Multigroup Cross Sections Research Articles

Calculation acceleration for fuel cycle simulation of molten salt reactor based on multi-group cross section method

The time-consuming issue of transport calculations is prominent in the burnup calculation of nuclear reactor. Multi-Group Cross Section (MGXS) method is an acceleration technique developed based on the characteristics of Monte Carlo simulation, which can significantly reduce the computation time required to solve a single group cross section in transportation calculations. The effectiveness of the method has been verified in the test calculations of water reactor pins. However, liquid molten salt reactors (MSRs) exhibit significant differences from conventional water reactors in terms of neutron energy spectra and fuel cycle mode. The effectiveness of the MGXS method in MSR burnup simulations remains to be validated, and targeted adjustments are required during its application. In this study, OpenMC and ORIGEN2 are coupled to develop an accelerated calculation method for MSR burnup simulations based on the MGXS approach. The reasonable grouping structure of the MGXS method is explored, and the performance of different grouping structures is tested. Results show that the transport calculation can be accelerated by an average factor of 2.4 for a single burnup zone by using MGXS method and the acceleration effect is generally independent of the grouping structure adopted. The nuclide mass bias compared to the traditional direct solution can be reduced to approximately 1% when the fuel burnup is 250MWd/kg for the LEU loading scheme with the 10000 groups structure. For the TRU loading scheme, the mass bias compared to the traditional direct solution of important nuclides (such as U-233, U-235, Pu-239 and so on) can be controlled below 0.5% at a burnup of 230 MW d/kg. The results indicate that the grouping strategy proposed in this study can achieve the adaptation of MGXS to MSRs, and the 10000 groups structure adopted in the study exhibits good accuracy.

Development and verification of an MC/MOC two-step scheme for neutronic analysis of FCM-fueled micro gas-cooled reactor

Gas-cooled microreactors are known for compact designs, high thermal-to-electric efficiencies, long refueling cycles, and flexible deployment capabilities, representing a groundbreaking solution to address the energy requisites of special scenarios. Fully ceramic microencapsulated (FCM) fuel is widely used in gas-cooled microreactors, bringing challenges to neutronic analysis methods. In this paper, an Monte Carlo/Method of Characteristics (MC/MOC) two-step scheme is developed and verified based on the reference case. In this scheme, the continuous-energy Monte Carlo calculations are used for reference calculation and multi-group cross-section generation. The multi-group Monte Carlo calculations are used for multi-group cross-section verification and the MOC solver verification. Fuel multi-group cross-sections are generated with the explicit fuel assembly model by continuous-energy Monte Carlo calculations, and structure multi-group cross-sections are generated with the simplified core model by continuous-energy Monte Carlo calculations. The core calculations are conducted with the MOC calculations. For verification, parameters such as power distribution, neutron spectrum, and control devices worth will be compared. Core calculation results show that the relative errors of MOC results are within −329 pcm, ±5%, ±6%, and ± 2 % for Keff, power distribution, neutron spectrum, and control device worth, separately. Moreover, the computation cost of MOC is only 6.6 % of the reference computation cost. The figure of merit results show that the MC-MOC scheme exhibits improved computational efficiency for neutronic analysis of FCM-fueled micro gas-cooled reactor.

Uncertainty Propagation of Monte Carlo Cross-Section Generation for Graphite-Moderated Pebble Bed Reactors

Monte Carlo codes have become increasingly popular for generating homogenized few-group cross-section data, especially for advanced reactor designs that have complex geometries and nontraditional compositions. However, the stochastic nature of Monte Carlo processes has the potential to introduce additional statistical uncertainties in the overall uncertainty in the prediction of core behavior. The work performed in this research quantified the additional uncertainty introduced by the use of Monte Carlo multigroup cross sections into the analysis of graphite-moderated pebble bed reactors. In this research, the objective was achieved by performing uncertainty quantification for the key output parameters in deterministic steady-state and transient safety calculations. The results show that when the homogenized multigroup cross sections are generated with a sufficient number of neutron histories in the Monte Carlo calculation, the uncertainties in the subsequent deterministic simulations caused by the Monte Carlo cross-section uncertainty are negligible compared to the contributions from the uncertainties of other input parameters.

Monte Carlo Workflow Unification for Nuclear Reactor Analysis with Metamodel-Driven Modeling

Monte Carlo (MC) transport codes are a cornerstone of nuclear reactor analysis frameworks, providing reference solutions and multigroup cross sections, and even as core components in multiphysics couplings. These applications can be seen in toolkits from the Nuclear Energy Advanced Modeling and Simulation program and the U.S. Nuclear Regulatory Commission’s BlueCRAB (Comprehensive Reactor Analysis Bundle). Contrary to their ubiquitousness in reactor physics modeling and simulation, popular MC codes, such as MCNP, Serpent, and KENO, are still reliant on antiquated textual input formats. These input languages use a plethora of keywords with terse syntax to specify all facets of a model, including its geometry, materials, physics settings, and tally options. This poses a steep learning curve and a poor user experience. Being tied to unique text-based input formats also significantly complicates programmatic input generation or modification that may be desired and/or required within a multiphysics framework. This work demonstrates how the development of programmatic interfaces for MC codes can support model unification and translation activities. Building on the Python application program interface (API) development of MCNPy, similar capabilities are being implemented for Serpent that are able to support model translation. In future work, the Serpent API capabilities will be made more robust and the work will be further expanded to include translations with KENO.

Improving tally efficiency and accuracy of multi-group scattering matrix calculations in the Monte Carlo code NECP-MCX

Two issues arise in the calculation of the multi-group scattering matrix when employing a continuous-energy Monte Carlo code for generating homogenized multi-group cross-sections. Firstly, the analog estimator is used to evaluate group-to-group elements, which leads to large statistical uncertainty. Secondly, employing the scalar flux as the weighting function in generating the high-order scattering matrix introduces errors in fast reactor calculations. For the first issue, the repeated collision approach and pre-tabulated cross-section approach are adopted to improve the tally efficiency. For the second issue, the average scattering cosine is calculated based on the conservation of the mean square displacement of neutrons, which is then used to correct the first-order self-scattering cross-section. To evaluate the effectiveness of the above approaches, a PWR pin-cell problem and fast reactor core problems are tested. The results demonstrate that: 1) The figure of merit for multi-group scattering matrix calculations was improved by 8–12 times with the pre-tabulated cross-section approach. 2) Biases of keff were reduced from over 500 pcm to less than 300 pcm when using the corrected self-scattering cross-section. 3) The corrected self-scattering cross-section also yielded higher accuracy for the assembly power calculations, where the maximum biases are reduced from 5 % to 1 %.

Development of neutron-photon coupling transport code IMPC-NP and optimization of method for fabrication of neutron-photon multi-group cross section

This paper introduces a Monte Carlo code IMPC-NP which can realize the simulation of neutron-photon coupling transport. In IMPC-NP, Delta-tracking algorithm and Weight delta-tracking algorithm are used for neutron and photon transport. A new method of fabrication of photon multi-group cross sections named "Scattering merging" is proposed, which is implemented and on IMPC-NP. The results of multiple benchmarks show that the new method can greatly improve the accuracy of neutron and photon calculation in deterministic code.

Study of MOX-fueled VVER-1000 pin cell using [formula omitted]-TRAC with ENDF/B-VIII.0 library

This paper compares the ENDF/B-VIII.0 library for the MOX-fueled VVER-1000 pin cell benchmark with ENDF/B-VII.0 library using the ν-TRAC code and demonstrates the modeling capability of the code. ν-TRAC is a MOC-based code for simulating neutron transport in fuel assembly lattices, with the ability to model cell heterogeneities. The material cross-section significantly impacts neutron transport calculations; therefore, a 172 multigroup cross-section library has been generated using the most recent version of ENDF/B-VIII.0 and the open-source NJOY-2016 code. This nuclear data file includes modifications to the cross-section of major actinides and other light nuclides. Five MOX fuel variants differing in fuel isotopic composition and five states differing in fuel temperature, the moderator, and poison in the moderator are investigated using the most recent library. The impact of new release on the infinite multiplication factor and reactivity change due to the different operating states is studied. Results of ν-TRAC code using multigroup data libraries based on ENDF/B-VIII.0 and ENDF/B-VII.0 are compared with corresponding results from SCALE/SAS2H, HELIOS, and MCU.

Analysis of transport-activation internal coupling method implemented in Monte Carlo code cosRMC

When fusion nuclear reactor is in operation, neutron activation causes a large number of radioisotopes. Activation calculation is a very important step in both of reactor shielding calculation and radiation safety analysis. The capability of transport-activation coupling calculation was developed in Monte Carlo code cosRMC though the built-in burnup solver Depth. In the process of neutron transport, the one-group cross section of activation-related was calculated by internal coupling method and the manipulation and transfer of input file for energy spectrum to external activation code was no longer necessary, which is more efficient and flexible than traditional external coupling. A cuboid iron model is established, and the activation calculation is performed by cosRMC and ALARA respectively. In the constant energy spectrum mode, the relative error of 56Fe atomic density between two codes is 0.0019 %, which verified the accuracy of capability of activation internal coupling calculation in the cosRMC code. The relative errors of 57Fe and 58Fe atomic density are 17.97 % and 36.75 % between constant and variable energy spectrum. This showed that whether energy spectrum remains constant has a significant impact on the results. Moreover, the one-group reaction rate with continuous energy/ multi-group cross section were different, which is because the pre-generated multi-group cross section libraries are independent of the geometry and energy spectrum of the specific problem. The resonance shielding effect of the specific problem cannot be accurately considered when using the multi-group cross section, resulted in relative errors of 60 % for the one-group cross section of 56Fe(n,γ) reaction. cosRMC can directly use the continuous energy method to calculate the problem dependent one-group section, which will give more accurate results.

Generating multi-group cross-sections using continuous-energy Monte Carlo method for fast reactor analysis

The deterministic two-step method, comprising multigroup cross-section generation and core calculation, is widely applied in fast reactor design and analysis. Monte Carlo (MC) methods with continuous energy and fine geometry provide high-precision cross-sections essential for advanced fast reactor neutronics analysis. This paper presents an analysis of integrating MC-generated homogenized cross-sections with various core solvers, demonstrating their effectiveness and potential improvements in fast reactor simulations. For diffusion core calculations, the superhomogénéisation (SPH) technique reduces control rod worth overestimation from 13.5% to 0.35% in the MET-1000 benchmark, improving power distribution predictions. In transport core calculations, the flux-moment homogenization technique (MHT) addresses reactivity overestimation by incorporating cross-section anisotropy, reducing error by 698 pcm. For Method of Characteristics (MOC) core calculations, transport-corrected multigroup cross-sections yield high precision in pin-by-pin power distribution for a 100 MWe lead-based fast reactor benchmark. While MC methods require significant computational resources, such as 62 CPU-hours for the MET-1000 core and 85.5 CPU-hours for the 100 MWe lead-based fast reactor core, they offer flexibility in geometry modeling. This work highlights MC multigroup cross-section generation methods applicable to diffusion, MOC, and transport core calculations for fast reactor analysis, suggesting further exploration into their performance in various reactor parameters and computational efficiency.

Molten Salt Research Reactor (MSRR) shielding analysis using SCALE/MAVRIC sequence with continuous energy and multigroup cross sections

It is necessary to verify (and validate when experimental data are available) shielding codes and methodologies for Molten Salt Reactors (MSRs). This paper examines the impact of using a fine and coarse multigroup cross section library vs. the reference continuous energy data. Molten Salt Research Reactor (MSRR) being developed by the NEXT Research Alliance (NEXTRA) is used as a testbed. Shielding analyses are performed in support of MSRR development using the MAVRIC sequence of the SCALE 6.2.4 code package. The sequence uses deterministic forward and adjoint radiation transport calculations with FW-CADIS methodology to generate variance reduction parameters that are used by MONACO, a fixed source Monte Carlo code. Originally, MONACO was developed as a multigroup code, and a 200-group and 27-group neutron shielding-focused libraries were provided as part of the package. While the 200-group library provides adequate accuracy for many applications, it is highly desirable to confirm this for any specific analysis. In SCALE 6.2, continuous energy capability was implemented in MONACO, thus enabling direct and consistent evaluation and quantification of the impact of using a multigroup rather than the reference continuous energy library. This paper examines the impact of multigroup approximation on main radiation environment parameters in MSRR shielding analysis, including the fast flux and dpa.

Development of multigroup cross section library generation system TPAMS

Kylin-2 is an advanced neutronics lattice code, developed by Nuclear Power Institute of China. High-precision multigroup cross section library is need for KYLIN-2 to carry out simulation of current pressurized water reactor (PWR) and advanced reactor. In this paper a multigroup cross section library generation system named TPAMS was developed, the methods in TPAMS dealing with resonance data such as subgroup parameters, lambda factor, resonance integral were discussed. Moreover, the depletion chain simplification method was studied. TPAMS can produce multigroup library in binary and ASIIC formats, including detailed data contents for resonance, transport and depletion calculations. A multigroup cross section library has been generated for KYLIN-2 based on TPAMS system. The multigroup cross section library was verified through the analysis of various criticality and burnup benchmarks, the values of multiplication factor and isotope density were compared with the experiment data. Numerical results demonstrate the accuracy of the multigroup cross section library and the reliability of the multigroup cross section library generation system TPAMS.

Calculation and analysis of fast neutron fluence of pressure vessel in AP1000 reactor

The structural integrity of the reactor pressure vessel plays an important role in the safe operation of AP1000 nuclear power plant. Radiation damage of fast neutrons is the main factor leading to pressure vessel material deterioration. Therefore, it is necessary to accurately calculate the fast neutron fluence in the pressure vessel. Discrete ordmates method radiation shielding analysis code cosSN is used to calculate fast neutron fluence hi the pressure vessel and the calculation result is compare to measurement of actual AP1000 power plant. Bondarenko method is adopted to calculate multi-group cross section hi resonance energy region, and Bell-Hansen-Sandmeier(BHS) transport correct method is used to deal with anisotropic scattering effect. To improve computational efficiency, cosSN adopts the diffuse comprehensive acceleration and the multi-grid technique to accelerate source iteration, and adopts parallel computing to solve the storage limitations in large-scale calculations. For fast neutron fluence calculation, the calculation uncertainty conies from input parameters and approximation of theoretical model. The results hidicate that the calculated specific activity is conform to the actual measured value of the power plant. The calculation uncertainty is ± 13.28%. which meets the requirements of China domestic energy industry standards NB/T 20576-2019 and NRC RG 1.190.

Overview of Method of ChAracteristics based Neutron TRAnsport Code (MANTRA) and its validation

An in-house computer code MANTRA is developed to solve the neutron transport equation at lattice or assembly level (in 2D) applying Method of Characteristics (MOC) for reactor design calculation. The code has the capability to divide the lattice into triangular meshes. By default, the code assumes constant neutron source inside the meshes. If required, it is possible to use linear source assumption to reduce the number of meshes for speeding up the solution. Using MOC, the solution of transport equation is obtained along a number of parallel lines or rays traced through the meshes in different directions and connect them through reflective or periodic boundary condition. In the code, there is option to choose either Power or Krylov subspace iteration technique to converge the solution with desired accuracy. The code is coupled with multigroup cross section library WIMSD. Performance of MANTRA is tested against a number of benchmark problems and overall good agreement is observed with the results obtained from internationally recognized codes like WIMSD, DRAGON, MCNP etc.

A deep-learning representation of multi-group cross sections in lattice calculations

To compute few-group nodal cross sections, lattice codes must first generate multi-group cross sections using continuous energy cross-section libraries for each material in each fuel cell. Since the processing cost is significant, we propose representing the multi-group cross sections during lattice calculations using a pre-trained deep-learning-based model. The model utilizes a combination of Principal Component Analysis (PCA) and fully connected Neural Networks (NN). The model is specifically designed to manage extensive multi-group cross-section data sets, which contain data for several dozen nuclides and encompass more than 50 energy groups. Our testing of the trained model on a PWR assembly with a realistic boron letdown curve revealed an average relative error of around 0.1% for both fission and total macroscopic cross sections. The average time required for the model to generate the cross sections was approximately 0.01% of the time needed to execute the cross-section processing module.

Impact of the resonance elastic scattering on reactor-core physics calculation results based on the deterministic method

NECP-Atlas and similar nuclear data processing codes have developed the function of incorporating the resonance elastic scattering effect into the multi-group cross sections and scattering matrices. However, the hyper-fine group method is commonly used in deterministic-based lattice physics codes and whole-core neutronics codes for resonance self-shielding calculations. In this method, the neutron slowing-down equation is established based on the conventional asymptotic scattering model where the neutron up-scattering caused by the resonance elastic scattering is ignored. Consequently, the deterministic codes cannot directly use the multi-group data produced by the nuclear data processing codes. In this paper, a correction factor method is proposed to correct the multi-group cross sections and scattering matrices obtained by the hyper-fine group calculations to consider the resonance elastic scattering. The proposed method has been implemented in the lattice physics code LOCUST. The few-group constants produced by the LOCUST code are provided to reactor-core analysis code SPARK to simulate a CNP-1000 type PWR reactor operated in China. Some core parameters measured during zero-power physics tests at 600 K and operations are analyzed to show the effect of the resonance elastic scattering on the core parameters. The numerical results show that the boron concentration reduces by 10 ∼ 14 ppm at 900 K during operations, which is closer to the measured value and improves the accuracy of reactor-core physics calculation.

Coupled neutronics/thermal-hydraulic analysis of ANTS-100e using MCS/RAST-F two-step code system

The feasibility of using the Monte Carlo code MCS to generate multigroup cross sections for nodal diffusion simulations RAST-F of liquid metal fast reactors is investigated in this paper. The performance of the MCS/RAST-F code system is assessed using steady-state simulations of the ANTS-100e core. The results show good agreement between MCS/RAST-F and MCS reference solutions, with a keff difference of less than 77 pcm and root-mean-square differences in radial and axial power of less than 0.5% and 0.25%, respectively. Furthermore, the MCS/RAST-F reactivity feedback coefficients are within three standard deviations of the MCS coefficients. To validate the internal thermal-hydraulic (TH) feedback capability in RAST-F code, the coupled neutronic/TH1D simulation of ANTS-100e is performed using the case matrix obtained from MCS branch calculations. The results are compared to those obtained using the MARS-LBE system code and show good agreement with relative temperature differences in fuel and coolant of less than 0.8%. This study demonstrates that the MCS/RAST-F code system can produce accurate results for core steady-state neutronic calculations and for coupled neutronic/TH simulations.

Characterization of Fast Neutron Transmission Through an Iron Shield

In this paper we give an analysis of the neutron transmission through an iron sphere using Monte Carlo and transport theory methods based on ENDF/B-VII.1 general purpose library. The motivation for this investigation comes from a well-known deficiency in the iron inelastic data from the older library evaluation (ENDF/B-V), giving a concern for a fast neutron flux underestimation within the reactor pressure vessels. In order to benchmark the next-generation ENDF/B-VI iron data, the U.S. Nuclear Regulatory Commission and the former Czechoslovakian National Research Institute have jointly preformed several experiments in 1990s, addressing neutron leakage spectra obtained for a 252Cf fission source in a centre of an iron sphere. It was shown that the ENDF/B-VI iron cross section, containing several improvements over previous evaluations, will not entirely resolve the neutron spectrum discrepancies observed at high neutron energies. Since safety analyses of reactor pressure vessel embrittlement are often based on neutron transport calculations using specific multigroup cross section libraries, simulation of this benchmark was performed using a hybrid shielding methodology of ADVANTG3.0.3 and MCNP6.1.1b codes. Comparison of calculated and referenced dosimeter activation rates are presented for several "standard" nuclear reactions, often used in reactor pressure vessel dosimetry. For that purpose, the new IRDFF-II special library from the IAEA Nuclear Data Services was used as a reference source of dosimetry cross sections. The MCNP6.1.1b code was used for calculation of reaction rates, which were also compared with previous IRDFF-1.05 special library and general purpose ENDF/B-VII.1 library.

MGGC2.0: A preprocessing code for the multi-group cross section of the fast reactor with ultrafine group library

How to generate the precise broad group cross section is important for the fast reactor design. In this study, a fast reactor multi-group cross-section generation code MGGC2.0 are developed in-house for processing ultrafine group MATXS format library. Validation and verification are performed for MGGC2.0 code by applying the benchmarks of ICSBEP handbook, and the results of MGGC2.0 agree well with that of MCNP. The consistent PN method with critical buckling search is in good agreement that condensed with TWODANT flux and flux moment for the inner core and outer core region. For the radial blanket and reflector, two region approximation method has been applied in MGGC2.0 by using collision Probability Method neutron flux solver. The RBEC-M benchmark was used to verify the power distribution calculation, and the relative error of power distribution comparison with the reference are less than 0.8% in the fuel region and the maximum relative error is 5.58% in the reflector region. Therefore, the precise broad cross section can be generated by MGGC2.0 for fast reactor.

Development of OpenMC/Trivac two-step scheme for fast reactor core neutronics analysis

This research develops an open-source two-step scheme coupling the Monte-Carlo (MC) code OpenMC and the deterministic code Trivac for fast reactor neutronic modeling. The multigroup cross-sections are generated using OpenMC with a complete core model, continuous energy, and high-level heterogeneity. The core calculation is achieved with diffusion or simplified Pn (SPn) solvers in Trivac. The scheme is verified with a 1000 MWth metallic-fueled fast reactor. The MC/diffusion scheme in this work shows good performance in the prediction of core reactivity, sodium void worth, and Doppler constant. The overestimation of MC/SPn is discussed by combining a complete review of MC-based two-step schemes. The SPH correction in control rod assembly can improve significantly the prediction of control rod worth and power distribution. Based on the scheme developed in this research, the SPH correction at a full core level will be verified. The application in depletion, transient, and multiphysics analysis could be developed.

Analysis of the Influence of Energy Group Structure on Iron Shielding Calculation

The energy group structure of a multi-group cross section library matched with a deterministic method has a significant influence on shielding calculation. The complex resonance cross section of Fe-56 has a significant influence on accuracy with different energy group structures when processing multi-group cross section data. In this study, in order to more accurately test the influence of the iron resonance phenomenon on shielding calculations, this group structure is modified by the 199-group with 69 points interpolated into its group boundaries at an energy range from 1.1 keV to 3.1164 MeV. The new 269-group library is then tested with selected SINBAD iron sphere benchmarks and compared with the results of 199-group, 299-group, and 172-group libraries and measurements. Upon analysis, it is shown that the resonance of Fe-56 has a great influence on the accuracy of the calculated leakage. Further, it is noted that the finer the energy group division, the greater the calculated leakage fluctuation, and the deeper the neutron passes through the iron sphere, the larger the calculated leakage fluctuation. This study and its leakage results may provide a good reference for the development of new multi-group structures for present and future shielding design.