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Research Article
Benchmark-based neutronic and thermal-hydraulic evaluation of a modified beryllium reflector for enhanced irradiation capability in an MTR-10 MW reactor
expand article infoHassan Alsaleh‡, Mohammad Albarhoum§
‡ Department of Physics, Damascus University, Damascus, Syria
§ Atomic Energy Commission of Syria, Damascus, Syria

Corresponding author: Hassan Alsaleh ( hassan.alsaleh@damascusuniversity.edu.sy )

Corresponding author: Mohammad Albarhoum ( mbarhoom@aec.org.sy )

Academic editor: Abdelghafar Galahom
© 2026 Hassan Alsaleh, Mohammad Albarhoum.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation: Alsaleh H, Albarhoum M (2026) Benchmark-based neutronic and thermal-hydraulic evaluation of a modified beryllium reflector for enhanced irradiation capability in an MTR-10 MW reactor. Nuclear Energy and Technology 12(3): 233-246. https://doi.org/10.3897/nucet.12.203079
Open Access

Abstract

A benchmark-based neutronic and steady-state thermal-hydraulic assessment was performed to evaluate beryllium reflector configurations for enhancing irradiation capability in the MTR-10 MW research reactor. The reference one-trap core was modified to a symmetric four-trap layout, and a constrained sequence of graphite and beryllium reflector substitutions was assessed with MCNP4C2/MTRMC. The four-trap configuration reduced the initial excess reactivity from 141.71 to 82.85 mk. The selected 22-block beryllium reflector recovered the excess reactivity to 139.38 mk, corresponding to 96.04% recovery of the reactivity loss relative to the shifted four-trap base case. The four-site average thermal neutron flux increased from the reference central-trap mean of 1.055 × 1014 to 1.319 × 1014 n·cm-2·s-1, an average gain of 25.0%, while the maximum site reached 1.904 × 1014 n·cm-2·s-1. After applying a comparable active neutron-history basis, OpenMC reproduced the same recovery trend, giving 96.94% recovered reactivity. The steady-state thermal-hydraulic assessment used CAUDVAP/TERMIC-1H at 550 m3/h, giving a total mass flow rate of 151.607 kg/s and a mean pressure drop of 5.372 kPa. The maximum plate power in the hottest fuel element was 28.93 kW, giving a hot-plate peaking factor of 1.24 and a hot-plate heat-flux input of 49.4 W/cm2. The TERMIC-B2 case at 50 W/cm2 therefore represents the rounded-up hot-plate condition for the final configuration, with redistribution and DNB ratios above unity over the assessed hot-channel velocity interval.

Keywords

MTR-10 MW, beryllium reflector, irradiation capability, MCNP4C2, hot-channel analysis

Introduction

The MTR-10 MW reactor was introduced by the International Atomic Energy Agency as a benchmark problem for comparing reactor-calculation methods used in different institutes. The benchmark results were reported in an IAEA technical document published in 1980 (International Atomic Energy Agency 1980). In that work, the participating groups analyzed nearly the same reactor model, with a horizontal cross section similar to that shown in Fig. 1.

Figure 1. 

Cross section of the MTR-10 MW core showing the graphite reflector blocks as represented by the MTRMC package (Al-Saleh et al. 2015), where W = water, CE = control element, and GRE = graphite. Fa and Fb are MTRMC display labels for fuel-element positions that form the central trap.

The benchmark core is represented by a rectangular X–Y grid including 9 × 8 positions. These positions represent fuel assemblies, reflector blocks, irradiation positions, and surrounding coolant regions. The active core region comprises a 5 × 6 array of standard and control fuel elements. The remaining positions are occupied by reflector blocks and coolant regions. Depending on the studied reference case, the reflector blocks are represented by graphite or beryllium, while water regions correspond to coolant and irradiation-trap positions.

In the reference arrangement considered in this work, the central water trap is the only irradiation site. It is designated as “W” in the MTRMC display of Fig. 1. The modification examined here converts this single central water trap into a symmetric four-water-trap arrangement within the same benchmark lattice.

Several Monte Carlo studies have been carried out on the IAEA MTR-10 MW benchmark reactor. Bousbia-Salah et al. (2008) used MCNP5 to calculate the multiplication factor, neutron-flux distributions, and power distributions, and compared the results with previous international benchmark calculations. Dawahra et al. (2015) studied the effect of reflector material on the MTR-10 MW benchmark core using MCNP4C and showed that beryllium provides the highest multiplication factor among the studied reflector materials, whereas graphite gives the highest maximum thermal flux in the water trap. Additional MCNP-based studies on MTR-type reactor fuel parameters were reported by Al-Saleh et al. (2016). Multi-trap irradiation arrangements have also been examined in related MTR-type systems, including one-neutronic-trap and three-neutronic-trap configurations in the MTR-22 MW/ETRR-2 reactor (Shaaban and Albarhoum 2016).

The present study aims to enhance the irradiation capability of the MTR-10 MW benchmark reactor by increasing the number of central water traps from one to four. This modification reduces the excess reactivity because fuel positions in the central region are replaced by water-filled irradiation positions. The resulting reactivity penalty defines the reflector-compensation task.

A stepwise reflector-compensation sequence is therefore applied. First, the uncompensated four-trap core is established. Then, graphite compensation is examined. Finally, beryllium substitutions are introduced progressively to recover the lost excess reactivity while preserving the benchmark lattice, fuel-element geometry, and nominal core power. The candidate configurations are evaluated using multiplication factor, excess reactivity, irradiation-site thermal neutron flux, flux redistribution, control-rod worth, shutdown margin, power-peaking indicators, and steady-state hot-channel thermal-hydraulic margins.

The final configuration is independently checked with OpenMC for the principal reactivity-recovery trend and assessed with CAUDVAP/TERMIC-1H for steady-state thermal-hydraulic performance. The study therefore provides a benchmark-based neutronic and hot-channel thermal-hydraulic evaluation of a modified four-trap irradiation layout for the MTR-10 MW reactor.

Methodology

Neutronic model and reproducibility basis

The neutronic calculations were performed with MCNP4C2 (Briesmeister 2000) using the ENDF/B-VI continuous-energy cross-section libraries available in the MTRMC workflow. This code/data combination was retained to preserve continuity with the MTRMC benchmark model and earlier MTR-10 MW calculations. To provide an independent Monte Carlo verification calculation of the principal trend, the reference, uncompensated four-trap, and final 22-Be cases were also evaluated with OpenMC (Romano et al. 2015) using a separate Monte Carlo workflow.

The MTRMC system was used to generate the three-dimensional MCNP model, assign material regions, and post-process keff, neutron-flux, and power-distribution outputs. The reproducibility basis is the exported MCNP input/output set, supported by the OpenMC verification and CAUDVAP/TERMIC input decks. The MTRMC user interface is shown in Fig. 2 to identify the calculation environment. The main geometric basis is the 9 × 8 core-reflector grid, the 5 × 6 fuel/control-element region, a 60 cm active height, standard fuel elements with 23 fuel plates, and control fuel elements with 17 fuel plates plus 4 aluminum plates. The relevant input decks are listed in the Data availability section for supplementary submission.

Figure 2. 

User interface of the MTRMC system.

Criticality calculations were run in KCODE mode with 100 inactive cycles followed by 1000 active cycles. A total of 1 × 106 active neutron histories was used for each principal configuration. The starting source was the default KCODE fission-source distribution updated from previous cycles. The reported neutron fluxes were normalized to the nominal reactor power of 10 MW.

Tally definitions and comparison basis

Thermal neutron fluxes in the irradiation sites were obtained from cell-based neutron-flux tallies assigned to the water-trap cells of interest. The four final trap positions are denoted [0,0,0], [1,0,0], [1,1,0], and [0,-1,0] according to the MTRMC coordinate convention. Power distributions were obtained from the MTRMC power-output processing and normalized to the 10 MW core power. The radial power distribution is reported at the cassette level as Fxy,cassette = P_max,cassette/P_avg,cassette. The global axial factor was taken from the hottest-fuel-element axial distribution. A plate-resolved heat-flux correction was then applied using the maximum plate power in the hottest fuel element to define the TERMIC-B2 hot-plate input.

Published thermal-neutron flux values are used as contextual literature benchmarks because differences in tally volume, thermal cutoff, power normalization, nuclear-data library, and geometric representation affect absolute flux values. The main performance metric is therefore the relative change between the in-house reference and final models under a common MCNP4C2/MTRMC tally definition, with OpenMC used as an independent cross-check.

Reflector-configuration sequence and uncertainty checks

The reflector configurations were examined in a stepwise sequence within the fixed MTR-10 MW benchmark grid. The four water-filled irradiation sites and the relocated-fuel arrangement were kept fixed, while reflector material and block placement were varied in implementable grid positions. The sequence included the shifted four-trap base case, a graphite-compensation option, and 12-Be, 16-Be, and 22-Be configurations. The final layout was selected from this sequence using excess-reactivity recovery, four-site average thermal flux, minimum site flux, flux redistribution, cassette-level radial and axial power indicators, shutdown margin, control-rod worth, and hot-plate thermal-hydraulic behavior.

MCNP tally uncertainties and independent repeated runs were used to quantify the statistical spread of the principal neutronic quantities for the reference and final beryllium-reflector cores. The reactivity-recovery sequence was also examined with OpenMC, and the hydraulic model was checked through CAUDVAP forward/reverse consistency. These elements provide the numerical basis for comparing the selected final configuration with the reference core.

Independent OpenMC verification calculation

OpenMC was used as an independent Monte Carlo check for three principal configurations: the reference core, the four-trap configuration before beryllium compensation, and the final 22-Be configuration. The OpenMC model was reconstructed from the same core-layout basis to test the reproducibility of the main reactivity-recovery sequence with a separate Monte Carlo workflow.

The OpenMC calculation used continuous-energy HDF5 cross sections through the OPENMC_CROSS_SECTIONS environment setting, with the tested workflow based on OpenMC 0.15.3 and an ENDF/B-VII.1 HDF5 data set. The eigenvalue calculation was rerun with a comparable active neutron-history basis to the MCNP4C2/MTRMC principal cases: 100 inactive batches followed by 1000 active batches with 1000 particles per batch, corresponding to 1 × 106 active histories. Thermal-flux tallies used a 0.625 eV upper cutoff and were volume-normalized for comparison between the reference trap and the four final irradiation sites.

The main OpenMC verification settings are summarized in Table 1.

Table 1.
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OpenMC verification-model settings used for the independent neutronic trend check.

Item OpenMC verification setting Interpretation
Code OpenMC 0.15.3 workflow (Romano et al. 2015) Independent Monte Carlo verification calculation
Nuclear data ENDF/B-VII.1 HDF5 library through cross_sections.xml Independent modern-library check
Cases Reference core; four-trap no-Be core; final 22-Be core Checks the principal neutronic trend
Eigenvalue settings 100 inactive batches + 1000 active batches; 1000 particles/batch; 1 × 106 active histories Comparable active-history basis to the principal MCNP cases
Thermal cutoff <0.625 eV Consistent broad thermal-group definition
Flux normalization Volume-normalized OpenMC tallies for relative comparison Independent comparison of the same recovery trend

For the MCNP4C2/MTRMC and OpenMC comparison, the recovered reactivity after adding the final beryllium reflector was normalized to the reactivity loss caused by the shifted four-trap base case in each workflow. This metric compares the reference, uncompensated four-trap, and final compensated configurations on a consistent relative basis.

Steady-state thermal-hydraulic and hot-plate method

The final 22-block Be-reflector configuration was evaluated with CAUDVAP 2.6 and TERMIC-1H from the MTR_PC v2.6 package. The neutronic and thermal-hydraulic calculation chain is one-way coupled: MCNP4C2/MTRMC provides the fuel-power distribution, hottest fuel-element power, maximum plate power, and axial peaking factor; these outputs are converted into TERMIC-B2 heat-flux inputs, while the thermal-hydraulic calculation does not feed back into the neutronic model. CAUDVAP was run in imposed-flow mode for a reference flow condition of 550 m3/h using the reconstructed channel counts 25/49/22/0/5 for the inner fuel-channel, inter-element, grid-edge, uncovered-hole, and control-fuel-element paths, respectively. A reverse pressure-drop calculation was then performed at the forward-run pressure drop to check hydraulic consistency. TERMIC-1H was used as TERMIC-B2 for the mapped hot-channel evaluation of the final core.

The TERMIC heat-flux input, FIO, was derived directly from the MCNP power distribution. The average heat flux of the hottest fuel element was 39.8 W/cm2 after applying the final-core axial peaking factor. The maximum plate power in the same fuel element was 28.93 kW, while the average plate power was 23.32 kW, giving a hot-plate peaking factor of 1.24. This value matches the statistical heat-flux hot-channel factor Fq = 1.24 reported by Woodruff (1997) for research-reactor hot-channel analysis. Applying the factor gives a hot-plate FIO of 49.4 W/cm2; therefore, the TERMIC-B2 case at 50 W/cm2 represents the rounded-up hot-plate case for the final configuration.

Reactor model and benchmark calculation

The reactor geometry is summarized in Table 2, and the standard fuel-element cross section is shown in Fig. 3. The three-dimensional model was generated through MTRMC and exported to MCNP4C2. The benchmark keff comparison is summarized in Table 3, and the modeled core cross section is shown in Fig. 4.

Figure 3. 

Schematic representation of a horizontal cross section of the standard fuel element (SFE).

Figure 4. 

A cross section in the MTR-10 MW core as modeled using the MCNP code.

Table 2.
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General characteristics of the MTR-10 MW benchmark reactor.

Parameter Description
Reactor type Pool type MTR
Steady-state power level, MW 10
Active core height, cm 60
Fuel grid 5 × 6 positions
Reflector Separate H2O, Be, and graphite regions
Fuel plates/SFE 23
Fuel plates/CFE 17 + 4 of Al
Fuel meat material U-Al
Meat density, g/cm3 5.36
Uranium enrichment (%) 20
Table 3.
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Comparison between the present keff result and international benchmark results for the MTR-10 MW reactor, including percentage deviation relative to the current MCNP4C2/MTRMC reference value (International Atomic Energy Agency 1980).

keff Organization (code) %Δk vs current work
1.16511 ± 0.00085 Current work 0.000%
1.16636 SERPENT (ENDF/B-VII) +0.107%
1.1683 ANL (DIF2D) +0.274%
1.15937 EIR (CODIFF) –0.493%
1.1813 OESGAE (EXTERMINATOR) +1.390%
1.187 CEA (NEPTUNE) +1.879%
1.18339 JAERI (ADC) +1.569%
1.1815 CNEA (EXTERMINATORII) +1.407%

The agreement of the reference keff with the benchmark range provides the basis for comparing modified core configurations under the same calculation workflow.

Results and discussion

Since the MTRMC package is essential for preparing reactor calculations and representing their results on a horizontal cross section of the core, this system was used to prepare the MCNP calculations and to represent the thermal-neutron flux and power distributions in the reactor.

The system can process the MCNP output file, read the power distribution and the neutron-flux distribution for three energy groups, draw a horizontal cross section of the reactor core, and register the corresponding flux and power values for each cell in the core. The system can also distinguish between the different filling materials of the cells and color each cell according to its material, independently of the coloring method adopted in the MCNP code. Fig. 5 shows the reference-core thermal-neutron flux distribution used as the starting state for the configuration sequence.

Figure 5. 

Thermal neutron flux distribution in the MTR-10 MW reactor for the actual configuration, where red = FE, yellow = CE, blue = water, white = IPs, and aqua = graphite.

In the configuration sequence, FE denotes fuel element, NT denotes neutron trap, RC denotes reference core, TNF denotes thermal neutron flux, IER denotes initial excess reactivity, DNB denotes departure from nucleate boiling, and FIO denotes the TERMIC heat-flux input.

If two FEs are removed from the center of the core and substituted by water (Fig. 6), the two NTs have higher thermal fluxes, increasing by 65.08%–75.77%, but a lower keff (1.12542) than the RC. The TNF increased in the new ISs with the decrease of the IER in the core, because the latter decreased from 141.71 mk to 111.44 mk, corresponding to a loss of 30.27 mk. The reactivity was calculated from the following relation (Duderstadt and Hamilton 1976):

ρ(mk)= k eff − 1 k eff × 10 3 (1)

The IER decreased for two reasons: first, because two FEs were removed, with a consequent decrease of the fuel mass in the core; and second, because of the different core configuration resulting from removing two FEs from the center of the core. If the two FEs are shifted to the corners of the fuel rectangle (Fig. 7), the IER of the reactor becomes 118.97 mk (keff = 1.13504), with 7.53 mk recovered by restoring the fuel mass, while the remaining loss relative to 141.71 mk (22.74 mk) is due to shifting the FE positions.

Figure 6. 

Thermal neutron flux distribution in the MTR-10 MW reactor for a configuration in which two central FEs were substituted by two water traps (using the same color convention as Fig. 5).

Figure 7. 

Cross section of the MTR-10 MW core with two NTs in the center and two FEs shifted to the corners of the fuel rectangle, as modeled by the MCNP code.

Four FEs were then substituted with water cells to form four neighboring irradiation positions in the central region of the reactor (Fig. 8). The arrangement follows the discrete MTR-10 MW benchmark grid and places the four water traps within a compact high-flux zone suitable for comparable irradiation conditions.

Figure 8. 

Cross section of the MTR-10 MW core with four NTs in the central region after substituting central fuel positions by water cells, as modeled by the MCNP code.

In this case, the IER of the reactor would be only 71.93 mk (keff = 1.07751), because part of the fuel mass in the core was removed. The TNF values in the four ISs are shown in Table 4, where the position [0, 0, 0] indicates the first IS to the left in the central FEs row, the position [1, 0, 0] indicates the second IS in the central FEs row shifted on the X-axis by only one unit, the position [1, 1, 0] indicates the upper IS, and the position [0, -1, 0] indicates the lower one.

Table 4.
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Thermal neutron flux in the ISs of the reactor for the configuration of Fig. 8.

Position [0, 0, 0] [1, 0, 0] [1, 1, 0] [0, -1, 0]
TNF (n·cm-2·s-1) 1.207 × 1014 1.227 × 1014 1.150 × 1014 4.643 × 1013

If the four FEs were only shifted (Fig. 9), then the IER of the reactor would be 82.85 mk (keff = 1.09034). The new TNF values in the four ISs are shown in Table 5.

Figure 9. 

Cross section of the MTR-10 MW core with four NTs in the center and four FEs shifted to the corners of the fuel rectangle, as modeled by the MCNP code.

Table 5.
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Thermal neutron flux in the irradiation sites of the reactor for the configuration of Fig. 9.

Position [0, 0, 0] [1, 0, 0] [1, 1, 0] [0, -1, 0]
TNF (n·cm-2·s-1) 1.237 × 1014 1.223 × 1014 1.048 × 1014 4.719 × 1013

After shifting the fuel elements and replacing them with four irradiation sites, 58.86 mk of reactivity still had to be recovered. As a first technical solution for reactivity recovery, additional reflector blocks were introduced by replacing selected water cells around the core. Graphite was first tested as a reflector material because it already exists in the reference configuration and can improve neutron economy without changing the fuel mass.

When additional graphite blocks were added to form complete reflector rows on both sides of the core, as shown in Fig. 10, the initial fuel mass was kept the same as in the reference case (RC). However, the resulting multiplication factor increased only to keff = 1.09874, corresponding to an IER of 89.87 mk. This configuration produced a 16.6% increase in the TNF at the central irradiation site, but only 7.02 mk of the lost reactivity was recovered (Table 6).

Figure 10. 

Cross section of the MTR-10 MW core with four NTs in the center and 12 graphite blocks, as modeled by the MCNP code.

Table 6.
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Thermal neutron flux in the irradiation positions of the reactor for the configuration of Fig. 10.

Position [0, 0, 0] [1, 0, 0] [1, 1, 0] [0, -1, 0]
TNF (n·cm-2·s-1) 1.219 × 1014 1.219 × 1014 1.112 × 1014 4.674 × 1013

Because graphite compensation recovered only 7.02 mk of the lost reactivity, beryllium was evaluated as a higher-worth reflector alternative (Fig. 11). Beryllium has favorable neutron-reflection properties and a relatively low neutron absorption probability. The substitution improves neutron economy and brings the modified core closer to the reference-core neutronic state while preserving the relocated fuel arrangement and four irradiation sites.

Figure 11. 

Cross section of the MTR-10 MW core with four NTs in the center and 12 Be blocks added, as modeled by the MCNP code.

This use of beryllium is consistent with the reflector-material study of Dawahra et al. (2015), in which Be was identified as the most efficient reflector for increasing the multiplication factor of the 10 MW MTR benchmark reactor. In the present sequence, Be is used primarily for reactivity recovery after creation of the additional irradiation sites, with the trap fluxes tracked throughout the reflector substitutions.

Replacing graphite with beryllium increased the reactivity and provided a larger recovery than the graphite case. The effective multiplication factor increased to keff = 1.13223, corresponding to ρ = 116.78 mk. The TNF values in the irradiation sites are listed in Table 7.

Table 7.
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Thermal neutron flux in the irradiation positions of the reactor for the configuration of Fig. 11.

Position [0, 0, 0] [1, 0, 0] [1, 1, 0] [0, -1, 0]
TNF (n·cm-2·s-1) 1.793 × 1014 1.355 × 1014 1.140 × 1014 4.833 × 1013

Compared with the reference-case IER of 141.71 mk, the remaining reactivity difference was 24.93 mk.

To recover part of the remaining reactivity, four additional water cells around the core were substituted by beryllium blocks: two blocks in the upper row and two blocks in the lower row (Fig. 12). This modification further increased the effective multiplication factor to keff = 1.14099, corresponding to ρ = 123.57 mk. The remaining reactivity difference was 18.14 mk. The TNF values in the four irradiation sites for this configuration are shown in Table 8.

Figure 12. 

Cross section of the MTR-10 MW core with four NTs in the center and 16 Be blocks added, as modeled by the MCNP code.

Table 8.
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Thermal neutron flux in the irradiation positions of the reactor for the configuration of Fig. 12.

Position [0, 0, 0] [1, 0, 0] [1, 1, 0] [0, -1, 0]
TNF (n·cm-2·s-1) 1.208 × 1014 1.227 × 1014 1.113 × 1014 4.521 × 1013

Among the examined reflector configurations, the layout shown in Fig. 13 was selected. In this configuration, six additional beryllium reflector blocks were added on both sides of the core relative to the 16-block case, giving 22 added Be blocks in total. The fuel mass remained unchanged relative to the shifted-fuel arrangement, while four neutron traps were maintained in the central region.

Figure 13. 

Cross section of the final MTR-10 MW core configuration with four neutron traps (NTs) in the central region and 22 beryllium reflector blocks added around the core, as modeled by the MCNP code.

The calculated effective multiplication factor was keff = 1.16196, corresponding to an initial excess reactivity (IER) of 139.38 mk. The selected configuration therefore provided four irradiation sites instead of one while retaining high thermal neutron flux (TNF) values (Table 9).

Table 9.
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Thermal neutron flux in the irradiation positions of the reactor for the configuration of Fig. 13.

Position [0, 0, 0] [1, 0, 0] [1, 1, 0] [0, -1, 0]
TNF (n·cm-2·s-1) 1.904 × 1014 1.165 × 1014 1.114 × 1014 1.093 × 1014

Table 10 reports the statistical relative errors of the MCNP4C2 thermal-flux tallies used for the final configuration.

Table 10.
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Statistical relative errors for thermal neutron flux tallies (MCNP4C2, 1 × 106 active histories, 1000 active cycles).

Irradiation site Thermal flux (n·cm-2·s-1) Relative error (%)
[0,0,0] 1.904 × 1014 0.72
[1,0,0] 1.165 × 1014 0.68
[1,1,0] 1.114 × 1014 0.71
[0,-1,0] 1.093 × 1014 0.74
Reference central trap (average) 1.055 × 1014 0.65

Note: The listed relative errors are the MCNP thermal-flux tally uncertainties for the final configuration. All values are below 1%, satisfying the statistical convergence criterion adopted in this work.

From Table 9, the final four-site average thermal neutron flux is 1.319 × 1014 n·cm-2·s-1, giving a 25.0% average increase relative to the reference central-trap mean of 1.055 × 1014 n·cm-2·s-1. The reference mean was calculated from the two central-trap tally estimates retained in the MTRMC reference calculation, 1.036 × 1014 and 1.074 × 1014 n·cm-2·s-1, and is used as a single-position reference basis rather than as an average over several irradiation sites. The maximum single-site thermal flux reached 1.904 × 1014 n·cm-2·s-1 and is reported as a local flux indicator, while the four-site average is used as the principal irradiation-capability metric.

Reflector-configuration sequence

Table 11 summarizes the configuration path used to select the Be-reflector layout. The table reports the discrete cases for which numerical evidence is presented. The irradiation-site flux varies non-monotonically across the Be sequence because reflector-block position modifies neutron return and the local redistribution of moderated neutrons around each trap. The decrease in the [0,0,0] flux from the 12-Be case to the 16-Be case is therefore a local redistribution effect rather than a simple reflector-worth trend. For this reason, the final layout is judged from reactivity recovery, four-site average flux, minimum site flux, and power-peaking indicators together.

Table 11.
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Reflector-configuration sequence.

Case Central traps Added reflector blocks keff IER (mk) Main irradiation-site result Derived reactivity / flux indicator
Reference core 1 0 added Be 1.16511 ± 0.00085 141.71 Central-trap TNF = 1.036 × 1014 and 1.074 × 1014 n·cm-2·s-1 Reference basis: IER = 141.71 mk; central-trap mean TNF = 1.055 × 1014 n·cm-2·s-1.
Two traps, central FEs removed 2 0 added Be 1.12542 111.44 Two central NT TNF = 1.821 × 1014 and 1.779 × 1014 n·cm-2·s-1 IER loss = 21.36% vs RC; TNF gain = +65.08%–75.77% vs reference central-trap tally basis.
Two traps, shifted FEs 2 0 added Be 1.13504 118.97 Fuel mass restored by shifting two FEs to the fuel-rectangle corners 7.53 mk recovered relative to the removed-fuel two-trap case; remaining loss = 22.74 mk vs RC.
Four traps, central FEs removed 4 0 added Be 1.07751 71.93 Maximum TNF = 1.227 × 1014; four-site average = 1.012 × 1014 n·cm-2·s-1 IER loss = 49.24% vs RC; maximum TNF gain = +16.3% vs RC mean.
Four traps, shifted FEs 4 0 added Be 1.09034 82.85 [0,0,0] TNF = 1.237 × 1014 n·cm-2·s-1 IER loss = 41.54% vs RC; recovery = 0% relative to shifted four-trap base; [0,0,0] TNF gain = +17.3% vs RC mean.
Four traps + graphite reflector option 4 12 graphite blocks 1.09874 89.87 [0,0,0] TNF = 1.219 × 1014 n·cm-2·s-1 Recovery = 11.93% of lost reactivity; [0,0,0] TNF gain = +15.5% vs RC mean.
Four traps + 12 Be blocks 4 12 Be blocks 1.13223 116.78 [0,0,0] TNF = 1.793 × 1014 n·cm-2·s-1 Recovery = 57.64% of lost reactivity; [0,0,0] TNF gain = +69.9% vs RC mean.
Four traps + 16 Be blocks 4 16 Be blocks 1.14099 123.57 [0,0,0] TNF = 1.208 × 1014 n·cm-2·s-1 Recovery = 69.18% of lost reactivity; local redistribution lowers [0,0,0] TNF to +14.5% vs RC mean.
Final selected configuration 4 22 Be blocks 1.16196 ± 0.00063 139.38 Maximum TNF = 1.904 × 1014; four-site average = 1.319 × 1014 n·cm-2·s-1 Recovery = 96.04%; maximum TNF gain = +80.5% and four-site average gain = +25.0% vs RC mean.

MCNP repeated-run uncertainty check

Ten independent MCNP runs were used to check the statistical robustness of the principal keff comparison. The repeated-run means were 1.16509 ± 0.00038 for the reference core and 1.16192 ± 0.00042 for the final Be core. Using the displayed means, standard deviations, and n = 10 runs for each case, the two-sample t-test gives t ≈ 17.7 with p < 0.001 for 18 degrees of freedom. This supports the conclusion that the final-core keff is statistically lower than the reference value while remaining close enough to recover 96.04% of the lost excess reactivity.

The repeated-run MCNP statistics are summarized in Table 12.

Table 12.
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Repeated-run MCNP uncertainty check for keff.

Configuration Number of independent runs Mean keff Standard deviation Interpretation
Reference core 10 1.16509 0.00038 Baseline repeated-run value
Final 22-Be core 10 1.16192 0.00042 Close to reference after four-trap modification
Two-sample t-test - t ≈ 17.7 p < 0.001 Difference is statistically resolved; final core remains close to the reference core after four-trap modification

Independent OpenMC verification

An independent OpenMC calculation was performed to confirm the principal neutronic response with a separate modern Monte Carlo workflow. After using a comparable active-history basis, OpenMC predicted keff = 1.163284 (±0.000655) for the reference core, keff = 1.086227 (±0.000666) for the four-trap no-Be configuration, and keff = 1.160765 (±0.000647) for the final 22-Be configuration. Using the same recovery definition as MCNP4C2/MTRMC, OpenMC recovered 59.12 mk out of the 60.98 mk lost after the four-trap modification, corresponding to 96.94% recovery. This agrees closely with the MCNP4C2/MTRMC result of 56.53 mk recovered out of 58.86 mk, or 96.04%.

The updated OpenMC verification results are summarized in Table 13.

Table 13.
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Independent OpenMC verification check using the same recovery definition as MCNP4C2/MTRMC, with absolute keff deviations reported as code-to-code consistency indicators.

Configuration / metric OpenMC result Reactivity, ρ (mk) Interpretation Code-to-code %Δk vs MCNP4C2/MTRMC
Reference core keff = 1.163284 ± 0.000655 140.36 OpenMC reference value with comparable active-history basis –0.157%
Four traps, no Be keff = 1.086227 ± 0.000666 79.38 Four-trap base case before Be compensation –0.377%
Final 22-Be configuration keff = 1.160765 ± 0.000647 138.50 Final reflector configuration –0.103%
Reactivity loss after four-trap modification 140.36–79.38 = 60.98 mk - Loss relative to the OpenMC reference core -
Recovered reactivity after 22-Be selection 138.50–79.38 = 59.12 mk; recovery = 96.94% - Same recovery definition as MCNP4C2/MTRMC -

The OpenMC verification confirms the same physical sequence obtained with MCNP4C2/MTRMC: the four-trap modification reduces excess reactivity, and the 22-block beryllium reflector restores nearly all of the lost reactivity while preserving the four irradiation sites.

Neutron spectrum in the final irradiation sites

The final neutron traps were also characterized in three broad energy groups. The thermal-to-fast ratios in Table 14 indicate that the selected sites retain a strongly thermal irradiation character. The tabulated spectrum supports the interpretation of the four positions as thermal-neutron irradiation sites.

Table 14.
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Neutron spectrum in irradiation sites for the final 22-Be configuration, including total flux and thermal/total ratio.

Site Thermal flux (<0.625 eV) n·cm-2·s-1 Epithermal flux (0.625 eV–100 keV) Fast flux (>100 keV) Thermal/fast ratio Total flux n·cm-2·s-1 Thermal/total ratio
[0,0,0] 1.904 × 1014 3.210 × 1013 2.150 × 1013 8.86 2.440 × 1014 0.780
[1,0,0] 1.165 × 1014 2.980 × 1013 2.010 × 1013 5.80 1.664 × 1014 0.700
[1,1,0] 1.114 × 1014 2.850 × 1013 1.950 × 1013 5.71 1.594 × 1014 0.699
[0,-1,0] 1.093 × 1014 2.790 × 1013 1.930 × 1013 5.66 1.565 × 1014 0.698

Comparison with reference and benchmark results

The final beryllium-reflector configuration was compared with the reference core and with selected benchmark values reported in the literature. The comparison includes the multiplication factor, initial excess reactivity, irradiation capability, independent OpenMC verification, power-distribution indicators, shutdown margin, control-rod worth, selected power-density indicators, and steady-state thermal-hydraulic quantities.

The present reference-core keff value of 1.16511 is close to the published MCNP benchmark calculations for the MTR-10 MW reactor. Bousbia-Salah et al. (2008) reported keff = 1.17238 (±0.00033) for the 20% fresh core, while Dawahra et al. (2015) reported keff = 1.16205 for the LEU 20% light-water reflector case and keff = 1.20382 for the corresponding Be-reflector case. The final configuration in the present work gave keff = 1.16196, which remains within the benchmark range while increasing the number of irradiation positions from one to four.

The literature flux values discussed in relation to Table 15 are used as contextual benchmarks because absolute flux comparisons depend on flux-trap volume, thermal cutoff, power-normalization basis, geometry, and nuclear data. The principal irradiation metric is therefore the in-house MCNP relative change between the reference central-trap basis and the final four-trap configuration.

Table 15.
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Comparison between the reference core, final beryllium-reflector core, and selected benchmark/literature values.

Parameter Original/benchmark value from references Final Be-reflector core (this work) Reference core (this work) Unit
Nominal reactor power 10 MW (International Atomic Energy Agency 1980) 10 10 MW
Fuel grid / active height 5 × 6 / 60 cm (International Atomic Energy Agency 1980) 5 × 6 / 60 5 × 6 / 60 - / cm
Number of irradiation sites 1 central flux trap in the original benchmark core (International Atomic Energy Agency 1980) 4 neutron traps 1 central trap site
Added Be reflector blocks Original benchmark reflector contains water, graphite, and beryllium regions (International Atomic Energy Agency 1980); Be was reported as the most efficient reflector for increasing keff (Dawahra et al. 2015). 22 0 block
Effective multiplication factor, keff 1.15937–1.1870 (IAEA intercomparison); 1.17238 ± 0.00033 for the 20% fresh core (Bousbia-Salah et al. 2008); 1.16205 for LEU 20% light-water reflector and 1.20382 for LEU 20% Be reflector (Dawahra et al. 2015); 1.1725 (Kamyab 2014). 1.16196 ± 6.3 × 10-4 1.16511 ± 8.5 × 10-4 -
Initial excess reactivity, IER 147.12 mk in Kamyab (2014) for the no-absorber benchmark core 139.38 141.71 mk
Remaining IER difference from reference - 2.33 mk lower than reference 0 mk
Recovered lost reactivity after final Be-reflector selection - 96.04% - %
Reference central-trap TNF values Contextual literature flux-trap values are not used as direct validation targets because tally volume, thermal cutoff, and normalization are not harmonized. - 1.036 × 1014 and 1.074 × 1014; average = 1.055 × 1014 n·cm-2·s-1
Maximum TNF in irradiation sites Contextual only; absolute literature flux values require harmonized tally definitions. 1.904 × 1014 1.074 × 1014 n·cm-2·s-1
Average TNF over irradiation sites Primary in-house relative comparison basis 1.319 × 1014 1.055 × 1014 n·cm-2·s-1
Average TNF increase Primary in-house relative comparison basis 25.0% (MCNP4C2/MTRMC) - %
Total fuel power 10 MW nominal benchmark power 9.970595 9.971674 MW
Average cassette power - 0.38348 0.3835 MW
Maximum cassette power - 0.536 0.518 MW
Cassette-level radial power factor / 2-D PPF 1.4171 without absorber; 1.4844 Ag-In-Cd; 1.5563 B4C; 1.5234 Hf (Kamyab 2014). 1.398 1.351 -
Maximum axial factor 1.30–1.35 with absorbers fully withdrawn; 1.50–1.55 for 50% withdrawn (International Atomic Energy Agency 1992) 1.290 1.297 -
Shutdown margin Ag-In-Cd: -6.65 mk in Kamyab (2014) (contextual comparison) -33.40 -6.05 mk
Total control-rod worth Ag-In-Cd: 153.77 (Kamyab (2014); absolute value converted to mk) 172.78 147.76 mk
Maximum point power density Ag-In-Cd: 155.72 (Kamyab 2014) 149.90 152.66 W/cm3
Minimum point power density Ag-In-Cd: 50.45 (Kamyab 2014) 45.21 48.9 W/cm3

Notes: The radial factor was calculated as a cassette-level quantity, Fxy,cassette = P_max,cassette/P_avg,cassette, using cassette powers from the MTRMC power-distribution output. The plate-resolved heat-flux correction used for TERMIC-B2 is reported separately in Table 19. The average final TNF was calculated over the four final irradiation sites. The comparison values from Kamyab (2014), Bousbia-Salah et al. (2008), and Dawahra et al. (2015) are used as benchmark or reference context for the present MCNP cases.

The OpenMC comparison supports this interpretation through the recovered-reactivity metric. MCNP4C2/MTRMC gave 96.04% recovery, while OpenMC gave 96.94% using a comparable active-history basis and the same recovery definition. The two Monte Carlo workflows therefore support the same reflector-recovery conclusion.

The final configuration recovered 96.04% of the reactivity loss measured from the shifted four-trap base case to the reference core. The cassette-level radial power factor increased slightly from 1.351 to 1.398, while the maximum axial factor remained nearly unchanged, decreasing slightly from 1.297 to 1.290. These results indicate that the final modification improves the irradiation capability while keeping the global neutronic performance close to that of the reference core.

Power redistribution and hot-channel indicators

The power distribution is redistributed by the reflector modification. The maximum point power density decreases slightly from 152.66 to 149.90 W/cm3, while the minimum point power density decreases from 48.9 to 45.21 W/cm3, indicating a broader spread of local power. The cassette-level value Fq,cassette combines cassette radial power and axial peaking for global comparison, while the hot-plate heat-flux treatment is calculated separately from the maximum plate power. As shown in Table 16, the final global power-distribution indicators remain within the adopted comparison envelope.

Table 16.
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Power-distribution and hot-channel indicators.

Parameter Reference core Final 22-Be core Reference/check basis
Cassette-level radial power factor, Fxy,cassette 1.351 1.398 Reference comparison value at cassette level (Kamyab 2014)
Maximum axial factor, Fz 1.297 1.290 IAEA comparison range for axial factor (International Atomic Energy Agency 1992)
Combined cassette/axial peaking indicator, Fq,cassette = Fxy,cassette × Fz 1.752 1.803 Internal comparison envelope; plate-level heat flux treated separately in Table 19
Maximum point power density 152.66 W/cm3 149.90 W/cm3 No increase relative to reference case in the reported point-power output
Minimum point power density 48.9 W/cm3 45.21 W/cm3 Power-spread indicator in the reported point-power output
Total control-rod worth 147.76 mk 172.78 mk Higher absolute worth is favorable
Shutdown margin –6.05 mk –33.40 mk Same modeled rod-state convention for both configurations

The shutdown-margin indicator in the final configuration is –33.40 mk, compared with –6.05 mk for the reference core under the same modeled rod-state convention. The more negative value indicates a larger calculated sub-criticality for that rod-state sequence, and the total control-rod worth increases from 147.76 to 172.78 mk.

A steady-state thermal-hydraulic calculation was performed for the final Be-reflector configuration using CAUDVAP 2.6 and TERMIC-1H within the MTR_PC v2.6 package. CAUDVAP was first used in imposed-flow mode for the 550 m3/h reference-flow condition to determine the flow distribution, fuel-channel velocities, and mean core pressure drop. The same hydraulic model was checked in pressure-drop mode by imposing the calculated 5372 Pa core pressure drop and verifying that the total flow and velocity distribution were reproduced. TERMIC-1H was then used with the corrected B2 upflow hot-channel model using the MCNP-derived hot-element and hot-plate heat-flux inputs.

The CAUDVAP flow distribution and forward/reverse consistency check are summarized in Tables 17, 18.

Table 17.
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Reconstructed CAUDVAP hydraulic flow-distribution results for the final Be-reflector configuration.

Hydraulic parameter CAUDVAP result Basis Comment
Total core flow rate 550 m3/h Input value Imposed-flow mode
Flow direction Bottom-to-top CAUDVAP output Upflow hydraulic calculation
Channel counts 25 / 49 / 22 / 0 / 5 Input values Inner / between / grid-edge / uncovered / control
Total mass flow rate 151.607 kg/s CAUDVAP result Total coolant mass flow
Mean core pressure drop 5.372 kPa (0.05372 bar) CAUDVAP result Common pressure drop of parallel channels
Inner fuel-channel flow fraction 0.7069 Dominant heated path 25 inner fuel-channel modules
Inter-element flow fraction 0.1284 Bypass/inter-element paths 49 channel modules
Grid-edge flow fraction 0.0466 Peripheral paths 22 channel modules
Control-FE flow fraction 0.1181 Control FE paths 5 channel modules
Inner fuel-channel velocity distribution 0.880–2.132 m/s Full reconstructed inner-channel range Full CAUDVAP channel range; TERMIC-B2 mapped velocities are listed in Table 20.
Overall channel velocity range 0.726–2.270 m/s Full reconstructed path range Hydraulic characterization of all reported paths
Table 18.
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CAUDVAP forward/reverse hydraulic consistency check.

CAUDVAP mode Input condition Calculated result Interpretation
Forward imposed-flow run 550 m3/h Total flow = 151.607 kg/s; mean core ΔP = 5.372 kPa; inner-channel distribution = 0.880–2.132 m/s Reference hydraulic distribution used for mapped hot-channel assessment
Reverse imposed-pressure run ΔP = 5372 Pa Total flow = 151.600 kg/s; flow fractions and inner-channel distribution reproduced the forward run Confirms the reconstructed hydraulic distribution

The CAUDVAP velocity range describes the full set of reconstructed hydraulic channels, whereas the TERMIC-B2 limiting calculation is mapped to the channel associated with the hottest fuel element and its maximum-power plate. In this location-consistent mapping, the 50 W/cm2 case represents the rounded hot-plate heat flux derived from the MCNP plate-power distribution. Lower-velocity paths in the CAUDVAP distribution correspond to other hydraulic locations and are therefore not paired with the maximum plate heat flux. This treatment follows the hot-channel-factor methodology used for plate-type research-reactor thermal-hydraulic assessment (Woodruff 1997), in which power peaking and hydraulic conditions are evaluated for the same limiting channel.

The MCNP-derived heat-flux derivation and the mapped TERMIC-B2 results are summarized in Tables 19, 20.

Table 19.
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MCNP-based derivation and mapping basis of the TERMIC hot-channel and hot-plate heat flux (FIO).

Quantity Value Source / calculation Comment
Hottest fuel-element power 0.536427 MW MCNP fuel-power tally Includes cassette-level radial peaking in the selected hot element
Fuel plates per SFE 23 MTR-10 geometry Used for plate-average power
Plate active width 6.3 cm Fuel-plate geometry Two cooled faces per plate
Active heated length 60 cm MTR-10 active height TERMIC-B2 axial model
Heat-transfer area of hot FE 17,388 cm2 23 × 2 × 6.3 × 60 Converts hot-element power to average heat flux
Average heat flux in hottest FE 30.85 W/cm2 0.536 × 106 / 17,388 Hot-element average over cooled area
Axial peaking factor, Fz 1.290 Final-core MCNP axial distribution Used for TERMIC FIO
Nominal TERMIC FIO 39.8 ≈ 40 W/cm2 30.85 × 1.290 Hot-element average case
Average plate power in hottest FE 23.32 kW/plate 536.427 kW / 23 Average plate power inside the hottest element
Maximum plate power 28.93 kW MCNP plate-power output Hot plate in the hottest fuel element
Hot-plate peaking factor 1.24 28.93 / 23.32 Consistent with Woodruff (1997) statistical heat-flux HCF Fq = 1.24
Hot-plate FIO 49.4 W/cm2 (28.930 × 103 / 756) × 1.290 MCNP-derived hot-plate heat flux
Rounded TERMIC hot-plate case 50 W/cm2 Rounded upward from 49.4 W/cm2 Hot-plate-resolved TERMIC-B2 case
Intermediate TERMIC case 45 W/cm2 40 × 1.13 Intermediate hot-channel comparison case
Hottest-element / hot-plate selection basis Maximum-power standard fuel element and maximum-power plate in the final-core power distribution MTRMC/MCNP power-distribution output Defines the mapped TERMIC-B2 hot-channel basis
Table 20.
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TERMIC-B2 up-flow mapped hot-channel assessment using MCNP-derived hot-element and hot-plate heat-flux inputs.

FIO (W/cm2) Velocity (m/s) Redistribution Mirshak Bernath Maximum coolant temperature (°C)
40 1.4 1.126 6.378 2.153 84.02
40 2.0 1.598 7.333 3.654 70.21
40 2.4 1.912 7.839 4.596 64.84
45 1.6 1.141 5.806 2.147 83.30
45 2.2 1.560 6.612 3.467 70.94
45 2.4 1.699 6.839 3.887 68.20
50 1.6 1.027 5.061 1.724 88.33
50 2.4 1.530 6.039 3.318 71.55

The CAUDVAP calculation predicted a total mass flow rate of 151.607 kg/s and a mean core pressure drop of 5.372 kPa for the reconstructed 550 m3/h reference-flow case. The TERMIC-B2 up-flow model was then evaluated over mapped hot-channel velocities. For the MCNP-derived hot-element heat flux, FIO ≈ 40 W/cm2, TERMIC-B2 predicted redistribution and DNB ratios above unity over the assessed interval. The MCNP-derived hot-plate case gave FIO ≈ 49.4 W/cm2; the corresponding rounded-up TERMIC-B2 calculation at 50 W/cm2 retained redistribution, Mirshak, and Bernath DNB ratios greater than unity at the mapped hot-channel velocity points (Mirshak et al. 1959; Bernath 1960).

Modern plate-fuel thermal-hydraulic studies provide context for the present hot-channel assessment. Khedr (2008) summarized one-dimensional steady-state thermal-hydraulic modeling for plate-type research reactors and compared THDSN predictions with IAEA TECDOC-233, PARET, RELAP5, and TERMIC results. More recent code-development studies include COTENP validation for plate-type research-reactor thermal-hydraulic calculations with pressure-drop discrepancies below 10.7% (Castellanos-Gonzalez et al. 2018), SubChanFlow extension and validation for MTR cores with plate-type fuel assemblies (Almachi et al. 2021), and PLTEMP/ANL verification and validation for experimental and test reactor thermal-hydraulics analysis (Kalimullah et al. 2023).

Thermal-hydraulic input basis

The main inputs of the CAUDVAP/TERMIC calculation are summarized in Table 21 to define the thermal-hydraulic calculation basis.

Table 21.
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Thermal-hydraulic input basis.

Item Reported basis Use in the assessment
Total core flow rate 550 m3/h explicitly reported and used in imposed-flow CAUDVAP mode Defines the reference hydraulic case
Flow direction Bottom-to-top in CAUDVAP; upflow TERMIC-B2 model used Makes CAUDVAP and TERMIC consistent with the intended coolant-flow direction
CAUDVAP channel counts 25 / 49 / 22 / 0 / 5 for inner, between, grid-edge, uncovered, and control-channel groups Provides a reproducible hydraulic grouping for the reconstructed reference run
Forward/reverse CAUDVAP check Flow-given and pressure-drop-given modes reproduce the same flow distribution Supports internal consistency of the hydraulic model
Inlet temperature and pressure 38 °C and 1.5 bar absolute reported as operating conditions Defines the modeled coolant state
Active height and plate count 60 cm active height; 23 plates/SFE and 17 + 4 Al plates/CFE reported in Table 2 Provides the plate-fuel geometry basis
Hot-channel heat flux FIO = 40 W/cm2 from hot-element average; FIO = 50 W/cm2 from MCNP hot-plate correction Connects MCNP power distribution to TERMIC-B2 hot-channel cases
Heated-channel geometry Flow area S1 = 1.4049 cm2 and hydraulic diameter D = 0.431 cm used in TERMIC-B2 Supplies the main hot-channel hydraulic parameters
Heat-transfer/DNB correlations Redistribution, Mirshak, and Bernath ratios reported as implemented in TERMIC-1H Reports redistribution, Mirshak, and Bernath margin ratios

Conclusions

Four neutron traps were introduced in the MTR-10 MW benchmark reactor by shifting selected fuel elements to peripheral positions and introducing additional beryllium reflector blocks while keeping the fuel mass unchanged. The four-trap modification reduced the excess reactivity from 141.71 to 82.85 mk. Among the examined reflector configurations, the final 22-Be-block layout restored the excess reactivity to 139.38 mk, corresponding to 96.04% recovery of the reactivity loss relative to the shifted four-trap base case.

The final configuration increased the four-site average thermal neutron flux to 1.319 × 1014 n·cm-2·s-1, corresponding to a 25.0% average increase relative to the in-house reference-core flux basis. The maximum single-site thermal flux reached 1.904 × 1014 n·cm-2·s-1. The OpenMC verification, performed with a comparable active neutron-history basis, gave 96.94% reactivity recovery using the same definition as the MCNP4C2/MTRMC calculation. The repeated-run MCNP check and the OpenMC verification therefore support the same reactivity-recovery conclusion for the selected 22-block Be-reflector configuration.

The steady-state CAUDVAP/TERMIC-1H calculation gave a total mass flow rate of 151.607 kg/s and a mean core pressure drop of 5.372 kPa for the imposed 550 m3/h flow case. The reverse CAUDVAP pressure-drop calculation at 5372 Pa reproduced the same total flow and velocity distribution. The MCNP-derived hottest fuel-element heat flux was 39.8 W/cm2 after axial peaking and was rounded to 40 W/cm2 for TERMIC-B2. The maximum plate power in the hottest fuel element was 28.93 kW, corresponding to a hot-plate peaking factor of 1.24 and a hot-plate FIO of 49.4 W/cm2. The rounded-up 50 W/cm2 TERMIC-B2 case retained redistribution, Mirshak, and Bernath ratios above unity over the mapped hot-channel velocity interval.

The 22-block beryllium-reflector layout increases the available central irradiation positions from one to four while preserving a reference-like neutronic state and maintaining acceptable steady-state hot-channel behavior. The compact four-trap arrangement provides a practical benchmark-based configuration for comparative irradiation studies in MTR-type cores.

References

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Additional information

Conflict of interest

The authors have declared that no competing interests exist.

Ethical statement

No ethical statement was reported.

Artificial Intelligence (AI) Use

The authors accept full responsibility for the content of the manuscript, including the disclosure of any use of AI.

Regarding the use of AI in the preparation of this manuscript, the authors declare the following: GPT used for language, style and writing. AI-assisted language-editing tools were used to improve clarity, grammar and consistency. All calculations, data verification, scientific interpretation and final manuscript content were reviewed and approved by the authors, who take full responsibility for the work.

Funding

No funding was reported.

Author contributions

H. Alsaleh: conceptualization, methodology, MCNP4C2/MTRMC calculations, OpenMC verification, thermal-hydraulic analysis, data analysis, manuscript drafting and revision. M. Albarhoum: supervision, scientific discussion, review of reactor-physics methodology, and manuscript revision. Both authors reviewed and approved the final manuscript.

Author ORCIDs

H. Alsaleh https://orcid.org/0009-0007-4792-359X

Data availability

The MCNP, OpenMC, and MTR_PC input decks corresponding to the reported reference and final configurations are intended for supplementary submission or availability from the corresponding author. These files include the three-dimensional geometry, tally definitions, random seeds for repeated MCNP runs, OpenMC inputs using the comparable active-history basis, CAUDVAP channel counts and flow-distribution settings, and TERMIC hot-channel input decks required to reproduce the reported neutronic and thermal-hydraulic assessment.

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