Neutron Transport Code Research Articles

Comparison of calculation methods for lead cooled fast reactor reactivity effects

This study analyzes three different reactivity feedback coefficients of the Advanced Lead-cooled Fast Reactor Demonstrator (ALFRED) reactor. During the evaluations, the central difference Direct Perturbation Method (DPM) and the Linear Perturbation Theory (LPT) were applied to determine the feedback coefficients and their uncertainties due to cross-section data. The continuous energy SERPENT Monte Carlo code, the multigroup TSUNAMI-3D sequence of the SCALE program package, and PARTISN discrete ordinate neutron transport code coupled with SEnTRi developed by the authors was applied, and the properties of these fundamentally different calculations are presented. In order to validate the methodologies, lead void coefficient calculations were performed for the Comet critical assembly, which confirmed that a good agreement could be reached between the different methods and measurement results. Besides the high-level transport approximation, the calculations indicated that the appropriate spatial resolution has outstanding importance in describing the high flux gradient.

Partial Cross-Section Calculations for PGNAA Based on a Deterministic Neutron Transport Solver

The measurement facility QUANTOM is being developed for the material analysis of radioactive waste packed up in 200-L drums. QUANTOM enables a spatially resolved elemental analysis based on prompt gamma neutron activation analysis. The evaluation of the spatially resolved gamma spectra relies on the calculation of partial cross sections. Hereby, the neutron flux spectrum enters as a parameter, which needs to be simulated in the full three-dimensional geometry of the measurement facility. To ensure that the simulations can be carried out within an acceptable time frame, we use a deterministic neutron transport code specially developed for this purpose based on the SPN approximation of the linear Boltzmann equation. The following question arises: Does the approximation in the neutron transport model still allow a calculation of the partial cross sections at a sufficient level of accuracy. Therefore, in this paper, we study the calculation of partial cross sections in light of the approximation in the neutron transport model in the geometrical setting of the measurement facility. In a simulation study we consider four typical matrix materials and compare cross sections for all elements of the periodic table to reference results obtained by Monte Carlo simulations.

Current Status and On-Going Development of VTT’s Kraken Core Physics Computational Framework

The Kraken computational framework is a new modular calculation system designed for coupled core physics calculations. The development started at VTT Technical Research Centre of Finland in 2017, with the aim to replace VTT’s outdated legacy codes used for the deterministic safety analyses of Finnish power reactors. In addition to conventional large PWRs and BWRs, Kraken is intended to be used for the modeling of SMRs and emerging non-LWR technologies. The main computational modules include the Serpent Monte Carlo neutron and photon transport code, the Ants nodal neutronics solver, the FINIX fuel behavior module and the Kharon thermal hydraulics code, all developed at VTT. The core physics solution can be further coupled to system-scale simulations. In addition to development, significant effort has been devoted to verification and validation of the implemented methodologies. The reduced-order Ants code has been successfully used for steady-state, transient and burnup simulations of PWRs with rectangular and hexagonal core geometry. The Ants–Kharon–FINIX code sequence is actively used for the core design tasks in VTT’s district heating reactor project. This paper is a general overview on the background, functional description, current status and future plans for the Kraken framework. Due to the short history of development, Kraken has not yet been comprehensively validated or applied to full-scale core physics calculations. A review of previous studies is instead provided to exemplify the practical use.

Improvement of Geant4 Neutron-HP package: From methodology to evaluated nuclear data library

An accurate description of interactions between thermal neutrons (below 4 eV) and materials is key to simulate the transport of neutrons in a wide range of applications such as criticality-safety, reactor physics, compact accelerator-driven neutron sources, radiological shielding or nuclear instrumentation, just to name a few. While the Monte Carlo transport code Geant4 was initially developed to simulate particle physics experiments, its use has spread to neutronics applications, requiring evaluated cross-sections for neutrons and gammas between 0 and 20 MeV (the so-called neutron High Precision – HP – package), as well as a proper offline or on-the-flight treatment of these cross-sections. In this paper we will point out limitations affecting the Geant4 (version 10.07.p01) thermal neutron treatment and associated nuclear data libraries, by using comparisons with the reference Monte Carlo neutron transport code Tripoli-4®, version 11, and we will present the results of various modifications of the Geant4 Neutron-HP package, required to overcome these limitations. Also, in order to broaden the support of nuclear data libraries compatible with Geant4, a nuclear processing tool has been developed (the code is available on a GitLab repository) and validated allowing the use of the code together with ENDF/B-VIII.0 and JEFF-3.3 libraries for example. These changes will be taken into account in an upcoming Geant4 release.

REX: An analytical tool for reactor operating envelope expansion through fuel-clad thermo-mechanics

REX, an analytical reactor design tool for the identification and expansion of reactor operating envelopes, is introduced and detailed. Written in MATLAB, REX takes core geometries and axially discretized detector and depletion output from the Serpent neutron transport code and performs full-core, pin-specific thermal-hydraulic and thermo-mechanical calculations. REX identifies the operating envelopes of advanced, solid-fuel nuclear reactors on the basis of their fuel-cladding, fuel-gas, and coolant-cladding interfacial thermo-mechanics. It iteratively pushes coolant inlet temperatures and modifies fuel pin geometries to induce mechanical failure in their original cladding materials at the fullest extent of their fuel cycle lengths and permissible coolant inlet temperatures. It then attempts to expand their operating envelopes by determining the mechanical responses of alternative cladding materials under the same geometric conditions. The result of the REX calculation sequence is a set of 5-D variables describing the temperatures, pressures, geometries, and mechanics of the core as functions of assembly, fuel pin, axial zone, depletion step, and coolant inlet temperature for each candidate cladding material with the limiting fuel pin geometry for the original material.

Uncertainty propagation of prompt fission neutron spectrum for physics analysis of fast and thermal reactors

This paper presents a strategy for processing the covariance matrix of the prompt fission neutron spectrum (PFNS) and propagating the PFNS uncertainties to the neutronic calculation of fast and thermal reactors. Due to their great significance to the accurate prediction of nuclear criticality, the sensitivity and uncertainty of core parameters for PFNS are analyzed in this study. The propagation of PFNS uncertainties from the evaluated nuclear data files (ENDF) to the core parameters is divided into two phases. In the first phase, the covariance data in the ENDF is transformed into the multi-group form, in which the “zero-sum” constraint is considered and a corresponding functional module is developed in the updated NECP-Atlas nuclear data processing code. In the second phase, the neutron transport code is coupled as a “black box” to propagate the uncertainties in the multi-group form to the core parameters. Sensitivity and uncertainty (S&U) analysis function is implemented in the NECP-UNICORN uncertainty quantification code. As for its application, S&U analysis for PFNS has been performed to the fast and thermal reactors. The numerical results indicate that the influence of PFNS uncertainties to the confidence interval of reactivity prediction and power distribution should be considered in the nuclear reactor analyses.

Application of genetic algorithms in optimization of SFR nuclear reactor design

Abstract This work presents a demonstrational application of genetic algorithms (GAs) to solve sample optimization problems in the generation IV nuclear reactor core design. The new software was developed implementing novel GAs, and it was applied to show their capabilities by presenting an example solution of two selected problems to check whether GAs can be used successfully in reactor engineering as an optimization tool. The 3600 MWth oxide core, which was based on the OECD/NEA sodium-cooled fast reactor (SFR) benchmark, was used a reference design [1]. The first problem was the optimization of the fuel isotopic inventory in terms of minimizing the volume share of long-lived actinides, while maximizing the effective neutron multiplication factor. The second task was the optimization of the boron shield distribution around the reactor core to minimize the sodium void reactivity effect (SVRE). Neutron transport and fuel depletion simulations were performed using Monte Carlo neutron transport code SERPENT2. The simulation resulted in an optimized fuel mixture composition for the selected parameters, which demonstrates the functionality of the algorithm. The results show the efficiency and universality of GAs in multidimensional optimization problems in nuclear engineering.

Sub-space iteration based Monte Carlo scheme for simultaneous computation of multiple dominant k-eigenmodes and acceleration of fission source iterations

Monte Carlo neutron transport codes are widely used for criticality simulation of full reactor core owing to their ability to model complex geometry in exact details, and of using the best available nuclear data. These codes are generally based on the Power Iteration (PI) method which is used to estimate only the fundamental eigenmode, and suffers from poor convergence rate specially when the dominance ratio is close to unity. Estimation of higher modes are required for various applications such as modal analysis, perturbation theory, etc. Computation of the dominance ratio is essential for determining the convergence rate of the power iterations. To overcome these issues, we have utilized a more robust Sub-Space Iteration (SSI) based Monte Carlo algorithm for simultaneous and efficient computation of multiple dominant eigenmodes for the general geometry full-core reactor problems. We have done an extensive investigation of the scheme on variety of problems with multi-group cross-section data, including the realistic full-core reactor benchmark (OECD/NEA 3D C5G7) to exemplify its validity, accuracy, and effectiveness. It was observed that the scheme works well for various kinds of systems, with good accuracy and has distinctly superior convergence properties than the PI method. The SSI based Monte Carlo scheme is built on top of the PI based neutron transport algorithm, and hence can be easily incorporated in the existing PI-based Monte Carlo codes for accelerating the fission source convergence and also for simultaneous computation of multiple eigenmodes.

Experimental validation of an integrated modelling approach to neutron emission studies at JET

An integrated modelling methodology for the calculation of realistic plasma neutron sources for the JET tokamak has been developed. The computational chain comprises TRANSP plasma transport and DRESS neutron spectrum calculations, and their coupling to the MCNP neutron transport code, bridging plasma physics and neutronics. In the paper we apply the developed methodology to the analysis of neutron emission properties of deuterium and helium plasmas at JET, and validate individual modelling steps against neutron diagnostic measurements. Two types of JET discharges are modelled—baseline-like and three-ion radio-frequency scenarios—due to their diversity in plasma heating, characteristics of the induced fast ion population, and the imprint of these on neutron emission properties. The neutron emission modelling results are quantitatively compared to the total neutron yield from fission chambers, neutron emissivity profiles from the neutron camera, neutron spectra from the time-of-flight spectrometer, and neutron activation measurements. The agreement between measured and calculated quantities is found to be satisfactory for all four diagnostic systems within the estimated experimental and computational uncertainties. Additionally, the effect of neutrons not originating from the dominating D(D, n)3He reactions is studied through modelling of triton burnup DT neutrons, and, in mixed D-3He plasmas, neutrons produced in the 9Be(D, nγ)10B reaction on impurities. It is found that these reactions can contribute up to several percent to the total neutron yield and dominate the neutron activation of samples. The effect of MeV-range fast ions on the neutron activation of 115In and 27Al samples is measured and computationally validated.

Validation of Light Water Reactor Ex-Core Calculations with VERA

The Consortium for Advanced Simulation of Light Water Reactors (CASL) Virtual Environment for Reactor Applications (VERA) is a reactor simulation software. It offers unique capabilities by combining high-fidelity in-core radiation transport with temperature feedback by using MPACT (a deterministic neutron transport code) and COBRA-TF (a thermal-hydraulic code) with follow-on, fixed-source transport calculations using the Shift Monte Carlo code to calculate ex-core quantities of interest. In these coupled calculations, MPACT provides Shift with the fission source for follow-on ex-core calculations. These ex-core simulations can be set up to calculate detector responses, as well as the flux and fluence in ex-core regions of interest, such as the reactor pressure vessel, nozzle, and irradiated capsules. A Watts Bar Nuclear Plant Unit 1 (WBN1) ex-core model was developed, as described in this paper, and this model was used to perform coupon calculations. The results for the coupon flux calculations show close agreement with the reference values for cycle 1 produced by the two-dimensional Discrete Ordinates Transport (DORT) code and presented in a BWXT Services Inc. report. However, differences in the results (10%) seen in cycles 2 and 3 and the reasons for these differences are discussed in this paper. The VERA WBN1 model was also used to perform a vessel fluence calculation for cycle 1. Additionally, a collaboration between CASL and Duke Energy led to the first code-to-code validation of VERA for reactor ex-core applications that used a model for the Shearon Harris reactor. Results from this collaboration show excellent agreement between VERA and the Monte Carlo N-Particle Transport Code for the detector response calculations. The work performed under this collaboration is also detailed in this paper.

Generalized Perturbation Theory Based Total Sensitivity and Uncertainty Analysis for High-Fidelity Neutronics Calculation

Neutronics calculation for nuclear reactor with high-fidelity technology can significantly reduce the uncertainties propagated from numerical approximation error and model error. However, the uncertainty of input parameters inevitably exists, especially for nuclear data. On the other hand, resonance self-shielding calculation is essential for multi-group assumption based high-fidelity neutronics calculation, which introduce the implicit effect for calculation responses. In order to fully consider the implicit effects in the process of uncertainty quantification, a generalized perturbation theory (GPT) based implicit sensitivity calculation method is proposed in this paper. Combining the explicit sensitivity coefficient, which can be quantified using classic perturbation theory, the total sensitivity coefficient of calculation responses is obtained. Then the total sensitivity and uncertainty module is established in self-developed neutron transport code with high-fidelity technology-HNET. To verify the accuracy of the sensitivity calculation methods proposed in this paper, a two-dimensional fuel pin problem is chosen to verify the sensitivity results, and the numerical results show good agreement with results calculated by a direct perturbation method. Finally, uncertainty analysis for two-dimensional fuel pin problem is performed and some general conclusions are obtained from the numerical results.

Domain decomposition in the GPU-accelerated Shift Monte Carlo code

The GPU solver within the Shift continuous-energy Monte Carlo neutron transport code has been extended to provide domain decomposition in addition to domain replication to enable the solution of problems with memory requirements exceeding the capacity of a single GPU. The strategy follows the Multiple Set, Overlapping Domain (MSOD) approach that is used in Shift’s CPU solver and integrates into the event-based algorithm used for Shift’s GPU solver. Furthermore, the ability to assign processors to spatial domains non-uniformly has been maintained. Two different approaches for communicating particle data between domains are considered, and multiple criteria for load balancing problems have been investigated. Numerical results are presented for both fresh and depleted small modular nuclear reactor (SMR) cores. A parallel efficiency of approximately 80% was achieved with up to 16 spatial domains measured relative to full domain replication. A scaling study on the Summit supercomputer demonstrates a weak scaling parallel efficiency of over 90% on over 24000 GPUs.

Propagation of VHTRC manufacturing uncertainties with RAVEN/PHISICS

The International Atomic Energy Agency recently concluded a Coordinated Research Program (CRP) to evaluate the effect of propagation of uncertainties on design and safety parameters in High Temperature Gas-cooled Reactors (HTGRs). This CRP catalyzed the development of novel software and methods relevant to HTGR uncertainty analysis. In the framework of this CRP, the statistical analysis code RAVEN was coupled to the neutron transport code PHISICS, using 6-group cross section libraries generated with the modules TRITON/NEWT from SCALE 6.2.1. This article describes the mechanics of the RAVEN/PHISICS sequence, and reports the effects of manufacturing uncertainties on integral parameter uncertainties found in the Very High Temperature Reactor Critical (VHTRC) core.The VHTRC experimental results included propagation of manufacturing uncertainties to obtain eigenvalue (keff) and temperature coefficient (αT) uncertainties. RAVEN/PHISICS was used to reproduce this analysis and to compare the predicted output uncertainties to the experimental measurements on the three VHTRC cores (HC-I, HP, HC-II). Results from the sequence agree with the experimental values (σ[keff] ~ 0.00300).The analysis also focuses on the interpretation of input uncertainties. The simulations conducted with RAVEN/PHISICS demonstrated the input uncertainties can induce a threefold increase in the resulting output uncertainties, depending on the mathematical modeling of the raw input uncertainties. In particular, the use of a unique uncertainty value repeated over lattice elements constitutes the major contribution to the keff and αT uncertainties, while modeling these uncertainties with random independent values leads to negligible keff and αT uncertainties, due to cancellation of errors. The propagation of the manufacturing uncertainties was also repeated using 56 energy groups in the neutron transport calculations, and showed a moderate impact on the output (keff, αT) uncertainties (~10 % difference) compared to the base-case 6-group simulations.

Exploratory tritium breeding performance study on a water cooled lead ceramic breeder blanket for EU DEMO using Serpent-2

• Explored the tritium breeding performance of WLCB Breeder blanket using Serpent-2. • Analyzed the sensitivity of TBR to materials in first wall and breeder zone. • Analyzed the effect of first wall and breeder zone structure on TBR. • Compared the effect of Lead-alloy and Lead on TBR. Innovative Water cooled Lead Ceramic Breeder (WLCB) blanket concepts are being developed at Karlsruhe Institute of Technology (KIT) to explore alternative options for the European demonstration fusion power plant (DEMO). Compared to the Helium Cooled Pebble Bed blanket (HCPB, which is one of the two driver blanket concepts of the European DEMO), Lead/ Lead-alloy is used as neutron multiplier instead of Be/Be-alloy and pressurized subcooled water is used as coolant instead of Helium in the WLCB. The tritium self-sufficiency is the vital function that a Breeding Blanket has to achieve. The absorption of neutrons by water leads to a decrease in the number of neutrons, so the requirement to improve the tritium breeding capacity of the water-cooled blankets is particularly prominent. The Monte Carlo neutron transport code Serpent-2 developed by VTT in Finland has already been benchmarked to be applicable to neutronics calculations in the fusion reactors in a previous study. In this paper, an exploratory TBR study on Water cooled Lead Ceramic Breeder Blanket is presented.

PHWR Reactivity Device Incremental Macroscopic Cross Sections and Reactivities for a Molybdenum-Producing Bundle and a Standard Bundle

A new 37-element PHWR fuel bundle, designed for molybdenum-99 production, has been proposed previously. The new bundle has been shown to have lattice properties and reactivity feedback effects equivalent to the standard PHWR bundle. This study looks at the effect the use of molybdenum-99-producing bundles has on the reactivity worth of reactivity devices, through the prism of reactivity-device macroscopic-cross-section increments. The study utilizes three-dimensional supercell configurations and the neutron transport code DRAGON to calculate and compare the incremental macroscopic cross sections and supercell reactivity for adjuster absorbers, shutoff absorber rods and liquid zone controllers when surrounded by molybdenum-99-producing bundles and by regular bundles. Two geometrical representations of fuel bundles are used: a detailed, cluster, representation, whereby all fuel pins are modeled separately, and an annularized representation, whereby each ring of fuel pins and corresponding coolant is represented as a homogeneous annulus. The latter model is the one customarily used in production calculations for finding cross-section increments of reactivity devices. The study finds that reactivity-device cross-section and supercell reactivity increments are very similar (< 2% difference in reactivity increments) for the case of the molybdenum-producing bundle and the regular bundle. The study also finds that the use of a detailed, cluster, geometrical representation of the fuel bundle produces slightly different cross-section increments and supercell reactivity increments than the use of an annularized geometrical representation. The supercell reactivity-increment difference between the two representations is found to be ~8.0% for adjuster absorbers and ~11.0% for shutoff absorber rods.

Nuclear criticality calculations using Geant4

A method for determining the parameters of importance to nuclear reactor kinetics and nuclear criticality analysis using the general-purpose Monte Carlo simulation toolkit Geant4 has been developed. The demonstration of the proposed method is first illustrated by a set of six Godiva-like criticality problems consisting of hypothetical spherical subcritical and supercritical configurations of highly enriched uranium. Next, the performance of the application of Geant4 for criticality evaluations is shown using selected experimental benchmarks from the International Criticality Safety Benchmark Evaluation Project ICSBEP. Results were compared with those obtained by a set of the most used neutron transport codes such as MCNP, TRIPOLI-4®, KENO, APOLLO and SERPENT.

Application of material-mesh algebraic collapsing acceleration technique in method of characteristics–based neutron transport code

Application of material-mesh algebraic collapsing acceleration technique in method of characteristics–based neutron transport code

Optimizing the RMC Code Using the Decay Chain Method for Large-Scale Decay Calculations

Decay calculations play an important role in reactor physics simulations. In particular, the isotopic decay of the burned fuel during refueling is important for predicting the startup reactivity of the following burn-up cycle. In addition, there is a growing interest in high-fidelity simulations where the mesh in the burn-up region can involve millions of regions. However, existing models repeatedly solve the same Bateman equations for each region, which is a waste of calculational resources. RMC is a Monte Carlo neutron transport code developed for advanced reactor physics analysis including criticality calculations and burn-up calculations. This paper presents a decay calculation method named the Decay Chain Method (DCM) to optimize the RMC code for large-scale decay calculations. Unlike traditional methods, the Decay Chain Method solves the Bateman equations one decay chain at a time rather than one region at a time. The decay calculation in the burn-up mode then treats the decay steps as zero power burn-up steps with some optimized calculational methods to further reduce the calculational time. These methods were evaluated for a single pin example and for a Virtual Environment for Reactor Applications (VERA) full-core example. The calculations for the single pin example verify the accuracy of the decay step treatment in the burn-up mode and show the improved efficiency. The single pin is divided into 1–1,000,000 decay regions to study the efficiency differences between the Transmutation Trajectory Analysis (TTA) and DCM methods. Both methods have a linear complexity with respect to the number of regions but DCM costs just one-sixtieth of the TTA time. In the simplified VERA full core example, the DCM method reduces the decay calculation time to 0.32 min from 75.26 min while the accuracy remains unchanged.

Applicability of the Krško nuclear power plant core Monte Carlo model for the determination of the neutron source term

A detailed geometrical model of a Krško reactor core was developed using a Monte Carlo neutron transport code MCNP. The main goal of developing an MCNP core model is for it to be used in future research focused on ex-core calculations. A script called McCord was developed to generate MCNP input for an arbitrary fuel cycle configuration from the diffusion based core design package CORD-2, taking advantage of already available material and temperature data obtained in the nuclear core design process. The core model was used to calculate 3D power density profile inside the core. The applicability of the calculated power density distributions was tested by comparison to the CORD-2 calculations, which is regularly used for the nuclear core design calculation verification of the Krško core. For the hot zero power and hot full power states differences between MCNP and CORD-2 in the radial power density profile were <3%. When studying axial power density profiles the differences in axial offset were less than 2.3% for hot full power condition. To further confirm the applicability of the developed model, the measurements with in-core neutron detectors were compared to the calculations, where differences of 5% were observed.

Development, verification, and validation of the parallel transport code AZTRAN

AZTRAN is a 3D parallel SN neutron transport code developed for the AZTLAN Platform project, an initiative devoted to developing a Mexican platform for analysis and design of nuclear reactors. AZTRAN solves the multi-group discrete-ordinates form of the neutron transport equation in 3D Cartesian geometry applying the nodal RTN-0 method and the domain decomposition method for its parallelization. To verify and start the validation process, the C5G7 MOX Benchmarks were used. The accuracy of the serial solver was demonstrated by comparing the numerical results of the keff and normalized pin powers with the reference solutions. Excellent agreement and good consistency were obtained, showing errors reduce as the spatial and angular discretizations refine. The parallel implementation is also demonstrated. The speed-up is significant as the number of processors increases without losing quality in the numerical results and reaching efficiencies over 80% in the 2D cases and 85% in the 3D cases.