Annals of Nuclear Energy

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1 Annals of Nuclear Energy 82 (2015) Contents lists available at ScienceDirect Annals of Nuclear Energy journal homepage: CAD-based Monte Carlo program for integrated simulation of nuclear system SuperMC Yican Wu, Jing Song, Huaqing Zheng, Guangyao Sun, Lijuan Hao, Pengcheng Long, Liqin Hu, FDS Team Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, Hefei, Anhui , China article info abstract Article history: Received 21 April 2014 Accepted 25 August 2014 Available online 7 October 2014 Keywords: Monte Carlo simulation CAD-based Multi-physics Nuclear system SuperMC Monte Carlo (MC) method has distinct advantages to simulate complicated nuclear systems and is envisioned as a routine method for nuclear design and analysis in the future. High-fidelity simulation with MC method coupled with multi-physics phenomena simulation has significant impact on safety, economy and sustainability of nuclear systems. However, great challenges to current MC methods and codes prevent its application in real engineering projects. SuperMC, developed by the FDS Team in China, is a CAD-based Monte Carlo program for integrated simulation of nuclear systems by making use of hybrid MC and deterministic methods and advanced computer technologies. The design objective, architecture and main methodology of SuperMC are presented in this paper. SuperMC2.1, the latest version, can perform neutron, photon and coupled neutron and photon transport calculation, geometry and physics modeling, results and process visualization. It has been developed and verified by using a series of benchmarking cases such as the fusion reactor ITER model and the fast reactor BN-600 model. SuperMC is still in its evolution process toward a general and routine tool for the simulation of nuclear systems. Ó 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( 1. Introduction Complicated nuclear systems such as advanced nuclear reactors have particularities in simulation over the traditional nuclear systems. The geometry is extremely complicated for modeling. Neutrons are strongly anisotropic in large energy range with complex energy spectrum structure. The nuclear system may run in critical or subcritical status with external or internal sources. The system is equipped with various coolants of different characteristics, multiple configurations of reactor core and blanket and new type fuels. The complexity and high requirements on design and safety margin of nuclear systems make the Monte Carlo (MC) methods the preferred option due to its capability of dealing complex problems with high accuracy. Many experts in the reactor community have begun to envision a bright future in which inherent advanced MC methods could be used as routine tools with the continuous improvement of high-performance computing (Smith and Forget, 2013; Brown, 2011). Although several MC codes for nuclear systems have been developed such as MCNP (X-5 Monte Carlo Team, 2003), Serpent (Leppänen, 2007), MC21 (Griesheimer et al., 2013), McCARD (Shim et al., 2012) and TRIPOLI (Diop et al., 2007), but many Corresponding author. address: yican.wu@fds.org.cn (Y. Wu). challenges prevent the applications of MC methods in real engineering projects, such as for reactor-physics problems: tediousness, intensive labor and error-prone in complex calculation geometry model generation (Wilson et al., 2008), prohibitive computational time for acceptable statistics especially when considering multi-physics feedback and coupling (Turinsky, 2012), excessive demand of computer memory, slow convergence of the fission source, apparent versus true variance, uncertainty propagation (Martin, 2005), adaptation to future computer architectures (Brown, 2011). Traditional stand-alone static solver should be transited to an integrated analysis system for simulation of multi-physics and multi-scale phenomena in reactors (Palmiotti et al., 2005). SuperMC, a Computer Aided Design (CAD)-based Monte Carlo program for integrated simulation of nuclear system, is under development by FDS Team in China. SuperMC2.1 is the latest version and can perform neutron, photon and coupled neutron and photon transport calculation, geometry and physics modeling, results and process visualization. In this paper, the overview of SuperMC and the latest development progress are presented. The intended design objective and architecture of SuperMC are described in Section 2. The main methodology which have been developed and are under development are introduced in Section 3. Functions and benchmarking cases of SuperMC2.1 are presented in Sections 4 and 5 separately, /Ó 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (

2 162 Y. Wu et al. / Annals of Nuclear Energy 82 (2015) whereas the fusion reactor ITER model (Wilson et al., 2008) and pool-type sodium cooled fast reactor BN-600 model (IAEA, 2010) are given as benchmarking examples of complex nuclear energy systems. 2. Design objective and architecture SuperMC is a CAD-based Monte Carlo program for integrated simulation of nuclear system by making use of hybrid MC-deterministic method and advanced computer technologies. As a general-purpose Monte Carlo program, SuperMC is designed for high-fidelity simulation of nuclear-system problems such as reactor physics, radiation physics, medical physics, nuclear detection. SuperMC intends to perform transport calculation of various types of particles, depletion and activation calculation including isotope burnup, material activation and shutdown dose, and multi-physics coupling calculation including thermo-hydraulics, fuel performance and structural mechanics. The bi-directional automatic conversion between general CAD models and calculation models can be easily performed. Results and process of simulation can be visualized with dynamical 3D dataset and geometry model. Continuous-energy cross section, burnup, activation, irradiation damage, material data, etc. are used to support the multi-process simulation. Advanced cloud computing framework makes the simulation which is extremely intensive in computation and data storage more attractive just as a network service. The modular design and generic interface promotes its flexible manipulation and coupling of external solvers. The architecture of SuperMC is shown in Fig Cloud computing framework The integrated simulation is highly intensive in computation and storage, especially for the simulation of large-scale nuclear systems with high-fidelity. Cloud computing framework makes the calculation and analysis more attractive as a service. Users just face simple networking GUI to access the resource pool and execute the simulation task. Users are no longer required large capital outlays in the hardware of high-performance computing cluster and do not need pay special attention to operation circumstance. The graphically and neatly defined calculation routines or coupling schemes based on uniform data exchange and task execution monitor make the system more user-friendly and intelligent Transport calculation Based on the hybrid MC and deterministic transport method, transport simulation of various particles such as neutron, photon, electron, and proton can be performed with continuous-energy cross-section libraries and mature physical models in broad energy range. Various quantities for nuclear design and analysis can be tallied by running in either fixed source mode or criticality mode. Parameters of assemblies or pins such as discontinuity factors can be generated as the input of few-group diffusion or transport calculations for whole core or assemblies. Structured mesh, unstructured mesh, continuous and large scale tallies and temperature-dependent cross section treatment are developed considering multi-physics feedback. The tally functions are easy to extend due to the hierarchical structure of particles trajectory tracking. Criticality search based on optimization algorithm aiming for specified eigenvalue within a specified confidence interval is designed exclusively for reactor design and engineering application of determining assembly configurations, fuel loadings, control device positions, soluble boron concentrations, etc Depletion and activation calculation The kernel function of this module is to calculate nuclide inventory following particles irradiation and also give details of the pathways by which these nuclides are formed. With the built-in depletion solver based on the matrix exponential method (Leppänen, 2007), users just need to specify the depletion zones in just one calculation model and depletion calculation tallies will be automatically generated. By the procedure control and inner calculation data exchange of transport and depletion solver, isotope burnup, material activation, shutdown dose can be performed. Fig. 1. Architecture of SuperMC.

3 Y. Wu et al. / Annals of Nuclear Energy 82 (2015) Multi-physics coupling calculation The transport calculation solved by hybrid MC and deterministic approach is coupled with thermal-hydraulics, fuel performance and structural mechanics module in an integrated, consistent and flexible way. Iteration scheme can also be defined graphically by the user for considering the nonlinear nature of the feedback process. Based on such a powerful coupling function, the multi-physics calculation can be used for the analysis of design basic accident (DBA), beyond design basic accident (BDBA) of advanced reactors, prediction of fuel-rod vibration, hence grid-to-rod-fretting (GTRF), etc. Sensitivity and uncertainty of the calculated parameters, cross section, etc. from single step MC calculation and the propagated uncertainties of the multi-step calculation such as MC and deterministic coupling transport, depletion calculation, multi-physics coupling can be quantified Nuclear data library The nuclear data libraries (Zou et al., 2010; Xu et al., 2010) in SuperMC for nuclear analysis include fine-group, coarse-group, fine-group and point-wise nuclear data for transport, burnup, activation, irradiation damage calculation and material data etc. The applied nuclear data libraries are designed for nuclear systems by selecting suitable energy structure and weight functions. The evaluated data are selected from international evaluated nuclear data source, such as ENDF, JENDL, and JEFF. The physical effect corrections include resonance self-shielding, thermal neutron upscattering and temperature Doppler effect Geometry and physics modeling Since text-based manual geometry description is a tedious, labor-intensive and error-prone process, especially for complex geometries of reactors, an automatic and intelligent CAD-based modeling functional module in SuperMC is developed to significantly reduce the manpower and enhance the reliability of calculation model (Wu and FDS Team, 2009). This module consists of geometry creator, physics modeling, convertor and invertor. CAD models can be imported or created and preprocessed by geometry creator. In geometry creator, users can also assign the heat transfer and coolant flow paths in the geometry. Physics modeling can interactively construct materials, sources, tallies, etc. Convertor can automatically convert CAD models with physical properties into simulation models. Conversion from unified models to calculation geometry represented by Constructive Solid Geometry (CSG), structured mesh and unstructured mesh are used to support multi-physics coupled calculation. Such approach ensures the coherence between the input data models of the solvers of different disciplines and scale. Invertor can reconstruct CAD models or facet models from simulation models for observing and modifying models by 3D visualization (Wang et al., 2011; Li et al., 2007; Zeng et al., 2006; Hu et al., 2007). Besides CAD geometry, CT, MRI, segmented images and other scan data can be converted for human body dose assessment in radiation shielding or medical physics (Cheng et al., 2011) Results and process visualization The output data can be automatically and intelligently visualized by mixing with the input models according to users interests, which simplifies information extraction from massive data (Luo et al., 2010). For static results visualization, some normal visualization functions such as curve plot, 2D map plot, mesh plot, geometry-coupled visualization and geometry-based data cutting and advanced visualization functions such as unified color mapping for various data maps are supported. Dynamical process visualization are used for assisting simulation. For example, the trajectories of particles are visualized to guide users to set cell importance in using variance reduction techniques. The calculation results can be visually analyzed in various styles such as mixed visualization with geometries, iso-surface, color map and volume rendering. 3. Main methodology 3.1. Hybrid MC and deterministic transport method In order to deal with the shielding problem of complex geometry and deep penetration of radiation, three dimensional domain hybrid MC and discrete ordinates (S N ) modeling and transport calculation method has been developed (Zhang et al., 2011). After importing the CAD model, the whole model is divided into three parts by selecting common surface: the complex region (for MC calculation using CSG geometry), the regular region (for S N calculation using mesh geometry) and coupling domain (for MC and S N calculation). The geometry domains are automatically converted into corresponding calculation model. Tally data of MC particle tracks crossing the specified surface should be mapped to discrete quadrature direction for calculating the angular flux distribution with S N method. The procedure is shown in Fig. 2. Also such hybrid transport method coupled with thermo-hydraulics will be efficient for complex transient accident analysis in which the configuration of core may change. Advanced variance reduction techniques and source convergence acceleration method play a key role in shielding calculation and criticality calculation. The adaptive variance reduction method Consistent Adjoint Driven Importance Sampling (CADIS) for localized tally region, Forward Weighted CADIS (FW-CADIS) for optimizing distributions or multiple localized tally regions, Multi Step CADIS (MS-CADIS) for shutdown dose rate calculation (Wagner et al., 2011) by using the S N method to get weight target and biased source for MC calculation are used in SuperMC. The Coarse Mesh Finite Difference (CMFD) (Lee et al., 2014) method which has been widely applied in deterministic calculation are used for accelerating MC source convergence. Deterministic solver is inner coupled for obtaining fission source distribution and neutrons in each energy group should be mapped consistently to coarse mesh cell. Parameters of assemblies or pins such as discontinuity factors and homogenized multi-group cross sections taken as the input of diffusion or transport code are generated based on homogenizing of assemblies or pins using MC method Particle interactions treatment method For particle interaction with nuclei, the status of particles after collision is sampled from continuous energy cross section according to the ENDF law or calculated using standard physical model for the energy range lacking cross section data. Thermal scattering effect of neutron is treated with S(a, b) scattering law data and free-gas approximation model wherein the velocities of the target nuclei obey Maxwellian distribution. Besides, Doppler Broadening Rejection Correction (DBRC) method (X-5 Monte Carlo Team, 2003) is adopted to treat the scattering of neutron in epithermal energy range. Probability tables in many nuclides data are used for accurate treatment of self-shielding effect in the unresolved resonance range which have obvious effect on the accuracy of results for problems which have appreciable flux spectrum in unresolved resonance energy range. Removal neutrons are individually sampled from the corresponding data block in nuclear data

4 164 Y. Wu et al. / Annals of Nuclear Energy 82 (2015) Fig. 2. The domain coupling MC-SN modeling and transport method. library. In photon-transport simulation, incoherent scattering functions which modify the scattered energy, angular and total cross section of Compton scattering, as given by the Klein-Nishina (X-5 Monte Carlo Team, 2003) relationship, are used to approximate electron binding effects. For the treatment of pair-production reaction of photon, the incident photon is replaced by a MeV photon with twice in weight and isotropic direction distribution. Possibility of fluorescent emission after photoelectric absorption are considered. Photonuclear reactions are treated with exclusive tabulated cross sections. With the On-the-Fly (OTF) Doppler-broadening (Yesilyurt et al., 2009) routine which is based on a combination of Taylor series expansions and asymptomatic series expansions, cross sections can be adjusted according to different region temperatures based on stored 0 K cross sections for each isotope without pre-generating cross section on temperature mesh or using in-line cross section processing routine Multi-physics coupling calculation method A fluid-dynamics calculation model which contains multidimension, multi-velocity-field, multiphase, multicomponent and Eulerian model and a structure heat and mass transfer model are used to perform the transient investigations of reactors. The overall fluid-dynamics solution algorithm is based on a time-factorization approach. In addition, an analytical equation-of-state model is introduced to close and complete the fluid-dynamics conservation equations. Consistent interpolation, averaging methods, etc. for the data transfer from one module to another or, within one given physics module, from one scale to another are developed for more accurate coupling simulation. Different from the traditional loose multiphysics coupling way which may have just one-way feedback and assume some prescribed normal plant operating conditions, a tighter integration of multi-physics considering multiple ways coupling is performed based on Jacobian-free Newton Krylov (JFNK) (Knoll and Keyes, 2004) method. It minimizes the need to employ operator splitting type mathematical coupling. Feedback with fidelity will improve the design and safety margins and save the cost Automatic geometry modeling and geometry processing method CAD models represented by Boundary Representation method, can be automatically converted to MC calculation geometry models which are represented in CSG based on primitive solids. Using this conversion function, CAD solids are firstly decomposed into convex solids and then represented as intersections of the surface wrapping of the convex solids. Then each surface is represented by primitive solid which would at last hierarchically represent the whole solid. Similar primitive solids are fusioned into one to simplify the geometries. During this process, automatic geometry fixing and high-order free surfaces simplification method are developed to make the CAD model standardized for conversion into high quality simulation models. Conversely, inversion from the calculation model to the CAD model for visualization to locate the defects and errors and further updates which will accelerate the redesign process is also introduced to SuperMC. It works by sequentially parsing the calculation model, constructing the CSG tree, making primitive solids and building real solids from the bottom to the top of the CSG tree (Wu and FDS Team, 2009; Wang et al., 2011). The unified multi-physics modeling is based on the identity CAD model. Materials with attributes for all the simulations are assigned to each cell in the model. Then BREP-CSG convertor and mesh creator will convert them into models for neutronics and other physics calculations. With unified geometry/material and smooth output/input bridging, it would reach the goal of accurate multi-physics simulation. Hierarchical tree structure is adopted to describe geometry and material and support geometry navigation during particles transport process. The main GSG geometry classes in SuperMC are: entity, volume, component and lattice. Volumes are geometry domains defined by Boolean operation of general entities (primitive bodies and auxiliary surfaces). The layout of components consists of multiple volumes with different materials can be further specified hierarchically with respect to other components according to the loading pattern. Through this hierarchical definition logic, the repeated structure can be easily specified by component and lattice. Additionally, a cuboid must be defined as a world volume and the root node of the geometry hierarchy to completely contain all components. Thus it is not needed to define all spatial areas such as cavity to avoid particles loss due to the precision of computers while other geometry representation method may need to consider such a problem. Advanced geometry acceleration methods derived from computer graphics field, such as the neighbor search method, axisaligned bounding box method and 3D spatial subdivision method are designed to enhance the efficiency of geometry navigation in simulation. Stochastic geometry can be handled by direct sampling of the spatial distribution of particles in fuel compact or pebbles Intelligent data analysis and visualization method Several efficient and effective visual analysis methods for huge data post-processing and analysis have been developed (Long et al.,

5 Y. Wu et al. / Annals of Nuclear Energy 82 (2015) ; He et al., 2012). Besides common visualization methods for data analysis, such as contour, 2D section map, 3D iso-surface and 3D mesh map, two innovative visual methods which are specialized in nuclear analysis have been proposed. One is the data visualization coupled with calculation geometries, including 2D map coupled with geometry wire-frame and mapping result data onto geometry surface. Such data analysis approach allows users to intuitively relate the simulation results to the geometry of components or whole space. Such function is especially important when the simulation results and geometry are complex. The other method is the visualization of simulation process and real-time dose visualized assessment. Such data analysis method can be used to test and evaluate the operational or maintenance tasks and assist the supervisors to plan better working activities Elastic cloud computing technology and parallel calculation method Hardware virtualization technology, parallel storage technology, task scheduling and load balancing algorithm with performance supervision on high performance computing cluster guarantee the intelligent and elastic calculation service with low cost in the cloud computing framework. The open source cloud computing toolkit is adopted for the development. Distributedmemory parallelism based on MPI and shared-memory parallelism based on OpenMP to solve the continued growth in concurrency via increasing numbers of cores per processor. Parallel scheme on particles, overlapping domain decomposition and data decomposition are adopted aiming to enhance the calculation efficiency and relieve memory burden limitation, especially for large-scale, depletion and multi-physics coupling calculation problems. 4. Functions of SuperMC2.1 In SuperMC2.1 for neutron, photon and coupled neutron and transport calculation, CAD models can be automatically converted for further MC transport calculation. Users can fix possibly existing errors, create 3D geometry models and edit physics attributes of materials, sources and tallies graphically. Inversely, the calculation model can be transformed back to CAD model for visualization. With the hierarchical definition method, the basic solids, Boolean operation, the repeated structure geometry can be easily specified in the GUI. Reflective boundary can be assigned by defining virtual surface which does not exist in actual geometry domain. Rotation and translation of different components in the geometry which is convenient for defining irregular rectangular lattice geometry such is possible. Tallies for various nuclear parameters such as volume flux, surface flux, integral leakage rate, energy deposition, fission energy deposition, various kinds of reaction rate corresponding the assigned reaction channel, power, k eff, removal neutron life time, b and b eff, neutron generation time, reactor period and etc. can be performed. For neutron, inelastic scattering including (n, xn), (n, f), (n, c), etc., elastic and various absorption reaction process from to 150 MeV are considered. Thermal scattering effect of neutron, self-shielding effect in the unresolved resonance energy range and removal neutron are treated. For photons, the code accounts for Compton scattering, coherent scattering, possibility of fluorescent emission after photoelectric absorption, electron positron pair production and photonuclear reaction from 1 kev to 100 GeV. Continuous energy nuclear data governing the interaction of neutron and photon and including thermal scattering data of molecules or crystalline solids for thermal neutrons are represented by the ACE format which is ordinarily used by MC codes. Some basic variance reduction techniques including implicit capture, cutoff, splitting and Russian rouletting of geometry and energy, weight window, forced collision and adaptive variance reduction technique coupled with deterministic method for local tally have been implemented to increase the figure-of-merit, especially for shielding problem of large scale geometry problem. The parallel computation on particles is implemented using hybrid parallel computing technology based on MPICH and OpenMP on the Windows platform. The output data can be automatically and intelligently visualized mixed with the input models according to users interest to simplify the information extraction from massive data. Besides, some ordinary functions such as curve plot, 2D map plot, mesh plot and advanced functions such as unified color mapping for various data maps, dynamical visualization are supported. Particles trajectory can be visualized to assist weight window setting for variance reduction. 5. Benchmarking and preliminary application of SuperMC2.1 Validation and verification methods of software engineering were adopted to guarantee the quality of SuperMC. Testing period was divided into several stages including unit testing, integrated testing, a testing, b testing. And the test methods such as black/ white box, static/dynamic testing etc. were adopted. A number of international benchmarks have been adopted for validation and verification by comparing with MCNP which has been extensively validated. Since the same ACE format cross sections are used, differences in results between the two codes will be limited to those arising from the geometry and physics algorithms. Handbook of International Criticality Safety Benchmark Evaluation Project (ICS- BEP) (OECD, 2006), Shielding Integral Benchmark Archive Database (SINBAD) (Kodeli et al., 2006) are mainly used to verify the basic physical corrections. A series of international reactor benchmarks including ITER benchmark model, BN600 model and cases from International Handbook of Evaluated Reactor Physics Benchmark Experiments (IRPhE) (OECD, 2013) for validating its capability of dealing with reactors. Two cases were taken as examples in this paper to test the capability of SuperMC2.1 on dealing with complicated advanced nuclear energy systems. As for fusion reactors, fixed-source calculation is mostly performed wherein flux is the key parameter and divertor cassette is the most complicated component on geometry, flux of divertor cassette in fusion reactor ITER benchmark model was taken as a typical case. For fission reactors, criticality calculation is mostly performed wherein k eff is the key parameter, the whole core k eff of pool-type sodium cooled fast reactor BN-600 was taken as another typical case Fusion reactor: ITER (Song et al., 2014) ITER benchmark model was created by ITER International Organization, saved into STEP format and used for testing and comparison of CAD/Monte Carlo codes developed by institutes and universities. This CAD model includes blanket, divertor, vacuum vessel, cryostat, bioshield, central solenoid coils, TF coils, PF coils, lower, upper and equatorial ports, etc. All the important parts and components of the ITER device are involved. The model is substantially simplified in comparison to the full detailed design drawings, based only on 2nd-order surfaces and including partial or full homogenization of some components. This model can fully test the capacity of the neutronics codes. The model is a 40 sector in toroidal direction of the full ITER machine from the central solenoid to the outer magnet coils. The plasma source is located in a structured cylindrical grid with probability distribution between R-Z grid cells and uniformly distributed in each grid cells.

6 166 Y. Wu et al. / Annals of Nuclear Energy 82 (2015) Some necessary and reasonable modification (Li et al., 2007) on geometry were performed during the conversion of the original CAD model. Additionally, material properties, source distribution and tally setting were modeled completely in graphical user interface for benchmarking SuperMC, as shown in Fig. 3. The same fusion nuclear data library FENDL 2.1 was used and ENDF/B-VI was used as alternatives for missing isotope Ba138. In testing with ITER benchmark model, the major differences between SuperMC 2.1 and MCNP are following: (1) Generally, SuperMC 2.1 directly starts from importing CAD models and converts geometry internally for further particles transport calculation while MCNP calculation starts from the ASCII text input file. The physical properties including materials, sources and tallies can be assigned and converted in SuperMC. In the benchmarking process, the input file of MCNP was automatically converted from the same CAD models with MCAM (Wu and FDS Team, 2009). (2) Complex spatial distribution of sources such as plasma source in ITER benchmark model can be converted from CAD model and probability distribution can be assigned in visualized and interactive manner. Then the source configuration can be converted internally for further transport calculation in SuperMC 2.1. However, source subroutine is necessary for problems of complex source distribution and should be compiled with other source codes in MCNP. (3) SuperMC 2.1 adopts hierarchical solid geometry description method assisted with surface description method while MCNP mainly adopts surface description method. It is an advantage of SuperMC that there is no need to describe or convert cavity cells so that particles loss due to the precision of computers is avoided. Neutron flux in the structural elements of the divertor cassette of the 40 degree toroidal segment model equipped with reflected boundary surfaces was presented as one case to test the capability to model complex geometry. As in Fig. 4, outer vertical W, outer vertical CFC, inner vertical CFC, inner vertical W and cassette body of the divertor cassettes were marked as Group1-Group5. Each group was divided into 7 segments numbered 1 to 7. The calculated total neutron fluxes were shown in Fig. 5. The average deviation of total neutron flux value between SuperMC and MCNP is % (from 0% to %) and the average standard error for all segments is (from to ). The flux distribution in divertor cassette using mesh tally is visualized as shown in Fig. 6. It s clear from the visualization results that neutron fluxes in inner vertical W and outer vertical W of the divertor cassette facing plasma directly are higher than neutron fluxes in other parts. Fig. 4. Divertor cassettes model. Fig. 5. Neutron flux in divertor cassettes Pool-type sodium cooled fast reactor: BN-600 Fig. 6. Visualization of neutron flux distribution in divertor cassettes. Fig. 3. ITER model conversion in SuperMC. BN-600 is a Russian pool type sodium cooled fast reactor, which was the subject of IAEA Coordinated Research Project (CRP) to validate, verify and improve methodologies and computer codes used for the calculation of reactivity coefficients in fast reactors. Different spatial discretization schemes were used during the first three phases of the CRP. Ten organizations (ANL from the USA, CEA and SERCO Assurance (SA) from EU, CIAE from China, FZK/IKET from Germany, IGCAR from India, JNC from Japan, KAERI from the Republic of Korea, IPPE and OKBM from the Russian Federation) have participated in the CRP with their own state-of-the-art basic data and codes. In this study, the three-dimensional Hex-Z homogeneous benchmark model was employed. The benchmark model

7 Y. Wu et al. / Annals of Nuclear Energy 82 (2015) (a) Radial view height is also not taken into account either. However, difference of the axial blanket compositions as a function of height has been retained. Besides, all fuel isotopes have been modeled at a uniform temperature of 1500 K and all structural and coolant isotopes are at a uniform temperature of 600 K. More information of the benchmark model can be found in reference (IAEA, 2010). The first step is to construct model in SuperMC modeling GUI. The position of assemblies as shown in Fig. 7 was arranged using the automatic repeat structure array modeling function. After materials were assigned and source configuration was defined in the GUI, k eff of the whole core was calculated directly without human effort. For benchmark purposes, MCNP was used to calculate k eff using the same data library. Calculation results of k eff by the participant organizations using different codes and nuclear data libraries were listed in Table 1 for comparison. 6. Summary (b) Axial view Fig. 7. Three-dimensional CAD model of BN600 in SuperMC for radial and axial view. corresponds to the 1470 MWth power BN-600 reactor at the beginning of an equilibrium cycle. The core consists of a low enrichment inner zone (LEZ), a middle enrichment zone (MEZ) and a high enrichment outer zone (HEZ). Between MEZ and HEZ a mixed oxide zone (MOX) is located. Three control rod zones (SHRs) and one scram rod zone (SCR), consisting of 19 shim control rods and 6 scram control rods respectively, are interspersed radially in LEZ. The outer core zone is bounded by two steel shielding zones (SSAs), followed by one row of radial reflector (RR). In this benchmark model, the heterogeneous structure of the core subassemblies is ignored. Difference of fissile fuel compositions as a function of core Table 1 Effective multiplication factors. Diffusion Participants Value Rel. Dev. 1 (%) Transport Value Rel. Dev. 2 (%) ANL CEA/SA CIAE IGCAR IPPE JNC KAERI OKBM Mean FDS Team (MCNP) (0.005%) FDS Team (SuperMC) (0.005%) 1 Relative Deviation = (Value-Mean)/Mean 100%. 2 Relative Deviation = (Diffusion value-transport value)/ Transport value 100%. The SuperMC code, a CAD-based Monte Carlo program for integrated simulation of nuclear system, is being developed by FDS Team in China. As a general-purpose MC program, it is designed for the simulation of nuclear-system problem such as reactor physics, radiation shielding, nuclear detection, and medical physics. Using hybrid Monte Carlo and deterministic method as a faithful core transport simulation approach and coupled by multi-physics processes promotes the evolution to full nuclear system simulation with high-fidelity. Advanced computer technologies such as automatic geometry modeling, intelligent data analysis and visualization, high performance parallel computing and cloud computing make the code intelligent and high efficient. SuperMC2.1, the latest version, for neutron, photon and coupled neutron and photon transport calculation has been developed and verified by a series of benchmarking cases such as the ITER model and the fast reactor BN-600 model. SuperMC is still in its evolution process toward a general and routine tool for nuclear systems. Acknowledgments This work was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (No. XDA ), and the National Natural Science Foundation of China (No ). References Brown, F.B., Recent advances and future prospects for Monte Carlo. Prog. Nucl. Sci. Technol. 2, 1 4. 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