Fast Reactor Analysis Research Articles

A hybrid method to generate few-group cross sections for fast reactor analysis

ABSTRACTThe accuracy of fast reactor core calculation is usually determined by the accuracy of self-shielded few-group cross sections. To further improve the accuracy of cross section generation, a hybrid method is proposed. In the hybrid method, the Monte-Carlo method is used to deal with the resonance effect in both the resolved and unresolved resonance range. The self-shielded ultrafine-group total, fission and elastic scattering cross sections are tallied by the Monte-Carlo method. The scattering transfer matrices are then generated in a synthesis way by using the tallied elastic scattering cross sections and a problem-independent elastic scattering function. The angular flux moments for the group condensation are calculated in an explicit deterministic way. Several tests are done to verify the hybrid method. The results show that the hybrid method avoids the disadvantages of both the traditional deterministic method and the pure Monte-Carlo method. It is a more accurate method to generate the few-group cross sections for fast reactor cores.

Multi-physics models for design basis accident analysis of sodium fast reactors. Part I: Validation of three-dimensional TRACE thermal-hydraulics model using Phenix end-of-life experiments

The demonstrated technological feasibility of Sodium-cooled Fast Reactors (SFRs) makes them stand out among the other reactor concepts proposed by Generation IV International Forum (GIF) for short-term deployment. The availability of reliable computational tools in support of safety analyses and plant simulations under complex transient scenarios is essential to assure SFR’s compliance with the highest safety goals.Answering this need, a multi-physics three-dimensional core and system model is being developed to enable a more detailed representation of the physics of the plant and to anticipate more accurately plant behaviour, even under wider three-dimensional scenarios, such as asymmetric transients. The coupling will be performed using the U.S.NRC system codes TRACE-PARCS, modified to simulate more accurately when using sodium as coolant.The publicly available end-of-life tests conducted in the French SFR Phenix were chosen as baseline to perform a first validation of the computational model. The development of the tool started with a three-dimensional thermal-hydraulic nodal system of Phenix using the TRACE system code.The system simulates the Phenix end-of-life natural circulation test and the result have been compared with published experimental and benchmark results. The main physical phenomena of the 3 phases of the transient (rise in temperature in the low part of the reactor vessel, establishment of natural convection and subsequent cooling of the lower and upper part of the vessel) are predicted by the developed nodal system. More specifically, the analysis of parameters such as Intermediate Heat Exchangers (IHX), primary pumps and core temperatures, shows that the developed system is able to predict and study natural convection phenomena in Phenix-type reactors.The three-dimensional nodal system is able to clearly illustrate the existing thermal stratification in the hot pool, which is neglected by one-dimensional systems and enables the modelling of thermal hydraulic asymmetric behaviour, as it is shown by the uneven flow distribution in Phenix’s primary IHXs as they are asymmetrically located in the reactor vessel.

SARAX: A new code for fast reactor analysis part II: Verification, validation and uncertainty quantification

This paper introduces the verification and validation (V&V) work on the newly developed fast reactor code SARAX. The verifications were done based on numerical benchmark calculations and code-to-code comparisons with the Monte-Carlo code. The validation works were performed and compared with evaluated reactor physics experiments. In this paper, results from different calculation schemes are discussed, and the uncertainty from nuclear data is quantified. The results show that SARAX has good accuracy in modeling a sodium fast reactor regardless of the integration parameters, such as keff, or the distributed parameters like the sub-assembly power/reaction rate. The uncertainty quantification shows that, for a MOX-fueled SFR, the greatest uncertainty in contributed nuclear data is from the inelastic scattering cross section of U-238, which requires further improvement to reduce the uncertainty of keff.

Design and performance analysis of passive residual heat removal system for a lead-cooled fast reactor

Lead-cooled Fast Reactor (LFR) has been chosen as one of the six Generation-IV reactor concept candidates due to its high performance in neutronics, thermal hydraulics and inherent safety features. Passive residual heat removal system (PRHRS) is a passive system that guarantees the residual heat removal of LFR even in the hypothetical beyond-design basis conditions. Based on a 1000 MWth lead-bismuth cooled fast reactor, the design and performance analysis of PRHRS were conducted using RELAP5 code. First, a PRHRS removing heat by Independent Heat EXchanger (IHEX) was designed, which utilizes natural circulation, gravity field and has the characteristics of high reliability and inherent safety. Secondly, the lead-bismuth heat transfer model was developed and verified based on RELAP5/MOD 4.0 code, as the heat transfer model of Pressurized Water Reactor (PWR) is not suitable for the lead-bismuth heat transfer calculation. The RELAP5 model of LFR was established and verified by comparison with design parameters. The PRHRS performance was investigated under Loss of Power (LOP) transient to assess the feasibility of the PRHRS design. The results demonstrated that the heat removal rate of the PRHRS removing heat by IHEX exceeded the core decay rate at about 5 h. The cladding peak temperature of the PRHRS reached 562 °C, which was below the limit (750 °C). Therefore, the PRHRS removing heat by IHEX has the capability to remove the LFR residual heat and has the characteristics of high performance and inherent safety, which can be used as an independent residual heat removal system for commercial LFR. The work provides reference for the design and performance analysis of LFR PRHRS in the future.

Application of Tone’s and embedded self-shielding methods to pressurized water reactor assemblies

The Tone’s and embedded self shielding methods are based on a heterogeneous-homogeneous equivalence principle. They both provide a formula for an equivalent dilution parameter that can be used to interpolate pretabulated effective cross sections for the infinite homogeneous medium. These two methods have been traditionally applied to fast reactor analysis with fine or ultrafine group energy mesh. We are investigating the accuracy of these two methods for the generation of self-shielded cross sections for typical pressurized water reactor assemblies.

MC2-3: Multigroup Cross Section Generation Code for Fast Reactor Analysis

This paper presents the methods and performance of the MC2-3 code, which is a multigroup cross-section generation code for fast reactor analysis, developed to improve the resonance self-shielding and spectrum calculation methods of MC2-2 and to simplify the current multistep schemes generating region-dependent broad-group cross sections. Using the basic neutron data from ENDF/B data files, MC2-3 solves the consistent P1 multigroup transport equation to determine the fundamental mode spectra for use in generating multigroup neutron cross sections. A homogeneous medium or a heterogeneous slab or cylindrical unit cell problem is solved in ultrafine (2082) or hyperfine (~400 000) group levels. In the resolved resonance range, pointwise cross sections are reconstructed with Doppler broadening at specified temperatures. The pointwise cross sections are directly used in the hyperfine group calculation, whereas for the ultrafine group calculation, self-shielded cross sections are prepared by numerical integration of the pointwise cross sections based upon the narrow resonance approximation. For both the hyperfine and ultrafine group calculations, unresolved resonances are self-shielded using the analytic resonance integral method. The ultrafine group calculation can also be performed for a two-dimensional whole-core problem to generate region-dependent broad-group cross sections. Verification tests have been performed using the benchmark problems for various fast critical experiments including Los Alamos National Laboratory critical assemblies; Zero-Power Reactor, Zero-Power Physics Reactor, and Bundesamt für Strahlenschutz experiments; Monju start-up core; and Advanced Burner Test Reactor. Verification and validation results with ENDF/B-VII.0 data indicated that eigenvalues from MC2-3/DIF3D agreed well with Monte Carlo N-Particle5 MCNP5 or VIM Monte Carlo solutions within 200 pcm and regionwise one-group fluxes were in good agreement with Monte Carlo solutions.

New version of the reactor dynamics code DYN3D for Sodium cooled Fast Reactor analyses

Abstract The reactor dynamics code DYN3D being developed at the Helmholtz-Zentrum Dresden-Rossendorf is currently under extension for Sodium cooled Fast Reactor analyses. This paper provides an overview on the new version of DYN3D to be used for SFR core calculations. The current article shortly describes the newly implemented thermal mechanical models, which can account for thermal expansion effects of the reactor core. Furthermore, the methodology used in Sodium cooled Fast Reactor analyses to generate homogenized few-group cross sections is summarized. The conducted and planned verification and validation studies are briefly presented. Related publications containing more detailed descriptions are outlined for the completeness of this overview.

Application of the virtual density theory in fast reactor analysis based on the neutron transport calculation

The geometry distortion introduces one of the most important reactivity feedbacks in the fast reactor. To evaluate the reactivity caused by the geometry distortion, this paper presents a new approach applied in the steady-state fast reactor code SARAX. This approach is based on the discrete ordinates nodal method, first-order perturbation approximation and virtual density theory. In this way, the virtual material density is changed instead of changing the geometry in modeling the distortion. Compared with other methods to get geometry distortion reactivity, this method has better geometric adaptability and better efficiency in the multi-case evaluation. A series of verification are carried on, including the uniform expansion, the non-uniform expansion and the local geometry distortion. The results show that the virtual density method has good accuracy and efficiency in evaluating the geometry distortion reactivity.

Improvement and verification of the fast reactor neutronics code NECP-SARAX

The NECP-SARAX code developed by NECP research team is used for the fast reactor analysis. In order to consider the complex neutron slowing down effects from scattering resonance of nuclides with medium mass and inelastic scattering, the Monte-Carlo method was used previously but brought big uncertainty in tallying the spectrum in low energy. Besides, the efficiency is extremely low. In the improvement, a new resonance method based on ultra-fine group and point-wise cross section was involved. It generated effective multi-group cross sections with similar accuracy of Monte-Carlo method but avoided its disadvantages. In the core calculation, the multi-group cross sections were used for the 3D transport calculation. The first-order and exact perturbation theories were used in calculating the reactivity coefficients of fast reactor. To be capable of handling the geometric distorting in fast reactor, a new pseudo density method based on neutron transport and perturbation theory was proposed. Both the point kinetic and quasi-steady method were used in the transient calculation as two options to fit the requirement of fast reactor and ADS. The OECD fast reactor benchmarks were tested to verify the SARAX code, the results show good accuracy in the fast reactor calculations, which is similar to other widely accepted fast reactor code. The relative error of keff is less than 300 pcm compared with the Monte-Carlo code. Based on the pseudo density model and three-dimensional spatially dependent kinetics model, the SARAX code has more complete functions to fit the requirements of fast reactor design better.

Numerical simulations on self-leveling behaviors with cylindrical debris bed

The postulated core disruptive accidents (CDAs) are regarded as particular difficulties in the safety analysis of liquid-metal fast reactors (LMFRs). In the CDAs, core debris may settle on the core-support structure and form conic bed mounds. Then debris bed can be levelled by the heat convection and vaporization of surrounding coolant sodium, which is named “self-leveling behavior”. The self-leveling behavior is a crucial issue in the safety analysis, due to its significant effect on the relocation of molten core and heat-removal capability of the debris bed. Considering its complicate multiphase mechanism, a comprehensive computational tool is needed to reasonably simulate transient particle behavior as well as thermal-hydraulic phenomenon of surrounding fluid phases. The SIMMER program is a successful computer code initially developed as an advanced tool for CDA analysis of LMFRs. It is a multi-velocity-field, multiphase, multicomponent, Eulerian, fluid dynamics code coupled with a fuel-pin model and a space- and energy-dependent neutron kinetics model. Until now, the code has been successfully applied in numerical simulations for reproducing key thermal-hydraulic phenomena involved in CDAs as well as performing reactor safety assessment. However, strong interactions between massive solid particles as well as particle characteristics in multiphase flows were not taken into consideration in its fluid-dynamics models. To solve this problem, a new method is developed by combining the discrete element method (DEM) with the multi-fluid models of SIMMER code to reasonably simulate the particle behaviors as well as the thermal-hydraulic phenomena of multiphase fluid flows. In this paper, the coupling method is validated by performing numerical simulations on a series of experiments with cylindrical particle bed in 3D situation. Based on various experimental conditions, Reasonable agreement between simulation results and corresponding experimental data can demonstrate the applicability of the method in reproducing the self-leveling behavior of debris bed. Sensitivity analysis on some model parameters of DEM is also performed to assess their impacts in the simulation. It is expected that the present method can be used as a computational tool to estimate self-leveling process of debris beds as well as the following behaviors in real reactor environment.

Pumps modelling of a sodium fast reactor design and analysis of hydrodynamic behavior

One of the goals of Generation IV reactors is to increase safety from those of previous generations. Different research platforms have been identified the need to improve the reliability of the simulation tools to ensure the capability of the plant to accommodate the design basis transients established in preliminary safety studies. The paper describes the modelling of primary pumps in advanced sodium cooled reactors using the TRACE code. Following the implementation of the models, the results obtained in the analysis of different design basis transients are compared with the simplifying approximations used in reference models. The paper shows the process to obtain a consistent pump model of the ESFR (European Sodium Fast Reactor) design and the analysis of loss of flow transients triggered by pumps coast–down analyzing the thermal hydraulic neutronic coupled system response. A sensitivity analysis of the system pressure drops effect and the other relevant parameters that influence the natural convection after the pumps coast–down is also included.

An Advanced One-Dimensional Finite Element Model for Incompressible Thermally Expandable Flow

This paper provides an overview of a new one-dimensional finite element flow model for incompressible but thermally expandable flow. The flow model was developed for use in system analysis tools for whole-plant safety analysis of sodium fast reactors. Although the pressure-based formulation was implemented, the use of integral equations in the conservative form ensured the conservation laws of the fluid. A stabilization scheme based on streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations is also introduced. The flow model and its implementation have been verified by many test problems, including density wave propagation, steep gradient problems, discharging between tanks, and the conjugate heat transfer in a heat exchanger.

Few-group condensation via two-material coexisting ring model for fast reactor core analysis

To improve the currently used simplified fast reactor analysis method for few-group condensation, a two-material coexisting ring model is proposed in this study. In the two-material coexisting ring model, the θ-direction homogenized model from the R–θ–Z geometry is solved, but the neutron flux for each material in the homogenized region is obtained separately. In the numerical results on simple 2-D fast reactor test problems, the newly proposed two-material coexisting ring model shows excellent neutron spectrum agreement with the reference, as compared to the conventional simplified model. In addition, the few-group calculation result shows better keff estimation when a two-material coexisting ring model is used for group condensation. Because relative errors on the neutron spectrum are much flattened when the newly proposed model is used, accurate few-group cross sections can be generated even if a small few-group structure is selected for condensation.

Use and Impact of Covariance Data in the Japanese Latest Adjusted Library ADJ2010 Based on JENDL-4.0

The current status of covariance applications to fast reactor analysis and design in Japan is summarized. In Japan, the covariance data are mainly used for three purposes: (1) to quantify the uncertainty of nuclear core parameters, (2) to identify important nuclides, reactions and energy ranges which are dominant to the uncertainty of core parameters, and (3) to improve the accuracy of core design values by adopting the integral data such as the critical experiments and the power reactor operation data. For the last purpose, the cross section adjustment based on the Bayesian theorem is used. After the release of JENDL-4.0, a development project of the new adjusted group-constant set ADJ2010 was started in 2010 and completed in 2013. In the present paper, the final results of ADJ2010 are briefly summarized. In addition, the adjustment results of ADJ2010 are discussed from the viewpoint of use and impact of nuclear data covariances, focusing on 239Pu capture cross section alterations. For this purpose three kind of indices, called “degree of mobility,” “adjustment motive force,” and “adjustment potential,” are proposed.

Russian Codes for Safety Analysis of Sodium-Cooled Fast Reactors

An approach to validating the safety of sodium-cooled fast reactors which was devised in Russia as these reactors were developed is presented. The collection of computational codes used for validating safety is described. Attention is focused on a group of codes which are intended for systematic analysis of all phases of a serious beyond design-basis accident resulting in the destruction of the core. The domestic approach to the analysis of the consequences of serious accidents is compared to the methodology developed abroad. Up to now the code system under development has made it possible to perform the main tasks of design validation, but the chosen path of development, where a separate computational code was developed for each individual problem, is not exhausted. On the one hand the complexity of the mathematical models drawn into the analysis has increased significantly, while on the other hand significant advances have been made in the development of computational technologies. The answer to the present situation is the tendency observed in the world nuclear community toward developing integrated codes and multipurpose computational systems. In Russia, this tendency is realized in the program for the development of a new generation of code systems within the framework of a special federal program.

Analysis of the Neutronic Properties of the Prototype FBR Monju Based on Several Evaluated Nuclear Data Libraries

In this work three major evaluated nuclear data libraries (JENDL-4.0, JEFF-3.1.2, ENDF/B-VII.1) are used to analyze the prototype FBR Monju. Cross section libraries were generated for the fast reactor analysis code ERANOS. The purpose is to validate our ERANOS libraries, the Monju core model and estimate the performance of the nuclear data sets. The result is that the libraries give adequate performance for applications where a reasonable accuracy is sufficient (e.g. conceptual design, scoping studies), with JENDL-4.0 giving the best results. The uncertainties of various reactor parameters are larger than the future target values for FBR analysis. For analysis with very high accuracy (e.g. detailed design, licensing), data adjustment is necessary.

Development of comprehensive and versatile framework for reactor analysis, MARBLE

A comprehensive and versatile reactor analysis code system, MARBLE, has been developed. MARBLE is designed as a software development framework for reactor analysis, which offers reusable and extendible functions and data models based on physical concepts, rather than a reactor analysis code system. From a viewpoint of the code system, it provides a set of functionalities utilized in a detailed reactor analysis scheme for fast criticality assemblies and power reactors, and nuclear data related uncertainty quantification such as cross-section adjustment. MARBLE includes five sub-systems named ECRIPSE, BIBLO, SCHEME, UNCERTAINTY and ORPHEUS, which are constructed of the shared functions and data models in the framework. By using these sub-systems, MARBLE covers all phases required in fast reactor core design prediction and improvement procedures, i.e. integral experiment database management, nuclear data processing, fast criticality assembly analysis, uncertainty quantification, and power reactor analysis. In the present paper, these functionalities are summarized and system validation results are described.

Overview of major HZDR developments for fast reactor analysis

The upgrading of the DYN3D code for the application for fast reactors is described. After extension and validation, a diverse code with the possibility for steady state and transient core analysis on the basis of coupled thermal hydraulics/neutronics calculations is available. The work on the use of fine distributed moderating material in SFR cores is discussed with the target on enhancing the feedback effects in SFR cores without influencing the operational. Newly developed analytical solutions without separation of space and time for the analysis of ADS experiments are shown with good agreement for the YALINA experiment. The analytical solutions are a very promising tool for the development of a new method for the analysis of ADS experiments.

Development and Application of an Integrated Fuel Performance and Subchannel Model for Analysis of Sodium Fast Reactors

A metal fuel performance code was coupled to a subchannel analysis code to predict, in a computationally efficient way, critical phenomena that could lead to pin failure for steady-state and transient scenarios in sodium-cooled fast reactors. The fuel performance and subchannel codes coupled are FEAST-METAL and an updated version of COBRA-IV-I, respectively. In coupling the codes, the importance of azimuthal temperature and stress effects in the fuel pin were analyzed; it was concluded that azimuthal temperature averaging around the fuel pin is an acceptable approximation. The codes were coupled using a wrapper, the COBRA And FEAST Executer (CAFE), written in the Python programming language. Data from EBR-II was used to confirm and verify CAFE. Finally, CAFE was used to predict the maximum allowable burnup of three different fuel assembly designs (driver fuel, radial blanket, and tight-pitch breed-and-burn fuel) as a function of operating temperature, linear power, fuel composition, cladding thickness, and smear density.

Analysis of the MZA/MZB benchmarks with modern nuclear data sets

For fast reactor design and analysis, our laboratory uses, amongst others, the ERANOS code system. Unfortunately, the publicly available version of ERANOS does not have the most recent nuclear data. Therefore, it was decided to implement an integrated processing system to generate cross sections libraries for the ECCO cell code, as well as covariance data. Cross sections are generated from the original ENDF files. For our purposes, it is important to ascertain that the ECCO cross section libraries are of adequate quality to allow design and analysis of advanced fast reactors in an academic context. In this paper, we present an analysis of the MZA/MZB benchmarks with nuclear data from JENDL-4.0, JEFF-3.1.2 and ENDF/B-VII.1. Results are that reactivity is generally well predicted, with an uncertainty of about 1% due to covariances of the nuclear data. Reaction rate ratios are satisfactorily calculated, as well as the flux spectrum and reaction rate traverses. Some problems remain: the magnitude of the void effect is not satisfactorily calculated, and reaction rate traverses are not always satisfactorily calculated. On the whole, the ECCO libraries are sufficient for design and analysis tasks in an academic context. For high-precision calculations, such as required for licensing tasks and detailed design calculations, data adjustment is still necessary as the “native” covariance data in the ENDF files is not accurate enough.