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The objective of this paper is to quantify the coupling effect on the power distribution of sodium-cooled fast reactors (SFRs), specifically the European SFR. Calculations are performed with several state-of-the-art reactor physics and Multiphysics codes (TRACE/PARCS, DYN3D, WIMS, COUNTHER, and GeN-Foam) to build confidence in the methodologies and validity of results. Standalone neutronic calculations were generally in excellent agreement with a reference Monte Carlo-calculated power distribution (from Serpent). Next, the impact of coolant density and fuel temperature Doppler feedback was calculated. Reactivity coefficients for perturbations in the inlet temperature, coolant heat up and core power was shown to be negative with values of around −0.5 pcm/°C, −0.3 pcm/°C, and −3.5 pcm/%, respectively. Fuel temperature and coolant density feedback was found to introduce a roughly −1%/+1% in/out power tilt across the core. Calculations were then extended to axial expansion for cases where fuel is linked and unlinked to the clad. Core calculations are in good agreement with each other. The impact of differential fuel expansion is found to be larger for fuel both linked and unlinked to the clad, with the in/out power tilt increasing to around −4%/+2%. Thus, while broadly confirming the known result that standalone physics calculations give good results, the expansion coupling effect is perhaps more than anticipated a priori. These results provide a useful benchmark for the further development of Multiphysics codes and methodologies in support of advanced reactor calculations.

The coupled DYN3D/ATHLET code system was recently adapted for Sodium cooled Fast Reactors (SFRs) applications. The main objective of this study is to validate further the DYN3D/ATHLET code system by performing a coupled 3D neutron kinetics/thermal-hydraulics analysis of six transient start-up tests conducted at the French Superphenix (SPX) reactor. The tests were a part of the startup test program aiming at evaluation of the core reactivity feedback characteristics. Peculiarity of these transients is the necessity of accounting for the thermal expansions of the primary system structural elements influencing the position of control rods in the core. The paper includes a brief summary on the benchmark specification, description of the neutronics and thermal-hydraulics models, and comparison of the simulation results to the available experimental data. For all six transients, a good agreement between simulations and experiments was observed confirming a reasonable performance of DYN3D/ATHLET.

The paper presents a transient simulation phase of the new benchmark on a large sodium fast reactor core. This phase of the benchmark was devoted to the modelling of selected operational transients performed during start-up tests of French SFR Superphénix in order to evaluate its reactivity characteristics and core response to certain perturbations. Six operational transients were selected for the analysis. The specification of a simplified thermal hydraulic model equipped with point kinetics reactivity data and boundary conditions for the selected transients are given in the paper and the results of simulations with several system codes are reported. The study uses the results of the reference Serpent 2 Monte Carlo solution obtained during the first phase of the benchmark related to static neutronic characterization of the core. The developed model contains necessary thermal hydraulic description of primary system components and assumptions to account for thermal expansion reactivity feedbacks from in-reactor structures, neutron kinetics parameters, power distribution and reactivity coefficients. Thus the transient benchmark appears as an effective tool for validation and cross comparisons of system codes including approbation and comparison of different modelling features for thermal expansion of the in-reactor structures, giving a reference core behaviour with use of relatively simple models. The results of the modelling demonstrate a reasonable agreement between all solutions and with the experimentally measured evolution of the core parameters. Particular discrepancies with experimental data could not be resolved using the simplified benchmark model and available experimental data reconstructed from the published analysis of start-up tests. Because of that, the future steps for achieving the improved agreement between the simulated results and the experimental data were proposed.

In this study, the isothermal physics tests performed on the fully loaded core of the Fast Flux Test Facility (FFTF) are analyzed with the Monte Carlo code Serpent and with the deterministic core simulator DYN3D. The selected tests comprise two neutron spectra measurements and a multitude of reactivity effect measurements (32 cases with control rod movements and one case for isothermal temperature coefficient). While the flux spectra are calculated only with the Monte Carlo code, the reactivity effects are evaluated with both codes, Serpent and DYN3D. The homogenized few-group cross sections for DYN3D calculations are generated with Serpent. The obtained numerical results are in a very good agreement as compared to the experimental data. Additionally, a comparison of radial power distributions is presented between DYN3D and Serpent calculations, demonstrating an adequate performance of the nodal code DYN3D. This paper provides an additional contribution to the validation of both codes for neutronic analyses of Sodium cooled Fast Reactor cores.

Recent developments of the reactor dynamics code DYN3D have introduced the micro-depletion model which allows for explicit calculation of radioactive decay heat. Such a unique combination of nodal diffusion, thermal hydraulic (T/H) and depletion solvers allows DYN3D to perform fuel cycle depletion and obtain detailed core isotopic concentration and decay heat distributions. More importantly, this capability allows for the generation of time-dependent spatial decay heat distribution, which is essential to predict the behavior of the reactor under off-nominal scenarios. The new sequence utilizes considerably less computational resources than coupled Monte Carlo-T/H-depletion systems, but with comparable accuracy. This capability was recently tested on a limited number of simple unit cell models. The main objective of this work is to further verify the decay heat calculation capabilities of DYN3D by applying it to a considerably more realistic and detailed full core model. For the purpose of the current analysis a 3D full core model of Advanced Burner Reactor (ABR) was adopted from the OECD/NEA Benchmark for Neutronic Analysis of Sodium-Cooled Fast Reactor Cores with Various Fuel Types and Core Sizes. In this work, the Monte Carlo code Serpent was used to generate macro- and microscopic parameters, and the neutron diffusion code, DYN3D, was used to perform neutronic and depletion analyses. Detailed spatial isotopic and decay heat distributions obtained with DYN3D were verified against the equivalent Serpent reference 3D full core solution. Results indicate very good agreement between the Serpent-DYN3D code sequence and the reference Serpent solutions, with a discrepancy in total decay heat on the order of 0.5%.

In the framework of the Horizon 2020 project ESFR-SMART (2017–2021), the European sodium fast reactor (ESFR) core was updated through a safety-related modification and optimization of the core design from the earlier FP7 CP-ESFR project (2009–2013). This study is dedicated to neutronic analyses of the improved ESFR core design. The conducted work is reported in two parts. Part I deals with the evaluation of the safety-related neutronic parameters of the fresh beginning-of-life (BOL) core carried out by eight organizations using both continuous energy Monte Carlo and deterministic computer codes. In addition to the neutronics characterization of the core, a special emphasis was put on the calibration and verification of the computational tools involved in the analyses. Part II is devoted to once-through and realistic batchwise burnup calculations aiming at the establishing of the equilibrium core state, which will later serve as a basis for detailed safety analyses.

This study explores the feasibility of applying the Serpent-DYN3D sequence to the analysis of Sodium-cooled Fast Reactors (SFRs) with complex core geometries, such as the ASTRIDlike design. The core is characterised by a highly heterogeneous configuration and was likely to challenge the accuracy of the Serpent-DYN3D sequence. It includes axially heterogeneous fuel assemblies, non-uniform fuel assembly heights and large sodium plena. Consequently, the influence of generation and correction methods of various homogenised, few-group crosssections (XS) on the accuracy of the full-core nodal diffusion DYN3D calculations is presented. An attempt to compare the approximate time effort spent on models preparation against the accuracy of the result is made. Results are compared to reference full-core Serpent MC (Monte Carlo) solutions. Initially, XS data was generated in Serpent using traditional methods (2D single assemblies and 2D super-cells). Full core calculations and MC simulations offered a moderate agreement. Therefore, XS generation with 2D fuel-reflector models and 3D single assembly models was verified. Super-homogenisation (SPH) factors for XS correction were applied. In conclusion, the performed work suggests that Serpent-DYN3D sequence could be used for the analysis of highly heterogeneous SFR designs similar to the studied ASTRID-like, with an only small penalty on the accuracy of the core reactivity and radial power distribution prediction. However, the XS generation route would need to include the correction with SPH factors and generation of XS with various MC models, for different core regions. At a certain point, there are diminishing returns to using more complex XS generation methods, as the accuracy of full-core deterministic calculations improves only slightly, while the time effort required increases significantly.

The Horizon 2020 ESFR-SMART project investigates the behaviour of the commercial-size European Sodium-cooled Fast Reactor (ESFR) throughout its lifetime. This paper reports work focused on the End of Equilibrium Cycle (EOEC) loading of the ESFR, including neutronic analysis, core- and zone-wise reactivity coefficients, and more detailed local mapping of important safety-relevant parameters. Sensitivity and uncertainty analysis on these parameters have also been performed and a detailed investigation into decay heat mapping carried out. Due to the scope of this work the results have been split into three papers. The nominal operating conditions and both zone-wise and local mapping of reactivity coefficients are considered in this paper; the sensitivity and uncertainty analysis are detailed in Margulis et al. and the decay heat mapping calculations are reported in Jimenez-Carrascosa et al. The work was performed across four institutions using both continuous-energy Monte Carlo and deterministic reactor physics codes. A good agreement is observed between the methods, verifying the suitability of these codes for simulation of large, complicated reactor configurations; and giving confidence in the results for the most limiting ESFR EOEC core state for safety analysis. The results from this work will inform the transient calculations planned for the next stage of work on the ESFR, allowing for more in-depth studies to be performed on the multiphysics behaviour of the reactor.

The ESFR-SMART project is the latest iteration of research into the behaviour of acommercial-size SFR core throughout its lifetime. As part of this project the ESFR corehas been modelled by a range of different reactor physics simulation codes at its end ofcycle state, and the important safety relevant parameters evaluated. These parameters arefound to agree well between the different codes, giving good confidence in the results.A detailed mapping of the local sodium void worth is also performed due to the problemsassociated with the positive void coefficient seen in large SFR designs. The local voidworth maps show that the use of zone-wise coefficients replicates the important reactivityfeedbacks to a high degree, indicating their suitability for use in SFR simulations.

In the framework of the FP7 Euratom project FREYA, the Serpent Monte Code was used to characterize a number of critical VENUS-F core configurations. Several neutronic parameters calculated by Serpent were compared to the available experimental data and reported in a previous study. Although a generally reasonable agreement between the calculated and experimental values was obtained, the study also revealed some important issues related to the modeling results such as a systematic overestimation of reactivity and a systematic underestimation of U238 to U235 fission rate ratio (designated as F28/F25 spectral index). The objective of the current follow-up study is to assess the impact of nuclear data uncertainties on the Monte Carlo estimates of reactivity and spectral indices. The analysis is carried out for two critical VENUS-F cores using a recently upgraded version of Serpent which is capable to perform sensitivity analysis, based on the collision history method and to propagate and quantify nuclear data uncertainties using multi-group covariance libraries in an automated way. The criticality calculations were performed using the ENDV/B-VII.1 based cross sections while the uncertainties due to nuclear data were obtained using 56-group neutron cross section covariance library from the SCALE-6.2 package. The estimated uncertainties due to nuclear data are of the order of 2200 pcm and 8% on k-eff and F28/F25 spectral index, respectively. It was found that the major contributor to the k-eff uncertainty is the capture cross section of U235. In the F28/F25 case, the total uncertainty is dominated by inelastic scattering cross section of U238, fission spectrum of U235, and capture cross section of U235.

The reactor dynamics code DYN3D, initially developed for LWR applications, is being extended for steady state and transient analyses of Sodium cooled Fast Reactor (SFR) cores. The extension includes the development of the few-group cross section generation methodology, updating of the thermal-hydraulic database with thermal-physical properties of sodium, and development of the thermal-mechanical model to account for thermal expansion effects of the core components. Part I of the paper provided a detailed description of the recently implemented thermal expansion models able to treat axial expansion of fuel rod and radial expansion of diagrid. The results of the initial verification tests were also presented in Part I of the paper. The capability of the extended version of DYN3D to perform steady state and transient analyses of SFR cores was validated using selected tests from the end-of-life experiments conducted at the Phenix reactor. Steady state analysis of the control rod withdrawal tests is covered in Part II of the paper. Part III of the paper reports on the results of the transient analysis of the initial stage of the natural circulation test from the Phenix end-of-life experiments.

The reactor dynamics code DYN3D, initially developed for LWR applications, is being extended for steady state and transient analyses of Sodium cooled Fast Reactor (SFR) cores. The extension includes the development of the few-group cross section generation methodology, updating of the thermal-hydraulic database with thermal-physical properties of sodium, and development of the thermal-mechanical model to account for thermal expansion effects of the core components. Part I of the paper provided a detailed description of the recently implemented thermal expansion models able to treat axial expansion of fuel rod and radial expansion of diagrid. The results of the initial verification tests were also presented in Part I of the paper. The capability of the extended version of DYN3D to perform steady state and transient analyses of SFR cores was validated using selected tests from the end-of-life experiments conducted at the Phenix reactor. Part II of the paper reports on the results of the steady state analysis of the control rod withdrawal tests from the Phenix end-of-life experiments. The transient analysis of the initial stage of the natural circulation test is covered in Part III of the paper.

The reactor dynamics code DYN3D, initially developed for LWR applications, is being extended for steady-state and transient analyses of Sodium cooled Fast Reactor (SFR) cores. In contrast to LWRs, thermal expansions of SFR core and reactor components such as fuel, cladding, diagrid, control rod (CR) drivelines, vessel, etc. provide essential reactivity feedbacks under normal and transient conditions. Since DYN3D was originally oriented to the LWRs analyses, the modeling of thermal expansion mechanisms was not considered in the code. Therefore, the development of a new thermal-mechanical module accounting for thermal expansions has been initiated as a part of the SFR related activities. At first step, the DYN3D code was extended with the capability of treating two important thermal expansion effects occurring within the core, namely axial expansion of fuel rod and radial expansion of diagrid. Part I of the paper provides a detailed description of the newly implemented models and presents the results of the initial verification study performed on a full core level using a large oxide SFR core from the OECD/NEA benchmark and a Phenix end-of-life core from the static neutronic IAEA benchmark. Two IAEA benchmarks on the Phenix end-of-life experiments were used for a more detailed validation of the extended version of DYN3D. While Part II presents the validation study performed against the static neutronic benchmark of the control rod withdrawal tests, the results of the initial stage of the natural circulation test are covered in Part III of the paper.

Part I of this study introduced a novel methodology for the optimization of energy group structures to be used in diffusion calculations of Sodium cooled Fast Reactors. The goal of the optimization is to speed up calculations, particularly in transient analyses, while maintaining an acceptable accuracy of the results. The proposed methodology is based by either direct or simulated annealing search techniques. The capabilities of the method were preliminarily demonstrated on a single core state of the Superphenix reactor by using the DYN3D nodal diffusion code. The scope of Part II is the further demonstration of the methodology efficiency through its application to more challenging “real-life” cases. In this respect, a static Superphenix neutronic benchmark comprising 13 different core states and a transient test initiated by an increase of the core inlet temperature at the Phenix reactor are considered. For both Superphenix and Phenix reactor cores, 2- to 12-group optimal condensed energy group structures are identified using the 24-group structure as a starting point. The obtained optimal structures are thus employed in DYN3D and compared to the reference 24-group DYN3D solutions. The outcomes show that also for a broader range of core configurations and under transient conditions the optimal energy group structures allow for significant acceleration of the DYN3D performance with practically negligible degradation of the solution accuracy.

The FP7 EURATOM project FREYA has been executed between 2011 and 2016 with the aim of supporting the design of fast lead-cooled reactor systems such as MYRRHA and ALFRED. During the project, a number of critical experiments were conducted in the VENUS-F facility located at SCK·CEN, Mol, Belgium. The Monte Carlo code Serpent was one of the codes applied for the characterization of the critical VENUS-F cores. Four critical configurations were modeled with Serpent, namely the reference critical core, the clean MYRRHA mock-up, the full MYRRHA mock-up, and the critical core with the ALFRED island. This paper briefly presents the VENUS-F facility, provides a detailed description of the aforementioned critical VENUS-F cores, and compares the numerical results calculated by Serpent to the available experimental data. The compared parameters include keff, point kinetics parameters, fission rate ratios of important actinides to that of U235 (spectral indices), axial and radial distribution of fission rates, and lead void reactivity effect. The reported results show generally good agreement between the calculated and experimental values. Nevertheless, the paper also reveals some noteworthy issues requiring further attention. This includes the systematic overprediction of reactivity and systematic underestimation of the U238 to U235 fission rate ratio.

The China Experimental Fast Reactor (CEFR) is the first SFR operated in China. The CEFR physical start-up tests, conducted in 2010, included control rod (CR) worth (CRW) measurements by the rod drop method. In this study, the transient simulations of the actual course of eigth CR drop experiments have been performed with the Monte Carlo code Serpent using a detailed 3D heterogeneous CEFR core model. For each of the eight cases, the calculated time-depended neutron population, dynamic reactivity, and CRW have been compared to the measurements. The experimental and calculated reactivity curves have shown a very close behavior for the entire simulated time interval. With regard to the CRW results, a very good compliance between the experiment and simulations as well as among the applied computational approaches has been observed. The obtained results indicate that Serpent can be routinely applied to transient simulations, the area which until recently was limited to deterministic methods.

The X2 VVER-1000 benchmark provides a unique set of the operational data of a VVER-1000 reactor. This includes fresh core hot zero power (HZP) experiments, operational history of first four fuel cycles, and information on the operational transients occurred on the unit during first cycles. Since a publication of the initial versions of the benchmark, numerous updates, corrections and refinements become available. The current paper is a first in a series of publications on the revised X2 VVER-1000 benchmark. It is dedicated to the fresh core HZP experiments and includes description of the fuel and core geometries, the material compositions, description and results of the measurements taken during fresh core start-up. In addition, the paper includes the reference Monte Carlo solution for the HZP experiments obtained with Serpent 2. The calculated and measured values are in a good agreement. Further extension of the benchmark definition is foreseen in the near future.

During the EURATOM FP7 project FREYA, a number of experiments were performed in a critical core assembled in the VENUS-F zero-power reactor able to reproduce the ALFRED lead-cooled fast reactor spectrum in a dedicated island. The experiments dealt with the measurements of integral and local neutronic parameters, such as the core criticality, the control rod and the lead void reactivity worth, the axial distributions of fission rates for the nuclides of major interest in a fast spectrum, the spectral indices of important actinides (238U, 239Pu, 237 Np) with respect to 235U. With the main aim to validate the neutronic codes adopted for the ALFRED core design, the VENUS-F core and its characterization measurements were simulated with both deterministic (ERANOS) and stochastic (MCNP, SERPENT) codes, by adopting different nuclear data libraries (JEFF, ENDF/B, JENDL, TENDL). This paper summarizes the main results obtained by highlighting a general agreement between measurements and simulations, with few discrepancies for some parameters that are discussed here. Additionally, a sensitivity and uncertainty analysis was performed with deterministic methods for the core reactivity: it clearly indicates that the small over-criticality estimated by the different codes/libraries resulted to be lower than the uncertainties due to nuclear data.

The paper presents a general hybrid method that combines the micro-depletion technique with correction of micro- and macro-diffusion parameters to account for the spectral history effects. The fuel in a core is subjected to time- and space-dependent operational conditions (e.g. coolant density), which cannot be predicted in advance. However, lattice codes assume some average conditions to generate cross sections (XS) for nodal diffusion codes such as DYN3D. Deviation of local operational history from average conditions leads to accumulation of errors in XS, which is referred as spectral history effects. Various methods to account for the spectral history effects, such as spectral index, burnup-averaged operational parameters and micro-depletion, were implemented in some nodal codes. Recently, an alternative method, which characterizes fuel depletion state by burnup and 239Pu concentration (denoted as Pu-correction) was proposed, implemented in nodal code DYN3D and verified for a wide range of history effects. The method is computationally efficient, however, it has applicability limitations. The current study seeks to improve the accuracy and applicability range of Pu-correction method. The proposed hybrid method combines the micro-depletion method with a XS characterization technique similar to the Pu-correction method. The method was implemented in DYN3D and verified on multiple test cases. The results obtained with DYN3D were compared to those obtained with Monte Carlo code Serpent, which was also used to generate the XS. The observed differences are within the statistical uncertainties.

The article provides an overview of the reactor dynamics code DYN3D. The code comprises various 3D neutron kinetics solvers, a thermal-hydraulics reactor core model and a thermo-mechanical fuel rod model. The implemented models and methods and the capabilities and features of the code are described. Latest developments of models and methods are delineated. An overview on the status of verification and validation is given. Code applications for selected safety analyses are described. Furthermore, multi-physics code couplings to thermal-hydraulic system codes, CFD and sub-channel codes as well as to the fuel performance code TRANSURANUS are outlined. Developments for innovative reactor concepts, in particular Molten Salt Reactor, High Temperature Gas-cooled Reactor and Sodium Fast Reactor are delineated. The management of code maintenance is briefly described. An outlook on further code development is given.

This paper describes the methods used in the Serpent 2 Monte Carlo code for producing homogenized group constants for nodal diffusion and other deterministic reactor simulator calculations. The methodology covers few-group reaction cross sections, scattering matrices, diffusion coefficients and poison cross sections condensed in infinite and B 1 leakage-corrected critical spectra, as well as the calculation of discontinuity factors, pin-power form factors, delayed neutron parameters and total and partial albedos. Also included is a description of an automated burnup sequence, which was recently implemented for the handling of restart calculations with branch variations. This capability enables covering the full range of local operating conditions required for the parameterization of group constants within a single run. The purpose of this paper is to bring the methodological description provided in earlier publications up to date, and provide insight into the developed methods and capabilities, including their limitations and known flaws.

This paper investigates the feasibility of a once-through thorium fuel cycle for the novel reactor-design concept named the pressure tube light water reactor with variable moderator control (PTVM LWR). The PTVM LWR operates in a “breed & burn” mode, which makes it an attractive system for utilizing thorium fuel in a once-through mode. The “breed & burn” mode can emphasize the in situ generation as well as incineration of 233U, which are the basic foundations of the once-through thorium fuel cycle. The PTVM LWR concept makes use of a seed–blanket geometry, whereby the core is divided into separated regions of thorium-based fuel channel assemblies (blanket) and low-enriched uranium (LEU) based fuel channel assemblies (seed). A novel fuel in-core management scheme based on two separate fuel flow routes (i.e., seed route and blanket route) is proposed and analyzed. Neutronic performance analysis indicates that the proposed novel fuel in-core management scheme has the potential to utilize both LEU- and thorium-based fuel in an efficient manner. The once-through thorium cycle, presented and discussed in this paper, provide interesting research leads and can serve as a bridge between current LEU-based fuel cycles and a thorium fuel cycle based on recycling of 233U.

This research focuses on the verification of a recently developed methodology accounting for spectral history effects in 3D full core nodal simulations. The traditional deterministic core simulation procedure includes two stages: (1) generation of homogenized macroscopic cross section sets and (2) application of these sets to obtain a full 3D core solution with nodal codes. The standard approach adopts the branch methodology in which the branches represent all expected combinations of operational conditions as a function of burnup (main branch). The main branch is produced for constant, usually averaged, operating conditions (e.g. coolant density). As a result, the spectral history effects that associated with coolant density variation are not taken into account properly. Number of methods to solve this problem (such as micro-depletion and spectral indexes) were developed and implemented in modern nodal codes. Recently, we proposed a new and robust method to account for history effects. The methodology was implemented in DYN3D and involves modification of the few-group cross section sets. The method utilizes the local Pu-239 concentration as an indicator of spectral history. The method was verified for PWR and VVER applications. However, the spectrum variation in BWR core is more pronounced due to the stronger coolant density change. The purpose of the current work is investigating the applicability of the method to BWR analysis. The proposed methodology was verified against recently developed BGCore system, which couples Monte Carlo neutron transport with depletion and thermal-hydraulic solvers and thus capable of providing a reference solution for 3D simulations. The results clearly show that neglecting the spectral history effects leads to a very large deviation (e.g. 1700 pcm in multiplication factor) from the reference solution. Application of the Pu-correction method results in a very good agreement between DYN3D and BGCore on the order of 200 pcm in k inf .

External or internal hazards, combined with multiple failures of components and safety systems or human errors can lead to a reactor core melt. In that case the reactor pressure vessel is the last barrier to keep the molten materials inside the reactor and to prevent further challenges to the nuclear power plant structures and consequently to the environment. In-vessel melt retention by external vessel cooling is a possible mitigative severe accident measure. Up to the moment it is not considered as a severe accident management strategy for VVER-1000 reactors. In this paper we analyse the possibility of in-vessel melt retention for a generic pressurized water VVER-1000 reactor during the late in-vessel phase of a postulated station blackout scenario. We developed a numerical model describing the thermal behaviour of a segregated molten pool situated in the lower plenum of the reactor pressure vessel and the thermo-mechanic behaviour of the vessel wall. The finite element code ANSYS® was used for the simulations. The results show that the highest thermo-mechanical loads are observed in the vertical part of the vessel wall, which is in contact with the molten metal. Parameter studies on the thickness of the metal layer have also been performed. Without flooding, the vessel wall will fail, as the necessary temperature for a balanced heat release from the external surface via radiation is near to or above the melting point of the steel. However, the external flooding could help the retention of the corium within the reactor pressure vessel.

This study explores the possibility of designing a high conversion (HC) Th-U233 core for current generation of Pressurized Water Reactors (PWRs). Increasing the conversion ratio in existing PWRs can potentially improve the utilization of natural resources, through the exploitation of vast thorium reserves and reduction in natural uranium demand. HC can be achieved through the use of heterogeneous seed-blanket (SB) Th-U233 fuel assembly design where the supercritical seed works as a neutron supplier, while the subcritical blanket acts as U233 breeder. One of the main challenges associated with the heterogeneous SB fuel assembly designs is a significant power imbalance between the seed and blanket regions caused by the concentration of fissile material primarily in the seed zone and consequently requiring a substantial reduction in the core average power density. The main objectives of the current work are: (1) to design a HC SB Th-U233 fuel assembly which is directly retrofittable into existing PWRs without introducing significant modifications into the core and plant design; (2) to estimate the reasonably achievable core power density level at which reactor safety is not compromised by performing 3D coupled neutronic and thermal–hydraulic (T–H) analysis of a typical PWR core fully loaded with HC Th-U233 SB fuel. Part I of the two-part paper presents the results of the assembly-level parametric study aiming at the selection of a number of SB fuel assembly configurations for the following whole-core analysis. The assembly configurations are selected according to their potential to satisfy the specified fuel cycle requirements and comply with the T–H safety limits. The results of the 3D full core analysis are reported in Part II of the paper.

This study explores a possibility of designing a high conversion (HC) Th–U233 core for current generation of pressurized water reactors (PWRs). Increasing the conversion ratio in existing PWRs can potentially improve the utilization of natural resources, through the exploitation of vast thorium reserves and reduction in natural uranium demand. HC can be achieved through the use of heterogeneous seed-blanket (SB) Th–U233 fuel assembly design, where the supercritical seed works as a neutron supplier, while the subcritical blanket acts as U233 breeder. One of the main challenges associated with the heterogeneous SB fuel assembly designs is significant power imbalance between the seed and blanket regions caused by the high concentration of fissile material in the seed region and consequently requiring a substantial reduction in the core average power density. The main objectives of the current work are: (1) to design a high conversion SB Th–U233 fuel assembly which is directly retrofittable into existing PWRs without introducing significant modifications into the core and plant design; (2) to estimate the reasonably achievable core power density level at which reactor safety is not compromised by performing 3D coupled neutronic and thermal–hydraulic (T–H) analysis of a typical PWR core fully loaded with HC Th–U233 SB fuel. Part II of the two-part paper reports on the steady-state whole core analysis of 100% Th–U233 fueled PWR. The results of this study demonstrate the feasibility in principle of achieving conversion ratio close to unity for a Th–U233 PWR core operating at power density of 60 W/cc, in three-batch annual fuel cycle and without exceeding the main safety limits.

Experimental results for the Xe depletion in the matrix of high burn-up fuel are presented from the High Burnup Rim Project (HBRP). In this project a number of UO 2 fuel discs with 235 U enrichment of 25.8 wt.% were irradiated. The Xe content of the fuel discs was analysed by means of electron probe microanalysis (EPMA). The influence of the burn-up and irradiation temperature on the Xe concentration was investigated using a multi-physics approach involving various simulation tools. The temperature influence was modelled by means of the temperature dependent effective burn-up. Good agreement was found between the modelled temperature threshold of the effective burn-up and the experimental temperature threshold between un- and restructured fuel in the HBRP. However, a systematic difference is observed between the onset burn-up derived from the Xe measurements in highly enriched discs such as those of HBRP and the corresponding values derived from irradiated Light Water Reactor (LWR) fuel rods and reported in the open literature. A sensitivity study identified the neutron flux spectrum and the fission product yields as the main reasons for the observed differences.

The reactor code DYN3D was developed at the Helmholtz-Zentrum Dresden-Rossendorf to study steady state and transient behavior of Light Water Reactors. Concerning the neutronics part, the multigroup diffusion or SP3 transport equation based on nodal expansion methods is solved both for hexagonal and square fuel element geometry. To deal with Block-type High Temperature Reactor cores DYN3D was extended to a version DYN3D-HTR. A 3D heat conduction model was introduced to include 3D effects of heat transfer and heat conduction and the detailed structure of the fuel element. Homogenized neutronic cross sections were generated by applying a Monte Carlo approach with resolution of each individual TRISO fuel particle. Results of coupled steady state and transient calculations with 12 energy groups are presented. Transient case studies are control rod insertion, a change of the inlet coolant temperature and a change of the coolant gas mass flow rate. It is shown that DYN3D-HTR is an appropriate code system to simulate steady states and short time transients. Furthermore the necessity of the 3D heat conduction model is demonstrated.

This paper presents the methodology developed for the Serpent 2 Monte Carlo code for the calculation of adjoint-weighted reactor point kinetics parameters: effective generation time and delayed neutron fractions. The calculation routines were implemented at the Politecnico di Milano, and they are based on the iterated fission probability (IFP) method. The developed methodology is mainly intended for the modeling of small research reactor cores, and the results are validated by comparison to experimental data and MCNP5 calculations in 31 critical configurations.

An innovative light water reactor constructed as a multitude of modular, horizontal fuel channels has been proposed. The basic novelty of the proposed design is an implementation of the “breed & burn” mode of operation by a dynamic variation of the moderator content in the core. This paper describes the novel reactor core design and explores the physical principles underlying its operation. Initially, a single fuel channel assembly was analyzed in order to evaluate the impact of the moderator variation on the reactivity and “breed & burn” processes. At the second stage, a full core model was analyzed, demonstrating a possibility of a realistic fuel management scheme with on-power moderator addition. The BGCore Monte-Carlo based depletion code was used for the analyses. It has been shown that the proposed design has a potential to increase the fuel utilization, attain negative reactivity coefficients and reduce the excess core reactivity during the power operation. The physical observations, presented and discussed in this paper, provide an interesting research lines for future investigation and continuous design developments.

In this study, HELIOS-2 deterministic transport code and Serpent Monte–Carlo (MC) reactor physics code were considered as tools for preparation of few-group constants for sodium cooled fast reactor (SFR) analysis. Initially, applicability of the mainly LWR-oriented HELIOS-2 code to the modeling of SFR lattices was investigated and recommendations for methodological modifications were given. At the next stage the methodology for few-group cross section generation for fuel and non-multiplying regions of SFR core was proposed. Afterward, few-group constants produced by HELIOS-2 and Serpent employing the proposed methodology were used by nodal diffusion code DYN3D for the analysis of a reference SFR core. Finally, the DYN3D results were verified against the full core Serpent MC solution. The full core DYN3D results obtained using few-group constants produced by Serpent agreed very well with that of the reference full core MC simulations. The use of HELIOS-2 based few-group constants led to somewhat reduced agreement between reference MC and DYN3D results. The implementation of the suggested modifications to the HELIOS-2 methodology can potentially improve its modeling accuracy for SFR lattices.

DYN3D reactor dynamics nodal diffusion code was originally developed for the analysis of Light Water Reactors. In this paper, we demonstrate the feasibility of using DYN3D for modeling of fast spectrum reactors. A homogenized cross sections data library was generated using continuous energy Monte-Carlo code Serpent which provides significant modeling flexibility compared with traditional deterministic lattice transport codes and tolerable execution time. A representative sodium cooled fast reactor core was modeled with the Serpent–DYN3D code sequence and the results were compared with those produced by ERANOS code and with a 3D full core Monte-Carlo solution. Very good agreement between the codes was observed for the core integral parameters and power distribution suggesting that the DYN3D code with cross section library generated using Serpent can be reliably used for the analysis of fast reactors.

During the GUINEVERE FP6 European project (2006-2011), the zero-power VENUS water-moderated reactor was modified into VENUS-F, a mock-up of a lead cooled fast spectrum system with solid components that can be operated in both critical and subcritical mode. The Fast Reactor Experiments for hybrid Applications (FREYA) FP7 project was launched in 2011 to support the designs of the MYRRHA Accelerator Driven System (ADS) and the ALFRED Lead Fast Reactor (LFR). Three VENUS-F critical core configurations, simulating the complex MYRRHA core design and one configuration devoted to the LFR ALFRED core conditions were investigated in 2015. The MYRRHA related cores simulated step by step design peculiarities like the BeO reflector and in pile sections. For all of these cores the fuel assemblies were of a simple design consisting of 30% enriched metallic uranium, lead rodlets to simulate the coolant and Al2O3 rodlets to simulate the oxide fuel. Fission rate ratios of minor actinides such as Np-237, Am-241 as well as Pu-239, Pu-240, Pu-242 and U-238 to U-235 were measured in these VENUS-F critical assemblies with small fission chambers in specially designed locations, to determine the spectral indices in the different neutron spectrum conditions. The measurements have been analyzed using advanced computational tools including deterministic and stochastic codes and different nuclear data sets like JEFF-3.1, JEFF-3.2, ENDF/B7.1 and JENDL-4.0. The analysis of the C/E discrepancies will help to improve the nuclear data in the specific energy region of fast neutron reactor spectra. © The Authors, published by EDP Sciences, 2017.

The residual radioactive decay heat plays an important role in some accident scenarios and, therefore, needs to be accurately calculated when performing accident analyses. The current reactor simulation codes used for accident analysis account for the residual decay heat by means of simplified models. Typically, these models rely on semi-empirical correlations which are defined over a limited range of burnup and fuel types. Therefore, the applicability of such correlations is limited and any deviation from the definition range may lead to high uncertainties, which is detrimental in evaluating safety margins. Reactor dynamic code DYN3D was originally developed for transient and accident analysis of LWRs. In DYN3D, the residual radioactive decay heat calculation is based on the German national standard DIN Norm 25463 model. The applicability of this model is limited to a low enriched uranium dioxide fuel for light water reactors. This paper describes a new general decay heat calculation model implemented in DYN3D. The radioactive decay rate of each nuclide in each spatial node is calculated by recently implemented depletion module and the cumulative released heat is used to obtain the spatial distribution of the decay power for every time step. Such explicit approach is based on first principles and is free from approximations and, thus, can be applied to any reactor system (e.g. thermal and fast) and fuel type. The proposed method is verified through code-to-code comparison with the Serpent 2 Monte Carlo code results.

DYN3D is a three-dimensional nodal code for steady-state and transient analyses of Light Water Reactors applicable for square and hexagonal fuel assembly geometries. Several versions of the DYN3D code are available including a multigroup diffusion and a simplified P3 (SP3) neutron transport option. The multi-group SP3 method based on a trigonal geometry was developed recently. This method is applicable to the analysis of reactor cores with hexagonal fuel assemblies and allows flexible mesh refinement. In this paper, the theoretical background for the SP3 method is briefly described. The consistency of the implementation of the trigonal SP3 methodology in DYN3D is demonstrated by means of a simplified VVER-440 core test example. The corresponding few-group homogenized cross sections and reference solutions were produced by the Monte Carlo code Serpent. The DYN3D results are in good agreement with the reference solutions.

This work shows the effect of the use of moderating layers on the sodium void effect in sodium cooled, MOX fuelled fast breeder reactors. The moderating layers are consisting of either zirconium boride ZrB2 or zirconium hydride ZrH2. The two investigated ZrH2 layers (0.1mm and 0.2 mm thick) cause a strong reduction of the sodium void effect. Additionally these layers improve the fuel temperature effect and the coolant effect of the system significantly. All changes caused by the insertion of the ZrH2 layers cause a significantly increased stability of the fast reactor system against transients. The moderating layers have only a small influence on the breeding effect and on the production of minor actinides.

BGCore reactor analysis system was recently developed at Ben-Gurion University for calculating in-core fuel composition and spent fuel emissions following discharge. It couples the Monte Carlo transport code MCNP with an independently developed burnup and decay module SARAF. Most of the existing MCNP based depletion codes (e.g. MOCUP, Monteburns, MCODE) tally directly the one-group fluxes and reaction rates in order to prepare one-group cross sections necessary for the fuel depletion analysis. BGCore, on the other hand, uses a multi-group (MG) approach for generation of one group cross-sections. This coupling approach significantly reduces the code execution time without compromising the accuracy of the results. Substantial reduction in the BGCore code execution time allows consideration of problems with much higher degree of complexity, such as introduction of thermal hydraulic (TH) feedback into the calculation scheme. Recently, a simplified TH feedback module, THERMO, was developed and integrated into the BGCore system. To demonstrate the capabilities of the upgraded BGCore system, a coupled neutronic TH analysis of a full PWR core was performed. The BGCore results were compared with those of the state of the art 3D deterministic nodal diffusion code DYN3D ( Grundmann et al., 2000 ). Very good agreement in major core operational parameters including k-eff eigenvalue, axial and radial power profiles, and temperature distributions between the BGCore and DYN3D results was observed. This agreement confirms the consistency of the implementation of the TH feedback module. Although the upgraded BGCore system is capable of performing both, depletion and TH analyses, the calculations in this study were performed for the beginning of cycle state with pre-generated fuel compositions.

This work shows the effect of the use of moderating layers on the sodium void effect in sodium cooled fast breeder reactors. The moderating layers consisting of either boron carbide B4C or uranium-zirconium hydride UzrH cause a strong reduction of the sodium void effect. Additionally these layers improve the fuel temperature effect and the coolant effect of the system. The use of the UZrH is significantly more effective for the reduction of the sodium void effect as well as for the improvement of the fuel temperature and the coolant effect. All changes cause by the insertion of the UZrH layer cause a significantly increased stability of the fast reactor system against transients. The moderating layers have only a small influence on the breeding effect and on the production of minor actinides.

Current practice of Pu recycling in existing Light Water Reactors (LWRs) in the form of U–Pu mixed oxide fuel (MOX) is not efficient due to continuous Pu production from U-238. The use of Th–Pu mixed oxide (TOX) fuel will considerably improve Pu consumption rates because virtually no new Pu is generated from thorium. In this study, the feasibility of Pu recycling in a typical pressurized water reactor (PWR) fully loaded with TOX fuel is investigated. Detailed 3-dimensional 100% TOX and 100% MOX PWR core designs are developed. The full MOX core is considered for comparison purposes. The design stages included determination of Pu loading required to achieve 18-month fuel cycle assuming three-batch fuel management scheme, selection of poison materials, development of the core loading pattern, optimization of burnable poison loadings, evaluation of critical boron concentration requirements, estimation of reactivity coefficients, core kinetic parameters, and shutdown margin. The performance of the MOX and TOX cores under steady-state condition and during selected reactivity initiated accidents (RIAs) is compared with that of the actual uranium oxide (UOX) PWR core. Part I of this paper describes the full TOX and MOX PWR core designs and reports the results of steady state analysis. The TOX core requires a slightly higher initial Pu loading than the MOX core to achieve the target fuel cycle length. However, the TOX core exhibits superior Pu incineration capabilities. The significantly degraded worth of control materials in Pu cores is partially addressed by the use of enriched soluble boron and B 4 C as a control rod absorbing material. Wet annular burnable absorber (WABA) rods are used to flatten radial power distribution. The temperature reactivity coefficients of the TOX core were found to be always negative. The TOX core has a slightly reduced, as compared to UOX core, but still sufficient shutdown margin. In the TOX core β eff is smaller by about a factor of two in comparison to the UOX core and even lower than that of the MOX core. The combination of small β eff and reduced control materials worth may potentially deteriorate the performance under RIA conditions and requires an additional examination. The behavior of the considered cores during the most limiting RIAs, such as rod ejection, main steam line break, and boron dilution, is further investigated and reported in Part II of the paper.

Nowadays nuclear power is the only greenhouse-free source that can contribute appreciably to the solution of the increasing world-wide energy demand problem. The use of Thorium in the nuclear energy production may offer some unique advantages to accomplish this task. Extensive research and development on the thorium fuel cycle has been conducted in many countries around the world. Starting from the current nuclear waste policy as well as from the (V)HTR good capabilities of Pu burning, the EU PUMA project focus on core physics investigations, in order to further demonstrate the potential benefits of using the HTR core as a Pu/MA transmuter. In this paper the following aspects have been analyzed: – The state of art about the studies focusing on the use of Th in different core concepts – The use of Th in HTRs, with a particular emphasis on Th-Pu fuel cycles – An original assessment of Th-Pu fuel cycles in HTR, on the basis, the energy produced totally, per initial Pu and the ratio between discharged and loaded Pu mass Some aspects related to Thorium exploitation were outlined, with a particular emphasis on its suitability for working in pebble-bed HTR as a fertile element in a Th-Pu fuel cycle, that is a promising kind of fuel considered in the framework of the EU PUMA project. Particularly, the influence of the Th/Pu weight fraction at BOC in a typical HTR pebble was analyzed as far as the reactivity trend vs. burn-up, the energy produced per Pu unit mass, and the Pu isotopic composition at EOC are concerned. The obtained results suggest us that there is not a best composition for the PBMR Pu/Th fuel. However deeper investigations need to be performed in order to draw final conclusions. Thus, at the moment it is possible to state that some optimized Th percentage in the initial Pu/Th fuel could be suggested on the basis of the aim we are trying to reach.

Coupled Monte Carlo depletion systems provide a versatile and an accurate tool for analyzing advanced thermal and fast reactor designs for a variety of fuel compositions and geometries. The main dr...

In the previous studies, reported in Parts I and II of the paper, a High Conversion (HC) Th–U233 fuel design for current generation of PWRs was proposed and investigated in details on a single fuel assembly and 3D full core levels. One of the important limitations of the previous studies was the reliance on the availability of pure U233 as a fissile driver. In reality however, U233 will always be accompanied by other U isotopes with changing relative fractions until equilibrium is reached. Part III of the paper deals with a number of fuel cycle aspects associated with the use of HC Th–U fuel in PWRs including: (1) More realistic estimation of neutronic characteristics and conversion performance of HC Th–U fuel by accounting for the evolution of U isotopic composition with the number of recycle stages; (2) Reassessment of the HC Th–U PWR core performance through 3D full core coupled neutronic and T–H analysis using the equilibrium Uranium isotopic vector; (3) Demonstration of a feasible way of generating U233; (4) Evaluation of potential savings in available resources that can be achieved by using HC Th–U fuel cycle as compared to the current fuel cycle practices. The obtained results imply that the self-sustainable mode of operation for the proposed HC Th–U fuel assembly design cannot be achieved under the specified fuel cycle length constraint when a realistic U vector is taken into account in the analysis. Nevertheless, the introduction of HC Th–U fuel cycle can notably improve the utilization of available resources.

The nodal diffusion code DYN3D (Grundmann et al., 2000, 2005) is under extension for Sodium cooled Fast Reactor (SFR) application. As a part of the extension new models for thermal expansion reactivity feedbacks are needed. One of these is the reactivity feedback of the axial fuel rod expansion, which is dependent on local temperatures. The difficulty in the modeling of this effect with nodal codes can be attributed to the inflexibility of the nodal mesh i.e. all nodes in a same axial layer have to be of an identical height. This restricts the modeling to a simplified case of the radially uniform axial expansion. In this study a new model for the treatment of axial fuel rod expansions was developed and implemented in DYN3D. The idea of the model was to preserve the axial size of the nodes and to account for the axial expansion effects by manipulation of homogenized few-group cross sections (XS). In this way the rigid nodal discretization can remain unchanged, and each node can be treated separately depending on its degree of expansion. The model recombines (“mixes”) the XS for the affected nodes, depending on the contribution of the expanded materials inside of the node.

This paper investigates the basic feasibility of using reactor-grade Pu in fertile-free fuel (FFF) matrix in pressurized water reactors (PWRs). Several important issues were investigated in this work: the Pu loading required to achieve a specific interrefueling interval, the impact of inert matrix composition on reactivity constrained length of cycle, and the potential of utilizing burnable poisons (BPs) to alleviate degradation of the reactivity control mechanism and temperature coefficients Although the subject was addressed in the past, no systematic approach for assessment of BP utilization in FFF cores was published. In this work, we examine all commercially available BP materials in all geometrical arrangements currently used by the nuclear industry with regards to their potential to alleviate the problems associated with the use of FFF in PWRs. The recently proposed MgO-ZrO 2 solid-state solution fuel matrix, which appears to be very promising in terms of thermal properties and radiation damage resistance, was used as a reference matrix material in this work. The neutronic impact of the relative amounts of MgO and ZrO 2 in the matrix were also studied. The analysis was performed with a neutron transport and fuel assembly burnup code BOXER. A modified linear reactivity model was applied to the two-dimensional single fuel assembly results to approximate the full core characteristics. Based on the results of the performed analyses, the Pu-loaded FFF core demonstrated potential feasibility to be used in existing PWRs. Major FFF core design problems may be significantly mitigated through the correct choice of BP design. It was found that a combination of BP materials and geometries may be required to meet all FFF design goals. The use of enriched (in most effective isotope) BPs, such as 167 Er and 157 Gd, may further improve the BP effectiveness and reduce the fuel cycle length penalty associated with their use.

This paper presents results of a feasibility study aimed at developing a zero-transuranic-discharge fuel cycle based on the U-Th-TRU ternary cycle. The design objective is to find a fuel composition (mixture of thorium, enriched uranium, and recycled transuranic components) and fuel management strategy resulting in an equilibrium charge-discharge mass flow. In such a fuel cycle scheme, the quantity and isotopic vector of the transuranium (TRU) component is identical at the charge and discharge time points, thus allowing the whole amount of the TRU at the end of the fuel irradiation period to be separated and reloaded into the following cycle. The TRU reprocessing activity losses are the only waste stream that will require permanent geological storage, virtually eliminating the long-term radiological waste of the commercial nuclear fuel cycle. A detailed three-dimensional full pressurized water reactor (PWR) core model was used to analyze the proposed fuel composition and management strategy. The results demonstrate the neutronic feasibility of the fuel cycle with zero-TRU discharge. The amount of TRU and enriched uranium loaded reach equilibrium after about four TRU recycles. The reactivity coefficients were found to be within a range typical for a reference PWR core. The soluble boron worth is reduced by a factor of ∼2 from a typical PWR value. Nevertheless, the results indicate the feasibility of an 18-month fuel cycle design with an acceptable beginning-of-cycle soluble boron concentration even without application of burnable poisons.

Allowing Monte Carlo (MC) codes to perform fuel cycle calculations requires coupling to a point depletion solver. In order to peiform depletion calculations, one-group cross sections must be provided in advance. This paper focuses on generating accurate one-group cross-section values using Monte Carlo transport codes. The proposed method is an alternative to the conventional direct reaction rate tally approach, which requires substantial computational effort. The method presented here is based on the multigroup approach, in which pregenerated multigroup sets are collapsed with MC calculated flux. In our previous studies, we showed that generating accurate one-group cross sections requires their tabulation against the background cross section (σ 0 ) to account for the self-shielding effect in the unresolved resonance energy range. However, in previous studies, the model used for the calculation of σ n was simplified by relying on user-specified Bell and Dancofffactors. This work demonstrates that the one-group cross-section values calculated under the previous simplified model assumptions may not always agree with the directly tallied values. More specifically, the assumption is not universally applicable to the analysis of reactor systems with different neutron spectra and may be inaccurate when the number of energy groups is reduced (i.e., from tens of thousands to hundreds of groups). Therefore, the original background cross-section model was extended by implicitly accounting for the Dancoff and Bell factors. The method developed here reconstructs the correct value of a 0 by utilizing statistical data generated within the MC transport calculation by default. The proposed method was implemented in the BGCore code system. The one-group cross-section values generated by BGCore were compared with those tallied directly from the MCNP code. Very good agreement in the one-group cross-section values was observed. The method does not carry any additional computational burden, and it is universally applicable to the analysis of thermal as well as fast reactor systems. Adopting this multigroup methodology, which accounts for self-shielding, allows generation of highly accurate cross sections even if the number of energy groups is significantly reduced (to hundreds versus tens of thousands of groups). This reduction considerably improves the computational efficiency, which makes the analysis of large-scale reactor problems feasible.