Multigroup Calculations Research Articles

Insights into calculating Reference Discontinuity Factors with Serpent Monte Carlo code

This study explores the calculation of Reference Discontinuity Factors (RDFs) using the Serpent Monte Carlo code, focusing on the methodology and potential pitfalls. In two-step reactor analyses, consistently generated RDFs are crucial for aligning homogeneous nodal diffusion results with the reference heterogeneous transport solution. However, the Serpent internal diffusion solver, based on the Analytic Function Expansion Nodal (AFEN) method, may not be compatible with other nodal methods such as the Nodal Expansion Method (NEM). Additionally, the solver can suffer from instabilities, particularly in multi-group calculations, leading to erroneous RDFs. Despite these challenges, Serpent can generate the necessary raw data for RDF calculation, which can be accurately processed using external diffusion solvers. Two numerical examples − a 1D fuel-reflector model and a 2D SMR core model − illustrate the effects of consistent and inconsistent RDFs on simulation accuracy. The study emphasizes the importance of using compatible diffusion solvers and thoroughly assessing RDFs to avoid errors in reactor simulations.

Generating a system of group constants for neutron-physical calculations of fast reactors based on ROSFOND-2020.2 library files

The subject of constant support development is currently becoming increasingly important in connection with the national strategy of transition to a closed nuclear fuel cycle. At the same time, the importance of the tasks of refining calculation models and minimizing methodological, statistical, and constant errors is increasing. In this connection, the idea of creating a universal system of constants describing with equal accuracy both uranium loading and loading with mixed oxide uranium-plutonium fuel and the possibility to perform on its basis both precision Monte Carlo calculations (data format – ACE) and multigroup calculations (formats – ABBN and ANISN) was laid in the basis of this work. In this paper we analyze the freely available libraries of evaluated nuclear data in order to justify the choice of source files for the formation of a new system of group constants for neutron-physical calculations of fast reactor cores, describe the process of formation of a new library of reactor constants, and verify the obtained system on computational test models of BN-800 reactor and critical systems. The process of formation of the new system of group constants included selection of initial neutron data files, updating of data tables of basic neutron cross-sections, self-shielding factors and Doppler coefficients, as well as data on fission spectra for the main fuel nuclides. The methodological component of the error for test models of the BN-800 core was evaluated. Using the ABBN-RF22 system of group constants it was possible to estimate the correction in the 299 groups calculation, which amounted to 0.3%. Previously, when using the ABBN-93 library, there was no such possibility due to the lack of continuity between the files of evaluated neutron data and the group constants used.

A simplified SP3 NEM solver within a unified formulation for pin-by-pin core multi-group calculations

This study addresses the development and verification of a pin-by-pin core multigroup SP3 solver CTRP-Clouds that employs NEM (Nodal Expansion Method) and three simplified NEM methods within a unified formulation for simultaneously solving the coupling 0th and 2nd SP3 equations. In this work, the solver using this unified formulation does not only include the original NEM and its simplifications but also the EFEN (Exponential Function Expansion Nodal) method and FDM (Finite Difference Method) for the comprehensive evaluation. Also, the solver was accelerated using CMFD (Coarse Mesh Finite Difference) method and parallelized using OpenMP. The computational efficiency of different solution methods was investigated for the 2D KAIST benchmark problems and their modified one for considering 3D extension. The results showed the simplified NEM with flat leakage approximation gives acceptable accuracies of less than 1.2 % in RMS of pin-power discrepancies of all the cases with 1x1 mesh per pin-cell, with a reduction of 20 % computing time compared to the original NEM. Particularly, the calculation time of flat leakage NEM is comparable to EFEN while the pin-wise accuracy is better. Besides, the simplified NEM with 2nd-order flux expansion gives substantially improved accuracy in comparison with FDM within comparable computing time.

Shock cooling emission from explosions of red supergiants: II. An analytic model of deviations from blackbody emission

ABSTRACT Light emission in the first hours and days following core-collapse supernovae (SNe) is dominated by the escape of photons from the expanding shock-heated envelope. In a preceding paper, Paper I, we provided a simple analytic description of the time-dependent luminosity, L, and colour temperature, Tcol, valid up to H recombination (T ≈ 0.7 eV), for explosions of red supergiants with convective polytropic envelopes without significant circumstellar medium (CSM). The analytic description was calibrated against ‘grey’ (frequency-independent) photon diffusion numeric calculations. Here, we present the results of a large set of 1D multigroup (frequency-dependent) calculations, for a wide range of progenitor parameters (mass, radius, core/envelope mass ratios, metalicity) and explosion energies, using opacity tables that we constructed (and made publicly available), including the contributions of bound–bound and bound–free transitions. We provide an analytic description of the small, ${\simeq}10\ \hbox{per cent}$ deviations of the spectrum from blackbody at low frequencies, hν < 3Tcol, and an improved (over Paper I) description of ‘line dampening’ for hν > 3Tcol. We show that the effects of deviations from initial polytropic density distribution are small, and so are the effects of ‘expansion opacity’ and deviations from LTE ionization and excitation (within our model assumptions). A recent study of a large set of type II SN observations finds that our model accounts well for the early multiband data of more than 50 per cent of observed SNe (the others are likely affected by thick CSM), enabling the inference of progenitor properties, explosion velocity, and relative extinction.

Generation method and verification of pebble type VHTR multigroup cross sections based on OpenMC

Very high temperature reactor (VHTR) is a Generation-IV (Gen-IV) type of reactor which could nominally operate at a high temperature. In traditional two-step core neutronics calculation method of VHTR, the high precision multigroup cross sections are required. Therefore, a new Monte Carlo based generation scheme for multigroup cross sections of pebble type VHTR, based on open source code OpenMC, is proposed in this paper. The new method can effectively deal with the double heterogeneity effect of pebble type VHTR. And the generated multigroup cross sections can be applied to the deterministic neutronics calculations and OpenMC multigroup calculations. Moreover, a unit cell model and a simplified pebble bed lattice model of VHTR were developed to be used for verification of the method. According to the verification results, the new developed method using OpenMC to generate multigroup homogenized cross sections for pebble type VHTR is feasible and enough accurate.

Convergence analysis of the non-linear CMFD schemes for acceleration of multi-group fixed source neutron transport calculations

The coarse mesh finite difference (CMFD) and related methods have been some of the most extensively used schemes to accelerate the convergence of neutron transport iterations. Despite its predominant application on multi-group problems, the convergence behavior of this class of acceleration methods has been traditionally characterized for the one-group form and results extended to multi-group domain. Theoretical convergence analysis of the multi-group variants of CMFD scheme has not been previously performed and is an important work related to neutron transport studies. Fourier analysis of the coarse mesh finite difference (CMFD), partial current CMFD (pCMFD) and optimally diffusive CMFD (odCMFD) methods for acceleration of the multi-group fixed source neutron transport calculations has been presented in this paper. The multi-group error transition matrix and intermediate Fourier analysis expressions have been found to be analogous to those for one-group system. Sensitivity studies to characterize the effect of various parameters on the overall convergence behavior have also been presented. The results extend current understanding and provide deeper insight into the application of CMFD class of acceleration schemes for more realistic multi-group calculations.

METHODS OF XS DATA PREPARATION FOR GEOMETRY WITH FUEL DUMMY

3D deterministic core calculation represents important category of the nuclear fuel cycle and safe Nuclear Power Plant operation. The appropriate solution was not published yet. Data preparation process for non-fuel elements of the core represents the challenge for scientists. This report briefly introduce the problem of the data preparation process and gives the information about new input format for macrocode PARCS (PMAXS). The best homogenization process approach is to prepare data in infinite lattice cell for fuel assemblies, which are placed next to the another fuel assembly. Data for fuel assembly located next to the non-fuel region are better with preparation in the real geometry with the real boundary conditions. Results of the neutron spectra study show that the PMAXS file format is well prepared for the 2 group calculation, but it is not well prepared for the multigroup calculations, however the XSEC file format still gave reasonable results.

Verification of on-the-fly homogenization method based on the analysis of HTTR

An on-the-fly homogenization (OTFHom) method coupled with depletion based on Monte Carlo method was proposed and implemented in Reactor Monte Carlo code (RMC), which uses continuous energy cross sections to generate multi-group cross sections for specified problems and then uses them in Monte Carlo multi-group calculations to get more convergent results. In order to coupling with depletion, some modifications are made in continuous energy and multi-group calculation procedures to get one-group depletion cross sections and flux for each depletion region. A verification of OTFHom method is carried out to investigate the accuracy and efficiency using HTTR benchmark, which is a prismatic block-type high temperature gas cooled reactor designed by Japan. The criticality and depletion results show that OTFHom method can capture double heterogeneity effect accurately and reduce calculation time considerably because of the spatial homogenization of massive TRISO particles embedded in the graphite matrix. In terms of HTTR model, the time used by CE calculation is about 3 times of that used by OTFHom calculations.

ИССЛЕДОВАНИЕ ВЛИЯНИЯ ГЕТЕРОГЕННОЙ БЛОКИРОВКИ НА КРИТИЧНОСТЬ БЫСТРОГО ФИЗИЧЕСКОГО СТЕНДА

The study investigated the effect of heterogeneous shielding on the preparation of macroconstants for various mixtures. By comparing the effective multiplication factor calculated using multigroup macroconstants of the mixtures obtained for the “infinite” and final geometries, it was determined how significantly the cross sections are shielded and how much this affects the criticality of the entire system. The study is part of the research work on the analysis of the criticality of a fast physical stand (BFS) and is intended to work out the methodology for carrying out multigroup and continuous-energy calculations. The work is carried out on the model of the benchmark BFS2-62-3A, which was carried out on the critical stand BFS-2 (IPPE, Obninsk) in 2000 to simulate the core of the BN-600 reactor with a hybrid U-Pu fuel load and a stainless reflector become. BFS is a set of tubes filled with pellets with different mixtures (uranium, sodium, steel, etc.). The research tool is the software package SCALE-6.2.1. It consists of various control modules united by a common user interface. The calculations of Keff and reaction rates were carried out by the CASAS6 criticality sequence of the SCALE software package using the KENO-VI Monte-Carlo code. During the work, the library ENDF/B-VII.1 was used with continuous and multi-group views of cross sections (252 and 56 groups). The preparation of the macroconstant libraries was done by the XSProc sequence of the SCALE soft-ware package using two different methods: BONAMI and CENTRM. In addition to the experimentally obtained values, the values obtained using the MMKKENO, TRIGEX and Serpent software complexes were used for comparison.

The SCALE/AMPX multigroup cross section processing for fast reactor analysis

The SCALE/AMPX multigroup (MG) cross section processing procedure has been updated to minimize reactivity differences for fast reactor designs and boiling water reactors (BWRs) with very high void fractions to provide excellent agreement with continuous-energy reference calculations. SCALE MG calculations are widely applied to thermal spectrum light-water reactor (LWR) systems as well as fast spectrum metallic systems of interest to National Nuclear Security Administration. With growing interest from industry and regulators in applying SCALE for the design of fast spectrum reactors, both sodium and molten salt, and in the licensing of power up rates for BWRs, it is desirable to review the SCALE/AMPX procedure for unresolved resonance self-shielded data and high energy neutron spectra. The data were improved by generating MG unresolved resonance data based on the analytic probability table method with the narrow resonance approximation as well as the use of a very fine group structure typically used in fast system analysis. This study focused on verifying the probability table and the SCALE/AMPX MG cross section processing procedure by performing reaction rate analysis and benchmark calculations for various fast reactor and high void BWR systems. Results indicate that the improved SCALE/AMPX MG cross section processing provides excellent results for the fast reactor analysis.

Refinement of the Pseudosource Method of Calculating RBMK Cluster Cells

The KLARA option is now being used to perform multigroup calculations of VVER and RBMK cluster cells and to prepare few-group characteristics of cells in the WIMS-SH-2.0 and SVL systems. The transition to 69-group calculations of RBMK cluster cells has revealed instability. Analysis has shown that the instability is associated with a discrepancy in the type of pole in several integrals arising in the calculation of the angular moments of the sinusoidal components of the Greens function. The removal of this singularity by adding two lines of the angular moments of the sinusoidal components eliminated this instability. The difference of K∞ calculated using the KLARA and PIJ options was less than 0.2% for cluster cells with and without fuel.

SHOULD ONE USE THE RAY-BY-RAY APPROXIMATION IN CORE-COLLAPSE SUPERNOVA SIMULATIONS?

ABSTRACT We perform the first self-consistent, time-dependent, multi-group calculations in two dimensions (2D) to address the consequences of using the ray-by-ray+ transport simplification in core-collapse supernova simulations. Such a dimensional reduction is employed by many researchers to facilitate their resource-intensive calculations. Our new code (Fornax) implements multi-D transport, and can, by zeroing out transverse flux terms, emulate the ray-by-ray+ scheme. Using the same microphysics, initial models, resolution, and code, we compare the results of simulating 12, 15, 20, and 25 M ⊙ progenitor models using these two transport methods. Our findings call into question the wisdom of the pervasive use of the ray-by-ray+ approach. Employing it leads to maximum post-bounce/pre-explosion shock radii that are almost universally larger by tens of kilometers than those derived using the more accurate scheme, typically leaving the post-bounce matter less bound and artificially more “explodable.” In fact, for our 25 M ⊙ progenitor, the ray-by-ray+ model explodes, while the corresponding multi-D transport model does not. Therefore, in two dimensions, the combination of ray-by-ray+ with the axial sloshing hydrodynamics that is a feature of 2D supernova dynamics can result in quantitatively, and perhaps qualitatively, incorrect results.

Two-dimensional radiative transfer calculations of the laser-target hohlraum

High non-LTE issue of ionization and radiative transfer are important physical characteristics of the laser-target hohlraum. Detailed multi-group transport approximation under non-LTE atomic physics is necessary for precisely describing radiation transfer and its interaction with matter. Using the recently developed LARED-integration code, we have accomplished multi-group radiative transfer calculations of the laser-target experimental hohlraum in 2D. Numerical results reflect the radiative illumination ununiformity inside the hohlraum. The ratio of X-ray intensity of the laser spot versus other regions along the gold wall agrees well with that of the experimental result, meanwhile the measured and simulated fuel shape resembles each other closely.

Evaluation of the HTTR criticality and burnup calculations with continuous-energy and multigroup cross sections

The High Temperature Engineering Test Reactor (HTTR) in Japan is a helium-cooled graphite-moderated reactor designed and operated for the future development of high-temperature gas-cooled reactors. Two detailed full-core models of HTTR have been established by using SCALE6 and MCNP5/X, respectively, to study its neutronic properties. Several benchmark problems were repeated first to validate the calculation models. Careful code-to-code comparisons were made to ensure that two calculation models are both correct and equivalent. Compared with experimental data, the two models show a consistent bias of approximately 20–30mk overestimation in effective multiplication factor for a wide range of core states. Most of the bias could be related to the ENDF/B-VII.0 cross-section library or incomplete modeling of impurities in graphite. After that, a series of systematic analyses was performed to investigate the effects of cross sections on the HTTR criticality and burnup calculations, with special interest in the comparison between continuous-energy and multigroup results. Multigroup calculations in this study were carried out in 238-group structure and adopted the SCALE double-heterogeneity treatment for resonance self-shielding. The results show that multigroup calculations tend to underestimate the system eigenvalue by a constant amount of ∼5mk compared to their continuous-energy counterparts. Further sensitivity studies suggest the differences between multigroup and continuous-energy results appear to be temperature independent and also insensitive to burnup effects.

Introduction of corrections taking into account interdependence of multigroup constants to the results of multigroup perturbation theory calculations

In multigroup calculations of reactivity and sensitivity coefficients, methodical errors can appear if the interdependence of multigroup constants is not taken into account. For this effect to be taken into account, so-called implicit components of the aforementioned values are introduced. A simple technique for computing these values is proposed. It is based on the use of subgroup parameters.

The Fast Neutron Fluence and the Activation Detector Activity Calculations Using the Effective Source Method and the Adjoint Function

Abstract This paper describes the application of effective source in forward calculations and the adjoint method to the solution of fast neutron fluence and activation detector activities in the reactor pressure vessel (RPV) and RPV cavity of a VVER-440 reactor. Its objective is the demonstration of both methods on a practical task. The effective source method applies the Boltzmann transport operator to time integrated source data in order to obtain neutron fluence and detector activities. By weighting the source data by time dependent decay of the detector activity, the result of the calculation is the detector activity. Alternatively, if the weighting is uniform with respect to time, the result is the fluence. The approach works because of the inherent linearity of radiation transport in non-multiplying time-invariant media. Integrated in this way, the source data are referred to as the effective source. The effective source in the forward calculations method thereby enables the analyst to replace numerous intensive transport calculations with a single transport calculation in which the time dependence and magnitude of the source are correctly represented. In this work, the effective source method has been expanded slightly in the following way: neutron source data were performed with fewgroup method calculation using the active core calculation code moby-dick. The follow-up neutron transport calculation was performed using the neutron transport code tort to perform multigroup calculations. For comparison, an alternative method of calculation has been used based upon adjoint functions of the Boltzmann transport equation. Calculation of the three-dimensional (3-D) adjoint function for each required computational outcome has been obtained using the deterministic code tort and the cross section library BGL440. Adjoint functions appropriate to the required fast neutron flux density and neutron reaction rates have been calculated for several significant points within the RPV and RPV cavity of the VVER-440 reactor. Both of calculation methods are briefly described and the results are compared.

Development and testing of multigroup library with correction of self-shielding effects in fusion–fission hybrid reactor

A multigroup library HENDL2.1/SS (Hybrid Evaluated Nuclear Data Library/Self-Shielding) based on ENDF/B-VII.0 evaluate data has been generated using Bondarenko and flux calculator method for the correction of self-shielding effect of neutronics analyses. To validate the reliability of the multigroup library HENDL2.1/SS, transport calculations for fusion–fission hybrid system FDS-I were performed in this paper. It was verified that the calculations with the HENDL2.1/SS gave almost the same results with MCNP calculations and were better than calculations with the HENDL2.0/MG which is another multigroup library without self-shielding correction. The test results also showed that neglecting resonance self-shielding caused underestimation of the K eff, neutron fluxes and waste transmutation ratios in the multigroup calculations of FDS-I.

Calculation of Photon Exposure and Ambient Dose Slant-Path Buildup Factors for Radiological Assessment

Slant-path photon buildup factors for nine radiation shielding materials (air, aluminum, concrete, iron, lead, leaded glass, polyethylene, stainless steel, and water) are calculated with the most recent cross-section data available using Monte Carlo and discrete ordinates methods. Discrete ordinates calculations use a 244-group energy structure based on previous research at Los Alamos National Laboratory (LANL) and focus on the effects of group widths in multigroup calculations for low-energy photons. Buildup-factor calculations in discrete ordinates benefit from coupled photon/electron cross sections to account for secondary photon effects. Also, ambient dose equivalent buildup factors were analyzed at lower energies where corresponding response functions do not exist in the literature. The results of these studies are directly applicable to radiation safety at LANL, where the dose-modeling code PANDEMONIUM is used to estimate worker dose in plutonium-handling facilities. Buildup factors determined in this work will be used to enhance the code’s modeling capabilities but also should be of general interest to the radiation shielding community.

A global approach to the physics validation of simulation codes for future nuclear systems

This paper presents a global approach to the validation of the parameters that enter into the neutronics simulation tools for advanced fast reactors with the objective to reduce the uncertainties associated to crucial design parameters. This global approach makes use of sensitivity/uncertainty methods; statistical data adjustments; integral experiment selection, analysis and “representativity” quantification with respect to a reference system; scientifically based cross-section covariance data and appropriate methods for their use in multigroup calculations. This global approach has been applied to the uncertainty reduction on the criticality of the Advanced Burner Reactor (both metal and oxide core versions) presently investigated in the frame of the GNEP initiative. The results obtained are very encouraging and allow to indicate some possible improvements of the ENDF/B-VII data file.

Monitoring the distribution of energy release in BN-600 by γ scanning fuel assemblies

A complex of computational and experimental measures for monitoring the distribution of energy release in the core has been perfected over the 25-year history of BN-600 operation in the Beloyarskaya nuclear power plant. Continual monitoring is conducted together with calculations based on three-dimensional multigroup calculations and periodic γ scanning of regular BN-600 fuel assemblies with upgrading of the core of this reactor. At the present time, in the course of switching BN-600 to a new core with four refuelings and maximum fuel burnup increased to 11.1% h.a., the experimental procedure has been upgraded and optimized taking account of the experience gained, three series of such measurements have been completed, and new experimental data on the character of the radial and axial neutron-field distribution have been obtained.