Simulation of NuScale-Like SMR Benchmark with OpenMC Code

Abstract

Compared to traditional large-scale reactors, the more heterogeneous, boron-free SMR cores create additional challenges for accurate multiphysics simulations. Therefore, advanced modelling and simulation tools should be used to create high-fidelity, high-accuracy, and computationally efficient multiphysics and multiscale solvers. These solvers can evaluate the safety and performance of SMRs and could be attractive for industrial applications if the computational power requirements were reasonably low. The first crucial step in building a computationally efficient simulation model is to define an SMR benchmark model. This model is a reference for validating the simulation results. In this paper, the benchmark model is a NuScale-like SMR, where the Serpent code has been utilized to run the neutronic simulation. The neutronic simulation was then performed again in the benchmark model, this time utilizing OpenMC code. The results of the Serpent and OpenMC codes were compared in terms of the reactivity coefficient, control rod worth and radial and axial power distribution. By comparing two different codes to validate the simulation of the NuScale-like benchmark, OpenMC will be utilized for future work, such as generating the nuclear material cross-section data for core simulators.

1. Introduction

Nuclear energy is one of the very few available low-carbon technologies capable of delivering energy 24/7 on demand, which is crucial for successfully transitioning to a net-zero society. The UK needs to expand its nuclear reactor fleet to meet the necessary production capacity. A key solution to this demand will be the successful development and deployment of Small Modular Reactors (SMRs) [1].

SMRs have recently gained attention as an appealing alternative to large-scale modern nuclear power plants. They offer several advantages, including enhanced nuclear safety by incorporating primary system components into a single vessel and implementing passive safety systems. Additionally, SMRs potentially feature shorter deployment times, lower upfront capital costs, and the capability to be installed in remote locations [2]. However, it is essential to note that, although the single investment per unit is lower, significant uncertainties remain in assessing the overall economic competitiveness of SMRs, and the levelized cost of electricity (LCOE) may be comparable to that of large-scale plants when full lifecycle costs are considered [3]. Consequently, various companies around the world are developing their own SMR designs, such as SMART (South Korea), NuScale (USA), and Rolls-Royce SMR (UK) [4]. Also, SMRs can be utilised in seawater desalination, hydrogen production, industrial district heat supply, and other industrial applications [5].

In the context of reactor simulation, multiphysics refers to the coupling of different physical disciplines such as neutronics, thermal hydraulics, and thermo-mechanics within a unified computational framework to model their complex interactions. Multiscale modeling, conversely, connects phenomena across different spatial or temporal scales, bridging, for example, the microscopic behavior of materials with the macroscopic performance of a full reactor core [6,7].

Multiphysics and multiscale modelling and simulation of SMRs differ from conventional large-scale nuclear reactors for various reasons. The SMR has a lower core coolant mass flow rate, a greater coolant temperature gradient, a lower core coolant bypass ratio, and higher neutron leakage when compared to a traditional PWR [8]. This high leakage rate impacts the reactivity and, therefore, the economic performance of SMRs, which must be compensated for in other areas such as the transition to boron-free cores [9]. However, it is necessary to consider the interactions of numerous physical phenomena such as neutron transport, fluid dynamics, and heat transfer, while considering the multiscale effects when modelling and simulating both SMRs and large-scale nuclear reactors.

For example, there is a difference in size between SMRs and large-scale nuclear reactors; the SMR core utilized in this study consists of 37 fuel assemblies with an average active fuel height of 2 m and an active core diameter of around 1.5 m. At the same time, the European Pressurised Reactor (EPR) being constructed at Hinkley Point C in the UK will have 241 fuel assemblies with an average active fuel height of 4.2 m and a core active diameter of around 3.8 m [10].

The modelling and simulation of nuclear reactors are crucial for their design and operation, as they enable the analysis of critical aspects such as neutronic behaviour, power distribution, coolant flow, heat transfer, and fuel performance. These processes are essential to ensure reactor safety, optimize performance, and prevent potential failures that could compromise efficiency and reliability [11].

In addition, SMRs’ increased reliance on natural circulation and passive safety systems, particularly for core cooling and decay heat removal, requires highly improved simulation models considering, for example, the mutual interaction of different passive safety systems, start-up behaviour, unique components, and a broader range of correlations for containment heat transfer [12]. Designing SMRs with boron-free cores eliminates boron-boric acid-induced corrosion risks and reduces the amount of radioactive waste produced during the reactor’s lifetime, particularly tritium production. They also enhance operational stability to a certain extent by increasing the moderator temperature coefficient [13]. However, due to the lack of soluble boron acid in the coolant, burnable absorbers or control rods must compensate for the excess reactivity. This process can lead to localized power distribution changes and potential issues during overcooling accidents. This approach makes the boron-free core more heterogeneous and creates additional challenges for accurate multiphysics simulations of such cores [13]. Therefore, simulating boron-free cores requires applying advanced techniques for multiphysics modelling and simulation of the SMR cores.

It is worth noting that several Research Reactors (RRs) share key design and operational features with SMRs, such as compact cores, boron-free coolant circuits, and the use of burnable absorbers. Their power is mostly between 0.01 kWth and 100 MWth. Similarities in multiphysics coupling, particularly between neutronics and thermal hydraulics, make RR simulations a valuable analogue for SMR validation studies. This is exemplified by high-fidelity validation studies, such as the computational benchmarks of the JSI TRIGA Mark II reactor, which utilise coupled Monte Carlo and thermal–hydraulic methods to accurately predict core behavior [14,15].

Consequently, utilizing advanced multiphysics and multiscale simulation tools is essential for enabling engineers to predict the behaviour of these systems under various operating conditions and accident scenarios, facilitating better design optimization and safety assessment of SMRs. Furthermore, as the International Atomic Energy Agency (IAEA) recommended, accurate predictions of core conditions throughout a nuclear reactor’s lifecycle are necessary [16]. All computational codes must be thoroughly validated against empirical data, adhering to the standards set by the IAEA and the Office for Nuclear Regulation [17]. To ensure compliance, regulatory bodies require these codes to be tested against scenarios aligning with ONR’s Technical Assessment Guide [18].

To address the complexities of SMRs, the rigorous approach of integrating advanced multiphysics and multiscale simulation tools and coupling methodologies enhances the accuracy of reactor modelling and simulation. It allows for a comprehensive understanding and simulation of the complex behaviour of nuclear reactors. Since nuclear reactors involve different physical effects occurring at various scales, the multiscale approach allows for a balanced compromise between accuracy and computational efficiency [7]. This approach is particularly valuable in solving reactor core-related problems, such as neutron transport, power distribution, and thermal–hydraulic and thermo-mechanical analyses. Coupling methods are crucial in integrating different codes and models to simulate the interactions between various physical phenomena within nuclear reactors.

Figure 1 presents a proposed integrated approach that combines advanced modelling and simulation tools, including the full-core simulator DYN3D [19], the neutron transport solver LOTUS [20], and the subchannel thermal hydraulics code CTF [21]. This approach aimed to develop a high-fidelity, high-accuracy, computationally efficient multiphysics and multiscale solver. The solver is designed to couple reactor physics at the assembly level for the entire core while enabling detailed pin-by-pin simulations in selected assemblies for SMRs. This capability makes it a valuable tool for assessing the safety and performance of SMRs, with strong potential for industrial applications.

The stochastic Monte Carlo-based code OpenMC [22] will generate the nuclear material cross-section data for this high-fidelity, computationally efficient solver. Additionally, the OpenMC model developed in this study, along with its results, will be used to verify and validate the proposed methodology, ensuring its accuracy and applicability in SMR simulations. While this paper focuses on neutronics, the developed OpenMC model provides a foundation for future multiphysics coupling. OpenMC is well-suited for this role, as its high-fidelity transport data and flexible Python (version 3.11.10) API facilitate integration with thermal–hydraulic and mechanical solvers [22].

Advanced tools such as stochastic modelling and simulation tools, including Monte Carlo codes, are important in addressing the complexities of reactor design. While Monte Carlo methods provide a detailed snapshot of the reactor at a single point in time and are useful for benchmarking, they can be part of a broader toolset to assess variations in reactor behaviour and improve the robustness of SMR designs. OpenMC, a Monte Carlo code, is a community-developed code for stochastic random neutronics that estimates the probability of outcomes based on uncertainties. It is effective for studying neutron movements and interactions. OpenMC can perform fixed-source, k-eigenvalue, and subcritical multiplication calculations using constructive solid geometry. Its application in various studies has provided valuable insights into neutron flux and power distribution, which are essential for optimizing SMR designs to ensure safety, efficiency, and economic viability [7].

The primary objective of this study is to create an OpenMC model of a benchmark core for SMRs, which will serve as a reference for validating advanced simulation tools used in multiphysics and multiscale approaches for SMRs. The calculated results are compared with the benchmark using Serpent to evaluate OpenMC’s accuracy and consistency in simulating SMR performance. This work also lays the groundwork for application of the OpenMC code for generating of the multigroup cross-section libraries for coupled multiphysics simulations of SMRs. A brief overview of the benchmark is provided in Section 2, while Section 3 details the key configurations and settings employed for the OpenMC simulation. The results and their discussion are presented in Section 4. The executable scripts are provided to support ongoing research in advanced reactor modelling and facilitate community-wide collaboration.

OpenMC was selected for this study because it combines the high-fidelity accuracy of established Monte Carlo codes such as Serpent with the advantages of a modern, open-source platform. Its native Python API and modular C++ architecture facilitate automation, parallel computing, and seamless integration into multiphysics frameworks. These features address the limitations of proprietary or licensed codes and make OpenMC particularly suitable for research and academic applications where transparency, extensibility, and coupling capabilities are essential [22,23].

2. Benchmark Specification

The NuScale-like SMR core was selected as the benchmark for this study due to its strong foundation in both regulatory approval and advanced research initiatives. As the first SMR certified by the U.S. Nuclear Regulatory Commission, the NuScale design represents a well-established and widely studied reference model, making it a suitable choice for validation purposes [24]. Additionally, this core is part of the Euratom McSAFER project, which was launched in September 2020 to enhance safety analysis methodologies for SMRs. The project integrates high-fidelity multiphysics tools and builds upon established methods from previous European research efforts, ensuring a comprehensive and validated approach to SMR simulations [25].

The Monte Carlo code Serpent [26] performed static neutronics calculations on the benchmark core at its Beginning of Life (BOL) state. This approach provides a detailed core description, a list of expected outputs, and a reference solution for the benchmark exercises [27].

The NuScale-like core is a nuclear reactor with an expected power output of 160 MWth. It consists of 37 fuel assemblies of 7 different types, as shown in Figure 2, left. Four fuel assemblies contain 16 pins with Gd₂O₃ burnable poison. The fuel assembly (FA), as shown in Figure 3, has a typical 17 × 17 lattice comprising 264 fuel rods and 24 guide tubes (GT) into which control rods can be inserted. The fuel rod pitch inside the assembly is 1.2598 cm, and the fuel assembly pitch inside the core is 21.5036 cm. In addition, the assemblies contain a central instrumentation tube, which is modelled as an empty guide tube in this benchmark. The fuel assemblies with the highest U-235 enrichment contain 16 gadolinia (Gd₂O₃) poison burnable rods. The fuel assemblies incorporate two types of spacer grids (SG): the HTP^TM grid type is made of Zircaloy-4, while the HMP^TM spacer grid is composed of Alloy 718 (Inconel). The UO₂ fuel stack has a total height of 200 cm and is constructed from a single material. The control rods (CRs) are made up of regions containing boron carbide (B₄C) and silver-indium-cadmium (Ag-In-Cd) as absorbers, in addition to a plenum and an end plug. The reactor core is managed by 16 control rod assemblies (CRAs), which are strategically divided into two regulating (RE) banks and two shutdown (SH) banks, as shown in the right panel of Figure 2.

In addition,

Table 1. Materials to be used for different parts of the NuScale-like core model. Reprinted from [27].

Part	Material
Fuel pellets	UO2 or UO2 + Gd2O3
Fuel rod cladding	Zr-4
Fuel rod plenum springs	Inconel
Fuel rod lower end cap	Zr-4
Fuel rod upper end cap	Zr-4
Coolant	H2O with 1000 ppm boron
Guide tube	Zr-4
HMP™ spacer grid	Inconel
HTP™ spacer grid	Zr-4
Control rod absorber	AIC or B4C
Control rod cladding	304L stainless steel (SS)
Control rod upper end plug	304L SS
Control rod bottom plug	304L SS
Core barrel	304L SS

summarize the materials used for the different parts of the NuScale-like model and the nuclide compositions of all fuel types, control rods, homogeneous mixtures, and coolants with 1000 ppm boron. Finally, the fixed operating conditions applied to the neutronics benchmark are presented in

Table 2. Operating conditions applied to the benchmark. Reprinted from [27].

Parameter	Value
Power	160 MW
Uniform fuel temperature	900 K
Uniform coolant temperature	600 K
Soluble boron content	1000 ppm
Uniform structures temperature	600 K
Initial CR position	100% withdrawal
Power	160 MW

.

The benchmark model, NuScale-like core, is used to compare the results of the simulations of the developed model with the available results. The neutronics tools utilised for analysing, verifying and comparing the SMR benchmark are the Serpent and OpenMC codes. The NuScale-like core is designed to operate with boron as a soluble neutron absorber for reactivity control. However, this work focuses on developing and refining modelling techniques for boron-free SMRs, enabling more accurate simulations and supporting alternative strategies for reactivity control. A reference solution to the benchmark exercises was obtained using the Monte Carlo code Serpent to facilitate cross-comparisons with the other Monte Carlo code, OpenMC [28].

3. OpenMC Model (Configuration and Setting)

The NuScale-like core was modelled using the OpenMC code (version 0.15.0). The geometry plot of the developed model is presented in Figure 4. The ENDF/B-VII.1 [29] nuclear data library was utilised to obtain cross-section data corresponding to a uniform fuel temperature of 900 K and uniform coolant and structural temperatures of 600 K used in this benchmark model. The library was downloaded from the official Serpent website, which can be found at [30].

The nuclear cross-section data used in Serpent calculations were initially stored in ACE (A Compact ENDF) format. To ensure compatibility with OpenMC, these cross-section files were converted to HDF5 format using the dedicated data processing scripts provided by OpenMC. Additionally, since the cross-section data files for the C12 and C13 isotopes are not included in the Serpent ENDF/B-VII.1 library, these files were processed separately to ensure the completeness of the OpenMC simulation. While this conversion process may introduce minor numerical differences, previous studies have indicated that such differences are of limited magnitude and do not significantly affect reactor simulation outcomes [22].

For the simulation setup, to ensure consistency with the benchmark, the unresolved resonance probability table sampling was enabled, and the thermal scattering law (i.e., S(α,β)) was applied to hydrogen in the coolant, where the ENDF/B-VII.1 thermal scattering library is provided within Serpent’s cross-section set. Doppler Broadening Rejection Correction (DBRC) was disabled, and gamma-smearing was not employed. Vacuum boundary conditions are applied to the outer surface of the core’s surrounding barrel, as well as the core’s top and bottom surfaces. In contrast, a reflective boundary condition is imposed on the inner surface of the surrounding barrel. The simulation was conducted with 2500 active and 200 inactive cycles, using 1,000,000 neutron histories per cycle.

It is essential to clarify that the pitch value of 21.5036 cm mentioned in the benchmark specifically refers to the fuel assembly pitch within the core, not the side length of the square fuel assembly. This distinction is crucial when determining the positioning of the lower-left lattices for modelling the fuel assemblies and the gaps between them. Neglecting this detail could lead to inaccuracies in the dimensions of the fuel assemblies, adversely affecting the accuracy of gap modelling and causing asymmetry in corresponding areas of the reactor core.

4. The Results and Discussion

A neutronic simulation of the NuScale-like benchmark core was previously conducted using the Serpent code. The same simulation was also performed using the developed OpenMC model of the benchmark core. The simulation input and benchmark results are available in an open-access dataset on Zenodo [31]. The results from both codes were compared based on the effective multiplication factor ($k_{eff}$), the reactivity worth of the control rod assemblies (CRA), and the radial and axial power distributions, as detailed below.

4.1. Effective Multiplication Factor ($k_{eff}$)

In this NuScale-like benchmark, reactor criticality is controlled exclusively through the placement of control rods, which consist of (B₄C) and Ag-In-Cd (AIC) absorbers. The effectiveness of the control rods in altering the reactor’s reactivity is quantified by the control rod or group of control rods reactivity worth. This parameter reflects the impact of inserting or withdrawing a CR on the reactor’s behaviour.

Table 3. Summary of the integral core parameters (Serpent and OpenMC).

Benchmark Model (Serpent)				OpenMC			Variation |X1 − X2| × 105 (pcm)
Core State	${\mathit{k}}_{\mathit{e}\mathit{f}\mathit{f}}$	$\mathit{\sigma }{\mathit{k}}_{\mathit{e}\mathit{f}\mathit{f}}$	CRW (pcm)	${\mathit{k}}_{\mathit{e}\mathit{f}\mathit{f}}$	$\mathit{\sigma }{\mathit{k}}_{\mathit{e}\mathit{f}\mathit{f}}$	CRW (pcm)	${\mathit{k}}_{\mathit{e}\mathit{f}\mathit{f}}$	CRW
All rods out	1.02768	0.00001	n/a	1.02786	0.00002	n/a	18	n/a
RE1 in	1.00723	0.00001	−1975	1.00751	0.00002	−1965	28	10
RE2 in	1.00313	0.00001	−2381	1.00333	0.00002	−2379	20	2
SH3 in	0.98978	0.00001	−3726	0.98994	0.00002	−3727	16	1
SH4 in	0.98971	0.00001	−3733	0.98993	0.00002	−3728	22	5
All rods in	0.85791	0.00002	−19,255	0.85822	0.00002	−19,231	31	24

presents the results of the $k_{eff}$, the standard deviation ($\sigma k_{eff}$) of the effective multiplication factor, and the CR reactivity worth taken from the benchmark, as well as those obtained from the neutronic simulation using the OpenMC code. The results are provided for various control rod insertion scenarios, including individual CRA banks (RE1, RE2, SH3, and SH4) and all CRA banks combined (SCRAM), as shown in Figure 2, right.

The comparison of $k_{eff}$ and control rod worths (CRW) between Serpent and OpenMC demonstrates good agreement, with variations ranging from 16 to 31 pcm in $k_{eff}$ values and from 1 to 24 pcm in CRW. The most significant deviations of 31 pcm in $k_{eff}$ and 24 in (CRW) occur when all control rods are fully inserted, this condition leads to significant neutron absorption and complex flux gradients, making accurate modelling more challenging. The discrepancies observed may be attributed to variations in the numerical methods, convergence criteria, and solution algorithms employed by Serpent and OpenMC. Although both codes use the same nuclear data library (ENDF/B-VII.1), differences in the processing tools, such as NJOY, that generate cross-section data files compatible with each code can lead to variations in results. These tools may handle resonance regions and thermal scattering laws differently, which impacts neutron interactions. As a result, discrepancies in cross-section processing can cause differences in the simulation outcomes between Serpent and OpenMC. Furthermore, the methods used for cross-section interpolation in both codes may also contribute to minor differences in the results.

It is worth mentioning that neutron source convergence in OpenMC was achieved after 72 batches, which corresponds to the 200 inactive cycles setting. This convergence is illustrated by the stabilization of Shannon entropy shown in Figure 5. However, the slightly higher standard deviation observed in OpenMC suggests increased statistical uncertainty in its results compared to Serpent, which may contribute to some of the observed discrepancies in the $k_{eff}$ values between the two codes. This difference in uncertainty may indicate that OpenMC requires a larger number of neutron histories or simulation cycles to achieve the same level of statistical precision as Serpent under comparable settings.

4.2. Power Distribution

In OpenMC, the radial and axial power distribution in the NuScale-like core is calculated by defining meshes with fine cells to discretize the core geometry. The tally filters in OpenMC are set to these meshes, and the tally scores correspond to the total fission reaction rate. The tally results provide the fission rate in each mesh cell, which can then be normalized by cell volume and average fuel density to determine the power density for each cell. The radial power distribution results for the fuel assemblies and fuel pins were compared between Serpent and OpenMC in two scenarios: the reference case (all rods out) and an asymmetric insertion of a single RE1 control rod at location D5, as shown in Figure 6.

4.2.1. Normalized Radial Power Distribution at the FA Level

Table 4. Normalized radial power distribution values at the FA level for the reference state (all rods out).

	Serpent								OpenMC
	A	B	C	D	E	F	G		A	B	C	D	E	F	G
1			1.0561	0.9810	1.0561			1			1.0544	0.9817	1.0548
2		0.9507	1.1662	0.8803	1.1662	0.9507		2		0.9495	1.1671	0.8808	1.1677	0.9506
3	1.0561	1.1662	0.8893	0.8200	0.8893	1.1662	1.0561	3	1.0537	1.1666	0.8891	0.8210	0.8899	1.1681	1.0553
4	0.9810	0.8803	0.8200	1.1362	0.8200	0.8803	0.9810	4	0.9809	0.8799	0.8204	1.1350	0.8210	0.8811	0.9823
5	1.0561	1.1662	0.8893	0.8200	0.8893	1.1662	1.0561	5	1.0542	1.1669	0.8891	0.8207	0.8897	1.1679	1.0555
6		0.9507	1.1662	0.8803	1.1662	0.9507		6		0.9496	1.1670	0.8804	1.1674	0.9504
7			1.0561	0.9810	1.0561			7			1.0540	0.9816	1.0548

and

Table 5. Normalized radial power distribution values at the FA level for the asymmetric insertion of a single RE1 CR.

	Serpent								OpenMC
	A	B	C	D	E	F	G		A	B	C	D	E	F	G
1			1.2977	1.2093	1.2977			1			1.2962	1.2107	1.2965
2		1.1187	1.3869	1.0481	1.3869	1.1187		2		1.1187	1.3900	1.0499	1.3895	1.1179
3	1.1907	1.3098	0.9766	0.8798	0.9766	1.3098	1.1907	3	1.1892	1.3124	0.9769	0.8811	0.9769	1.3107	1.1898
4	1.0575	0.9152	0.7681	0.9498	0.7681	0.9152	1.0575	4	1.0573	0.9151	0.7689	0.9489	0.7690	0.9157	1.0589
5	1.0807	1.1152	0.6995	0.3138	0.6995	1.1152	1.0807	5	1.0781	1.1149	0.6992	0.3131	0.6995	1.1172	1.0797
6		0.8544	0.9380	0.6363	0.9380	0.8544		6		0.8529	0.9371	0.6356	0.9388	0.8542
7			0.8742	0.7962	0.8742			7			0.8709	0.7951	0.8729

present the normalized radial power distribution calculated at the FA level for two scenarios: the reference case (all control rods out) and the asymmetric insertion of a single RE1 control rod. Figure 7 and Figure 8 illustrate these distributions accordingly. Additionally,

Table 6. Relative Percentage Difference (RPD) between Serpent and OpenMC results for normalized radial power distribution values at the FA level for the reference state (all rods out).

Relative Percentage Difference (RPD) |T1 − T2|/(T1) × 100%
	A	B	C	D	E	F	G
1			0.1610	0.0714	0.1231
2		0.1262	0.0772	0.0568	0.1286	0.0105
3	0.2273	0.0343	0.0225	0.1220	0.0675	0.1629
4	0.0102	0.0454	0.0488	0.1056	0.1220	0.0909	0.1325
5	0.1799	0.0600	0.0225	0.0854	0.0450	0.1458	0.0568
6		0.1157	0.0686	0.0114	0.1029	0.0316
7			0.1988	0.0612	0.1231

and

Table 7. Relative Percentage Difference (RPD) between Serpent and OpenMC results for normalized radial power distribution values at the FA level for the asymmetric insertion of a single RE1 CR.

Relative Percentage Difference (RPD) |T1 − T2|/(T1) × 100%
	A	B	C	D	E	F	G
1			0.1156	0.1158	0.0925
2		0.0000	0.2235	0.1717	0.1875	0.0715
3	0.1260	0.1985	0.0307	0.1478	0.0307	0.0687	0.0756
4	0.0189	0.0109	0.1042	0.0948	0.1172	0.0546	0.1324
5	0.2406	0.0269	0.0429	0.2231	0.0000	0.1793	0.0925
6		0.1756	0.0959	0.1100	0.0853	0.0234
7			0.3775	0.1382	0.1487

show the Relative Percentage Difference (RPD) between Serpent and OpenMC results for the normalized radial power distribution values at the FA level for both scenarios.

The results demonstrate a strong agreement between Serpent and OpenMC in both the reference case (all rods out) and the scenario involving the asymmetric insertion of a single RE1 control rod. The Root Mean Square Relative Difference (RMSRD) value stayed below 0.11% across all the FAs in the Reference state, while it reached 0.14% in the RE1 CR state.

The maximum RPD reached 0.227% at (A3-FA) Table 6 for the reference case and 0.377% at (C7-FA) Table 7 for the RE1 insertion case. Both values remain below 0.4%, indicating a high level of consistency between the two codes.

The differences in results can be traced back to variations in neutron transport modelling and cross-section interpolation methods between Serpent and OpenMC. Additionally, the inherent statistical uncertainties in Monte Carlo simulations also contribute to the discrepancies in the results. In the reference case, as shown in

Table 8. Relative Uncertainty (%) at the FA level for the reference state (all rods out).

	Serpent								OpenMC
	A	B	C	D	E	F	G		A	B	C	D	E	F	G
1			1.7 × 10−3	1.5 × 10−3	1.7 × 10−3			1			3.0 × 10−4	2.7 × 10−4	2.9 × 10−4
2		2.9 × 10−3	9.0 × 10−4	1.3 × 10−3	9.0 × 10−4	2.9 × 10−3		2		2.9 × 10−4	2.6 × 10−4	2.4 × 10−4	2.6 × 10−4	2.8 × 10−4
3	1.7 × 10−3	9.0 × 10−4	3.0 × 10−3	3.9 × 10−3	3.0 × 10−3	9.0 × 10−4	1.7 × 10−3	3	3.1 × 10−4	2.6 × 10−4	2.5 × 10−4	2.4 × 10−4	2.4 × 10−4	2.5 × 10−4	3.0 × 10−4
4	1.5 × 10−3	1.3 × 10−3	3.9 × 10−3	4.7 × 10−3	3.9 × 10−3	1.3 × 10−3	1.5 × 10−3	4	3.1 × 10−4	2.6 × 10−4	2.4 × 10−4	2.3 × 10−4	2.4 × 10−4	2.4 × 10−4	2.9 × 10−4
5	1.7 × 10−3	9.0 × 10−4	3.0 × 10−3	3.9 × 10−3	3.0 × 10−3	9.0 × 10−4	1.7 × 10−3	5	3.2 × 10−4	2.5 × 10−4	2.4 × 10−4	2.4 × 10−4	2.5 × 10−4	2.6 × 10−4	3.0 × 10−4
6		2.9 × 10−3	9.0 × 10−4	1.3 × 10−3	9.0 × 10−4	2.9 × 10−3		6		2.8 × 10−4	2.5 × 10−4	2.5 × 10−4	2.5 × 10−4	2.8 × 10−4
7			1.7 × 10−3	1.5 × 10−3	1.7 × 10−3			7			3.1 × 10−4	3.0 × 10−4	3.1 × 10−4

, Serpent exhibits significantly higher relative uncertainties, ranging from 9.0 × 10⁻⁴% to 4.7 × 10⁻³%. In the RE1 insertion case,

Table 9. Relative Uncertainty (%) at the FA level for the asymmetric insertion of a single RE1 CR.

	Serpent								OpenMC
	A	B	C	D	E	F	G		A	B	C	D	E	F	G
1			1.3 × 10−2	1.3 × 10−2	1.3 × 10−2			1			2.7 × 10−4	2.6 × 10−4	2.8 × 10−4
2		7.5 × 10−3	1.0 × 10−2	1.1 × 10−2	1.0 × 10−2	7.5 × 10−3		2		2.6 × 10−4	2.3 × 10−4	2.3 × 10−4	2.3 × 10−4	2.6 × 10−4
3	6.5 × 10−3	6.3 × 10−3	8.5 × 10−3	8.3 × 10−3	8.5 × 10−3	6.3 × 10−3	6.5 × 10−3	3	2.8 × 10−4	2.5 × 10−4	2.4 × 10−4	2.3 × 10−4	2.4 × 10−4	2.5 × 10−4	2.9 × 10−4
4	7.2 × 10−3	4.8 × 10−3	5.6 × 10−3	5.9 × 10−3	5.6 × 10−3	4.8 × 10−3	7.2 × 10−3	4	2.7 × 10−4	2.4 × 10−4	2.5 × 10−4	2.5 × 10−4	2.6 × 10−4	2.5 × 10−4	2.8 × 10−4
5	8.0 × 10−3	8.5 × 10−3	8.7 × 10−3	8.7 × 10−3	8.7 × 10−3	8.5 × 10−3	8.0 × 10−3	5	3.1 × 10−4	2.8 × 10−4	2.8 × 10−4	3.0 × 10−4	2.7 × 10−4	2.7 × 10−4	3.1 × 10−4
6		1.2 × 10−2	1.8 × 10−2	2.0 × 10−2	1.8 × 10−2	1.2 × 10−2		6		3.1 × 10−4	2.6 × 10−4	3.0 × 10−4	3.0 × 10−4	3.1 × 10−4
7			2.2 × 10−2	2.3 × 10−2	2.2 × 10−2			7			3.3 × 10−4	3.2 × 10−4	3.4 × 10−4

, these uncertainties increase further, ranging from 4.8E−03% to 2.3 × 10⁻²%. In contrast, OpenMC demonstrates much lower uncertainties, remaining between 2.3 × 10⁻⁴% and 3.2 × 10⁻⁴% for the reference case and 2.3 × 10⁻⁴% to 3.4 × 10⁻⁴% for the RE1 insertion case. Furthermore, the relative uncertainty in Serpent varies more dramatically between the two cases, while OpenMC maintains consistently low variations.

Focusing exclusively on the OpenMC results, the normalised radial power distribution shows slight asymmetries despite the expected symmetry in the core design. These discrepancies occur between geometrically equivalent positions, such as C1 (1.0544) and E1 (1.0548) in Table 4, where the relative difference is approximately 0.114%. When the simulation was refined to include 5000 active batches, 400 inactive batches, and 5 × 10⁶ neutron histories per cycle, the relative difference was reduced to 0.026%. This improvement confirms that the observed asymmetry was primarily caused by statistical noise. It should be noted that, in the benchmark definition, all Serpent radial power distributions were obtained by averaging ten independent calculations, which accounts for the better symmetry observed in those results [27]. The uncertainty values in

Table 10. Standard deviation values at the FA level for the reference state (all rods out).

	Serpent								OpenMC
	A	B	C	D	E	F	G		A	B	C	D	E	F	G
1			1.8 × 10−5	1.5 × 10−5	1.8 × 10−5			1			3.2 × 10−6	2.7 × 10−6	3.1 × 10−6
2		2.7 × 10−5	1.1 × 10−5	1.1 × 10−5	1.1 × 10−5	2.7 × 10−5		2		2.8 × 10−6	3.0 × 10−6	2.2 × 10−6	3.0 × 10−6	2.7 × 10−6
3	1.8 × 10−5	1.1 × 10−5	2.6 × 10−5	3.2 × 10−5	2.6 × 10−5	1.1 × 10−5	1.8 × 10−5	3	3.3 × 10−6	3.1 × 10−6	2.2 × 10−6	1.9 × 10−6	2.1 × 10−6	3.0 × 10−6	3.1 × 10−6
4	1.5 × 10−5	1.1 × 10−5	3.2 × 10−5	5.3 × 10−5	3.2 × 10−5	1.1 × 10−5	1.5 × 10−5	4	3.0 × 10−6	2.3 × 10−6	1.9 × 10−6	2.6 × 10−6	2.0 × 10−6	2.1 × 10−6	2.9 × 10−6
5	1.8 × 10−5	1.1 × 10−5	2.6 × 10−5	3.2 × 10−5	2.6 × 10−5	1.1 × 10−5	1.8 × 10−5	5	3.4 × 10−6	2.9 × 10−6	2.1 × 10−6	1.9 × 10−6	2.2 × 10−6	3.0 × 10−6	3.2 × 10−6
6		2.7 × 10−5	1.1 × 10−5	1.1 × 10−5	1.1 × 10−5	2.7 × 10−5		6		2.6 × 10−6	2.9 × 10−6	2.2 × 10−6	3.0 × 10−6	2.7 × 10−6
7			1.8 × 10−5	1.5 × 10−5	1.8 × 10−5			7			3.2 × 10−6	3.0 × 10−6	3.3 × 10−6

and

Table 11. Standard deviation values at the FA level for the asymmetric insertion of a single RE1 CR.

	Serpent								OpenMC
	A	B	C	D	E	F	G		A	B	C	D	E	F	G
1			1.7 × 10−4	1.6 × 10−4	1.7 × 10−4			1			3.5 × 10−6	3.2 × 10−6	3.6 × 10−6
2		8.4 × 10−5	1.4 × 10−4	1.1 × 10−4	1.4 × 10−4	8.4 × 10−5		2		2.9 × 10−6	3.1 × 10−6	2.4 × 10−6	3.2 × 10−6	3.0 × 10−6
3	7.7 × 10−5	8.3 × 10−5	8.3 × 10−5	7.3 × 10−5	8.3 × 10−5	8.3 × 10−5	7.7 × 10−5	3	3.3 × 10−6	3.2 × 10−6	2.3 × 10−6	2.1 × 10−6	2.3 × 10−6	3.3 × 10−6	3.5 × 10−6
4	7.6 × 10−5	4.4 × 10−5	4.3 × 10−5	5.6 × 10−5	4.3 × 10−5	4.4 × 10−5	7.6 × 10−5	4	2.9 × 10−6	2.2 × 10−6	1.9 × 10−6	2.4 × 10−6	2.0 × 10−6	2.3 × 10−6	3.0 × 10−6
5	8.6 × 10−5	9.5 × 10−5	6.1 × 10−5	2.7 × 10−5	6.1 × 10−5	9.5 × 10−5	8.6 × 10−5	5	3.3 × 10−6	3.1 × 10−6	1.9 × 10−6	9.4 × 10−6	1.9 × 10−6	3.0 × 10−6	3.4 × 10−6
6		1.0 × 10−4	1.7 × 10−4	1.2 × 10−4	1.7 × 10−4	1.0 × 10−4		6		2.6 × 10−6	2.5 × 10−6	1.9 × 10−6	2.8 × 10−6	2.6 × 10−6
7			2.0 × 10−4	1.8 × 10−4	2.0 × 10−4			7			2.8 × 10−6	2.5 × 10−6	3.0 × 10−6

represent only the statistical standard deviation (σ) derived from tally fluctuations; they do not include systematic sources of error. Such systematic discrepancies may arise from factors such as geometry discretisation, tally normalisation, or cross-section data interpolation. While statistical fluctuations explain most of the observed asymmetry, the persistent residual deviation suggests that minor systematic effects also contribute, a known challenge in particle transport simulations [32]. Therefore, the reported uncertainties should be interpreted strictly as statistical measures. In future work, additional OpenMC tests using simplified, highly symmetric configurations could be conducted to better isolate and quantify the respective roles of statistical and systematic effects, employing established methodologies developed for this purpose.

Overall, the results confirm that both codes effectively capture the expected physical behaviour of power distribution under different control rod configurations.

4.2.2. Radial Pin-Power Distribution

The radial pin power distributions for both the Reference and RE1 CR states were calculated in watts using Serpent and OpenMC. The results are presented in Figure 9 and Figure 10. Due to space limitations, detailed numerical values are available in a digital dataset [31].

A comparative analysis of the results from OpenMC and Serpent shows strong overall agreement, with RMSRD values remaining below 0.68% for the Reference state and 0.59% for the RE1 CR state in almost all corresponding regions. The RPD distribution of the results for both cases are illustrated in Figure 11. The figure highlights significant discrepancies observed at the core boundaries in both cases, particularly around the RE1 CR fuel assembly and its surrounding area in the RE1 CR state. In the Reference state, the maximum RPD observed between the two codes was 1.3%. In contrast, the CR state for RE1 showed a slightly higher RPD of 1.7%. These variations are likely influenced by neutron flux gradients and the complexity of local geometries, which increase statistical uncertainties and can affect the precision of the simulations.

The maximum relative uncertainty difference in both states is observed at fuel pins near the core edges and surrounding areas Figure 12 and Figure 13. In the Reference state, Serpent’s uncertainty ranges from 2.0 × 10⁻³% to 1.8 × 10⁻²%, while OpenMC’s ranges from 4.8 × 10⁻³% to 1.2 × 10⁻²%. For the RE1 CR state, OpenMC shows a slight change, with uncertainty ranging from 4.5 × 10⁻³% to 1.3 × 10⁻²%. In contrast, Serpent exhibits a more noticeable variation, with uncertainty increasing from 4.2 × 10⁻³% to 5.4 × 10⁻²%, differing from OpenMC.

Figure 12 and Figure 13 show that OpenMC generally maintains lower and more uniform relative uncertainty across both states, with only slight localized increases due to control rod insertion. Serpent, however, displays higher variations, particularly in the upper and lower core regions in the RE1 control rod case. These differences in statistical uncertainty between the two codes may impact result accuracy and consistency, affecting direct comparisons.

4.2.3. Axial Power Distribution

The radially axial power distribution values were calculated using the OpenMC code and compared with values obtained from the benchmark simulation conducted by the Serpent code. The corresponding power levels in megawatts (MW) are presented in

Table 12. Axial power profile.

Height (cm)	Axial Power Distribution (MW)
	Serpent		OpenMC		Power Relative Difference |PSer − POpe|/|PSer| × 100%
	Power (MW)	STD	Power (MW)	STD
11.365	0.6553.	7 × 10−5	0.6335	7 × 10−7	3.33
14.92	0.9184	9 × 10−5	0.8992	9 × 10−7	2.09
19.365	4.154	5 × 10−4	4.1181	3 × 10−6	0.86
31.017	6.3682	7 × 10−4	6.3492	3 × 10−6	0.30
42.67	8.3573	8 × 10−4	8.3574	4 × 10−6	0.00
54.322	10.0322	9 × 10−4	10.0599	4 × 10−6	0.28
65.974	4.0497	3 × 10−4	4.0668	2 × 10−6	0.42
70.419	11.9449	8 × 10−4	12.0051	4 × 10−6	0.50
82.071	12.9909	7 × 10−4	13.0686	4 × 10−6	0.60
93.724	13.5872	5 × 10−4	13.6681	4 × 10−6	0.60
105.376	13.7097	4 × 10−4	13.7890	4 × 10−6	0.58
117.028	4.9838	2 × 10−4	5.0107	2 × 10−6	0.54
121.473	13.3353	8 × 10−4	13.3967	4 × 10−6	0.46
133.125	12.6828	8 × 10−4	12.7291	4 × 10−6	0.37
144.778	11.578	9 × 10−4	11.6034	4 × 10−6	0.22
156.43	10.0769	8 × 10−4	10.0793	4 × 10−6	0.02
168.082	3.2594	2 × 10−4	3.2548	2 × 10−6	0.14
172.527	6.4714	5 × 10−4	6.4393	3 × 10−6	0.50
182.236	5.1145	4 × 10−4	5.0529	3 × 10−6	1.20
191.946	3.6038	4 × 10−4	3.5138	2 × 10−6	2.50
201.656	2.1263	3 × 10−4	1.9052	2 × 10−6	10.40
Total	160.000		160.000

. For recommended axial meshing which accounts for the position of the spacer grids, refer to the original benchmark article [27].

The comparison of results from Serpent and OpenMC, illustrated in Figure 14, demonstrates good agreement in the radially averaged axial power distribution. Both codes exhibit similar trends and peak positions, effectively capturing the influence of modelling the spacer grids, which shows power dips at corresponding heights. The RMSRD across most axial positions remains small, staying below 0.78%. This indicates a reliable consistency between the two codes.

However, noticeable deviations occur between the results obtained from the codes at the core extremities, with RPD reaching 10.4% at the top and 3.33% at the bottom. While both codes apply the recommended axial meshing, differences in their mathematical handling of the mesh, boundary conditions, methodologies, cross-section treatment, transport algorithms, and statistical convergence criteria could contribute to these discrepancies. Lower neutron populations due to leakage and limited fuel availability may amplify the variations further. Because Monte Carlo methods depend on statistical sampling, they are less effective in low-flux regions. In these areas, the statistical uncertainty increases, resulting in more pronounced RPD. Additionally, the presence of helium, coolant, plenum springs, and control rods at the top end of the core introduces spatial heterogeneities and sharp neutron flux gradients, adding to the complexity in that region. This increased complexity can lead to greater statistical uncertainties and numerical errors in the simulations, resulting in a larger discrepancy between the results generated from the code.

Further analysis of the uncertainty profiles illustrated in Figure 15 highlights a distinct trend in statistical uncertainty across the core. The statistical uncertainty associated with the power distribution in both codes exhibits a clear pattern: uncertainties are higher at the bottom of the core than at the top. This variation can be explained by the boundary conditions surrounding the core. At the top, the presence of water facilitates neutron scattering, which increases the neutron population and enhances statistical accuracy. In contrast, the neutron population is lower at the bottom due to structural components such as the bottom nozzle and the reactor vessel floor. This results in fewer neutron interactions and, consequently, a higher level of statistical uncertainty.

A closer examination of the statistical uncertainties presented in Figure 15, given the constraints outlined in Section 3, namely 1,000,000 neutron histories and 2500 active cycles, shows that OpenMC provides a more precise representation of power distribution variations, especially at key structural points such as the spacer grid. The results from OpenMC more effectively highlight the peak points and trends in the power distribution, while Serpent’s results, as presented in the benchmark dataset, tend to exhibit greater statistical noise [28]. This difference can be attributed to the standard deviation (STD) values reported for each code in Table 12, with Serpent generally showing higher uncertainties. A larger STD in Serpent indicates a broader spread in the sampled neutron histories, leading to less precise predictions compared to OpenMC. Consequently, OpenMC’s representation of uncertainty is more in-line with expected trends when considering structural variations and the resulting core’s axial power distribution.

5. Conclusions

SMRs represent a promising advancement in nuclear energy technology, which could offer significant benefits such as faster deployment, enhanced safety features, reduced operational costs, and improved adaptability for remote locations. The successful implementation of SMRs relies on advanced multiphysics and multiscale simulation tools that enable precise predictions of operational characteristics and the optimization of reactor designs. This study’s comparative analysis of the Serpent and OpenMC computational codes demonstrated notable consistency in simulating nuclear reactor performance. Comparisons of the $k_{eff}$ showed excellent agreement, with variations ranging from 16 to 31 pcm across different control rod configurations. Analyses of radial and axial power distribution revealed that RMSRD is consistently below 0.78% in most regions. The minor discrepancies observed can be attributed to the statistical uncertainties inherent in Monte Carlo simulation methods, as well as variations in numerical techniques, cross-section interpolation, and solution algorithms. Despite these small differences, both codes effectively captured complex neutron transport phenomena and power distribution characteristics under different reactor conditions. Nevertheless, OpenMC’s open-source framework, modular Python API, and flexibility for integration with thermal–hydraulic and mechanical solvers make it particularly suitable for future multiphysics applications, where interoperability and transparency are key for advancing SMR design and safety analysis. Looking ahead, the research will expand its computational approach by integrating advanced modelling and simulation tools such as DYN3D, LOTUS, and CTF. The goal is to develop a high-fidelity, computationally efficient multiphysics SMR solver with OpenMC generating macroscopic multigroup cross-section libraries to enable comprehensive full-core modelling of NuScale-like SMRs.