Deterministic Transport Code Research Articles

Development of NEMESI: A Multiparameter Library Generator Prototype for Industrial VVER and PWR Applications Based on APOLLO3®

A nuclear reactor’s design and safety assessment relies on a calculation platform consisting of a series of calculations performed using different simulation tools, each dedicated to modeling a specific phenomenon. The European Union H2020 CAMIVVER Work Package 4 aims to establish lattice neutronics calculation methodologies for VVER and pressurized water reactor fuel assemblies employing the new-generation deterministic multipurpose neutron transport code APOLLO3®, developed by the CEA (Commissariat à l’Énergie Atomique et aux Énergies Alternatives) with the support of EDF (Electricité de France) and Framatome. The present work aims to present NEMESI, an industrial prototype of a flexible lattice calculation tool developed as part of the CAMIVVER project, showing the applicability of APOLLO3 for industrial research and development and proposing dedicated VVER calculation schemes. Given the intense focus on the industrial issues of the entire CAMIVVER project, the elements constituting the rationale behind the development of such a computational platform are flexible modeling and analysis options, compliance with a series of specified requirements, implementation of innovative algorithms with improved precision, and a modern software and architectural base.

Comparison of MCNP and Microshield Dose Savings Determinations for Remote Methods of Transuranic Contamination Characterization.

The maturation of robotic and remote systems presents opportunities to expand the use of technologies that have typically been restricted to high-dose/high-risk nuclear work for moderate- or low-risk work to further reduce radiation exposure to workers. This study quantifies the potential dose savings achieved through the use of robotic techniques for characterizing transuranic-contaminated waste items and compares dose estimates from a simplistic, user-friendly deterministic radiation transport code and a more robust, complex Monte Carlo code. Three scenarios of transuranic-contaminated waste items described in published reports are modeled using representative source geometries in MicroShield and MCNP radiation transport codes. Estimated dose rates are determined at points ranging from 30 cm to 300 cm from the face of the waste item to represent the increase in distance allowed by robotic or remote system implementation for characterization activities. The dose rate savings are then converted to detriment cost savings using a dollar-per-person-dose conversion factor to provide a financial context. The radiation transport simulations show no consistent bias in estimated dose rate by varying simulation methodology or using geometrical simplifications-in some cases, MicroShield produces higher dose rate estimates while MCNP estimates are higher in other cases. In the MCNP simulations, the volume source geometry consistently produces a higher dose rate than the slab source geometry, but the MicroShield dose rate estimates do not display the same trend. Dose savings range from 1.60 × 10-5 μSv h-1 to 1.75 × 101 μSv h-1 with associated detriment cost savings from < 0.010 USD/person-h to 14 USD/person-h.

Poly(vinyl alcohol) gels cross-linked by boric acid for radiation protection of astronauts

Gels are soft materials composed of hydrophilic polymers cross-linked in water by physical or chemical bonds. Due to their lightweight and water-rich nature, these materials find application in various fields, including the space environment, for radiation protection purposes. In fact, thanks to their high hydrogen content, gels exhibit significant radiation stopping power, resulting in reduced fragmentation of incident particles. This suggests their potential utility in shielding electronic devices and safeguarding astronauts’ health. In this work, cross-linked gels based on poly(vinyl alcohol) (PVA) and boric acid (BA) were fabricated and their properties were investigated using different experimental and modeling techniques. The effect of parameters, such as time and temperature, used for fabricating the PVA/BA gels is assessed. Fourier transform infrared spectroscopy (FTIR) was employed to evaluate the ability of BA to form hybrid interpolymeric bonds with PVA macromolecules. To understand the thermo-mechanical properties and viscoelastic behavior of these gels, dynamic mechanical analysis (DMA) in compression mode was performed. The shielding properties were evaluated in different space radiation environments considering galactic cosmic rays, solar particle events, and low earth orbit radiation using deterministic transport codes. The High charge (Z) and Energy TRaNsport (HZETRN) code was employed to create different cross sections as first output for the selected materials, and then, propagate and transport the ionizing radiation inside the materials. The results highlight several advantages of PVA/BA gels fabricated at room temperature without heat treatments. Firstly, the incorporation of BA allows for a slight increase in water content compared to gels produced without the crosslinker. Additionally, an examination of elastic moduli reveals improved mechanical properties exhibiting approximately twice the elastic modulus of PVA gels. Moreover, the analysis of dosimetry quantities suggests that the radiation protection effectiveness of these gels is comparable to that of pure water, while heat-treated PVA/BA gels exhibit a reduced water content resulting in decreased shielding properties and decreased flexibility. Consequently, PVA/BA gels realized at room temperature appear to be the optimal material between PVA gels and the heat-treated counterparts, making them well-suited for integration into astronaut personal protective equipment.

A conservative first-collision source treatment for ray effect mitigation in discrete-ordinate radiation transport solutions

Deterministic transport codes play a fundamental role in the modeling and simulation of neutron transport. One of the most common deterministic methods is the method of discrete ordinates, also known as the Sn method. While offering significant advantages over other deterministic methods or stochastic methods like Monte Carlo, the method of discrete ordinates suffers from non-physical artifacts in its local solution due to its discretization of angle. These artifacts, referred to as ray effects because of their ray-like appearance, tend to be worse in problems with small sources in areas with little scattering. Significant effort has gone into developing methods to mitigate ray effects, such as the first-collision source treatment, which separates the angular flux into the uncollided and collided fluxes and solves them using non-traditional techniques such as ray tracing. Current ray tracing methods typically trace to a set of points inside a zone to compute an overall flux. However, this approach has significant drawbacks, such as a low potential for optimization, as well as not being conservative. A new method has been developed that traces instead to a set of points on each of a zone's surfaces and computes the currents, before using these to obtain the flux. A comparison between these two ray tracing methods shows significant advantages to the new surface method, including inherent particle conservation, similar convergence rate and increased potential for optimization through ray sharing.

Optimizations of the Accelerated Axial Polynomial Method of Characteristics of the APOLLO3® Deterministic Neutron Transport Code

For some years now, the TDT (two- and three-dimensional transport) solver of the APOLLO3® deterministic neutron transport code has been able to perform lattice calculations on three-dimensional extruded and unstructured geometries. A polynomial expansion of the angular flux has been implemented to better describe the flux gradient axially to reduce the number of computational meshes required to reach a given accuracy. Then the polynomial approximation was extended to macroscopic cross sections to perform evolution calculations. Besides these transport schemes, synthetic acceleration has also been implemented, relying on double PN approximations of the angular flux on the boundaries of the spatial regions. The solver has already introduced several techniques to reduce the transport and memory footprint; for example, for the storage of the surfaces crossed by a trajectory or the classification of chords. In this paper, new optimizations are presented. One deals with how monomials of the polynomial basis are integrated along trajectories. Another one concerns the computation of the source term of the transmission equation in the case of polynomial cross sections. The last optimization exploits the fact that, along horizontal trajectories, the flux and the cross sections are constant to speed up the sweep algorithm. Calculations on 5 × 5 and 7 × 7 pressurized water reactor assemblies were performed to assess the gains of these recently developed strategies. The results show good improvements both in computing time and in memory footprint reductions.

Computation of sensitivity coefficients in fixed source simulations with SERPENT2

Within the scope of the implementation of a nuclear data pipeline aiming at producing the best possible evaluated nuclear data files, a major point is the production of relevant sensitivity coefficients when including integral benchmark information. Thanks to recent code modifications in the Monte Carlo code Serpent2, it is now possible to produce these coefficients in fixed source simulations. The manuscript describes the verification of this implementation against the deterministic transport code susd3d. The study is completed by an analysis of the computational cost (running time and memory allocation) associated with such calculations with Serpent2. The relative difference between the sensitivity coefficients produced by Serpent2 and susd3d is of the order of the percent at most, except for the low energy range where the lack of neutrons prevents from reducing the Monte Carlo uncertainties. The computational cost of such calculation is similar to the one of criticality calculation mode, although the OpenMP scalability should be further improved.

Deterministic neutron transport and burnup code coupling assessment

Nuclide evolution is a key aspect in nuclear reactor design and operation. Burnup (or depletion) codes evaluate the isotopic inventory evolution. The inherent need for nuclear safety, the development in computational capabilities, and new discoveries in related areas, such as mathematical methods, result in constant software re-evaluation and improvement. Now, many stochastic-based burnup codes are being developed in comparison to deterministic-based ones, which also present advantages and interesting aspects. In this work, nuclear libraries, processing requirements, data workflow, and methodologies are studied for the development of a brand-new burnup code linked to the VALKIN-FVM-Sn deterministic transport code. As a result, the requirements to create, and couple, a burnup code have been assessed, establishing a methodology. The burnup code has been developed and contrasted with an industry reference. The resulting coupling is a lattice code foundation to be used in a Multiphysics platform.

Mitigating space radiation using magnesium(-lithium) and boron carbide composites

The health effects of galactic cosmic radiation are a serious impediment to crewed exploration of the solar system. OLTARIS, an interface for the 3DHZETRN deterministic radiation transport code, was used to assess the response of aerospace materials to this constant radiation exposure. Traditional aerospace structural materials like aluminum can, after a certain mass, increase the health effects of such radiation. However, materials with lower atomic mass may mitigate this build-up in secondary radiation with increasing areal density. As such, lower atomic mass structural alloys of magnesium and magnesium–lithium are promising candidates. These alloys may reduce the mass of structures when substituted for aluminum alloys. Reinforcement with boron carbide could further reduce atomic mass while also improving the mechanical properties of such lightweight alloys. This study found that the lower atomic mass of these materials increased nuclear fragmentation upon cosmic radiation interactions, leading to a softening of the secondary (neutron) radiation spectra. This softened spectra reduced the effective dose equivalent, a measure of health effects, for magnesium(-lithium) alloys and their boron carbide-reinforced composites when compared to aluminum.

Optimisation of the Tripathi model using a nuclear reaction cross-section database

Nuclear reaction cross-sections are an essential ingredient to reliable deterministic and stochastic radiation transport codes used for radiation protection in space and heavy-ion therapy applications. A recent study compared the existing literature data compiled within the open-access GSI-ESA-NASA cross-section database to the models implemented in the transport codes most commonly used for radiation protection in space and heavy-ion therapy applications. The outcome of the comparison was that none of the models fit well the experimental data for all projectile-target systems at all energy ranges. Therefore, the literature data were exploited to optimise the Tripathi–Cucinotta–Wilson model as reported in this work. This model is used as default in FLUKA, TRiP, and SpaceTRiP, it is part of the hybrid-Kurotama (HK) model used in particle and heavy ion transport code (PHITS), and it is implemented in Geant4. The consequences of using the proposed Tripathi–Cucinotta–Wilson optimisation in the HK model are also analysed.

Estimation of Continuous Distribution of Iterated Fission Probability Using an Artificial Neural Network with Monte Carlo-Based Training Data

The Monte Carlo neutron transport method is used to accurately estimate various quantities, such as k-eigenvalue and integral neutron flux. However, in the case of estimating a distribution of a desired quantity, the Monte Carlo method does not typically provide continuous distribution. Recently, the functional expansion tally (FET) and kernel density estimation (KDE) methods have been developed to provide a continuous distribution of a Monte Carlo tally. In this paper, we propose a method to estimate a continuous distribution of a quantity in all phase-space variables using a fully connected feedforward artificial neural network (ANN) model with Monte Carlo-based training data. As a proof of concept, a continuous distribution of iterated fission probability (IFP) was estimated by ANN models in two distinct fissile systems. The ANN models were trained on the training data created using the Monte Carlo IFP method. The estimated IFP distributions by the ANN models were compared with the Monte Carlo-based data that include the training data. Additionally, the IFP distributions by the ANN models were also compared with the adjoint angular neutron flux distributions obtained with the deterministic neutron transport code PARTISN. The comparisons showed varying degrees of agreement or discrepancy; however, it was observed that the ANN models learned the general trend of the IFP distributions from the Monte Carlo-based training data.

Development of transient Monte Carlo in a fissile system with β-delayed emission from individual precursors using modified open source code OpenMC(TD)

In deterministic and Monte Carlo transport codes, β-delayed emission is included using a group structure where all of the precursors are grouped together in 6 groups or families, but given the increase in computational power, nowadays there is no reason to keep this structure. Furthermore, there have been recent efforts to compile and evaluate all the available β-delayed neutron emission data and to measure new and improved data on individual precursors. In order to be able to perform a transient Monte Carlo simulation, data from individual precursors needs to be implemented in a transport code. This work is the first step towards the development of a tool to explore the effect of individual precursors in a fissile system. In concrete, individual precursor data is included by expanding the capabilities of the open source Monte Carlo code OpenMC. In the modified code – named Time Dependent OpenMC or OpenMC(TD)– time dependency related to β-delayed neutron emission was handled by using forced decay of precursors and combing of the particle population. The data for continuous energy neutron cross-sections was taken from JEFF-3.1.1 library. Regarding the data needed to include the individual precursors, cumulative yields were taken from JEFF-3.1.1 and delayed neutron emission probabilities and delayed neutron spectra were taken from ENDF-B/VIII.0. OpenMC(TD) was tested in a monoenergetic system, an energy dependent unmoderated system where the precursors were taken individually or in a group structure, and in a light-water moderated energy dependent system, using 6-groups, 50 and 40 individual precursors. Neutron flux as a function of time was obtained for each of the systems studied. These results show the potential of OpenMC(TD) as a tool to study the impact of individual precursor data on fissile systems, thus motivating further research to simulate more complex fissile systems.

An Analysis of Transport Effects in Steady-State Simulation of the Molten Salt Reactor Experiment

We use the deterministic neutron transport code QuasiMolto to simulate steady-state operation of the Molten Salt Reactor Experiment (MSRE). Comparisons are made to similar results from the MOST benchmark, the MOOSE-based code Moltres, and the design calculations for the MSRE. In the course of these comparisons, we calculate a value of 0.1799 for the graphite-to-fuel power density ratio, which differs significantly from that seen in other works. We also find uniform graphite heating inadequate to reproduce the characteristic graphite temperature distribution of the MSRE. Leveraging the multilevel projective methodology of QuasiMolto, the influence of transport effects on the modeled problem is found to produce average and maximum group flux variations of 2% to 5% and 30%, respectively, with a 12% variation in the reactivity loss due to delayed neutron precursor drift.

Feasibility of deterministic self-shielding models for Molten Salt Fast Reactor analysis using DRAGON5 code with ENDF/B-VIII.0 data library

Due to its complex geometry and neutron spectrum, the GenIV Molten Salt Fast Reactor was largely studied using the “one-step” calculation scheme, based on the Monte Carlo method. However, for whole-core simulations, this method requires a long computing time to get accurate results. A deterministic “two-step” calculation scheme must be considered and applied to minimize the computational resources. In general, the first step is to obtain multi-group homogenized and condensed cross-sections, while the second step is using those multi-group cross-sections to perform the whole-core simulations. The treatment of the resonance cross-section behavior is one of the biggest problems that affect the accuracy of the multi-group cross-section and handling such a problem is required before proceeding to the second step calculation. So, it is essential to choose a proper and accurate self-shielding model. In this paper, the different self-shielding models are performed with the deterministic code DRAGON5, using ENDF/B-VIII.0 with various energy group libraries on which the self-shielding model is implemented. The infinite multiplication factor Kinf and the radial distribution of absorption, nu-fission, and capture rates were calculated at the low temperature to demonstrate the rim effect. To guarantee accurate predictions of the results revealed by the self-shielding models, the temperature was increased in the range [893 K–1123 K], and a series of different parameters, such as Kinf, average percent error (AVG), root mean square (RMS), and mean relative error (MRE), were calculated as functions of temperature. The calculation’s accuracy is determined by comparing the results with the stochastic transport code OpenMC. It was found that the deterministic transport code DRAGON5 can accurately treat the effect of self-shielding behavior in the MSFR; hence, DRAGON5 code can be utilized as a tool to generate the multi-group homogenized cross-sections of MSFR for whole-core calculations.

Application of model-order reduction of non-linear time-dependent neutronics via POD-Galerkin projection and matrix discrete empirical interpolation

Presented here is an application of model-order reduction to non-linear neutronic transients. The effort described extends previous work (Elzohery and Roberts, 2021b) aimed to develop and assess a Reduced-order model (ROM) framework that can be used for different purposes, such as design optimization and propagating input parameter uncertainties like nuclear data. Here, the target applications is non-linear. The ROM was built with the use of the POD-Galerkin projection method and the matrix version of the Discrete Empirical Interpolation Method (MDEIM) for improved efficiency. Where applications of the ROM to the diffusion equation have been introduced before, this work focuses on treating the non-linearity induced by coupling with different physics. Previous work has used DEIM to approximate non-linear functions resulting from multiphysics coupling such as the temperature and the velocity field (German et al., 2019, 2022). Here, the MDEIM is used to approximate the projection of the problem operator that otherwise must be computed at each non-linear iteration within each time step, which increases the ROM cost. By applying the method to the LRA benchmark, speed ups from 6 to 40 were achieved depending on the full-order model (FOM) spatial fidelity. The maximum relative error in the assemblies power was in the order of 1×10−5%. Moreover, the ROM was parameterized by POD-greedy sampling, and a case study was performed where the kinetic data, i.e., the precursor decay constants and delayed-neutron fraction were assumed to be the model parameters of interest. For the parameterized ROM, the maximum relative error in the assembly power was 1×10−3%, The computational gain from the MDEIM-ROM was compared with that of a direct projection ROM and showed that employing the MDEIM is computationally advantageous, and the advantage grows with dimension of the problem. The method was implemented in the open-source deterministic transport code Detran (Roberts, 2014) where only access to the system operator was needed to construct the ROM, and; hence, the method is trivially invasive and could easily be implemented in many modern deterministic diffusion codes.

Validating NEUTRO, a deterministic finite element neutron transport solver for fusion applications, with literature tests, experimental benchmarks and other neutronic codes

Neutron reactions on fusion reactor materials are key phenomena to be understood to enable fusion as a feasible energy source for future reactors. We present significant improvements and validations of NEUTRO, a deterministic neutron transport code dedicated to solving the Boltzmann transport equation. The code is integrated as a module in the Alya system developed by the Barcelona Supercomputing Center and uses the discrete ordinates method over an angular portion, multigroup for energy discretization and the finite element method over unstructured meshes to treat special complex domains. Material anisotropy of the scattering medium is introduced into the scattering kernel using real base expressions for spherical harmonics. In order to build the total cross-section and the respective group matrix for the elastic cross-section, we use the NJOY code. We test the solver using different geometries and materials with varying levels of scattering properties. We compare our results on classic tests, benchmarks obtained from a Nuclear Energy Agency database and test cases using other neutron transport codes.

Verification and validation of the high-resolution code nTF with VVER-1000 hot zero power monte carlo calculations and experimental data

Novel codes allow the prediction of parameters with increased resolution, in comparison to the conventional approach, sometimes using meshing smaller than the size of the fuel pin. Optimally, complex geometric structures, like the ones included in the VVER core e.g. corner stiffeners, would be modeled explicitly by novel neutronic codes. In this paper, the performance of the deterministic neutron transport code nTF is studied for VVER geometries. The code is verified standalone with Monte Carlo reference solutions for a range of Hot Zero Power (HZP) models, from 2D pincells to the 3D full core of a VVER-1000, described in the X2 benchmark. Several modeling options and approximations are studied to optimize the nTF X2 3D core model. The updated version of nTF, including all necessary modifications to improve its VVER modeling capabilities, presents good agreement with the reference solutions for the simple VVER configurations and the critical state of the X2 core. Specifically for the full core critical state, the RMS of the pin power difference is 1.5% and the eigenvalue difference 74 pcm with respect to a Monte Carlo reference solution. Any resulting discrepancies are analyzed, the more significant ones with the use of the lattice code CASMO5-VVER that employs similar methods as nTF. The optimized nTF X2 full core model is validated with the experimental data included in the X2 benchmark, produced by HZP start-up tests. The differences of the nTF results with the measured and simulated data of the X2 benchmark remain within the accuracy limits set by the utilities and the literature of deterministic code verification for most cases. The related discrepancies are discussed in detail.

Verification of the direct transport code SHARK with the JRR-3M macro benchmark

The JRR-3M reactor is a water-cooled plate-type reactor for research. A macro benchmark based on the JRR-3M reactor is established with the Monte-Carlo code RMC and deterministic direct transport code SHARK with accurate and explicit geometry modeling. A series of cases from 2D lattice to 3D whole-core are adopted for the verification of SHARK. In the verification, sensitivity analyses are conducted with the 2D lattice case and applied in the 3D whole-core calculation. Numerical results indicate the good accuracy of SHARK for the plate-type JRR-3M macro benchmark.

Verification of the Parallel Transport Codes Parafish and AZTRAN with the TAKEDA Benchmarks

With the increase in computational resources, parallel computation in neutron transport codes is inherent since it allows simulations with high spatial-angular resolution. Among the different methodologies available for the solution of the neutron transport equation, spherical harmonics (PN) and discrete-ordinates (SN) approximations have been widely used, as they are established classical methods for performing nuclear reactor calculations. This work focuses on describing and verifying two parallel deterministic neutron transport codes under development. The first one is the Parafish code that is based on the finite-element method and PN approximation. The second one is the AZTRAN code, based on the RTN-0 nodal method and SN approximation. The capabilities of these two codes have been tested on the TAKEDA benchmarks and the results obtained show good behavior and accuracy compared to the Monte Carlo reference solutions. Additionally, the speedup obtained by each code in the parallel execution is acceptable. In general, the results encourage further improvement in the codes to be comparable to other well-validated deterministic transport codes.

On the Self-Shielding in the Unresolved Resonance Range

Abstract Resonance behavior is a feature of nuclear reaction cross sections. Resonance density increases with increasing incident particle energy and they begin to overlap, until they can no longer be resolved experimentally, but they still contribute to self-shielding and must be accounted for. This is usually done by representing them with statistical average parameters according to methods and approximations described in standard text-books. Self-shielding factors are commonly used in deterministic transport codes, while statistical Monte Carlo codes use probability tables or multiband parameters. An exercise was conducted at the International Atomic Energy Agency (IAEA) to validate codes and methods for generating data that account for self-shielding in deterministic and Monte Carlo codes. A simple numerical model problem was defined, considering a sphere of 1 m radius with a 20 MeV isotropic neutron source at the center. The chosen material for testing was 139La from the ENDF/B-VIII.0 library, which clearly showed anomalous behavior.

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.