Multigroup Transport Calculations Research Articles

Goal-based angular adaptivity with contributon theory for the discrete ordinates transport equation

A goal-based angular adaptivity has been described for solving the discrete ordinates transport equation. This method uses the linear discontinuous finite element quadrature sets, allowing for local angular refinement across space-energy dimensions. Anisotropy quantified factor derived by contributon theory is introduced in this adaptivity to locate spatial regions that require more angular unknowns in every energy group for a given goal region. The goal-based error metric is considered to trigger local refinement in angle, which requires the solutions of the contributon transport equation to determine the importance to a user-defined functional. Several problems that include both one-group and multi-group transport calculations are displayed to demonstrate the effectiveness of this method. Results indicate that our goal-based adaptivity can significantly reduce computational expenses in terms of angular unknowns and computational times for a similar accuracy, as compared to uniform quadrature sets. It is expected that this adaptivity has the potential to enhance the efficiency of an even wider range of transport problems.

Development of multi-group Monte-Carlo transport and depletion coupling calculation method and verification with metal-fueled fast reactor

Development of multi-group Monte-Carlo transport and depletion coupling calculation method and verification with metal-fueled fast reactor

Analysis of the fine-mesh subgroup method and its feasible improvement

The fine-mesh subgroup method (FSM) is proposed to treat the significant resonance self-shielding effect both effectively and accurately. Similar to the ultra-fine group method, the fine-mesh subgroup method adopts a fine group structure on the resonance energy range to avoid the extra resonance interference effect correction. To improve the efficiency, on the one hand, the one-group micro-level optimization is adopted, so the subgroup fixed-source equations will be only calculated on a certain number of pre-determined subgroup levels, and an interpolation process is employed to obtain the actual subgroup flux. On the other hand, the slowing-down calculation is carried out for group condensation for multigroup transport calculation. The main theory and feasible improvements of the fine-mesh subgroup method are analyzed in this paper. Several pin cell and lattice problems are applied to test the performance of the fine-mesh subgroup method, and the particle swarm optimization method is adopted to find the better group structure. The numerical results indicate a good performance both for accuracy and efficiency.

STRAUM-MATXST: A code system for multi-group neutron-gamma coupled transport calculation with unstructured tetrahedral meshes

In this paper, a new multi-group neutron-gamma transport calculation code system STRAUM-MATXST for complicated geometrical problems is introduced and its development status including numerical tests is presented. In this code system, the MATXST (MATXS-based Cross Section Processor for SN Transport) code generates multi-group neutron and gamma cross sections by processing MATXS format libraries generated using NJOY and the STRAUM (SN Transport for Radiation Analysis with Unstructured Meshes) code performs multi-group neutron-gamma coupled transport calculation using tetrahedral meshes. In particular, this work presents the recent implementation and its test results of the Krylov subspace methods (i.e., Bi-CGSTAB and GMRES(m)) with preconditioners using DSA (Diffusion Synthetic Acceleration) and TSA (Transport Synthetic Acceleration). In addition, the Krylov subspace methods for accelerating the energy-group coupling iteration through thermal up-scatterings are implemented with new multi-group block DSA and TSA preconditioners in STRAUM.

ACE-FRENDY-CBZ: a new neutronics analysis sequence using multi-group neutron transport calculations

ABSTARCT We propose a new neutronics analysis sequence using multi-group neutron transport calculations named ACE-FRENDY-CBZ. This sequence is free from uses of any application libraries; with the ACE files as the starting point, multi-group cross sections of media comprising a target system are calculated with the FRENDY code, and multi-group neutron transport calculations are performed with modules of the CBZ code system. The ACE-FRENDY-CBZ sequence was tested against the eight fast neutron systems, and good agreement in the neutron multiplication factors with the reference Monte Carlo results was obtained within 20 pcm differences in the bare systems and within 60 pcm differences in the reflected systems. It was also found that the adoption of the consistent P approximation increases the errors. In order to investigate this issue, we adopted the sub-group method to calculate spatially-dependent current-weighted total cross sections in the reflector regions, and it was suggested that the uses of the spatially-dependent cross sections with the consistent P approximation has a possibility to further improve the numerical accuracy.

Development and verification of neutron and photon multi-group cross sections processing code TXMAT2.0

TXMAT2.0 is an in-house code for processing neutron and photon cross sections from the MATXS format nuclear library, which provides multi-group macroscopic cross sections for transport and diffusion calculations. In developing the program, three improvements have been made in the code. First, TXMAT2.0 adopts Fortran2003 based on object-oriented programming techniques and uses allocatable memory management techniques. Second, TXMAT2.0 is capable of processing the ultrafine group (2082 groups) library using these memory management techniques; in comparison, the officially released TRANSX2.15 has difficulty with this task. Finally, TXMAT2.0 handles correctly self-shielding corrections for light nuclides such as 12C, 16O, whereas TRANSX 2.15 experiences problems. In performing the verification and validation of TXMAT2.0, ICSBEP benchmarks for criticality verification, and OKTAVIAN and IPPE benchmarks for shielding verification were selected. Several results were compared with results obtained from TRANSX2.15 as well as with experimental data. The results show that the accuracy of TXMAT2.0 is as good as TRANSX2.15. Moreover, TXMAT2.0 provides accurate neutron and photon cross sections for multi-group transport calculations. In addition, through the verification of a self-designed benchmark, TXMAT2.0 processes effectively and correctly self-shielding problems of light nuclides.

Convergence study of CMFD based acceleration schemes for multi-group transport calculations with fission source using fourier analysis

Application of the coarse mesh finite difference (CMFD) method and its variants to accelerate the convergence of criticality calculations has been extremely popular for neutron transport simulations. Despite their widespread use in the multi-group form, the convergence performance of these acceleration schemes is usually studied in the one-group domain and results extended to multi-group problems. Theoretical investigation of the convergence behavior of multi-group CMFD and related methods has not been previously performed and is an important work to complement existing studies. In this paper, we present the Fourier convergence analysis of multi-group CMFD, partial current CMFD (pCMFD), optimally diffusive CMFD (odCMFD) and linear prolongation CMFD (lpCMFD) schemes for acceleration of the fission source neutron transport calculations. The multi-group formulation of the error iteration matrix has been found to be analogous to the results obtained from one-group analysis. It has also been shown that for certain simplified cases, the spectral radius of multi-group CMFD is independent of the group coupling terms and can be determined as the maximum among individual energy groups. The results extend current understanding and provide deeper insight into the application of CMFD based acceleration techniques for more realistic multi-group neutron transport.

A new hexagonal-Z nodal SN method in SARAX code system

Multigroup transport calculation has become the preferred choice instead of diffusion calculation in the fast reactor core analysis due to the strong anisotropy in hard spectrum. Thus, a stable and efficient transport solver is crucial for fast reactor core-analysis. In this paper, a new hexagonal-Z nodal SN method is proposed. The advantages (improvements) mainly include a more stable and efficient nodal response relation, a simple but effective method for the high-order transverse leakages treatment, the acceleration methods, and the hybrid parallelization. Based on the algorithms, a code named DNTH has been developed in the SARAX code system. Three fast reactor cores including the small-size KNK-2 core, the medium-size CEFR core and the large-size BN-600 core were calculated. The numerical results showed that good accuracy could be achieved by the method, and the efficiency was obviously improved thanks to its stable convergence performance, the acceleration methods and the parallel schemes.

Effect and treatment of angular dependency of multi-group total cross section and anisotropic scattering in fine-mesh transport calculation

The whole core heterogeneous high-fidelity transport calculation is widely researched recently, where the spatial meshes reach sub-pin level to provide accurate results. In this context, two issues, namely angular dependency of total cross section and anisotropic scattering, which greatly affect the precision of multi-group transport calculation are assessed in this paper. Two pin cell problems respectively fueled with UO2 and MOX are calculated. The numerical results show that neglecting angular dependency of total cross section leads to over-estimation of flux in resonance groups in fuel pellet and under-estimation of eigenvalue. Using angular-flux-weighted total cross sections can effectively reduce the error of flux in resonance groups. For UO2 fuel pin cell, angular dependency of total cross section is more important than anisotropic scattering. While for MOX fuel pin cell, anisotropic scattering is more important. And then SPH method and a newly developed method called auxiliary term method are introduced and tested on UO2 and MOX pin cell and 3×3 super cell with control rod. The numerical results show that both of these two methods are capable of capturing the effect of the angular dependency of total cross section. The accuracies of the methods are comparable.

Improvement and optimization of the pseudo-resonant-nuclide subgroup method in NECP-X

The pseudo-resonant-nuclide subgroup method is a newly emerged self-shielding calculation method to treat resonance interference effect. It has been implemented in the NECP-X code which is developed for the high-fidelity neutronics calculation. Though this method has high accuracy, its computation time occupies more than half of the total computation time (mainly including resonance self-shielding calculation, multi-group transport calculation and depletion calculation). To improve the efficiency of the resonance self-shielding calculation, some analysis and optimization are performed in several aspects: firstly, the maximum number of subgroups is reduced from 7 to 5; secondly, the number of dilution cross section points is reduced from 21 to 9; thirdly, the number of fuel meshes in solving SFSE is reduced from 15 to 5; finally, number of fuel meshes in solving one-group fixed-source equation for the SPH factor is reduced from 15 to 1. The acceleration ratio of the self-shielding calculation is 3.45 for assembly without poison and 3.49 for assembly with poison. The time proportion of self-shielding calculation is reduced to less than 30%. The accuracy loss is negligible in the accelerations. Besides, it is found that the subgroup condensation scheme can obtain better self-shielded cross sections of component resonant nuclides than the dilution interpolation scheme.

A genetic algorithm for multigroup energy structure search

The generation of multigroup neutron cross-section libraries is a key issue of the multigroup transport calculations in reactor physics. The correct choice of the boundaries of the energy groups, in particular, is decisive for obtaining reliable results. Knowledge of the reactor physics, general and specific of the studied reactor, along with long and refined analyses are required for finding out a reasonable energy structure, which is specific for the considered reactor and might be unsuitable for other systems. The genetic algorithm presented in this work aims to choose the most appropriate energy structure for the considered system to collapse a fine multigroup library into a few-groups one, usable for transient transport calculations. The user is free to choose the number of energy groups of the final library, which is in direct relation with the precision required and the time available for the simulation. The methodology is coupled with SIMMER-III code and applied to 3 reactor systems: ESNII+ ASTRID, ESFR and MSFR. The results show that the algorithm can find representative energy structures, providing accurate results on the multiplication factor. The results of each test are analyzed, showing how different compositions, geometries and neutron spectra guide the algorithm choices, so demonstrating the effectiveness of the method.

A NOVEL APPROACH TO FIND OPTIMIZED NEUTRON ENERGY GROUP STRUCTURE IN MOX THERMAL LATTICES USING SWARM INTELLIGENCE

Energy group structure has a significant effect on the results of multigroup transport calculations. It is known that UO2–PUO2 (MOX) is a recently developed fuel which consumes recycled plutonium. For such fuel which contains various resonant nuclides, the selection of energy group structure is more crucial comparing to the UO2 fuels. In this paper, in order to improve the accuracy of the integral results in MOX thermal lattices calculated by WIMSD-5B code, a swarm intelligence method is employed to optimize the energy group structure of WIMS library. In this process, the NJOY code system is used to generate the 69 group cross sections of WIMS code for the specified energy structure. In addition, the multiplication factor and spectral indices are compared against the results of continuous energy MCNP-4C code for evaluating the energy group structure. Calculations performed in four different types of H2O moderated UO2–PuO2 (MOX) lattices show that the optimized energy structure obtains more accurate results in comparison with the WIMS original structure.

An Adaptive Energy Mesh Constructor for Multigroup Library Generation for Transport Codes

Users’ demands for multigroup transport calculations are wide and diverse, encompassing routine, rough, and fast calculations as well as very precise simulations. For these reasons, the use of accurate and efficient multigroup cross-section libraries is needed. In this work, we present an adaptive energy mesh constructor (AEMC) that builds a multigroup mesh from predefined requisites of precision and calculation time. For a given self-shielding model and number of groups, AEMC looks for the optimal bounds of a multigroup mesh that minimizes the errors of the multigroup transport solutions for a predefined set of infinite homogeneous medium problems. We have applied this methodology to define two energy meshes for fast sodium reactor applications: a 600-group mesh associated with an extension of the Livolant-Jeanpierre self-shielding method and a 1200-group mesh based on subgroup self-shielding. Tests in homogeneous media prove that the multigroup solutions are almost equivalent to Monte Carlo simulations. Simplified one-dimensional transport calculations confirm the accuracy of the 1200-group mesh and show that this mesh provides a precision similar to that obtained with the well-validated 1968-group ECCO mesh. The same tests reveal that the 600-group mesh optimized for subgroup self-shielding offers a good compromise between simulation time and precision.

3次元詳細メッシュ多群輸送計算に基づくPWR 炉心計算コードSCOPE2 の開発 (9) 動特性計算機能の実装

3次元詳細メッシュ多群輸送計算に基づくPWR 炉心計算コードSCOPE2 の開発 (9) 動特性計算機能の実装

Discontinuity factors for non-multiplying material in two-dimensional hexagonal reactor geometry

On the basis of methods developed recently for square-fuel-assembly reactor cores, discontinuity factors for hexagonal VVER (Russian PWR) control absorbers and reflector nodes have been derived. Partial currents from heterogeneous multi-group transport calculations are used for the determination of the discontinuity factors. As shown by suitable benchmark calculations, the application of these quantities in the two-group nodal diffusion code DYN3D clearly improves the results of assembly-power predictions. The advantage of reflector diffusion parameters, including discontinuity factors, over conventional albedos has been demonstrated.

Object-Oriented Three-Dimensional Fine-Mesh Transport Calculation on Parallel/Distributed Environments for Advanced Reactor Core Analyses

This paper describes a comprehensive study on the feasibility of advanced reactor core analyses within the framework of pin-by-pin multigroup transport calculations using a prototype of the object-oriented parallel core calculation code SCOPE. The SCOPE code enables the coupling of the diffusion theory method and the SPN transport theory method. The formulation of the method coupling and its verifications with benchmarks are presented.Quantitative estimation of the pin-cell homogenization effects within the octant core geometry of a three-loop-type pressurized water reactor (PWR) was performed. Comparisons between results by heterogeneous and homogeneous calculations revealed the effects on pin-cell homogenization in large-scale geometry. In order to preserve the neutronic property in the heterogeneous calculation within the framework of pin-cell homogenized pin-by-pin calculations, the applicability of the homogenized cross section corrected by the superhomogénéisation SPH method was studied. It was found that the pin-by-pin nine-group calculation by the SP3 transport theory method with the SPH-corrected cross sections gave good accuracy for the pin power distribution approximately <1% of the root-mean-square error. The calculation accuracy of the transport calculation and the effectiveness of the method coupling were also demonstrated through analyses of the initial core of an identical three-loop-type PWR.With fine-grained parallelism, the identical convergence property was obtained regardless of the number of processors. Parallel performance was almost scalable up to eight processors, 93% with eight processors in three-dimensional nine-group fine-mesh transport calculations with meshes of 180 × 180 × 30.

A Diffusion Iterative Model for Simulation of Reactivity Devices in Pressurized Heavy Water Reactors

A diffusion iterative scheme has been developed to analyze the basic three-dimensional supercell problem encountered in pressurized heavy water reactors (PHWRs). Multigroup transport calculations are performed essentially in one dimension for the fuel cluster cell and the reactivity device (RD) supercell problems. Iterative diffusion calculations are done in one and two dimensions such that the net transport leakages into the fuel cluster or RD are reproduced. The few-group parameters of the fuel cluster or the boundary conditions on the RD surface are modified for this purpose. With these modifications, the three-dimensional supercell problem is treated by diffusion theory. The accuracy of the new scheme is demonstrated against the corresponding transport solutions in both one and three dimensions

SIMULATE-3 Pin Power Reconstruction: Methodology and Benchmarking

Pin power reconstruction capability has recently been added to the SIMULATE-3 nodal rector analysis code. Detailed descriptions of the models employed are presented. This reconstruction method is based on single-assembly (not colorset) form functions, and a detailed treatment of spectral interaction between assemblies is introduced. This pin power reconstruction method produces accurate calculation of pin powers throughout depletion and fuel shuffling. Comparisons with multigroup transport calculations and with measured critical assembly power distributions demonstrate that the pin power reconstruction method is comparable in accuracy to fine-mesh methods. The high numerical efficiency of the reconstruction method permits economical calculation of three-dimensional pin power distributions in light water reactors.

Fusion nuclear systems design and analysis

Conceptual design of a power-producing fusion-fission hybrid reactor was carried out based on the new concept of the blanket containing equilibrium fissile fuel. The blanket safety performance was analysed on residual heat removal and accidental criticality. The concept of a direct enrichment fusion breeder blanket using UO 2 powder was also presented and studied. The impact of uncertainties in neutron cross section data on design parameters such as tritium breeding ratio was analysed including the uncertainties of the secondary angular and energy distribution of neutrons. The uncertainty of the tritium breeding ratio due to cross-sections is about 6% for a commercial tokamak reactor. The errors of the design parameters due to the approximations in the multigroup transport calculation were also quantitatively estimated. The methods for the analyses were developed. The computer codes for nuclear analysis and design were developed. Those are: (1) BISON for one-dimensional transport and burnup calculation, (2) SUSD for the cross section sensitivity and uncertainty analysis, (3) TRISTAN for three-dimensional radiation transport calculation and (4) MEDUSA-IB for one-dimensional hydrodynamic calculation of the implosion and thermonuclear burn of an ion beam driven ICF target.

Accuracy of Multi-Group Transport Calculation in D-T Fusion Neutronics

Both multi-group and point (continuous energy) Monte Carlo calculations have been performed on two types of benchmark problems, and the results have been compared to investigate the accuracy of the multi-group transport calculations in D-T fusion neutronics. In the multi-group calculations, space dependent self-shielding factors were used. As the first benchmark problem, spheres of four materials were analyzed. The discrepancy in the total fluxes obtained by the multi-group and point calculations was small in the lithium sphere, but it was great in the regions composed of iron. Nuclear design calculations of two types of fusion reactor blankets were performed as the second benchmark problem. The tritium breeding ratios obtained by the multi-group calculations agreed well with those obtained by the point calculations. However, the total fluxes in the reflectors or in the shields and the fast neutron leakage fluxes from the inboard shield were greatly underestimated by the multi-group calculations.