Continuous-energy Monte Carlo Code Research Articles

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 %.

Feasibility Study on Production of High-Purity Rhenium-185 by Nuclear Transmutation of Natural Tantalum

Rhenium-186 (Re-186) has attracted attention as a medical isotope. The feasibility of producing Re-185, the raw material for Re-186, using a fast reactor was evaluated using a continuous energy Monte Carlo code. The irradiation of natural tantalum (Ta) in the fast reactor can produce Re-185 with an isotopic purity of 99%. A two-step irradiation process with different moderators was found to improve the production rate of Re-185. Specifically, this can be achieved by using zirconium hydride (ZrH1.7) as a moderator in the first transmutation process from natural Ta to tungsten (W), and then zirconium deuteride (ZrD1.7) as a moderator in the second transmutation process from W to Re-185. Due to the two-step irradiation, the production rate of Re-185 from Ta can be increased up to a maximum of 470 times compared with irradiation without a moderator, and 2.3 g of Re-185 can be obtained from 1571 g of Ta in 1 year of irradiation. The proposed isotope production method is a new method that is different from the conventional electromagnetic enrichment process.

Research on the calculation method of sensitivity coefficients of reactor power to material density based on Monte Carlo perturbation theory

The ability to calculate the material density sensitivity coefficients of power with respect to the material density has broad application prospects for accelerating Monte Carlo-Thermal Hydraulics iterations. The second-order material density sensitivity coefficients for the general Monte Carlo score have been derived based on the differential operator sampling method in this paper, and the calculation of the sensitivity coefficients of cell power scores with respect to the material density has been realized in continuous-energy Monte Carlo code RMC. Based on the power-density sensitivity coefficients, the sensitivity coefficients of power scores to some other physical quantities, such as power-boron concentration coefficients and power-temperature coefficients considering only the thermal expansion, were subsequently calculated. The effectiveness of the proposed method is demonstrated in the power-density coefficients problems of the pressurized water reactor (PWR) moderator and the heat pipe reactor (HPR) reflectors. The calculations were carried out using RMC and the ENDF/B-VII.1 neutron nuclear data. It is shown that the calculated sensitivity coefficients can be used to predict the power scores accurately over a wide range of boron concentration of the PWR moderator and a wide range of temperature of HPR reflectors.

Criticality Evaluation During Fuel Debris Particle Sedimentation Using Coupled DEM-MPS Code

From the viewpoint of criticality management in the fuel debris retrieval operation at the Fukushima Daiichi Nuclear Power Station, it is important in criticality safety analyses to consider the behavior of fuel debris particles as they fall into the water, given that the neutron moderation condition of the fuel debris can dramatically change. In this study, we evaluated a reactivity insertion while fuel debris particles dropped into the water. Specifically, we considered the effects of the fuel debris particle-size distribution in either an erroneous operation or a postulated accident in the fuel debris retrieval operation. Three types of fuel debris particle-size distribution were assumed: monodisperse, uniform, and Rosin-Rammler. The behaviors of the fuel debris particles during sedimentation were evaluated using the coupled Distinct Element Method–Moving Particle Simulation (DEM-MPS) code. The multiplication factors corresponding to the behaviors of the falling fuel debris were calculated by a continuous-energy Monte Carlo code MVP3.0 with JENDL-4.0. Consequently, the multiplication factors changed with the particle motions during the sedimentation, and the trends of the multiplication factors differed between the particle-size distributions. Especially, the 2-cm monodisperse particle-size distribution showed the highest multiplication factor during sedimentation, the trend of which differed from the others in the fuel debris particles dispersing and piled-up phases in the water.

High-Performance and High-Fidelity GPU-Based Monte Carlo Solutions to the BEAVRS Benchmark

The BEAVRS benchmark is solved by PRAGMA, the graphics processing unit (GPU)–based continuous-energy Monte Carlo code. The solutions consist of the detailed simulation results for the two cycles that involve the reactivity and pin power distribution information for the zero-power physics tests and depletion. Primary results at hot zero power, such as the critical boron concentration at various rodded conditions, control rod bank worth, isothermal temperature coefficients, and assemblywise detector signal, are compared with the measured data. Core-follow calculations are performed with varied power, and the resulting boron letdown curves are compared with the measured one. Hot full-power depletion is also performed and the resulting pinwise power distributions of cycle 1 are compared with the nTRACER results. The comparison with the measured data and also with the nTRACER results demonstrates the high solution fidelity of PRAGMA. In all the calculations, PRAGMA uses a tremendously large number of histories, ranging from up to hundreds of millions per cycle, that are used to fully exploit the massive parallel computing capacity of GPUs. The execution time of the entire core-follow calculation with about 30 burnup steps takes less than 16 h on a single rack of computing nodes mounted with 24 gaming GPUs, which represents considerably high Monte Carlo core calculation performance.

Multiphysics Analysis System for Heat Pipe–Cooled Micro Reactors Employing PRAGMA-OpenFOAM-ANLHTP

A multiphysics analysis system for neutronics/thermomechanical/heat pipe thermal analysis of heat pipe–cooled micro reactors was developed using the PRAGMA code as the neutronics engine. PRAGMA, which was developed as a graphics processing unit (GPU)-based continuous-energy Monte Carlo code for power reactor applications, now has an extended geometry package to handle geometries with unstructured meshes generated by Coreform Cubit. The NVIDIA ray-tracing engine OptiX has been exploited for efficient neutron transport on unstructured mesh geometry. On the multiphysics side, the open-source computational fluid dynamics tool OpenFOAM and one-dimensional heat pipe analysis code ANLHTP have been adopted. The manager-worker system based on the message passing interface dynamic process management model enables efficient coupling of codes employing different parallelization schemes. With all the features, the multiphysics analysis of the 60-deg symmetrical sector model of the MegaPower three-dimensional core was performed for normal operation and heat pipe–failed conditions. The multiphysics coupling run time was about 2.5 h, in which the Monte Carlo simulation employing more than 10 billion histories was performed within half an hour on a single rack of computing nodes mounted with 24 NVIDIA Quadro GPUs. Accordingly, this demonstrates the soundness and robustness of the tightly coupled three-way multiphysics analysis system.

Reactivity Worth Measurement of Calcium Hydride Sample in UTR-KINKI Reactor

Small modular reactors (SMR) using calcium hydride (CaH2) as a moderator have attracted attention due to their passive safety and economic efficiency. In order to design the nuclear design of the SMR, the integral validation of the cross section considering the thermal neutron scattering law(S(α,β)) of CaH2 is necessary. However, there are no integral experiments using CaH2 in the reactor. As the first integral experiment in nuclear reactors, we performed reactivity worth measurements of CaH2 samples in a university training and research reactor (UTR-KINKI) of Kindai University. The measured sample reactivity worth was compared with the results calculated by the continuous energy Monte Carlo code MVP3 and JEFF-3.1, and integral validation of the CaH2 cross section stored in JEFF-3.1 was performed. To obtain the sample reactivity worth components, we carried out perturbation calculations.

Control rods’ position history effect on the Indonesian multipurpose research reactor RSG-GAS operation and safety parameters

The present work extends the analysis of the first working core of RSG-GAS to the burnup calculation. During the fuel management calculations of RSG-GAS, the control rods are usually assumed to be withdrawn from the core. Due to the exclusion of the control rod, it is hypothesized that the integral control rod worth shows significant differences compared to the experimental data. Therefore, a burnup calculation was performed in this study for the first core of RSG-GAS to evaluate the impact of operating control rods. The analyses were performed using continuous-energy Monte Carlo code, Serpent 2, and ENDF-B/VIII.0 nuclear data library for both cases with and without the inclusion of control rods. As a result, it is found that the calculated control rod worth, as well as the excess reactivity at the beginning of the cycle of the RSG-GAS second core from the burnup calculation considering the control rod position, agreed with the experimental data.

Improvement and benchmarking of the deterministic transport calculation code CBZ to design beam shaping assembly for BNCT

The quick and accurate neutron and photon transport calculations are desired in the optimization calculations for the neutron source design, and in the present work, we establish the deterministic neutron and photon transport calculation procedure with the nuclear reactor physics calculation code system CBZ. Numerical calculation conditions are carefully chosen, and the efficient and practical condition is determined. Test calculations are carried out for the simple cylindrical systems with various kinds of neutron moderators, and the results are compared with the reference solutions obtained by the continuous-energy Monte Carlo code PHITS. Generally good agreements are obtained for all the benchmark problems. In addition, another problem with the detailed geometry for the neutron source is prepared. In this realistic problem also, good agreement is obtained between CBZ and PHITS. These results demonstrate the high accuracy of CBZ in the application to the design optimization calculations for the neutron source.

CORE BURN-UP ANALYSIS OF THE RSG-GAS RESEARCH REACTOR USING DETERMINISTIC AND STOCHASTIC METHODSS

Due to several characteristics, such as geometry, compact core, high coolant flow, and high neutron flux, the burn-up study of the RSG-GAS multi-purpose reactor provides challenges when employing a neutronic calculation. For the burn-up analysis, two calculating methodologies are used in the RSG-GAS: deterministic and probabilistic methods. The deterministic codes such as WIMSD-5B and Batan-FUEL are utilized, whereas the continuous-energy Monte Carlo code Serpent 2 is used for the stochastic method. WIMSD-5B is being used to produce a four-group cross-section that is needed by Batan-FUEL to do full core diffusion calculations. Burn-up calculations were performed at the whole fuel assemblies inside the core to see if the deterministic code, WIMSD-5B/Batan-FUEL, could accurately replicate the burn-up behavior of the RSG-GAS research reactor. The Serpent 2 calculation was also done with the exact models to provide a comparison. The results show that both Serpent 2 and WIMSD-5B/Batan-FUEL can perform the RSG-GAS burn-up analysis if appropriate treatments are made to the deterministic codes at both the assembly and core levels. There is a 5% difference in calculated fuel burn-up between deterministic and stochastic approaches.

McCARD/MIG stochastic sampling calculations for nuclear cross section sensitivity and uncertainty analysis

In this study, a cross section stochastic sampling (S.S.) capability is implemented into both the McCARD continuous energy Monte Carlo code and MIG multiple-correlated data sampling code. The ENDF/B-VII.1 covariance data based 30 group cross section sets and the SCALE6 covariance data based 44 group cross section sets are sampled by the MIG code. Through various uncertainty quantification (UQ) benchmark calculations, the McCARD/MIG results are verified to be consistent with the McCARD stand-alone sensitivity/uncertainty (S/U) results and the XSUSA S.S. results. UQ analyses for Three Mile Island Unit 1, Peach Bottom Unit 2, and Kozloduy-6 fuel pin problems are conducted to provide the uncertainties of keff and microscopic and macroscopic cross sections by the McCARD/MIG code system. Moreover, the SNU S/U formulations for uncertainty propagation in a MC depletion analysis are validated through a comparison with the McCARD/MIG S.S. results for the UAM Exercise I-1b burnup benchmark. It is therefore concluded that the SNU formulation based on the S/U method has the capability to accurately estimate the uncertainty propagation in a MC depletion analysis.

Application of dynamic mode decomposition to Rossi-α method in a critical state using file-by-file moving block bootstrap method

ABSTRACT Prompt neutron decay constant in a critical state is useful information to validate the numerically predicted ratio of the point kinetics parameters , where and are the effective delayed neutron fraction and prompt neutron lifetime, respectively. To directly measure in a target critical system, this study proposes the application of the dynamic mode decomposition (DMD) to the reactor noise analysis based on the Rossi- method. The DMD-based Rossi- method enables us to robustly estimate the fundamental mode component of from the Rossi- histograms measured using multiple neutron detectors. Furthermore, the file-by-file moving block bootstrap method is newly proposed for the statistical uncertainty quantification of to prevent huge memory usage when the neutron count rate is high and/or the total measurement time is long. A critical experiment has been conducted at Kyoto University Critical Assembly to demonstrate the proposed method. As a result, the proposed method can uniquely determine the value of which the statistical uncertainty is smallest. By utilizing this experimental result of , numerical results of ratio using the continuous energy Monte Carlo code MCNP6.2 with recent nuclear data libraries, which are processed by the nuclear data processing code FRENDY, are validated.

Neutronic Characteristics of ENDF/B-VIII.0 Compared to ENDF/B-VII.1 for Light-Water Reactor Analysis

The Evaluated Nuclear Data File (ENDF)/B-VIII.0 data library was released in 2018. To assess the new data during development and shortly after release, many validation calculations were performed with static, room-temperature benchmarks. Recently, when performing validation of ENDF/B-VIII.0 for pressurized water reactor depletion calculations, a regression in performance compared to ENDF/B-VII.1 was observed. This paper documents extensive benchmark calculations for light-water reactors performed using continuous energy Monte Carlo code with ENDF/B-VII.1 and -VIII.0 and neutronic characteristics of ENDF/B-VIII.0 are discussed and compared to those of ENDF/B-VII.1. It is our recommendation that ENDF/B data library assessment should include reactor-specific benchmark assessments, including depletion cases, such that these types of regressions may be caught earlier in the data development cycle.

Additional Stylized 3-D Benchmark Problem Set Based on the Pin-Fueled SmAHTR

Previous work presented a set of stylized three-dimensional benchmark problems based on the Oak Ridge National Laboratory (ORNL) preconceptual design of a fluoride-salt-cooled small modular advanced high-temperature reactor, or SmAHTR, with prismatic assemblies fueled by tri-isotropic (TRISO) particles. That previous work created a detailed description of the benchmark problems by closing several outstanding design gaps from the ORNL preconceptual design report, notably by addressing the lack of active control mechanisms, for which control rod “bundles” were implemented. In this paper, the creation of two additional stylized benchmark problem sets based on that past work is detailed, offering two new control rod configurations. The fluoride salt, small size, and highly heterogeneous TRISO-fueled pins make these additional benchmark problem sets useful numerical validation references in benchmarking neutronics tools against continuous-energy stochastic Monte Carlo results. Detailed reference results, including the eigenvalue (keff) and 1/11th assembly-averaged relative fission density distributions, are provided for both control rod configurations in full-core cases with all control rods withdrawn and all control rods fully inserted. A near-critical core benchmark problem and results are provided for one configuration. The provided results are calculated using the continuous-energy Monte Carlo code MCNP.

Neutronic Analysis of the European Sodium Fast Reactor: Part II—Burnup Results

Abstract In the framework of the Horizon 2020 project ESFR-SMART (2017–2021), the European sodium fast reactor (ESFR) core was updated through a safety-related modification and optimization of the core design from the earlier FP7 CP-ESFR project (2009–2013). This study is dedicated to neutronic analyses of the improved ESFR core design. The conducted work is reported in two parts. Part I deals with the evaluation of the safety-related neutronic parameters of the fresh beginning-of-life (BOL) core carried out by eight organizations using both continuous energy Monte Carlo and deterministic computer codes. In addition to the neutronics characterization of the core, a special emphasis was put on the calibration and verification of the computational tools involved in the analyses. Part II is devoted to once-through and realistic batchwise burnup calculations aiming at the establishing of the equilibrium core state, which will later serve as a basis for detailed safety analyses.

Neutronic Analysis of the European Sodium Fast Reactor: Part I—Fresh Core Results

Abstract In the framework of the Horizon 2020 project ESFR-SMART (2017-2021), the European Sodium Fast Reactor (ESFR) core was updated through a safety-related modification and optimization of the core design from the earlier FP7 CP-ESFR project (2009-2013). This study is dedicated to neutronic analyses of the improved ESFR core design. The conducted work is reported in two parts. Part I deals with the evaluation of the safety-related neutronic parameters of the fresh Beginning-of-Life (BOL) core carried out by 8 organizations using both continuous energy Monte Carlo and deterministic computer codes. In addition to the neutronics characterization of the core, a special emphasis was put on the calibration and verification of the computational tools involved in the analyses. Part II is devoted to once-through and realistic batch-wise burnup calculations aiming at the establishing of the equilibrium core state, which will later serve as a basis for detailed safety analyses.

Optimization of neutron tracking algorithms for GPU-based continuous energy Monte Carlo calculation

The implementation and optimization strategies of the neutron tracking algorithms in the GPU-based continuous-energy Monte Carlo (MC) code PRAGMA are presented. The strategies consist of 1) a mixed precision technique, 2) an event-based tracking algorithm, 3) the history-based tracking algorithm improved for GPUs by imposing transition limits, 4) the region partitioning and energy sort schemes to vectorize macroscopic cross section calculations, 5) the unionized grid method improved by a linear hashing scheme, and 6) the GPU-specific implementation techniques such as the use of built-in vector types and an array-based race-free bank algorithm utilizing GPU atomic addition. The developed algorithms and strategies are examined for pin cell and full-core problems consisting of fresh and depleted fuels. PRAGMA turned out to be especially efficient in depleted fuel calculation; PRAGMA effectively overcame the performance drop in the depleted fuel calculation by vectorized cross section calculation. In the full-core calculations PRAGMA also rendered outstanding performance; calculations employing 11.5 billion histories and 20 consumer-grade GPUs could be finished within 15 min for a 3D APR1400 fresh core problem, and within half an hour for a mock-up depleted core problem.

Serpent and Monte Carlo Continuous Energy Burnup Code Comparison for Neutronics Calculations of the European Lead-Cooled Fast Reactor

Abstract As part of the generation IV reactors (GENIV), the European lead-cooled fast reactor (ELFR) is one of the most promising candidates to be part of the European energy framework in the near future. Alike most of the GENIV systems, the ELFR is still under development and having reliable computational tools that allow fast and accurate results become an important task in the modeling and simulation levels. In this work, the Serpent code is assessed. Serpent is a continuous-energy Monte Carlo (MC) code suitable for reactor physic calculations and is used for the modeling of the ELFR system. The results were compared with the reference data that were obtained with the Monte Carlo continuous energy burnup code (MCB). In order to verify the ELFR Serpent model, several neutronic parameters were compared to the reference results: the effective neutron multiplication factor (keff), the Doppler constant (KD), the reactivity effect of the coolant density, the effective delayed neutron fraction (βeff), and the effective prompt neutron lifetime (Λ). In addition, the axial and radial power distributions were also obtained and verified. A good approximation between Serpent and MCB values was obtained.

Improvement of sensitivity and uncertainty analysis capabilities of generalized response in Monte Carlo code RMC

The capability of performing nuclear data sensitivity and uncertainty analysis of reaction rates has been developed in continuous-energy Reactor Monte Carlo (RMC) code. The sensitivity coefficients of reaction rates are calculated by using new generalized perturbation theory (GPT) formulation which is also implemented in McCARD. The superhistory based generalized perturbation theory (SH-GPT) formulation is developed in this paper to overcome the huge memory consumption problem encountered by the new GPT formulation. This newly developed capability is tested on several benchmark problems. The sensitivity coefficients are shown to agree within 5% of reference results for most cases. Moreover, the region-specified sensitivity analysis capability enables RMC to be the first continuous-energy Monte Carlo code that can use the first-order uncertainty quantification method to perform uncertainty analysis of the power distribution. The uncertainty results calculated by first-order uncertainty quantification method also agree well with those obtained by using stochastic sampling method.

GENERALIZED SENSITIVITY ANALYSIS CAPABILITY WITH THE DIFFERENTIAL OPERATOR METHOD IN RMC CODE

Sensitivity analysis is an important way for us to know how the input parameters will affect the output of a system. Therefore, recently, there is an increased interest in developing sensitivity analysis methods in continuous-energy Monte Carlo Code due to the fact that Monte Carlo method can perform high-fidelity simulations of nuclear reactor. Previous studies mainly focused on developing sensitivity analysis method suitable for analyze eigenvalue. There are relatively few researches for performing sensitivity analysis of generalized response function by using continuous-energy Monte Carlo code. So, in this work, the differential operator method (DOM) has been investigated and implemented in continuous-energy Reactor Monte Carlo code (RMC) to perform sensitivity analysis of generalized response function in the form of ratios of reaction rate. The DOM implemented in RMC is based on the analog Monte Carlo transport mode and non-analog Monte Carlo transport mode. The correctness of the newly implemented method has been verified by comparing the results with those calculated by using the collision history-based method through the Jezeble and Flattop benchmark problems. In general, the results given by the DOM agree well with those obtained by the collision history-based method with an accuracy of 5%. Moreover, it is also shown that the non-analog Monte Carlo transport mode can obtain lower relative standard deviation of the sensitivity coefficients than the analog Monte Carlo transport mode.