Neutron Transport Calculations Research Articles

Neutron transport calculation for Activation Evaluation for Decommissioning of PET cyclotron Facility

In order to evaluate the state of activation in a cyclotron facility used for the radioisotope production of PET diagnostics, we measured the neutron flux by using gold foils and TLDs. Then, the spatial distribution of neutrons and induced activity inside the cyclotron vault were simulated with the Monte Calro calculation code for neutron transport and DCHAIN-SP for activation calculation. The calculated results are in good agreement with measured values within factor 3. Therefore, the adaption of the advanced evaluation procedure for activation level is proved to be important for the planning of decommissioning of these facilities.

Analysis of the WCLL European demo blanket concept in terms of activation and decay heat after exposure to neutron irradiation

This comparative paper describes the activation and decay heat calculations for water-cooled lithium-lead performed part of the EURO fusion WPSAE programme and specifications in comparison to other European DEMO blanket concepts on the basis of using a three-dimensional neutronics calculation model. Results are provided for a range of decay times of interest for maintenance activities, safety and waste management assessments. The study revealed that water-cooled lithium-lead has the highest total decay heat at longer decay times in comparison to the helium-cooled design which has the lowest total decay heat. In addition, major nuclides were identified for water-cooled lithium-lead in W armour, Eurofer, and LiPb. In addition, great attention has been dedicated to the analysis of the decay heat and activity both from the different water-cooled lithium-lead blanket modules for the entire reactor and from each water-cooled lithium-lead blanket module separately. The neutron induced activation and decay heat at shutdown were calculated by the FISPACT code, using the neutron flux densities and spectra that were provided by the preceding MCNP neutron transport calculations.

New evaluation of thermal neutron scattering libraries for light and heavy water

In order to improve the design and safety of thermal nuclear reactors and for verification of criticality safety conditions on systems with significant amount of fissile materials and water, it is necessary to perform high-precision neutron transport calculations and estimate uncertainties of the results. These calculations are based on neutron interaction data distributed in evaluated nuclear data libraries. To improve the evaluations of thermal scattering sub-libraries, we developed a set of thermal neutron scattering cross sections (scattering kernels) for hydrogen bound in light water, and deuterium and oxygen bound in heavy water, in the ENDF-6 format from room temperature up to the critical temperatures of molecular liquids. The new evaluations were generated and processable with NJOY99 and also with NJOY-2012 with minor modifications (updates), and with the new version of NJOY-2016. The new TSL libraries are based on molecular dynamics simulations with GROMACS and recent experimental data, and result in an improvement of the calculation of single neutron scattering quantities. In this work, we discuss the importance of taking into account self-diffusion in liquids to accurately describe the neutron scattering at low neutron energies (quasi-elastic peak problem). To improve modeling of heavy water, it is important to take into account temperature-dependent static structure factors and apply Skold approximation to the coherent inelastic components of the scattering matrix. The usage of the new set of scattering matrices and cross-sections improves the calculation of thermal critical systems moderated and/or reflected with light/heavy water obtained from the International Criticality Safety Benchmark Evaluation Project (ICSBEP) handbook. For example, the use of the new thermal scattering library for heavy water, combined with the ROSFOND-2010 evaluation of the cross sections for deuterium, results in an improvement of the C/E ratio in 48 out of 65 international benchmark cases calculated with the Monte Carlo code MCNP5, in comparison with the existing library based on the ENDF/B-VII.0 evaluation.

Molten salt reactor neutronics and fuel cycle modeling and simulation with SCALE

Current interest in advanced nuclear energy and molten salt reactor (MSR) concepts has enhanced interest in building the tools necessary to analyze these systems. A Python script known as ChemTriton has been developed to simulate equilibrium MSR fuel cycle performance by modeling the changing isotopic composition of an irradiated fuel salt using SCALE for neutron transport and depletion calculations. Improved capabilities in ChemTriton include a generic geometry capable of modeling multi-zone and multi-fluid systems, enhanced time-dependent feed and separations, and a critical concentration search. Although more generally applicable, the capabilities developed to date are illustrated in this paper in three applied problems: (1) simulating the startup of a thorium-based MSR fuel cycle (a likely scenario requires the first of these MSRs to be started without available 233U); (2) determining the effect of the removal of different fission products on MSR operations; and (3) obtaining the equilibrium concentration of a mixed-oxide light-water reactor fuel in a two-stage fuel cycle with a sodium fast reactor. The third problem is chosen to demonstrate versatility in an application to analyze the fuel cycle of a non-MSR system.In the first application, the initial fuel salt compositions fueled with different sources of fissile material are made feasible after (1) removing the associated nonfissile actinides after much of the initial fissile isotopes have burned and (2) optimizing the thorium concentration to maintain a critical configuration without significantly reducing breeding capability. In the second application, noble metal, volatile gas, and rare earth element fission products are shown to have a strong negative effect on criticality in a uranium-fueled thermal-spectrum MSR; their removal significantly increases core lifetime (by 30%) and fuel utilization. In the third application, the fuel of a mixed-oxide light-water reactor approaches an equilibrium composition after 20 depletion steps, demonstrating the potential for the longer time scales required to achieve equilibrium for solid-fueled systems over liquid fuel systems. This time to equilibrium can be reduced by starting with an initial fuel composition closer to that of the equilibrium fuel, reducing the need to handle time-dependent fuel compositions.

Nuclear-data uncertainty propagations in burnup calculation for the PWR assembly

In this paper, our home-developed lattice code NECP-CACTI has been implemented into our UNICORN code to perform sensitivity and uncertainty analysis for the lattice calculations. The verified multigroup cross-section perturbation model and methods of the sensitivity and uncertainty analysis are established and applied to different lattice codes in UNICORN. As DRAGON5.0 and NECP-CACTI are available for the lattice calculations in UNICORN now, the effects of different neutronics methods (including methods for the neutron-transport and resonance self-shielding calculations) on the results of sensitivity and uncertainty analysis were studied in this paper. Based on NECP-CACTI, uncertainty analysis using the statistical sampling method has been performed to the burnup calculation for the fresh-fueled TMI-1 assembly, propagating the nuclear-data uncertainties to k∞ and two-group constants of the lattice calculation with depletions. As results shown, for different neutronics methods, it can be observed that different methods of the neutron-transport calculation introduce no differences to the results of sensitivity and uncertainty analysis, while different methods of the resonance self-shielding calculation would impact the results. With depletions of the TMI-1 assembly, for k∞, the relative uncertainty varies between 0.45% and 0.60%; for two-group constants, the largest variation is between 0.35% and 2.56% for vΣf,2. Moreover, the most significant contributors to the uncertainty of k∞ and two-group constants varied with depletions are determined.

Simulation of a sodium fast core: Effect of B1 leakage models on group constant generation

Due to their complexity, neutronic calculations are usually performed in two steps. Once the neutron transport equation has been solved over the elementary domains that compose the core (cells or assemblies with translation or reflexion boundary conditions), a set of parameters – namely macroscopic cross sections and potentially diffusion coefficients – are generated in order to model the whole core as a simplified problem which is often treated in diffusion theory.The first calculation being over a periodic lattice of cells or assemblies, leakage between different domains of the core and out of the lattice needs to be explicitly taken into account by an additional term that must be added in the neutron transport equation. For historical reasons, the leakage term is in most cases modeled by a homogeneous and isotropic probability within a “homogeneous leakage model” that is compatible with the classical collision probability method often used to solve the neutron transport equation. Driven by technological innovation in the field of computer science, “heterogeneous leakage models” have been developed and implemented in several neutron transport calculation codes.The present work discusses the effect of the leakage model used for the generation of diffusion parameters on sodium fast reactor diffusion calculations. Homogenized and condensed cross sections as well as diffusion coefficients are calculated for hexagonal sodium fast reactor assemblies using the lattice code DRAGON-3. Three different calculations are performed for each assembly: without taking neutron leakage into account, using the classical homogeneous B1 procedure or with the heterogeneous B1 TIBERE model. Furthermore, a homogeneous core and a simple heterogeneous core are calculated within diffusion theory using the DONJON-5 code and the results are compared with a Monte Carlo calculation.It is shown that, even if a fissile assembly can be calculated without leakage, the heterogeneous TIBERE model is best suited for “cluster calculations” (a fertile or reflector assembly surrounded by fuel assemblies). Moreover, the homogeneous B1 model should be avoided in such calculations since it is not able to handle streaming effects between the different assemblies.

Effect of heat treatment on neutron attenuation characteristics of high density concretes (HDC)

In nuclear reactor and fuel cycle facilities, apart from ordinary concrete (2300 kg/m3) various special types of concrete of density varying in range 3600–4600 kg/m3have been effectively employed to achieve less shielding thickness. Radiation attenuation in concrete mainly depend on types of aggregate used; water to cement ratio, elemental composition and moisture content apart from density of concrete. In addition to this, operating temperature also plays a vital role in deciding its shielding properties due to loss of water content and microcracking. The effect of heat on neutron attenuation properties of HDC upon heat exposure is the scope of the study in this paper. Four types of concrete made of granite and having hematite and steel shots as aggregate were prepared with density varying from 2300 to 4300 kg/m3and exposed to 120 °C for durations (14, 28 and 56 days). Neutron Attenuation Factor (NAF) was obtained from experimental study and compared with results obtained with neutron transport calculations. The results of this study clearly indicate that the sustained and cyclic heat treatment at 120 °C up to 56 days reduced the neutron attenuation factor by a factor of two.

Synchronized forward-adjoint neutron transport using method of characteristics

The method of characteristics has been widely used for neutron transport calculations in lattice physics computations. This method recently has attracted a lot of attention for whole core calculation because of its flexibility in geometry definition and to highly impose parallelization. One area of whole core calculation is perturbation calculation that needs forward-adjoint flux. The objective of the work presented in this paper is to develop a synchronized forward-adjoint neutron transport solver embedding in FAMOC code.FAMOC is a new neutron transport code based on method of characteristics that is currently under development at Shahid Beheshti University (SBU). It is capable of simulating 2D models based on combinatorial geometry with first or second-order surfaces, and a multilevel lattice-universe base geometry model to rectangularly simulate. In this code, the same tracking data is used to compute forward and adjoint average flux. The forward and adjoint effective multiplication factor, and flux obtained by FAMOC code for 2D benchmark of C5G7 were found to be in good agreement with references.

An optimally diffusive Coarse Mesh Finite Difference method to accelerate neutron transport calculations

A new optimally diffusive Coarse Mesh Finite Difference (odCMFD) method is proposed. The new method generalizes the Coarse Mesh Finite Difference (CMFD) and partial current-based CMFD (pCMFD) methods by adding an artificial term to the diffusion coefficient. The standard CMFD and pCMFD methods preserve the net current and partial currents respectively and can greatly reduce the spectral radius for solving neutron transport problems. Linearized Fourier analysis shows that these methods essentially differ only by the definition of the diffusion coefficient – the pCMFD diffusion coefficient contains an additional “artificial” term, usually taken to be ¼ the coarse mesh size. In this paper, the magnitude of the artificially diffusive term is numerically investigated and optimized using Fourier analysis. The results show that the optimal coefficient increases as the coarse cell optical thickness increases. Also, the optimal value is always smaller than the pCMFD value. This indicates that the pCMFD method overcorrects the diffusion coefficient which increases the spectral radius. A simple polynomial fitting was found for implementing the odCMFD in the MPACT code to perform calculations for realistic problems. Numerical MPACT results for a two-region homogeneous problem, a 2D C5G7 problem, a VERA problem 5 and a 2D BWR Peach Bottom Unit 2 core problem agree well with the Fourier analysis and confirm previous research results that: (1) CMFD converges faster than pCMFD for optically thin coarse grids, but CMFD diverges for optically thick coarse grids; (2) pCMFD is unconditionally stable for all coarse grids; and show that the newly proposed odCMFD is the most efficient among these three methods for all cases. The new method has a similar convergence rate as CMFD for optically thin coarse grids, is faster than both CMFD and pCMFD for coarse grids with intermediate optical thickness, and is unconditionally stable and faster than pCMFD for optically thick coarse grids.

Shutdown dose rate analysis with CAD geometry, Cartesian/tetrahedral mesh, and advanced variance reduction

In fusion energy systems (FES) high-energy neutrons born from burning plasma activate system components to form radionuclides. The biological dose rate that results from photons emitted by these radionuclides after shutdown—the shutdown dose rate (SDR)—must be quantified for maintenance planning. This can be done using the Rigorous Two-Step (R2S) method, which involves separate neutron and photon transport calculations, coupled by a nuclear inventory analysis code. The geometric complexity and highly attenuating configuration of FES motivates the use of CAD geometry and advanced variance reduction for this analysis.An R2S workflow has been created with the new capability of performing SDR analysis directly from CAD geometry with Cartesian or tetrahedral meshes and with biased photon source sampling, enabling the use of the Consistent Adjoint Driven Importance Sampling (CADIS) variance reduction technique. This workflow has been validated with the Frascati Neutron Generator (FNG)-ITER SDR benchmark using both Cartesian and tetrahedral meshes and both unbiased and biased photon source sampling. All results are within 20.4% of experimental values, which constitutes satisfactory agreement. Photon transport using CADIS is demonstrated to yield speedups as high as 8.5·105 for problems using the FNG geometry.

Improvement of core design of small pebble bed reactor with accumulative fuel loading scheme

Innovative nuclear power plant designs and high-efficiency utilization of nuclear fuel are important issues in the field of nuclear power. Pebble bed reactors with an accumulative fuel loading scheme have been introduced to obtain high burnup and efficient uranium utilization. Monte Carlo codes, MVP/MVP-BURN, were used to perform the neutron transport and burnup calculation. Optimum fuel composition was obtained in the finite geometry using 6-g HM of uranium per pebble ball with 20% 235U enrichment. The results show that the maximum burnup was 223GWd/t with 10.2years of operation. However, a large amount of excess reactivity occurred in the initial condition. One of the options for minimizing this was to reduce the enrichment of 235U from 20% to 3.42%, only for the initial condition. The result showed a relatively small amount of excess reactivity during the operation period. However, the maximum burnup decreased to 199GWd/t with 8years of operation.

Dancoff factor analysis for pebble bed fluoride salt cooled high temperature reactor

In this work, an analytical expression based on a two-region spherical model for a High Temperature Gas cooled Reactor (HTGR), is applied to a Pebble Bed Fluoride salt cooled High temperature Reactor (PB-FHR) to calculate the average Dancoff factor for fuel kernel with various coated particle densities. The results are compared with those obtained by the Monte Carlo (MC) method. It is found that there is a good agreement between the analytical and MC, which implies that the two-region spherical model for the Dancoff factor calculation is applicable to PB-FHR. The Dancoff factors with and without FLiBe salt are both evaluated and compared to analyze the influence of FLiBe salt with different numbers of coated particles. The Dancoff factor with FLiBe salt is smaller than that without FLiBe salt from ∼ 11% to ∼ 3% when the number of coated particles in a fuel pebble increases from 5000 to 60,000. In addition, the effects of temperature and volume fraction of FLiBe salt on Dancoff factor are analyzed. Afterwards, the sensitivity of the infinite multiplication factor (k∞) to the Dancoff factor for a fuel cell of PB-FHR is further analyzed by the neutron transport calculation with a new developed routine. It is found that the infinite multiplication factor increases almost linearly with the increase of Dancoff factor, and a higher density of coated particles will lead to a sharper variation of k∞ with Dancoff factor.

Analysis of the ITER computational shielding benchmark with the Monte Carlo TRIPOLI-4® neutron gamma coupled calculations

With the growing interest in using the continuous-energy TRIPOLI-4® Monte Carlo radiation transport code for ITER applications, a key issue that arises is whether or not the released TRIPOLI-4 code and its associated nuclear data libraries are verified and validated for the D–T fusion neutronics calculations. Previous published benchmark results of TRIPOLI-4 code on the ITER related activities have concentrated on the first wall loading, the reactor dosimetry, the nuclear heating, and the tritium breeding ratio. To enhance the TRIPOLI-4 verification and validation on neutron-gamma coupled calculations for fusion device application, the computational ITER shielding benchmark of M. E. Sawan was performed in this work by using the 2013 released TRIPOLI-4.9S code and the associated CEA-V5.1.1 data library. First wall, blanket, vacuum vessel and toroidal field magnet of the inboard and outboard components were fully modelled in this 1-D toroidal cylindrical benchmark. The 14.1MeV source neutrons were sampled from a uniform isotropic distribution in the plasma zone. Nuclear responses including neutron and gamma fluxes, nuclear heating, and material damage indicator were benchmarked against previous published results. The capabilities of the TRIPOLI-4 code on the evaluation of above physics parameters were presented. The nuclear data library from the new FENDL-3.0 evaluation was also benchmarked against the CEA-V5.1.1 results for the neutron transport calculations. The results show that both data libraries can be run with TRIPOLI-4 for the fusion neutronics study. This work also demonstrates that the “safety factors” concept is necessary in the nuclear analyses of ITER.

Neutronic study of extended DONES irradiation module

IFMIF is considered as one of the main pillars in the international fusion program. Its double deuteron beam 125mA each will produce enough rate of damage behind the lithium target to make available in a few years information on materials damage at DEMO relevant doses. Furthermore the stripping reaction D-Li will produce in Fe-based materials under study a production of He and H similar to those expected in fusion reactor. DONES (DEMO Oriented Neutron Source) has been conceived as a simplified IFMIF-like plant to provide in a reduced time scale and with a reduced budget – both compared to IFMIF- the basic information on materials damage.In this work, radiation conditions behind the irradiation module, the so-called High Flux Test Module (HFTM), are analyzed with a double objective. First objective is to assess the impact of the second irradiation module on the material irradiation effects in the HFTM due to its potential use as optimization tool for the damage dose and gas production in the specimens. Second objective is to assess on the potential use of that volume for irradiation of additional specimens beyond the HFTM. Then, neutron transport calculations have been performed in order to evaluate the impact on the irradiation effects on the HFTM and to determine the radiation level in the experimental samples of the new module.

Reactor Dosimetry Aspects of the Service Life Extension of the Hungarian Paks NPP

The service life of the Hungarian Paks Nuclear Power Plant (NPP) will be extended from the originally planned 30 years to 50 years. To improve the reliability of the results obtained in frame of the old reactor pressure vessel (RPV) surveillance programme, new methods have been developed, and based on them, the old exposition data have been re-evaluated for all the four reactor units. At the same time, a new RPV surveillance programme has been developed and introduced, and long term irradiations have been performed to determine the radiation damage of the surveillance specimens due to the high fast neutron exposition. Neutron transport calculations have been performed with a validated neutron transport code system to determine the fast neutron exposition of the RPVs during the extended service life. The cavity dosimetry is in the introductory phase. This paper presents the new developments in the field of the RPV surveillance dosimetry and summarises the results obtained. According to the results the service life of the NPP can safely be extended for the planned 50 years.

Modernization of Cross Section Library for VVER-1000 Type Reactors Internals and Pressure Vessel Dosimetry

The broad-group library BGL1000_B7 for neutron and gamma transport calculations in VVER-1000 internals, RPV and shielding was carried out on a base of fine-group library v7-200n47g from SCALE-6 system. The comparison of the library BGL1000_B7 with the library v7-200n47g and the library BGL1000 (the latter is using for VVER-1000 calculations) is demonstrated on several calculation and experimental tests.

Impact of nuclear data on sodium-cooled fast reactor calculations

Neutron transport and depletion calculations are performed in combination with various nuclear data libraries in order to assess the impact of nuclear data on safety-relevant parameters of sodium-cooled fast reactors. These calculations are supplemented by systematic uncertainty analyses with respect to nuclear data. Analysed quantities are the multiplication factor and nuclide densities as a function of burn-up and the Doppler and Na-void reactivity coefficients at begin of cycle. While ENDF/B-VII.0 / -VII.1 yield rather consistent results, larger discrepancies are observed between the JEFF libraries. While the newest evaluation, JEFF-3.2, agrees with the ENDF/B-VII libraries, the JEFF-3.1.2 library yields significant larger multiplication factors.

Competing Energy Lookup Algorithms in Monte Carlo Neutron Transport Calculations and Their Optimization on CPU and Intel MIC Architectures

The Monte Carlo method is a common and accurate way to model neutron transport with minimal approximations. However, such method is rather time-consuming due to its slow convergence rate. More specifically, the energy lookup process for cross sections can take up to 80% of overall computing time and therefore becomes an important performance hotspot. Several optimization solutions have been already proposed: unionized grid, hashing and fractional cascading methods. In this paper we revisit those algorithms for both CPU and manycore (Intel MIC) architectures and introduce vectorized versions. Tests are performed with the PATMOS Monte Carlo prototype, and algorithms are evaluated and compared in terms of time performance and memory usage. Results show that significant speedup can be achieved over the conventional binary search on both CPU and Intel MIC. Further optimization with vectorization instructions has been proved very efficient on Intel MIC architecture due to its 512-bit Vector Processing Unit (VPU); on CPU this improvement is limited by the smaller VPU width.

Approaches to Accounting and Prediction of Fast Neutron Fluence on VVER Pressure Vessels for Estimation of RPV Residual Lifetime in Compliance with Russian Utility's Procedure

The Paper describes a new Russian Utility's regulatory document (RD EO) which has been recently developed and implemented since the beginning of 2013. This RD EO includes the procedure of RPV FNF monitoring and provides recommendations on how to predict fluence over the design lifetime taking into account results of FNF monitoring. The basic method of RPV neutron fluence monitoring is neutron transport calculations of FR in the vicinity of the RPV. Reliability of the calculation results should be validated by ex-vessel neutron-activation measurements, which were performed during different fuel cycles with different core loadings including new types of fuel.

Validation of VHTRC calculation benchmark of critical experiment using the MCB code

The calculation benchmark problem Very High Temperature Reactor Critical (VHTR) a pin-in-block type core critical assembly has been investigated with the Monte Carlo Burnup (MCB) code in order to validate the latest version of Nuclear Data Library based on ENDF format. Executed benchmark has been made on the basis of VHTR benchmark available from the International Handbook of Evaluated Reactor Physics Benchmark Experiments. This benchmark is useful for verifying the discrepancies in keff values between various libraries and experimental values. This allows to improve accuracy of the neutron transport calculations that may help in designing the high performance commercial VHTRs. Almost all safety parameters depend on the accuracy of neutron transport calculation results that, in turn depend on the accuracy of nuclear data libraries. Thus, evaluation of the libraries applicability to VHTR modelling is one of the important subjects. We compared the numerical experiment results with experimental measurements using two versions of available nuclear data (ENDF-B-VII.1 and JEFF-3.2) prepared for required temperatures. Calculations have been performed with the MCB code which allows to obtain very precise representation of complex VHTR geometry, including the double heterogeneity of a fuel element. In this paper, together with impact of nuclear data, we discuss also the impact of different lattice modelling inside the fuel pins. The discrepancies of keff have been successfully observed and show good agreement with each other and with the experimental data within the 1 σ range of the experimental uncertainty. Because some propagated discrepancies observed, we proposed appropriate corrections in experimental constants which can improve the reactivity coefficient dependency. Obtained results confirm the accuracy of the new Nuclear Data Libraries.