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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

Neutronic modeling and calculations of the ETRR-2 MTR reactor using COMSOL multiphysics code Ned Xoubi ⇑, Abdelfattah Y. Soliman Nuclear Engineering Department, King Abdulaziz University, P.O. Box: 80204, Jeddah 21589, Saudi Arabia

a r t i c l e

i n f o

Article history: Received 12 June 2016 Received in revised form 16 March 2017 Accepted 2 June 2017

Keywords: COMSOL ETRR-2 Research Reactor MTR WIMS Neutronics calculation

a b s t r a c t The second Egyptian Test and Research Reactor (ETRR-2) is a 22 MWth light water cooled and moderated open pool multipurpose reactor, with isotope production, thermal neutron scattering, neutron activation and materials irradiation capabilities. COMSOL Multiphysics is powerful finite element computational tool with diversified physics and engineering applications, and coupling phenomena capabilities, a feature that is very attractive for simulating nuclear reactors as well as neutronics and thermalhydraulics calculations. In this work, a full core, three-dimensional, multi-group model of ETRR-2 reactor is developed using detailed specifications and quality experimental data from IAEA Technical Report Series. This paper presents COMSOL-based neutronics calculations performed to study reactor physics parameters. The WIMS-D5 with 69-group neutron cross section library, was used to calculate the fivegroup constants for different reactor regions essential to solve the diffusion equations. The multigroup constants were applied in the COMSOL model to perform neutronics calculations using adaptive mesh refinement technique to increase the accuracy of the solution. The calculated effective multiplication factor (keff) for three specified cases compare well with experimental measurements. The study found a slight difference between the calculated $8.70 excess reactivity and the measured value of $9.11 for the core. The calculated reactivity worth of CR-1 at different positions, are in agreement with experimental measured values. The spectrums of thermal and fast fluxes were also calculated by the COMSOL model and are presented in this paper. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Research Reactors (RRs) are neutron-generating facilities used for scientific, educational, medical, and industrial purposes. Unlike nuclear power plants in which the most valuable criteria are the power output, research reactors are evaluated based on their neutron flux output, thus they are usually designed with a compact core to maximize the flux output, consequently resulting in high power density. Incessant neutronic and thermal-hydraulics analysis of sample irradiation, configuration changes and fuel reloading, is of utmost importance to improve the reactor design, performance and safety. Computer codes applying different computational techniques to simulate nuclear reactors complex processes and conditions have been in use for decades. Advances in computation power, code availability and ease of use, have enabled researchers to perform full core detailed calculations of neutronic, thermal-hydraulics, and transient scenarios on research reactors worldwide (Ferraro ⇑ Corresponding author. E-mail address: [email protected] (N. Xoubi). http://dx.doi.org/10.1016/j.anucene.2017.06.007 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.

and Villarino, 2016; Yang et al., 2011; Bonifetto et al., 2013; Rosenkrantz et al., 2014; Amin et al., 2016; Damian and Brun, 2015; Ali et al., 2016; Nacir et al., 2014; Khattab and Sulieman, 2011). Last year the IAEA published sets of verifiable experimental data (International Atomic Energy Agency, 2015), to be used in benchmarking and validation of computational techniques and codes used for research reactors safety analysis, operation, and utilization improvement (International Atomic Energy Agency, 2015). Several innovative methods and codes that have been proposed for the analysis and simulation of research reactors must be validated before being used. Lately, several studies have utilized the multiphysics code COMSOL (Multiphysics C.O.M.S.O.L., 2012) to perform complex and computationally intense neutronic, thermalhydraulic, and structural calculations, both on research reactors like the HFIR (Chandler et al., 2011) and on power reactors like LWR (Liu et al., 2015, 2016), Fast reactors (Aufiero et al., 2013), and CANDU (Bell and Lewis, 2012). The code is a powerful finite element computational tool with diversified physics and engineering applications, and coupling phenomena capabilities, a feature that is very

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attractive for simulating nuclear reactors as well as neutronic and thermal-hydraulics calculations. A full core three-dimensional, diffusion neutronics model of Egypt Test and Research Reactor (ETRR-2), can be a very powerful computational tool for the analysis, safety and improvement of the reactor. The purpose of this study is to construct a 3-D full core model of the ETRR-2 reactor using COMSOL multiphysics code, and to simulate the neutronic behavior of reactor by predicting the system criticality for different experimental cases, the excess reactivity of the core, the neutron flux distribution and the control rod worth. The study will compare calculated results with experimental measurements. The study also aims to use finite element method and adaptive mesh refinement technique to increase the accuracy of the solution. 2. Reactor description The second Egyptian Test and Research Reactor (ETRR-2) is a 22 MW light water cooled and moderated open pool type Material Test Reactor (MTR). The multipurpose reactor is equipped with isotope production, thermal scattering, neutron activation and materials irradiation facilities. The reactor is cooled and moderated by the forced upward circulation of light water. Its core consists of 6 5 grid matrix of 8.1 cm 8.1 cm square array, loaded with 29 fuel elements (8 cm 8 cm), leaving one flux trap central position (3D) for in core experimental facility. The space between the fuel elements is used as a water channel, allowing coolant to circulate, the detailed specifications and operating conditions of the reactor are given in Table 1 (Abdelrazek and Villarino, 2015). The reactor is controlled by six control plates, made of Ag–In– Cd alloy as a neutron absorber material with stainless steel cladding. Each plate is 14.57 cm wide, 100.0 cm long, and 0.53 cm thick. The control plates are inserted in and out of the core through two aluminum guide boxes, each housing three control plates. The control plates guide boxes are parallel, dividing the core grid into three zones, one central zone of 3 6 grid position and two side zones of 1 6 grid position, as shown in Fig_1. Second shut down system (SSS) consisting of four zircaloy double wall chambers surrounds the core on its four sides, the chambers are 3.0 cm thick and are normally filled with nitrogen. When triggered a gadolinium solution is injected into chamber to shut down the reactor, if the first shutdown system fails.

Table 1 Design specifications data of the ETRR-2 reactor. Fuel material Uranium Enrichment (wt) Uranium U3O8 density (g/cm3) Fuel plate dimensions (cm) Fuel plate active dimensions (cm) Cladding material Density of cladding material (g/cm3) No. of control plates Control plate material Control plate cladding material Control plate external dimensions (cm) Control plate active dimensions (cm) Reference pressure of the facility Coolant (flow direction) Water channel thickness between two fuel plates (cm) Water channel thickness between two fuel elements (cm) Moderator Reflector Max. heat flux (W/m2) Nominal flow rate (m3/h)

U3O8 19.7% 8.1 84.0 7.0 0.150 80.0 6.4 0.070 Al-6061 2.700 6 Ag–In–Cd AISI 316 L 100 14.57 0.53 82.0 14.40 0.36 0.2 MPa Light water (upwards) 0.270 0.390 Light water Beryllium 1,170,000 1900

An aluminum chimney extends above the core and sets on top of the second shut down system chambers, it conveys the water to the primary system outlet pipe. The chimney is open from the top to allow access to the core, and to allow water to naturally circulate to cool the reactor after shutdown (Abdelrazek and Villarino, 2015). The core has a beryllium reflector on two sides, the beryllium blocks are 7.67 7.67 cm, and are fixed in the innermost positions of the reactor external grid. The thermal column side has two rows of beryllium blocks and one row of aluminum blocks filling the grid positions between the core and the thermal column. The fuel element has 19 identical flat plates whose thickness is 1.5 mm, separated by 2.7 mm wide water-coolant channel between them as shown in Fig. 2. The fuel material is 19.7 wt% enriched uranium oxide (U3O8) in aluminum matrix sandwiched between two aluminum plates. The fuel element is 119.5 cm long, with an active length of 80.0 cm. Three different types of fuel elements are loaded in the core. The Standard Fuel Element (SFE) has 21.3 g of 235U in each plate, with meat density of 4.802 g/cm3 and a meat uranium density of 3.017 g/cm3. Fuel Element type one (FE1) has 7.8 g of 235U in each plate, with meat density of 3.299 g/cm3 and a meat uranium density of 1.105 g/cm3. Fuel Element type two (FE2) has 11.0 g of 235U in each plate, with meat density of 3.655 g/cm3 and a meat uranium density of 1.558 g/cm3. 2.1. Core 1/98 The 1/98 reactor core is loaded with 29 fuel elements of fresh fuel; 8 standard fuel elements (SFE), 13 type one fuel elements (FE-1), and 8 type two fuel elements (FE-2). The central flux trap is filled with water, and all experimental irradiation facilities are empty. The core has two beryllium blocks rows and one aluminum blocks row on the thermal column side, and one beryllium blocks row on the opposite side acting as a reflector, the 1/98 core is shown in Fig.1. 2.2. Computation codes 2.2.1. COMSOL multiphysics The COMSOL code is a finite element, multiphysics numerical analysis software with diverse physics and engineering applications, including coupled phenomena or multiphysics (Multiphysics C.O.M.S.O.L., 2012). This code has an integrated user interface, which allows users to input coupled systems of partial differential equations directly. In addition, the COMSOL code application builder can be used to construct specialized applications based on physics model. The adaptive mesh refinement algorithm of COMSOL, enable the user to increase the number of meshes only in the core regions with largest numerical errors, without the need to refine the meshes for the whole reactor core. Consequently reducing the spatial discretization errors, and making the calculation faster. This can be seen as an advantage over other codes, where the user is forced to refine the mesh for the whole core to reduce the errors in specific regions, which will affect the core calculation time. Thus trading between reducing spatial discretization errors, and computation time, especially in computer intensive calculations 2.2.2. WIMS WIMS-D5 is a general reactor lattice cell calculation code, which has been used extensively for nuclear computations in a wide range of reactor systems (Askew et al., 1966; WIMSD5, 2004). By using several techniques to solve the transport equation, WIMS can provide the exact spectrum computations in the 69 groups of the lattice main regions. As the equivalence theorems are applied

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Fig. 1. Cross sectional (x-y) view of the ETRR-2 MTR reactor core 1/98 configuration.

Fig. 2. Cross-sectional view of fuel element (dimensions in cm) Abdelrazek and Villarino (2015).

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Table 2 The experimental results of the ETRR-2 critical core and the control plate positions. Experiment Number

1 2 3

Control rod positions (% extraction) CR-1

CR-2

CR-3

CR-4

CR-5

CR-6

0.0 0.0 0.0

53.5 52.8 100.0

100 100 49.4

100 100 100.0

100 100 100.0

0.0 0.0 0.0

Table 3 Energy groups upper and lower boundaries (eV) used in WIMS calculations. Group No.

Energy lower boundary (eV)

Energy upper boundary (eV)

1 2 3 4 5

8.21E+05 5.53E+03 1.30E+00 6.25E01 0.00E+00

1.00E+07 8.21E+05 5.53E+03 1.30E+00 6.25E01

in the treatment of resonances, the moderator library has temperature-dependent thermal scattering matrices. A simplified geometry can be used to represent the complicated lattice cells, and the computed spectra can be used for collapsing the crosssections to the desired number of groups and for solving the transport equation with detailed geometry (Askew et al., 1966; WIMSD5, 2004). 3. Experimental measurements A set of neutronic experiments were performed to give the critical configurations of the ETRR-2 reactor core 1/98 (Abdelrazek and

Villarino, 2015). The data set was prudently prepared as a reliable resource of high quality experimental data, which can consequently be used to benchmark and validate neutronic codes (Abdelrazek and Villarino, 2015). The experimental results of three critical core with control plate positions are listed in Table 2. The excess reactivity of $9.11 was measured by control rod calibration. To convert reactivity units from pcm to $, and to compare measured and calculated data, the effective delayed neutron fraction was taken as beff = 750 pcm (Abdelrazek and Villarino, 2015). Control plate one (CR-1) was calibrated by the period method against CR-4, the experimental reactivity values as well as the initial position of both control rods for each calibration are shown in Table 5 (Abdelrazek and Villarino, 2015). In each step the initial positions of CR-1 and CR4 are critical positions and so are the final positions. The reactor is supercritical when CR-1 is at the final position while CR-4 remains at the initial position. The reactor period under the supercritical condition is measured by three fission chambers and converted to reactivity, using the asymptotic period method on a critical reactor at low power, no external neutron sources and negligible buildup of neutron poisons during the measurements.

Fig. 3. COMSOL 3-D mesh structure modeling of the ETRR-2 reactor.

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N. Xoubi, A.Y. Soliman / Annals of Nuclear Energy 109 (2017) 667–674 Table 4 The COMSOL calculated effective multiplication factor (Keff) for three critical cores.

DK

Critical Configuration Experiment Number

Calculated effective multiplication factor (keff)

pcm

$

1 2 3

1.00220 1.00247 1.00193

220 247 193

0.293 0.329 0.257

4. Methodology WIMS-D5 code was used to generate the reactor multigroup diffusion constants. Lattice calculations were performed using WIMSD5 (Askew et al., 1966; WIMSD5, 2004), which has its nuclear data library as well as the collision probability option in onedimensional geometry (slab) and 69 neutron energy groups. The results of the WIMS calculations were processed in order to obtain the multi-group constants for the different reactor regions. The 69 energy groups cross section were collapsed to generate five energy groups diffusion constants with the upper and lower boundaries set as shown in Table 3, and corresponding to the following WIMS groups; 5, 15 32, 45, and 69. COMSOL was used to build a 3-D model of the ETRR-2 reactor, based on actual geometrical dimensions and material compositions, the mesh structure model of the reactor core is presented in Fig. 3. Finite element calculations, using the WIMS generated multigroup constants, were performed by COMSOL using the adaptive mesh structure option. The calculations, were divided into two stages. The first stage was used to solve the five group diffusion equation in the eigenvalue study mode. The other stage was employed, as the stationary study mode with initial flux guess from the eigenvalue stage, by applying the criticality normalization condition to calculate the effective multiplication factor and the flux distribution. Partial differential equation (PDE) coefficient mode was chosen from COMSOL physics to write the equation of each region in the eigenvalue mode. The five group equation, which is in the form of eigenvalue mode, is presented in Eq. (1) (Hébert, 2010; Duderstadt, 1976).

r Dg ðrÞrug ðrÞ þ Rrg ðrÞug ðrÞ X X 1 Rsg0 !g ðrÞug0 ðrÞ þ vg m Rfg0 ðrÞug0 ðrÞ ¼ k g 0 –g g0

ð1Þ

where: Dg(r) is the neutron diffusion coefficient for the energy group g; /g(r) is the neutron scalar flux for the energy group g; Rrg(r) is the neutron removal cross section for the energy group g, Rrg ¼ Ra þ Rsg!g0 ; Rsg0 ?g(r) is the neutron scattering cross section from energy group g0 to g; vg is the fraction fission spectrum for the energy group g, R1 vðEÞdE ¼ 1; 0 m is the average number of neutrons emitted per fission; Rfg(r) is the neutron macroscopic fission cross section for the energy group g; k is the effective multiplication factor. 5. Results and discussion The calculation of the reactor lattice cell was performed using WIMS to generate the macroscopic cross-sections, and collision probability option in one-dimensional slab geometry, using the 69 energy groups for different core regions. The WIMS calculations results were collapsed into five-group structure (see Table 3), and processed in order to obtain the multi-group constants for different reactor regions. The multi-group constants were introduced to the 3-D reactor model for COMSOL neutronic core calculations. The COMSOL calculation, using the finite element method and the adaptive mesh structure option, were performed to solve the five group diffusion equation for the three critical core configurations of the ETTR-2. The calculation results of the effective multiplication factor (keff), for the three cases, are shown in Table 4. This study show that the COMSOL model criticality calculations are in fair agreement with measured values, having a difference (DK) of only 193–247 pcm, when compared with experimental results. This slight discrepancy can be ascribed to two factors; first, the different measurement methods of reactor criticality, such as by reactor period, and the uncertainty associated with these measurements, second to the diffusion equation approximation.

Table 5 The calculated and measured reactivity at different control rod withdrawal positions of CR-1 and CR-4. CR-1 Positions (% withdrawal)

CR-4 Positions (% withdrawal)

Reactivity ($)

ERROR %

Initial

Final

Initial

Final

Experimental

Calculated

Dq/qexp

0.0 15.3 23.4 29.1 33.6 36.9 39.6 42.6 45.3 49.1 52.7 55.9 59.5 63.0 66.9 72.5 78.8 87.0

15.3 23.4 29.1 33.6 36.9 39.6 42.6 45.3 49.1 52.7 55.9 59.5 63.0 66.9 72.5 78.8 87.0 100.0

100.0 90.9 82.2 75.6 70.1 65.9 62.6 59.2 55.6 51.7 47.8 44.7 41.2 38.0 34.3 29.1 22.7 10.5

90.9 82.2 75.6 70.1 65.9 62.6 59.2 55.6 51.7 47.8 44.7 41.2 38.0 34.3 29.1 22.7 10.5 CR2:52,4

0.130 0.220 0.220 0.22 0.21 0.18 0.19 0.21 0.23 0.23 0.20 0.22 0.19 0.20 0.23 0.21 0.20 0.17

0.1326 0.2209 0.2209 0.2203 0.2147 0.1842 0.1912 0.2141 0.2404 0.2369 0.2045 0.2220 0.1931 0.2082 0.2395 0.2140 0.2044 0.1783

2.0% 0.4% 0.4% 0.1% 2.3% 2.3% 0.6% 2.0% 4.5% 3.0% 2.2% 0.9% 1.6% 4.1% 4.1% 1.9% 2.2% 4.9%

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Table 6 The calculated and measured integral reactivity ($) of CR-1 at different withdrawal positions (%). CR-1 % withdrawal Experimental Calculated

0.0 0.00 0.00

15.3 0.13 0.13

23.4 0.35 0.35

29.1 0.57 0.57

33.6 0.79 0.79

36.9 1.00 1.01

39.6 1.18 1.19

42.6 1.37 1.38

45.3 1.58 1.60

CR-1 % withdrawal Experimental Calculated

52.7 2.04 2.08

55.9 2.24 2.28

59.5 2.46 2.50

63.0 2.65 2.70

66.9 2.85 2.90

72.5 3.08 3.14

78.8 3.29 3.36

87.0 3.49 3.56

100.0 3.66 3.74

Fig. 4. The integral reactivity ($) worth of control plate CR-1 vs. Percentage withdrawal.

Although the computation results are in agreement to the second digit, farther investigation by different methods might be able to reduce the discrepancy and improve the model criticality calculations. The calculated excess reactivity with all rods out is $8.70, this is in agreement with the measured value of $9.11. The slight difference of 4.5% between the calculated and measured values can be explained by the difference in the estimation method. The measured value is estimated against the control rods worth, as measurements can only be performed on a critical core. Thus errors

49.1 1.81 1.84

in control rods measurement worth will contribute to the uncertainty in the excess reactivity experimental estimation. The COMSOL model calculated value is estimated with all control rods out, thus the core is supercritical. The movement of control rods CR-1 and CR-4 was simulated by COMSOL model, and the results obtained for core reactivity at each position were used to calculate the rod worth of CR-1. The calculated results in study were found to be in agreement with experimental results, having a differential ratio (Dq/qexp) below 5% as shown in Table 5. The integral reactivity worth of CR-1 at different percentage withdrawal positions, from fully inserted to fully withdrawn position, was calculated and compared with measured values as shown in Table 6, and illustrated by Fig. 4. The thermal and fast neutron flux distributions as calculated with COMSOL, at the reactor midplane, are shown in Figs. 4 and 5, respectively, the values are normalized to the maximum flux value. The neutron flux is viewed by the color spectrum scale whereby dark red represents the largest flux, followed by yellow, turquoise and down to dark blue for the lowest flux value. The unsymmetrical horizontal fuel loading of the core, is shown clearly by both fluxes being shifted to one side of the core. The thermal flux at midplane is more dominant in the upper half of the core, where six standard fuel assemblies with higher enrichment (19.7%) are located. The flux increases with increasing penetration toward the center of the core, reaching its greatest value at the flux trap. The effect of the control rod on the thermal flux is clearly seen in Fig. 5a. The thermal flux decreases to the smallest value (blue) as a result of CR-1 control rod being fully inserted, while it continue to be red over the CR-4 location being fully withdrawn. The thermal flux 3-D surface plot at the reactor core mid-plane is shown in Fig. 5b.

Fig. 5. The thermal flux profile (a) contour and (b) 3D surface plot for at the reactor core mid-plane.

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Fig. 6. The fast flux profile (a) contour and (b) 3D surface plot at the reactor core mid-plane.

Fig. 7. COMSOL 3-D modeling of thermal flux spectrum in the ETTR-2 reactor core.

The fast flux at the midplane is increases at the top outer fuel elements, reaching its greatest value at the standard fuel element 4F. The fast flux decreases toward the thermal column side, reaching its lowest value at the bottom outer fuel elements, as shown in Fig 6a. In the flux trap, the fast flux is extremely low, since fast neutrons are produced in the fuel assemblies and slowdown in nonfuel regions due to scattering and moderating. Again the fully inserted CR-1 shifts the flux to the left, where flux is higher in the region of the withdrawn CR-4. The fast flux 3-D surface plot at the reactor core mid-plane is shown, as shown in Fig 6b. Fig. 7 shows a 3-D radial and axial view of flux spectrum in the reactor core.

6. Conclusions In this work, a COMSOL, full-core, three dimensional, neutronics model of the ETRR-2 reactor was developed using detailed specification and high quality experimental data. The model was used to perform COMSOL-based neutronics calculations to study reactor physics parameters, such as criticality, excess reactivity, control rod worth, and neutron flux spectrum. Five-group constants for different reactor regions essential to solve the diffusion equations were obtained from WIMS-D5 69-group neutron cross section library calculations. The calculated effective multiplication factor (keff) for three specified cases were in agreement with experimental

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measurements, having a difference (DK) of only 193–247 pcm. The study found a slight difference of 4.5% between the calculated $8.70 excess reactivity and the experimental measured value of $9.11 for the core. The calculated reactivity worth of control rod one (CR-1) at different positions, were found in good agreement with experimental measured values, having a differential ratio (Dq/qexp) below 5%. The thermal and fast flux spectrums were also calculated and discussed. The neutronics computation accuracy of the three-dimensional full core COMSOL-based model, in obtaining differences below 5% compared with experimental measurement, demonstrates its capabilities in providing a viable alternative for Research Reactor calculations. References Abdelrazek, I.D., Villarino, E.A., 2015. ETRR-2 nuclear reactor: Facility specification. IAEA Technical Reports Series no. 480. Ali, M., Rizwan, R., Khan, K.S., Chaudri, Stummer, T., 2016. Monte Carlo modeling of the Pakistan Research Reactor-1 (PARR-1). Ann. Nucl. Energy 87, 584–590. Amin, E.A., Bashter, I.I., Hassan, Nabil M., Mustafa, S.S., 2016. Full core analysis of IRIS reactor by using MCNPX. Appl. Radiation Isotopes 113, 70–74. Askew, J.R., Fayers, F.J., Kemshell, P.B., 1966. A general Description of the Code WIMS. J. British Nucl. Energy Soc., 564 Aufiero, M., Cammi, A., Fiorina, C., Luzzi, L., Sartori, A., 2013. A multi-physics timedependent model for the Lead Fast Reactor single-channel analysis. Nucl. Eng. Des. 256, 14–27. Bell, J.S., Lewis, B.J., 2012. CANDU fuel bundle deformation modelling with COMSOL multiphysics. Nucl. Eng. Des. 250, 134–141. Bonifetto, Roberto., Dulla, Sandra, Ravetto, Piero, Richard, L. Savoldi, Zanino, Roberto, 2013. A full-core coupled neutronic/thermal-hydraulic code for the modeling of lead-cooled nuclear fast reactors. Nucl. Eng. Des. 261, 85–94.

Chandler, David, Ivan Maldonado, G., Primm, R.T., Freels, J.D., 2011. Neutronics modeling of the high flux isotope reactor using COMSOL. Ann. Nucl. Energy 38 (11), 2594–2605. Damian, F., Brun, E., 2015. ORPHEE research reactor: 3D core depletion calculation using Monte-Carlo code TRIPOLI-4Ò. Ann. Nucl. Energy 82, 203–216. Duderstadt, James J., Hamilton, Louis J., 1976. Nuclear reactor analysis. Ferraro, Diego, Villarino, Eduardo, 2016. Full 3-D core calculations with refueling for the OPAL Research Reactor using Monte Carlo Code Serpent 2. Ann. Nucl. Energy 92, 369–377. Hébert, Alain, 2010. Multigroup neutron transport and diffusion computations. Handbook of Nuclear Engineering. Springer, pp. 751–911. International Atomic Energy Agency Report Series No. 480 – Research Reactor Benchmarking Database: Facility Specification and Experimental Data – STI/ DOC/010/480 (ISBN: 978-92-0-151714-2) – Vienna 2015. Khattab, K., Sulieman, I., 2011. Monte Carlo simulation of core physics parameters of the Syrian MNSR reactor. Ann. Nucl. Energy 38 (5), 1211–1213. Liu, R., Zhou, W., Shen, P., 2015. Fully coupled multiphysics modeling of enhanced thermal conductivity UO 2–BeO fuel performance in a light water reactor. Nucl. Eng. Des. 295, 511–523. Liu, Rong, Prudil, Andrew, Zhou, Wenzhong, Chan, Paul K., 2016. Multiphysics coupled modeling of light water reactor fuel performance. Prog. Nucl. Energy 91, 38–48. Multiphysics, C.O.M.S.O.L., 2012. COMSOL multiphysics user guide (Version 4.3 a). COMSOL, AB. Nacir, B., Boulaich, Y., Chakir, E., El Bardouni, T., El Bakkari, B., El Younoussi, C., 2014. Safety analysis and optimization of the core fuel reloading for the Moroccan TRIGA Mark-II reactor. Ann. Nucl. Energy 70, 312–316. Rosenkrantz, Adam, Avramova, Maria, Ivanov, Kostadin, Prinsloo, Rian, Botes, Danniëll, Elsakhawy, Khalid, 2014. Coupled 3D neutronics/thermal hydraulics modeling of the SAFARI-1 MTR. Ann. Nucl. Energy 73, 122–130. WIMSD5, Deterministic Multigroup Reactor Lattice Calculations, NEA-1507/04, 2004. Yang, Ping, Cao, Liangzhi, Hongchun, Wu, Wang, Changhui, 2011. Core design study on CANDU-SCWR with 3D neutronics/thermal-hydraulics coupling. Nucl. Eng. Des. 241 (12), 4714–4719.

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