Three-dimensional Neutron Transport Research Articles

A First collision source method using spherical harmonics method for arbitrary shape and order finite element mesh

The discrete ordinates (SN) method is a highly effective and accurate angular discretization method for the neutron transport equation, but suffers from the inherent ray effect in low-scattering regions. The first collision source (FCS) method employing the methods without ray effect to obtain the uncollided flux is a common ray effect mitigation technique. In this paper, a novel FCS method using the spherical harmonics (PN) method to calculate the uncollided flux is proposed. The PN for the first collision source (PN-FCS) method possesses distinctive advantages in several aspects: (1) it can be applied in the problem containing reflective boundary conditions that are difficult to handle with traditional FCS method, (2) it uses the discontinuous Galerkin method to perform spatial discretization, and thus can be easily applied in arbitrary shape and order finite element meshes, (3) it can be effectively calculated in parallel on distributed meshes, (4) the accuracy and computational cost can be flexibly adjusted. Besides, the filter technique is adopted to improve the performance of the PN method in stream-dominated regions. The PN-FCS method has been implemented in two- and three-dimensional neutron transport code and tested by various testing problems. Numerical results show that the PN-FCS method can effectively mitigate the ray effect.

Gamma ray diagnostics for high time resolution measurement in large helical device

A 1-inch LaBr3:Ce gamma ray scintillation detector, characterized by high time and energy resolution, was installed to advance energetic particle physics studies in Large Helical Device (LHD). We reduced the size of the scintillator from 3 inches to 1 inch to reinforce the radiation shielding to reduce the unwanted signal in the detector induced by fast neutrons and stray gamma rays according to the commissioning results. The radiation shielding composed of 10% borated polyethylene and lead was redesigned to suppress the gamma-ray induced signal based on the Monte Carlo three-dimensional neutron and gamma-ray transport code MCNP6. We increased the lead thickness from 50 mm to 77.5 mm to suppress the stray gamma ray effect. The gamma ray spectrum was measured in the hydrogen neutral beam heated deuterium plasma with 6LiF pellet injection. We might obtain a gamma ray peak near 0.48 MeV due to the 6Li(d,p'γ)7Li reaction.

Goal-Oriented Mesh Adaptivity of Three-Dimensional Neutron Transport Calculation Using Weighted Difference Scheme and Dual-Weighted Residual Error Indicators

Maintaining a reasonable balance between computational accuracy and overhead is important for neutron transport simulations of engineering problems. This paper presents a goal-oriented mesh adaptive algorithm applied to the multigroup discrete ordinates equation for fixed source and criticality problems. The dual-weighted residual (DWR) approach estimates numerical solution errors and drives local mesh refinement for specific targets, such as detector response, integral flux, and multiplication factor. We employ a reconstruction method to evaluate the spatial residuals of the fluxes obtained by the weighted difference scheme. To improve the performance of adaptive algorithms, new estimation models are proposed for adjoint fluxes needed by the DWR theory, including a regional goal model for fixed source problems and an inconsistent fission source model for k-eigenvalue problems. Additionally, we analyze the impact of the truncation of flux reconstruction and isotropic approximation of adjoint fluxes on grid error indicators and adaptive calculations. Numerical results demonstrate that for the quantities of interest, our adaptive approach saves more than 70% of computational effort and run time when obtaining a level of high accuracy comparable to that of uniform fine grids.

Spherical Harmonics and Discontinuous Galerkin Finite Element Methods for the Three-Dimensional Neutron Transport Equation: Application to Core and Lattice Calculation

The spherical harmonics or PN method is intended to approximate the neutron angular flux by a linear combination of spherical harmonics of degree at most . In this work, the PN method is combined with the discontinuous Galerkin (DG) finite elements method and yield to a full discretization of the multigroup neutron transport equation. The employed method is able to handle all geometries describing the fuel elements without any simplification nor homogenization. Moreover, the use of the matrix assembly-free method avoids building large sparse matrices, which enables producing high-order solutions in a small computational time and less storage usage. The resulting transport solver, called NYMO, has a wide range of applications; it can be used for a core calculation as well as for a precise 281-group lattice calculation accounting for anisotropic scattering. To assess the accuracy of this numerical scheme, it is applied to a three-dimensional (3-D) reactor core and fuel assembly calculations. These calculations point out that the proposed PN -DG method is capable of producing precise solutions, while the developed solver is able to handle complex 3-D core and assembly geometries.

Dosimetry data from fuel channel clips for benchmarking a new computational fluid dynamics model in neutron transport

Accurate neutron transport models for BWRs are needed to characterize neutron damage to the top guide, top guide cylinder, vessel nozzles, and to other upper internals. In the past, neutron transport calculations above top-of-active-fuel (TAF) have had large uncertainties (well in excess of ± 20%) mainly due to the fact that the steam density distribution in that region is not well known. An advanced three-dimensional (3D) neutron transport model, which incorporates computational fluid dynamics (CFD) in the code suite, has been developed. Retrospective dosimetry measurements were made to benchmark the transport results. Six fuel channel clips were removed from the top of the fuel bundles, and small disk-shaped dosimetry samples were cut from the clips. The cuts were made through the Inconel spring and through the stainless steel clip body. The clips were selected from bundles that cover regions of low, intermediate, and high steam density. The average C/M ratio for the 10 dosimeters is 1.06. It has been shown that all of the calculated dosimeter activities fall within ± 20% of the measurement. This meets the criterion set by RG 1.190 [1] for acceptability of the calculations.

Determination of the Activity Inventory in the Structural Components of the Dalat Nuclear Research Reactor for Its Decommissioning Planning

This report presents the methods and calculated results of the activity inventory in the structural components of the Dalat Nuclear Research Reactor (DNRR). These components include the shielding concrete, the reactor tank, and its inside irradiated facilities; the thermal and thermalizing columns; and the horizontal channels. The MCNP5 code with a three-dimensional neutron transport model was used to calculate the neutron flux distribution, neutron energy spectrum at different locations, and activation cross sections of long-lived radioactive nuclides in activated major materials, including heavy concrete, reflection graphite, and aluminum of the reactor. The calculated results of the energy spectrum and activation cross sections of MCNP5 were used in the ORIGEN2.1 point depletion code to calculate the neutron-induced activity of activated materials at different time points by modeling the irradiation history and radioactive decay. Radioactivity of long-lived key activation products such as 41Ca, 60Co, 55Fe, 63Ni, and 152Eu was modeled, and volumes of radioactive waste mainly of ordinary concrete, graphite, and aluminum in the structural components of the reactor were estimated. Experimental results of neutron flux and specific activities of some typical nuclides such as 60Co, 152Eu, 55Fe, and 63Ni in activated aluminum samples showed good agreement with the calculated results. As part of the national regulation requirements, the obtained data have been used to develop the decommissioning plan for the operational DNRR, with an estimation of about 10 years before its permanent shutdown.

Development of a GPU-based three-dimensional neutron transport code

A GPU-based three-dimensional (3D) neutron transport code, named ThorMOC, is developed in this work. A GPU-parallelized transport sweeping algorithm based on a planar method of characteristics (MOC) is implemented in ThorMOC and a two-level coarse mesh finite difference (CMFD) method is used to accelerate the convergence of the MOC transport solution. To reduce the memory burden of 3D calculation, the transport sweeping algorithm is improved by azimuthal angle decomposition. This developed ThorMOC code is verified by a Takeda benchmark and a C5G7 3D extension benchmark, and the performance of the azimuthal angle decomposition algorithm is evaluated by the whole core calculation of a C5G7 hexagonal benchmark. The numerical results obtained from ThorMOC show a good agreement with those from the Monte Carlo code OpenMC. Besides, the azimuthal angle decomposition algorithm can reduce the GPU storage requirement by more than 40% for the C5G7 hexagonal benchmark.

Evaluation of neutron flux distribution in structural components and activation products in aluminum alloy at 13-2 channel of the DNRR

The estimation of radiological properties of activated structural components of a nuclear reactor due to irradiation of neutron produced by fission is a very important task for radiation safety and reasonable cost of dismantling and radioactive waste management in the decommissioning plan of the reactor. In this work, the calculation approach was carried out by using three-dimensional neutron transport model with the Monte Carlo code MCNP5 to evaluate neutron fluxes and reaction rates. The Bateman equation was solved with neutron absorption reactions (fission and capture) and disintegration by ORIGEN2 code to obtain the activity of materials in reactor structures. This paper presents the evaluation results of the neutron flux distribution and the radioactivity of long-lived key activation products such as 60Co, 55Fe, 59Ni, 63Ni, etc. isotopes in the structural components of the Dalat Nuclear Research Reactor (DNRR). The validation of calculation methodology of the two codes was implemented by comparing calculation results with measured neutron fluxes at irradiation positions in the reactor core as well as specific activities at the bottom part of the aluminum guiding tube at 13-2 channel, which has been removed from the reactor core about six years. The calculation results were in good agreement under 7% difference with the experimental neutron flux value of (6.05±0.52) × 1012 n/cm2.s, and under 33% difference with the experimental specific activities of 60Co isotope being 1.86×104, 9.99×104, and 1.28×105 Bq/g at the positions of -32.5, -17.5 and -2.1 cm (the centerline of the reactor core is at 0 cm), respectively, in the aluminum guiding tube of irradiation channel 13-2. The neutron flux distributions in other structural components such as the graphite reflector, thermal column, thermalizing column, concrete shielding, etc. of the reactor were also evaluated. The obtained calculation results and experimental data are very valuable for the development of a suitable decommissioning plan and a reasonable dismantling strategy for the DNRR.

Third order adjoint sensitivity analysis of reaction rate responses in a multiplying nuclear system with source

Until recently, the 2nd-order sensitivities of reactor physics model responses to the nuclear data characterizing the respective model were impractical to compute exactly and exhaustively, because of the so-called “curse of dimensionality.” Hence, the effects of the 2nd-order sensitivities on the uncertainties produced in responses by the uncertain nuclear data have been routinely neglected. Recently, the author has developed a general 2nd-order adjoint sensitivity analysis methodology which overcame the “curse of dimensionality” to perform the first-ever complete computation of the exact 21,976 first-order, and 482,944,576 s-order sensitivities for a OECD/NEA reactor physics benchmark response to the uncertain nuclear data that characterize the neutron transport computational model of this benchmark. In particular, the numerical results obtained for the benchmark’s leakage response with respect to the benchmark’s group-averaged isotopic total cross sections indicated that, contrary to the widely held belief that the 2nd-order response sensitivities in reactor physics systems are negligible, the opposite turned out to be the case, i.e., many of the 2nd-order sensitivities were orders of magnitude larger than the corresponding 1st-order ones. Consequently, neglecting the 2nd-order sensitivities would cause very large non-conservative errors by under-reporting the response variance and erroneously reporting its expected value.The fact that a large number of 2nd-order response sensitivities are significantly larger than the 1st-order sensitivities has motivated the development of the general expressions presented in this work for the efficient and exact computation of the 3rd-order response sensitivities of reaction rate responses to nuclear data for subcritical reactor physics systems modeled by the neutron transport equation. The mathematical results derived in this work are currently implemented in production-oriented three-dimensional neutron transport code systems to enable the computation of 3rd-order sensitivities of reactor physics systems, commencing with the OECD/NEA benchmark mentioned above.

Developing 3D neutron transport kernel for heterogeneous structures in an improved method of characteristic (MOC) framework

Given the importance and complexity of the three-dimensional (3D) neutron transport equation solution, in the current research, a new Modular Ray Tracing (MRT) Algorithm and 3D characteristic kernel for heterogeneous structures are presented. Improvement of memory management and cache coherency are achieved to some acceptable level. Also, parallel implementation of transport algorithm utilizing OpenMP, cause significant reduction in runtime.To validate our Algorithm, first, a self-constituted pin cell and a lattice arrangement are modeled and results are compared with Monte-Carlo simulation. Second, the well-known 3D benchmark, Takeda model one and two, are investigated and results compared with the well-known MPACT code. Also, as a reliable trial, the obtained multiplication factors from the forward and adjoint form of MOC kernel are investigated. Meanwhile, for the multiplication factor, we achieved 3.5800E-04 and 3.3924E-04 |Δkeffkeff| the difference with Takeda reference models one and two respectively. Also, the maximum speedup that our parallel algorithm gained for the Takeda benchmark is 5.13.

Nuclear analysis of the Water cooled lithium lead DEMO reactor

In the frame of the EUROfusion roadmap, the development of a conceptual design for the Demonstration Fusion Power Reactor (DEMO), beyond ITER, is a key issue. The DEMO reactor shall guarantee the tritium self-sufficiency, generate electricity and operate as a test facility for the fusion power plant relevant technologies, such as the breeding blanket (BB). The Water Cooled Lithium Lead (WCLL) concept has been chosen as a candidate for the DEMO BB: it relies on liquid Lithium Lead as breeder and neutron multiplier, Eurofer as structural material and pressurized water as coolant.A detailed MCNP model of the latest WCLL BB layout has been generated and integrated in the DEMO MCNP generic model suitably designed for neutronic analyses. Three-dimensional neutron and gamma transport simulations have been carried out by means the MCNP Monte Carlo code and JEFF nuclear data libraries in order to assess the WCLL-DEMO performances in terms of tritium self-sufficiency and shielding effectiveness to protect the vacuum vessel and the toroidal field coils. Moreover, the impact on the Tritium production of the water content in the first wall (FW) and the effect of its pressure/temperature has been addressed.The outcomes of the present study provide guidelines for the optimization of the WCLL DEMO reactor nuclear performances through the assessment of the loads on sensitive components and the estimation of its potential tritium generation capabilities.

Neutronic analyses in support of the conceptual design of the DTT tokamak radial neutron camera

Abstract The Divertor Tokamak Test (DTT) facility, whose design phase is currently under finalization, is an Italian project aimed to investigate alternative power exhaust solutions for DEMO. It is designed to operate with significant power loads and enough flexibility to test innovative divertor configurations, different plasma edge and bulk conditions approaching, as much as possible, those planned for DEMO. Among the neutron diagnostics, a multi-channel neutron camera, most likely equipped with the liquid scintillators NE213, is foreseen to provide spatially resolved measurements of several plasma parameters needed for fusion power estimation, plasma control and plasma physics studies. This paper presents a preliminary study performed in support of the DTT neutron camera design. A detailed MCNP model representing a 20° sector of the machine integrating its main components and detectors assemblies has been developed and used for this study. Three-dimensional neutron transport simulations have been carried out by means of the MCNP Monte Carlo code coupled with the FENDL nuclear data libraries. The diagnostic design was optimized starting from the assessment of the expected detector performances obtained by using the calculated neutron fluxes and spectra and the NE213 response functions. The outcomes of this analysis provide the detectors requirements and guidelines for the development of the above-mentioned diagnostics, investigating its feasibility and suitability with the neutron emissivity foreseen for the DTT operational scenarios.

Nuclear analysis of the Single Module Segment WCLL DEMO

The latest design of the Water Cooled Lithium Lead blanket for the European DEMO reactor is based on a Single Module Segment (SMS) concept for the blanket segments: the removal of the gaps between the modules (present in the former Multi Module structure design), with the consequent reduction of the neutron streaming, improves the tritium production and the shielding capabilities. A nuclear analysis has been carried out with the Monte Carlo N-Particle transport code version 5 (MCNP5) and the Joint Evaluated Fission and Fusion nuclear data libraries version 3.2 (JEFF 3.2). A detailed three-dimensional MCNP DEMO model with the Single Module layout has been generated. Three-dimensional neutron and gamma transport simulations have been carried out in order to assess the tritium production, nuclear power deposition in each subcomponent of the blanket and nuclear heating density, neutron flux, neutron damage (dpa) and Helium production, relevant for the design of the system. The results confirm the fulfilment of tritium self-sufficiency and shielding requirements of DEMO. Furthermore, a parametric analysis has been carried out by varying the thickness of the first wall tungsten layer to evaluate how the blanket performances are influenced by the tungsten layer thickness.

Hybrid Monte Carlo-deterministic method for 3D neutron transport simulation based on energy region division

Monte Carlo (MC) and deterministic methods are widely used for neutron transport simulation. The MC method computes with an accurate description of geometry and cross section but with a long execution time, while the deterministic method has higher computational efficiency but poor accuracy, especially in the resonance energy range. To achieve both high efficiency and accuracy, a hybrid MC-deterministic method was developed for three-dimensional neutron transport simulation based on SuperMC. Using a directly delivered scattering source, the simulation was conducted in the fast region by the deterministic method, resonance region by the MC method, and thermal region by the deterministic method. Detailed analysis was conducted to verify the performance of the hybrid method. Based on the fixed-source case and criticality case, higher accuracy of the hybrid method compared to the deterministic method and better acceleration performance compared to the MC method was confirmed.

Application of the Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology to Compute First- and Second-Order Sensitivities of Flux Functionals in a Multiplying System with Source

This work presents an application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to the neutron transport Boltzmann equation that models a multiplying subcritical system comprising a nonfission neutron source to compute efficiently and exactly all of the first- and second-order functional derivatives (sensitivities) of a detector’s response to all of the model’s parameters, including isotopic number densities, microscopic cross sections, fission spectrum, sources, and detector response function. As indicated by the general theoretical considerations underlying the 2nd-ASAM, the number of computations required to obtain the first and second orders increases linearly in augmented Hilbert spaces as opposed to increasing exponentially in the original Hilbert space. The results presented in this work are currently being implemented in several production-oriented three-dimensional neutron transport code systems for analyzing specific subcritical systems.

Assessment of the Lagrange Discrete Ordinates Equations for Three-Dimensional Neutron Transport

The Lagrange Discrete Ordinates (LDO) equations, developed by Ahrens as an alternative to the traditional discrete ordinates formulation, have been implemented in Denovo, a three-dimensional radiation transport code developed by Oak Ridge National Laboratory. The LDO equations retain the formal structure of the classical discrete ordinates equations but treat particle scattering in a different way. Solutions of the LDO equations have an interpolatory structure such that the angular flux can be naturally evaluated at directions other than the discrete ordinates used in arriving at the solutions, and the ordinates themselves may be chosen in a strategic way for the problem under consideration. Of particular interest is that the LDO equations have been shown to mitigate ray effects at increased angular resolutions. In this paper we present scalar flux solutions of the LDO equations for a small number of test cases of interest and compare the results against flux solutions generated using standard quadrature types. The LDO equations’ flux solutions were found to be comparable to those resultant from the standard quadrature types in value; results from the LDO equations were also found to be commensurate with those of standard quadrature types when comparing the flux solutions in the context of the experimental benchmark test case examined.

Neutronic analyses in support of the WCLL DEMO design development

In the frame of the EUROfusion Consortium programme, the Water Cooled Lithium Lead (WCLL) option has been chosen as a candidate for the breeding blanket (BB) of the European fusion power demonstration plant (DEMO) conceptual design. Neutronic analyses play a fundamental role in the development of the WCLL blanket, providing guidelines for its design based on the evaluation of the nuclear performances.A detailed three-dimensional MCNP model of the latest WCLL layout has been generated and integrated in a DEMO MCNP generic model suitably designed for neutronic analyses. Three-dimensional neutron and gamma transport simulations have been performed using the MCNP5v1.6 Monte Carlo code and JEFF 3.2 nuclear data libraries, in order to assess the WCLL-DEMO tritium self-sufficiency and the shielding capabilities of the breeding blanket/manifold system to protect the vacuum vessel and toroidal field coils. Furthermore, radial profiles of the neutron flux, nuclear heating, neutron damage and he-production have been assessed in the inboard and outboard equatorial planes.The outcome of the present study highlights the potential and suitability of the WCLL breeding blanket for the application to DEMO, both in terms of tritium production and shielding performances.

In situ calibration of neutron activation system on the large helical device.

In situ calibration of the neutron activation system on the Large Helical Device (LHD) was performed by using an intense 252Cf neutron source. To simulate a ring-shaped neutron source, we installed a railway inside the LHD vacuum vessel and made a train loaded with the 252Cf source run along a typical magnetic axis position. Three activation capsules loaded with thirty pieces of indium foils stacked with total mass of approximately 18 g were prepared. Each capsule was irradiated over 15 h while the train was circulating. The activation response coefficient (9.4 ± 1.2) × 10-8 of 115In(n, n')115mIn reaction obtained from the experiment is in good agreement with results from three-dimensional neutron transport calculations using the Monte Carlo neutron transport simulation code 6. The activation response coefficients of 2.45 MeV birth neutron and secondary 14.1 MeV neutron from deuterium plasma were evaluated from the activation response coefficient obtained in this calibration experiment with results from three-dimensional neutron calculations using the Monte Carlo neutron transport simulation code 6.

A new approach to three-dimensional neutron transport solution based on the method of characteristics and linear axial approximation

A new approach based on the method of characteristics (MOC) is proposed to solve the neutron transport equation. A new three-dimensional (3D) spatial discretization is applied to avoid the instability issue of the transverse leakage iteration of the traditional 2D/1D approach. In this new approach, the axial and radial variables are discretized in two different ways: the linear expansion is performed in the axial direction, then, the 3D solution of the angular flux is transformed to be the planar solution of 2D angular expansion moments, which are solved by the planar MOC sweeping. Based on the boundary and interface continuity conditions, the 2D expansion moment solution is equivalently transformed to be the solution of the axially averaged angular flux. Using the piecewise averaged angular flux at the top and bottom surfaces of 3D meshes, the planes are coupled to give the 3D angular flux distribution. The 3D CMFD linear system is established from the surface net current of every 3D pin-mesh to accelerate the convergence of power iteration. The STREAM code is extended to be capable of handling 3D problems based on the new approach. Several benchmarks are tested to verify its feasibility and accuracy, including the 3D homogeneous benchmarks and heterogeneous benchmarks. The computational sensitivity is discussed. The results show good accuracy in all tests. With the CMFD acceleration, the convergence is stable. In addition, a pin-cell problem with void gap is calculated. This shows the advantage compared to the traditional 2D/1D MOC methods.

三次元中性子輸送・燃焼計算に基づくBWR使用済燃料内の中性子源核種<sup>242</sup>Cm・<sup>244</sup>Cm組成および中性子放出率の分布

Distributions of the TRU nuclide composition in spent fuels are important for radiation-shielding analyses in their storage and transport. In this research, detailed three-dimensional distributions of 242Cm and 244Cm compositions as the main neutron sources in spent fuel assemblies (BWR 8×8 and 9×9 types) were calculated with the three-dimensional neutron transport and fuel burnup code system. The distributions of 242Cm and 244Cm compositions become heterogeneous as fuel burnup increases. Horizontally, the distributions of both compositions in the fuel assemblies always show peaks at the corner rods. Vertically, in the corner rod, the distributions show peaks on the bottom nodes at the initial burnup, and the peak node gradually moves upward as fuel burnup increases until the fuel assemblies are unloaded. For example, in a 9×9 type fuel assembly at the final burnup (55 MWd/kgU), the horizontal peak ratio of the 244Cm composition was 1.78 at the corner rod and its vertical peak ratio was 1.67 on the upper node. 242Cm and 244Cm compositions mainly contribute to neutron emission rates in spent fuel. Accordingly, it is rational to consider those heterogeneous distributions for the neutron-shielding evaluation of spent fuels of higher burnup.