IAEA Benchmark Research Articles

Generalized Empirical Interpolation Method With H1 Regularization: Application to Nuclear Reactor Physics

The generalized empirical interpolation method (GEIM) can be used to estimate the physical field by combining observation data acquired from the physical system itself and a reduced model of the underlying physical system. In presence of observation noise, the estimation error of the GEIM is blurred even diverged. We propose to address this issue by imposing a smooth constraint, namely, to constrain the H1 semi-norm of the reconstructed field of the reduced model. The efficiency of the approach, which we will call the H1 regularization GEIM (R-GEIM), is illustrated by numerical experiments of a typical IAEA benchmark problem in nuclear reactor physics. A theoretical analysis of the proposed R-GEIM will be presented in future works.

Jacobian-free Newton Krylov nodal expansion method in three-dimensional cylindrical coordinates

A cylindrical version of Jaocbian-free Newton Krylov nodal expansion methods in cylindrical coordinates (CyliNEM_JFNK) are successfully developed to solve the three-dimensional and multigroup k-eigenvalue reactor problems in cylindrical geometry. Unlike nodal methods in Cartesian geometry, CyliNEM_JFNK adopts the special polynomial-expansion approximation and some separate treatments to solve the transverse-integrated equations in each direction and it is not a simple and trivial extension from Cartesian geometry to cylindrical geometry. To reduce the computational cost and the scale of residual systems constructed in the CyliNEM_JFNK as much as possible, the outgoing interface partial currents, node-averaged fluxes, third and fourth expansion coefficients are only chosen as the final-solving variables to obtain the residual functions by eliminating all the other variables including incoming interface partial currents, first and second expansion coefficients, source and leakage moments. Then the efficient physics-based preconditioners are successfully developed by making full use of the efficient Row-Column iteration and original power iteration framework. The cylindrical version of 3D LWR IAEA benchmark problem and a series of three-dimensional high temperature gas-cooled pebble bed reactor models are chosen to verify the numerical accuracy and computational efficiency of the CyliNEM_JFNK method. Numerical solutions show that the proposed CyliNEM_JFNK method can track the reference solutions very well and obtain higher computational efficiency than the CyliNEM method with efficient Row-Column iteration in three-dimensional cylindrical coordinates, which indicates the advantages of the developed CyliNEM_JFNK method that can serve as a potential nodal diffusion analysis tool for three-dimensional cylindrical advanced reactor problems.

New 3D Diffusion Code Based on The Nodal Polynomial Expansion

Nodal Expansion Method (NEM) is widely employed in the neutronic design of nuclear reactors core. The main reason is its higher computational performance and efficiency when compared with the conventional fine mesh difference method or finite element method. The NEM diffusion calculation uses coarse spatial meshes and the size can lie in assembly scale. This is the key for the computational efficiency and high accuracy calculations. The NEM consists mainly of basis polynomial function expansion for each nodal direction. The Nodal Expansion Method (NEM), as proposed by Finnemann in 1977, has been used to solve the multigroup neutron diffusion equations in three-dimensional (3D) rectangular geometry. The weighted residual technique has been applied to determine the higher order coupling coefficients. Resulting from the combination of nodal and finite element methods, NEM provides rigorously accurate equations obtained by integrating the neutron balance equation. The two group coarse mesh 3D IAEA benchmark has been simulated by NEM3D-1A using different nodes sizes. The VENTURE

CFD validation with optimized mesh using benchmarking data of pebble-bed high-temperature reactor

In this study, a computational fluid dynamics (CFD) analysis conducted to predict the thermo-hydraulic performance of the HTR-10, which is an experimental pebble bed reactor (PBR). The PBR with a modular model with a realistic approach and finite volume method (FVM) instead of porous media is used to predict the distribution of the critical thermal-hydraulics parameters like temperature, pressure, velocity, and heat transfer coefficient (HTC) over the pebbles as well as the reactor core. In the simulation study, an optimized mesh used as a replacement of the large size mesh. The simulation results, for the boundary conditions such as coolant inlet and outlet temperatures, mass flow, and other thermal-hydraulics parameters, were validated with the data published by the IAEA benchmark document. This study demonstrates that the CFD analysis using an optimized mesh is capable of predicting the nature thermo-hydraulic behavior of PBR core, maintaining design safety limits like maximum fuel temperature, and coolant flows distribution.

MONTE CARLO SIMULATION OF NEUTRONICS START-UP TESTS AT CHINA EXPERIMENTAL FAST REACTOR (CEFR)

China Experimental Fast Reactor (CEFR) is a small size sodium-cooled fast reactor (SFR) with a high neutron leakage core fueled by uranium oxide. The CEFR core with 20 MW(e) power reached its first criticality in July 2010, and several start-up tests were conducted from 2010 to 2011. The China Institute of Atomic Energy (CIAE) proposed to release some of the neutronics start-up test data for the IAEA benchmark within the scope of the IAEA’s coordinated research activities through the coordinated research project (CRP) on “Neutronics Benchmark of CEFR Start-Up Tests”, launched in 2018. This benchmark aims to perform validation and verification of the physical models and the neutronics simulation codes by comparing calculation results against collected experimental data. The six physics start-up tests considered for this CRP include evaluation of the criticality, control rod worth, void reactivity, temperature coefficient, swap reactivity, and foil irradiation. Twenty-nine participating research organizations are performing independent blind calculations during the first phase of the project. As a part of this coordinated research, IAEA performed neutronics calculations using Monte Carlo code SERPENT. Two kinds of 3D core models, homogenous and heterogeneous, were calculated using SERPENT, with ENDF/B-VII.0 continuous energy library. Preliminary results with a reasonably good estimation of criticality, as well as theoretically sound results of other five test cases, are available. The paper will discuss the core modelling assumptions, challenges and key findings of modelling a dense SFR core, preliminary results of the first phase of the CRP, heterogeneity impact analysis between homogenous core models and heterogeneous core models and future work to be performed as a part of this four-year project.

Numerical study on the thermal stratification characteristics in the upper plenum of sodium-cooled fast reactor (SFR)

In this paper, the IAEA benchmark, a trip transient scenario from 40% rated power of Monju reactor in Japan, was studied using CFD method. The reactor steady state and shutdown transient scenarios were simulated and the 3-D distributions of important thermal hydraulic parameters in the SFR upper plenum was achieved. The steady state calculated results agreed well with experimental data and acceptable deviations were obtained, which indicate the application and prediction accuracy of CFD method. The complex development of thermal stratification in the upper plenum of SFR under accident conditions were obtained. The detailed flow fields in the bottom of center measuring column and near with the through flow holes were revealed. The influence of different local structures on the thermal stratification in the SFR upper plenum were understood. This work could provide a certain basis for the SFR upper plenum structure design and operation strategy making.

Investigation of the IAEA benchmark problem using MCNP code

The PWR benchmark problem was intended to draw some conclusions about the accuracy of the different neutronic calculation codes used in the routine deterministic reactor calculation. The objective of this paper is to test the MCNP code against previously obtained solutions to provide new reference solutions to the IAEA benchmark with Monte Carlo method. The effective multiplication factor, radial and axial assembly power distributions and zone average group flux were calculated using Monte Carlo code (MCNP). The MCNP results are compared with the results of deterministic solutions in two and three dimensions. Good estimates of effective multiplication factor values and power distributionvalues in two and three dimensions were showed. To assess the MCNP results, the collective percent error measures were investigated. The results of AVG, MRE and RMS error measures were less than 1 % error. So all results presented here are considered an accurate reference solution and can using as Monte Carlo reference for IAEA PWR benchmark problem.

Benchmark analyses for EBR-II shutdown heat removal tests SHRT-17 and SHRT-45R – (2) subchannel analysis of instrumented fuel subassembly

Two kinds of Loss of Flow experiments conducted in EBR-II are the subject of an IAEA benchmark exercise. The present work discusses the subchannel analysis in an instrumented subassembly, analyzed with the COBRA-IV-I code. Boundary conditions are provided by a 1D thermal–hydraulic system code (NETFLOW++) for a protected loss-of-flow and an unprotected-loss-of-flow tests conducted at the EBR-II reactor. The instrumented subassembly with 61 pins is installed in the 5th row of the reactor core in order to measure the temperature profile across the mid-plane and the top region of the fuel subassembly. The pin lattice in the subassembly consists of 126 subchannels. Calculated temperature profiles at three levels are compared with the measured results. Biased temperature profiles with respect to the center line of the subassembly measured in the experiments are appropriately simulated by the code. The presence of the spacer wire by itself introduces a biased temperature profile. The biased temperature profile is also shown by a CFD calculation using a 7-pin partial model of the instrumented subassembly. In order to obtain close agreement with measured temperatures, the power profile within the subassembly must be taken into account. Temperature evolutions during the transients are simulated by the subchannel code.

Analysis of the IAEA benchmark on heat transfer in a 4 × 4 rod bundle with mixing grid

The IAEA is organizing a Coordinated Research Project (CRP) on the application of Computational Fluid Dynamics (CFD) for nuclear reactor design. Within this CRP, an open benchmark is organized on fluid mixing in rod bundles. KAERI has offered precise experimental data of the velocity field downstream of a mixed twist/split type mixing grid. Additionally, temperature measurements in various axial and azimuthal locations of a partly heated rod were made available by KAERI. The experimental set up consists of a 2000 mm long bundle of 4 × 4 rods with pitch to diameter ratio of 1.35, placed in a square housing of 142 × 142 mm. Each rod has a diameter of 25.4 mm. The mixing grid is located at 2/3 height of the channel with 5 spacer grids located upstream and 3 downstream of the mixing grid. These experiments are analysed with the TrioCFD code. Turbulence is treated with the RANS approach by using a non-linear eddy viscosity model. The comparison of measured and calculated mean velocity fields is presented. Measured profiles of velocity mean values were calculated correctly for the central sub-channel and the gap of rod-to-rod both close and far from the mixing grid. The measured temperature is underestimated by the calculations, on one hand due to the localization of the thermocouples inside the wall of the rod and on the other hand due to the used thermal boundary condition called “imposed heat flux”. A first order correction procedure helps to understand the detected discrepancy between experiment and calculation.

Thermal-hydraulic analysis of research reactor core with different LEU fuel types using RELAP5

Abstract In the current work, comparisons between the core performances when using different LEU fuels are done. The fuels tested are UA1X-A1, U3O8-Al, and U3Si2-Al fuels with 19.7 % enrichment. Calculations are done using RELAP5 code to evaluate the thermal-hydraulic performance of the IAEA benchmark 10 MW reactor. First, a reassessment of the slow reactivity insertion transient with UA1X-A1 LEU fuel to compare the results with those reported in the IAEA TECDOC [1]. Then, comparisons between the thermal-hydraulic core performances when using the three LEU fuels are done. The assessment is performed at initial power of 1.0 W. The reactor power is calculated using the RELAP5 point kinetic model. The reactivity feedback, from changes in water density and fuel temperature, is considered for all cases. From the results it is noticed that U3Si2-Al fuel gives the best fuel performance since it has the minimum value of peak fuel temperature and the minimum peak clad surface temperature, as operating parameters. Also, it gives the maximum value of the Critical Heat Flux Ratio and the lowest tendency to flow instability occurrence.

Criticality benchmark of VVER-1000 fresh fuel assembly with MCNP

IAEA benchmark problem for VVER-1000 reactor fresh fuel assemblies has been evaluated through Monte Carlo (MC) simulation. Infinite multiplication factor (k∞) values are calculated for different hexagonal fuel assemblies with 2 wt%, 3 wt%, 3.22 wt% and 3.3 wt% enriched U-235. MC simulations have been performed with the computer code MCNP at different temperatures 120°C, 278°C, 280°C, 302°C and 305°C for three different conditions: (i) 0 ppm soluble boron concentration, (ii) 1000 ppm soluble boron concentration, and (iii) full insertion of control rod clusters (absorber material, B4C) without boron in the moderator. The results are in good agreement with the deterministic calculations as reported in IAEA-TECDOC-847.

Criticality benchmark of VVER-1000 fresh fuel assembly with MCNP

IAEA benchmark problem for VVER-1000 reactor fresh fuel assemblies has been evaluated through Monte Carlo (MC) simulation. Infinite multiplication factor (k∞) values are calculated for different hexagonal fuel assemblies with 2 wt%, 3 wt%, 3.22 wt% and 3.3 wt% enriched U-235. MC simulations have been performed with the computer code MCNP at different temperatures 120°C, 278°C, 280°C, 302°C and 305°C for three different conditions: (i) 0 ppm soluble boron concentration, (ii) 1000 ppm soluble boron concentration, and (iii) full insertion of control rod clusters (absorber material, B4C) without boron in the moderator. The results are in good agreement with the deterministic calculations as reported in IAEA-TECDOC-847.

Analysis of a VVER-1000 in-core fuel management benchmark with DRAGON and DONJON

This paper discusses the calculation of the IAEA benchmark entitled In-core fuel management code package validation for WWERs (IAEA-TECDOC-847) with the Version5 code system (DRAGON and DONJON). Calculations were performed for VVER-1000 cores. Cell calculations are done with DRAGON. Core calculations are done with DONJON, using CLE-2000 procedures to determine the reactor state at each depletion step, taking into account the control rod insertion pattern, reactor power, coolant inlet temperature and coolant mass flow. A multi-variate cross-section database for the core calculations is made with DRAGON. Calculated results are the critical boron concentration at each depletion step, and axial and radial power profiles at a few depletion steps. The present work serves as a feasibility study for the application of DRAGON and DONJON to VVER cores, and results are generally acceptable. Suggestions are made to improve the quality of the simulations.

Benchmark of the non-parametric Bayesian deconvolution method implemented in the SINBAD code for X/γ rays spectra processing

Radionuclide identification and quantification are a serious concern for many applications as for in situ monitoring at nuclear facilities, laboratory analysis, special nuclear materials detection, environmental monitoring, and waste measurements. High resolution gamma-ray spectrometry based on high purity germanium diode detectors is the best solution available for isotopic identification. Over the last decades, methods have been developed to improve gamma spectra analysis. However, some difficulties remain in the analysis when full energy peaks are folded together with high ratio between their amplitudes, and when the Compton background is much larger compared to the signal of a single peak. In this context, this study deals with the comparison between a conventional analysis based on “iterative peak fitting deconvolution” method and a “nonparametric Bayesian deconvolution” approach developed by the CEA LIST and implemented into the SINBAD code. The iterative peak fit deconvolution is used in this study as a reference method largely validated by industrial standards to unfold complex spectra from HPGe detectors. Complex cases of spectra are studied from IAEA benchmark protocol tests and with measured spectra. The SINBAD code shows promising deconvolution capabilities compared to the conventional method without any expert parameter fine tuning.

Analytic function expansion nodal (AFEN) method for solving multigroup neutron simplified P3 (SP3) equations in hexagonal-z geometry

In this paper, analytic function expansion nodal (AFEN) method was developed to solve multi-group and multi-dimensional neutron simplified P3 (SP3) equation in reactor cores with hexagonal fuel assembly. In this method, the intranodal fluxes are expanded into a set of analytic basis functions for each group and Legendre moment. Fourteen boundary conditions has been considered that constrain the intranodal flux distributions in the hexagonal-z node, which include twelve radial surface-averaged partial currents and two axial surface-averaged partial currents. The code takes few-groups cross sections produced by a lattice code and calculates the effective multiplication factor (keff), flux in multi-group energy, reactivity, and the relative power density at each fuel assembly. Finally, the solution accuracy is tested for the two and three dimensional IAEA benchmark problem. The 3D IAEA problem has been calculated for three different cases. The numerical results demonstrate that the SP3 AFEN method exhibits better accuracy compared to diffusion method especially when the control materials are inserted in the core.

Monte Carlo and nodal neutron physics calculations of the IAEA MTR benchmark using Serpent/DYN3D code system

As part of recent efforts to utilize NPPs computational methodologies to safety analysis of research reactors, the Serpent and DYN3D codes were extensively compared with a variety of static and burnup calculations as defined in the IAEA benchmark for 10 MW MTR pool-type reactor. These calculations include unit cell calculations and few group constants generation, unit cell and full core k-eigenvalue and burnup calculations, and full core 3D flux and power distributions. The Serpent code capabilities as a lattice code for MTR plate-type fuel assemblies were evaluated and compared with EPRI-CELL and WIMS-D4 results and reference solutions for full 3D core models were compared with MCNP5 and OpenMC results. The DYN3D nodal diffusion code capabilities in modeling full 3D MTR cores were also evaluated using few group cross sections and assembly discontinuity factors obtained by Serpent unit cell calculations. The DYN3D results were compared with Serpent, MCNP5 and OpenMC.

Calculation of fuel burnup and radioactive inventory in the CANDU reactor using the GETERA and MCNP4C codes

A study of fuel burnup and radioactive inventory for the CANDU bundle (37 element NU) has been carried out to benchmark the GETERA and MCNP4C computer codes for cluster geometry. The infinite multiplication factor was calculated as a function of burnup and compared with available results (IAEA benchmark, KENO VI and MCNPX Monte Carlo codes). Good agreement was observed between the present calculations and the previously published results. The differences between the GETERA code and MCNP literature were −1.85 to −14.0 mk, the GETERA code and transport literature were −4 to −8 mk, the GETERA code and IAEA benchmark were 1 to −8 mk. The GETERA code was then used to calculate the 235U and the 239Pu number densities in the bundle with maximum relative difference less than 7% compared with IAEA benchmark codes. The inventories and the corresponding activities of some important fission products were also calculated. The total radioactivity of the CANDU bundle was calculated (using the GETERA code) summing the radioactivities of all the radionuclides at 3.1 MWd/kg (available in the literature) of fuel burnup and found to be 1.158E15 compared with the WIMSD4 code result (1.122E15 Bq) with relative difference less than 3.2%.

Realistic CFD simulation of HTR-10 reactor using a face centred cubic column

High-temperature gas-cooled reactors (HTGRs) have the potential to be used as possible energy generation sources in the near future, owing to their inherently safe performance, low power density design, and high conversion efficiency. However, safety is the most important issue for its commercialisation in the nuclear energy industry. The research of the thermal-hydraulic characteristics is very important for safe design and operation of an HTGR. In this article, the thermal-hydraulic simulation of compressible flow inside the core of the pebble bed reactor HTR-10 (High Temperature Reactor) using Computational Fluid Dynamics (CFD) is described. The realistic approach was considered, where every closely packed pebble is realistically modelled considering a graphite layer and sphere of fuel. Owing to the high computational cost it is impossible to simulate the full core; therefore, the geometry used is an FCC (Face Centred Cubic) cell with the total height of the core, with 41 layers of pebbles and 82 full pebbles. The input data used were taken from the thermal-hydraulic IAEA Benchmark. The results show the profiles of temperature of the coolant in the core, and the temperature distribution inside the pebbles. The maximum temperatures in the pebbles do not exceed the allowable limit for this type of nuclear fuel. The obtained results are consistent with the results of other authors using other simulation techniques and models.

Thermal hydraulic analysis of reactivity accidents in MTR research reactors using RELAP5

Abstract The present paper comes in the line with the international approach which use the best estimate codes, instead of conservative codes, to get more realistic prediction of system behavior under off-normal reactor conditions. The aim of the current work is to apply this approach using the thermal-hydraulic system code RELAP5/Mod3.3 in a reassessment of safety of the IAEA benchmark 10 MW Research Reactor. The assessment is performed for both slow and fast reactivity insertion transients at initial power of 1.0 W. The reactor power is calculated using the RELA5 point kinetic model. The reactivity feedback terms are considered in two steps. In the first step the feedback from changes in water density and fuel temperature (Doppler effects) are considered. In the second step the feedback from the water temperature changes is added. The results from the first step are compared with that published in IAEA-TECDOC-643 benchmarks. The comparison shows that RELAP5 over predicts the peak power and consequently the fuel, clad and coolant temperatures in case of fast reactivity insertion. The results from the second step show unjustified values for reactor power. Therefore, the model of reactivity feedback from water temperature changes in the RELAP5 code may have to be reviewed.

Study of Thorium Fuel Cycles for Light Water Reactor VBER-150

The main objective of this paper is to examine the use of thorium-based fuel cycle for the transportable reactors or transportable nuclear power plants (TNPP) VBER-150 concept, in particular the neutronic behavior. The thorium-based fuel cycles included Th232+Pu239, Th232+U233, and Th232+U and the standard design fuel UOX. Parameters related to the neutronic behavior such as burnup, nuclear fuel breeding, MA stockpile, and Pu isotopes production (among others) were used to compare the fuel cycles. The Pu transmutation rate and accumulation of Pu with MA in the spent fuel were compared mutually and with an UOX open cycle. The Th232+U233 fuel cycle proved to be the best cycle for minimizing the production of Pu and MA. The neutronic calculations have been performed with the well-known MCNPX computational code, which was verified for this type of fuel performing calculation of the IAEA benchmark announced by IAEA-TECDOC-1349.