008755749 0.030909671 0.109197209

0.161196124 0.068382612 0.029794724 −0.003254775 −0.001970519 −0.017789392 −0.025543352 −0.016788163 −0.023448574 −0.018917213 −0.024698384 −0.011592242 −0.02074474 −0.012875112 −0.00958622 0.033833983 0.066753761 0.1523274

0.197625349 0.12920396 0.105994614 0.045627986 0.006465351 −0.012660842 −0.012101125 −0.0214392 −0.018054157 −0.019966513 −0.021422148 −0.014135612 −0.005485427 0.009312221 0.037516774 0.10127133 0.140669529 0.204034057

0.105641305 0.026164034 0.004067657 −0.006326206 −0.013593838 −0.021965624 −0.025368398 −0.011760531 −0.021775991 0.002614108 0.02390098 0.108484853

0.129846417 0.066006067 0.043800513 0.011605549 0.0019072 −0.005494482 −0.000107845 −0.008126468 0.009757986 0.035881737 0.068579815 0.136485257

0.195958315 0.159213312 0.107170446 0.048451801 0.012203784 0.00821445 0.005362082 0.017775559 0.053945288 0.109940266 0.156976278 0.192671749

0.104119749 0.043617646 0.007598827 0.019747309 0.037219728 0.090936696

0.099189296 0.064831492 0.04634435 0.046843849 0.066221491 0.099268397

(%)

−3

Figure 11: Radial power difference (Serpent 2 versus PARCS).

of the core is within 3%with respect to Serpent 2. From safetyanalysis standpoint, these results are positive since the hottestrod will be most likely located in this area.

Since, as stated earlier, two different PARCS modelswere used to predict radial power distribution, additionalverification was carried out between these two models andthe Serpent 2 reference model. Table 2 shows the percent ofthe total power generated in each fuel lattice for the Serpent2 model and also for the two PARCS models.

Table 2 differences between PARCS models and Serpent2 are in the order of few percent. This could be potentiallylinked to the fact that while one PARCS model includes thewater gap in the inner lattice, the other model includes it inthe outer lattice.

Table 2: Radial power prediction comparison.

Model Percent of total powerInner lattice Outer lattice

Serpent 2 61% 39%𝐵1UO2 cell-size mesh 59% 41%𝐵1U-metal cell-size mesh 63% 37%

5. Thermal-Hydraulic Modeling

For more than 50 years, numerous computer codes havebeen written to calculate the thermal-hydraulic character-istics of reactor cores under steady-state and operationaltransient conditions as well as hypothetical accidents. Themain purposes of the continuing effort in the developmentof such computer codes have been improved computationaleffectiveness and improved ability to predict the response ofthe nuclear reactor. While thermal-hydraulic modeling playsa vital role in the design, operation, performance, and safetyof a nuclear reactor, the present paper focuses particularly onthe safety (or accident analysis) application.

Examples of codes used for research reactor thermal-hydraulic modeling are RELAP5 [21] for the NIST researchreactor [22], the IPR-R1 TRIGA Brazilian reactor [23], andtheHigh Flux reactor (HFR) inNetherlands [24].The PARETcode [25] has been used for theMcMaster University researchreactor [26], the University of Florida Training Reactor [27],and the NUR Algerian research reactor [28] among severalothers. Also, in many cases, thermal-hydraulic modelingwas performed with in-house designed codes, such as theMULCH-II code for the MIT research reactor [29] andPLTEMP for the GRR1 Greek research reactor [30]. In allcases, the neutronic behavior of the research reactors waspredicted using the point-kinetic approximation.

5.1. Current Methodology. The current safety analysis of theCROCUS reactor studies the reactor response under themax-imum hypothetical accident, which is initiated by the flood-ing of the reactor core with light water at 12∘C, the reactorbeing at nominal power (100W), and failure of the shutdownsafety systems. For the thermal-hydraulic modeling of thisreactor, the in-house designed code EX PUI [31] has beenused. EX PUI is based on a simple zero-dimensional model,assuming natural convection heat transfer and uniform tem-peratures in the fuel, moderator, and coolant. No two-phaseflow equations are available in the code since the currentaccident analysis predicts that the maximum fuel claddingtemperatures are of 60∘C. The EX PUI code also includes apoint-reactor kinetic subroutine with reactivity feedback topredict the reactor power evolution. No overpower or powerpeaking factors are included in the current analysis.

The kinetic parameters used by the EX PUI code werecalculated using another in-house code, CRO93DIF [31],which is based on one-dimension multigroup diffusion the-ory. The CRO93DIF model of the CROCUS core used one-dimensional cylindrical coordinates. Four cross-section sets(for UO

2fuel, water gap, U-metal fuel, and reflector) and 19

energy groups were used for the diffusion calculations. The


19-group macroscopic cross sections used by CROF93DIFcode were generated using the lattice code BOXER [32]. Also,the BOXER code was used to generate the reactivity feedbackcoefficients used by the point kinetic module of the EX PUIcode.

5.2. Proposed Methodology. The current CROCUS safetyanalysis relies on very simplemodels assuming a point reactorand all calculations are based on average values. A moredetailed analysis, including multidimensional effects, powerpeaking factors, and the hottest channel analysis, may revealrestrictions or add flexibility to the reactor day-to-day opera-tion. An additional driving force for this project results fromthe fact that the Swiss nuclear regulatory authority (ENSI)requested the Laboratory for Reactor Physics and SystemBehavior at EPFL, who is responsible for the CROCUSoperation, to update the Final Safety Analysis Report usingup-to-date tools andmethods.Thus, the proposed update canprovide additional details for the accident consequences andquantification of the conservatism in the original evaluations.

In general, many codes used for nuclear power plants canbe also used for research reactor analysis. However, the rangesof parameters of interest to research reactors are differentfrom those for nuclear power plants: this is namely true forfuel composition, system pressure, materials, and core geom-etry. Also, due to the large variety of research reactors, differ-ences on validation and applicationmay appear for each case.In this work, the proposed thermal-hydraulic analysis will becarried out using the TRACE code [33] since it is the currentstate-of-the-art tool for transient analysis of light water powerreactors. It may be, however, necessary to modify TRACEto make it applicable for the particular channel geometry,coolant velocities, heat fluxes, and subcooled core conditionsof theCROCUS reactor. As earlier described, research reactorthermal-hydraulics models have been coupled to point-reactor kinetic modules [34]; however, the proposed methodtakes advantage of the relatively simple coupling of TRACEto PARCS for the multiphysics modeling. By doing so, we arenot only utilizing state-of-the-art methods for research reac-tor analysis but also investigating TRACE/PARCS potentialapplications to small modular reactors (SMR).

In a first approach, the TRACE model of the CROCUSreactor will consist of a 3D vessel component for the reactorvessel. The core will be represented by several heat structuresthat will be coupled to the PARCS model, which solves theneutron kinetic problem. Thus, power evolution, peakingfactors, and reactivity feedback coefficients are computed byPARCS and transferred to TRACE. Several hydrodynamicchannels will be used within the vessel component to repre-sent the different areas of the core. Reactor parameters andoperating conditions considered in the safety analysis will bechosen assuming the most unfavorable conditions, that is,following a conservative approach.

6. Conclusions

In this paper, a methodology for the coupled neutronicsand thermal-hydraulics analysis of the CROCUS reactor atEFPL has been studied. The Serpent 2 Monte Carlo code has

been used to generate two-group parameters for the PARCScode. Since the Monte Carlo technique offers significantadvantages for detailed modeling of the complex geometricalconfiguration of the reactor core, a full Serpent 2 modelof CROCUS has been built. A steady-state benchmark hasbeen conducted between PARCS and Serpent 2 full-coremodels. Good agreement was achieved in terms of eigenvaluecalculations and control rod reactivity worth. Radial powerdistribution results show good agreement in the central coreregion; however, they reveal that PARCS models presentlimitations in predicting power near the water gap region.

Future work will address validations of the PARCSmodelfor the static and dynamic analysis. Also, since the full-scale heterogeneous problem represents the best availablereference solution for cross-section homogenization, it iscurrently under development to provide an alternative anda potential improvement over the pin-cell homogenizationscheme. Future testsmay also include the use of superhomog-enization factors (SPH) [35] to yield better approximation ofthe full heterogeneous problem.

The PARCS model will be coupled to a TRACE thermal-hydraulic model of CROCUS for transient analysis of thereactor. From an accident analysis perspective, the currentCROCUS safety analysis report shows room for improvementas it relies on very simple models that may unnecessarilylimit the range of operation of the reactor.Thus, reassessmentusing state-of-the-art tools would provide not only morerealistic predictions that reduce the deliberate conservatismbut also the possibility to add flexibility in the day-to-dayreactor operation.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

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