Four energy group neutron flux distributions in the Syrian Miniature Neutron Source Reactor using the WIMSD4 and CITATION codes

A 3-D (R, θ, Z) neutronic model for the Miniature Neutron Source Reactor (MNSR) was developed earlier to conduct the reactor neutronic analysis. The group constants for all the reactor components were generated using the WIMSD4 code. The reactor excess reactivity and the four group neutron flux distributions were calculated using the CITATION code. This model is used in this paper to calculate the pointwise four energy group neutron flux distributions in the MNSR versus the radius, angle and reactor axial directions. Good agreement is noticed between the measured and the calculated thermal neutron flux in the inner and the outer irradiation sites with relative differences less than 7% and 5%, respectively.     

直接三维中子输运特征线法并行计算软件的实现

作为中子输运问题的一种重要确定论方法,特征线法（MOC）具有强几何适应性、计算流程简洁、易于大规模并行的优点。ANT-MOC是自主开发的中国数值反应堆1.0（CVR1.0）中的三维特征线法中子输运计算程序,主要用于压水堆、快堆的堆芯输运计算。ANT-MOC支持基于构造实体几何（CSG）的复杂几何建模、高效的用户输入方式、面向矩形/六边形网格的射线追踪算法,以及基于轨迹链分解的并行算法和负载平衡策略。在国产超算上,ANT-MOC可以扩展到约10万处理器核,并行效率在50%以上。针对压水堆、快堆计算问题进行验证和参数敏感性分析,结果表明ANT-MOC计算结果具有较好的稳定性和准确度。     

Synergism of the method of characteristic, R-functions and diffusion solution for accurate representation of 3D neutron interactions in research reactors using the AGENT code system

This paper summarizes the theoretical and numerical aspects of the AGENT code methodology accurately applied for detailed three-dimensional (3D) multigroup steady-state modeling of neutron interactions in complex heterogeneous reactor domains. For the first time we show the fine-mesh neutron scalar flux distribution in Purdue research reactor (that was built over forty years ago).     

TRIPOLI-4® Monte Carlo code ITER A-lite neutronic model validation

3D Monte Carlo transport codes are extensively used in neutronic analysis, especially in radiation protection and shielding analyses for fission and fusion reactors. TRIPOLI-4^® is a Monte Carlo code developed by CEA. The aim of this paper is to show its capability to model a large-scale fusion reactor with complex neutron source and geometry. A benchmark between MCNP5 and TRIPOLI-4^®, on the ITER A-lite model was carried out; neutron flux, nuclear heating in the blankets and tritium production rate in the European TBMs were evaluated and compared. The methodology to build the TRIPOLI-4^® A-lite model is based on MCAM and the MCNP A-lite model. Simplified TBMs, from KIT, were integrated in the equatorial-port. A good agreement between MCNP and TRIPOLI-4^® is shown; discrepancies are mainly included in the statistical error.     

热管式空间反应堆燃耗计算研究

针对热管式空间反应堆,基于OpenMC程序产生均匀化截面参数,并由确定论快堆分析程序SARAX进行堆芯输运及燃耗计算。以蒙特卡罗程序（MCNP）的输运计算结果以及MVP程序的燃耗计算结果作为参考解,通过对比稳态输运计算和燃耗计算的结果,证明了耦合的OpenMC和SARAX程序系统对于空间堆中子学分析和燃耗分析的适用性和高效性。为热管式空间反应堆的设计分析提供了参考。      

Neutronic performance of new coolants in a fusion–fission (hybrid) reactor

Selection of coolant used in the fuel zone of a fusion–fission (hybrid) reactor affects the neutronic performance of the blanket much. Recently, two coolants namely, Flinabe and Li₂₀Sn₈₀ have been investigated to use in fusion reactors as tritium breeder and energy carrier due to their advantages of low melting point, low vapor pressure. In this study, neutronic performance of these coolants in a hybrid reactor using Canada Deuterium Uranium Reactor (CANDU) spent fuel was investigated for an operation period of 48 months. And also that of natural lithium and Flibe was also examined for comparison. Neutron transport calculations were conducted on a simple experimental hybrid blanket in a cylindrical geometry with the help of the SCALE4.3 system by solving the Boltzmann transport equation with the XSDRNPM code in 238 neutron groups and a S₈–P₃ approximation.     

Homogeneous zones definition in deterministic codes and effect on computed neutronic parameters

The design or modification and in general the analysis and control of nuclear reactors require complex calculations, which are carried out by numerical codes including neutronic and thermal-hydraulic components. Among the neutronic codes, the deterministic ones which solve the neutron transport/diffusion equation simulate the reactor core by dividing it into homogenized zones, i.e. volumes within which the macroscopic nuclear properties are considered uniform. These codes have been extensively used and tested for several decades and are shown to perform well when they analyze reactor cores containing regions with relatively homogeneous distributions of fuel, moderator and absorbing materials. In this work, the sensitivity of computed key neutronic parameters to the partitioning of the reactor core in homogenized zones is examined. Application is made for a configuration of the Greek Research Reactor (GRR-1) core, which is pool type, fueled by slab-type fuel elements. For the calculations, the neutronic code system consisting of XSDRNPM (cell-calculations) and CITATION (core analysis) is used with two different definitions of homogeneous zones for the special/control fuel assemblies. The effect on computations of neutron flux distribution, void-induced reactivity and total control rod worth is examined based on corresponding measurements. It is shown that with a more appropriate partition in homogeneous zones, the agreement of computed results with measurements can be remarkably improved concerning mainly the neutron flux, while the control rods worth is the less affected quantity.     

Finite element spherical harmonics (PN) solutions of the three-dimensional Takeda benchmark problems

A set of multi-group eigenvalue (K_eff) benchmark problems in three-dimensional homogenised reactor core configurations have been solved using the deterministic finite element transport theory code EVENT and the Monte Carlo code MCNP4C. The principal aim of this work is to qualify numerical methods and algorithms implemented in EVENT. The benchmark problems were compiled and published by the Nuclear Data Agency (OECD/NEACRP) and represent three-dimensional realistic reactor cores which provide a framework in which computer codes employing different numerical methods can be tested. This is an important step that ought to be taken (in our view) before any code system can be confidently applied to sensitive problems in nuclear criticality and reactor core calculations. This paper presents EVENT diffusion theory (P₁) approximation to the neutron transport equation and spherical harmonics transport theory solutions (P₃–P₉) to three benchmark problems with comparison against the widely used and accepted Monte Carlo code MCNP4C. In most cases, discrete ordinates transport theory (S_N) solutions which are already available and published have also been presented. The effective multiplication factors (K_eff) obtained from transport theory EVENT calculations using an adequate spatial mesh and spherical harmonics approximation to represent the angular flux for all benchmark problems have been estimated within 0.1% (100 pcm) of the MCNP4C predictions. All EVENT predictions were within the three standard deviation uncertainty of the MCNP4C predictions. Regionwise and pointwise multi-group neutron scalar fluxes have also been calculated using the EVENT code and compared against MCNP4C predictions with satisfactory agreements. As a result of this study, it is shown that multi-group reactor core/criticality problems can be accurately solved using the three-dimensional deterministic finite element spherical harmonics code EVENT.     

A comparative neutronic study of the standard HEU core and various potential LEU alternatives for a typical MNSR system

A comparative study has been performed for neutronic analysis of highly enriched in uranium (HEU) and potential low enriched in uranium (LEU) cores for the Pakistan Research Reactor-2 (PARR-2) taken as a typical miniature neutron source reactor (MNSR) system. The group constant generation has been carried out using transport theory code WIMS-D4 and a detailed five-group RZ-model has been used in the CITATION code for multigroup diffusion theory analysis. The neutronic analysis of the 90% HEU reference and potential LEU alternative: UO₂, U₃Si₂ and U9Mo, cores has been carried out yielding 11%, 20.7% and 14.25% enrichments with corresponding values of excess reactivity: 4.33, 4.30 and 4.07 mk. These results have been found in good agreement with recently reported Monte Carlo-based transport theory calculations. The diffusion theory-based calculated values of thermal flux profiles for axial as well as for radial directions have been found to agree well with the corresponding experimental measurements. The UO₂-based LEU core has been found having flux spectrum closest to the reference core while U9Mo core has significantly harder flux spectrum at irradiation site.     

Application of wavelets scaling function expansion method in resonance self-shielding calculation

The wavelets expansion method is widely used in various fields due to its powerful ability to simulate the oscillating functions. This method is applied to discretize the energy variable of neutron angular flux within the resonant energy range. Meanwhile, the conventional multi-group method is applied in fast and thermal energy ranges. This coupled method can obtain the problem-dependent continuous-energy neutron flux spectrum within the resonant energy range. The method of characteristics (MOC) is employed as a space-variable solver in this paper to keep the powerful capability of dealing with the complex geometry problems. A pressurized water reactor (PWR) fuel cell problem with UO2 fuel (UOX) and mixed oxide fuel (MOX), and a cylindrical cluster fuel problem are calculated by utilizing this coupled method. Results of these problems are all in good agreement with the results of the Monte Carlo statistical transport code MCNP. It is concluded that this is a valuable method to solve the resonance self-shielding calculation problems in a complex geometry, and it is promising to be applicable for realistic reactor problems.     

Parallelization of Monte Carlo Code MCACE for Shielding Analysis and Estimation of Its Efficiency by Simulator

An improved coarse-mesh discrete ordinates method has been developed for three-dimensional hexagonal transport calculations of high-conversion light water reactors and fast reactors. This method employs a new weighted diamond difference approximation which is obtained by using the neutron balance equations in divided submeshes. The weight is a function of neutron direction and scaler flux, and this method can be easily incorporated into conventional discrete ordinates transport codes.

The present method was applied to hexagonal fuel assembly calculations of high-conversion reactor and fast reactor core calculations, and the results were compared with those of Monte- Carlo calculations. The values of kefi and power distributions agreed with each other within 0.5 and 3%, respectively, verifying accuracy of the present improved coarse-mesh discrete ordinates transport calculation method.     

Prediction of MgO volume fraction in an ADS fresh fuel for the scenario code CLASS

Subcritical reactors, also called Accelerator Driven Systems (ADS), are specifically studied for their capacity in transmuting Minor Actinides (MA). Nuclear fuel cycle scenarios involving MA transmutation in ADS are widely researched. The nuclear fuel cycle simulation tool code CLASS (Core Library for Advanced Scenarios Simulations) is dedicated to the inventory evolution calculation induced by a complex nuclear fleet. For managing reactors, the code CLASS includes physic models. Loading models aim to provide the fuel composition at beginning of cycle according to the stocks isotopic composition and the reactors requirements. A cross section predictor aims to provide mean cross sections needed for solving Bateman equations. Physic models are built from reactors calculation set ahead of the scenario calculation. An ADS standard composition at BOC is a mixture of plutonium and MA oxide. The high number of fissile isotopes present in the subcritical core leads to an issue for building an ADS fuel loading model. A high number of isotopic vector at BOC is needed to get an exhaustive simulation set. Also, ADS initial reactivity is adjusted with an inert matrix which induces an additional degree of freedom. The building of an ADS fuel loading model for CLASS requires two steps. For any heavy nuclide composition at beginning of cycle, the core reactivity must be imposed at a subcritical level. Also, the reactivity coefficient evolution should be maintained during the irradiation. In this work, the MgO volume fraction is adjusted to reach the first requirement. The methodology based on a set of reactor simulations and neural network utilization to predict the MgO volume fraction needed to reach a wanted k_eff for any initial composition is presented. Also, a complete neutronic study is done that highlight the effect on MgO on neutronic parameters. Reactor simulations are done with the transport code MCNP6 (Monte Carlo N particle transport code). The ADS geometry is based on the EFIT (European Facility for Industrial-Scale Transmutation) concept. The simulation set is composed of more than 8000 randomized runs from which a neural network has been built. The resulting MgO prediction method allows reaching a k_eff at 0.96 and the distribution standard deviation is around 200 pcm.     

数字化反应堆高保真中子学程序SHARK研发

SHARK程序是由中国核动力研究设计院新近研发的基于全堆芯确定论非均匀输运理论体系的数字化反应堆软件。该软件从多群数据库的截面与共振数据出发,采用改进子群方法刻画有效共振截面的复杂非均匀效应,采用二维/一维或准三维特征线方法开展堆芯层面非均匀输运计算。目前该程序的定态微观问题计算能力已建立完毕。数值结果显示,SHARK程序对于商用压水堆相关基准问题具有良好的计算精度和效率。     

Utilization of Ceramic Uranium Fuels in ARIES-RS Fusion Reactor

This study presents the neutronic performance of the ARIES-RS fusion reactor design using different natural ceramic uranium fuels, namely UO₂, UN or U₃Si₂, dispersed in graphite matrix. These fissionable fuels inserted as micro spheres into the first range quadratic channels at the immediate neighborhood of the first wall in the inboard blanket to amplify fusion power and breed fissile fuel. Neutron transport calculations were performed with the help of the SCALE4.3 system by solving the Boltzmann transport equation with the XSDRNPM code in 238 neutron groups and a S₈–P₃ approximation. Among the investigated fuels, UN showed the best neutronic performance while UO₂ and U₃Si₂ had similar performances. Numerical results pointed out that inserting fissionable fuel zone even with a small thickness (10 cm) in a pure fusion reactor increased fusion power from 2170 MW to 4500, 5250 and 4150 MW depending on the fuel type. Furthermore significant amount of fissile fuel was produced to be charged to light water reactors.     

Transmission probability method for solving neutron transport equation in three-dimensional triangular-z geometry

This paper presents a transmission probability method (TPM) to solve the neutron transport equation in three-dimensional triangular-z geometry. The source within the mesh is assumed to be spatially uniform and isotropic. At the mesh surface, the constant and the simplified P₁ approximation are invoked for the anisotropic angular flux distribution. Based on this model, a code TPMTDT is encoded. It was verified by three 3D Takeda benchmark problems, in which the first two problems are in XYZ geometry and the last one is in hexagonal-z geometry, and an unstructured geometry problem. The results of the present method agree well with those of Monte-Carlo calculation method and Spherical Harmonics (P_N) method.     

First 3-D calculation of core disruptive accident in a large-scale sodium-cooled fast reactor

The SIMMER-IV computer code is a three-dimensional fluid-dynamics code coupled with a fuel-pin model and a space- and energy-dependent neutron transport kinetics model. The present study has attempted the first application of SIMMER-IV to a core disruptive accident in a large-scale sodium-cooled fast reactor. A principal point of this study was to investigate reactivity effects with fuel relocation under three-dimensional core representation including control rods. The calculation has indicated that the fuel discharge from the core was disturbed by a significant flow resistance at the entrance nozzle in the current design. Additional static neutronic calculations have been performed to compare basic neutronic characteristics between different scale cores. The static neutronic calculations have clarified that the outward fuel compaction within the inner core increased the reactivity in the large-scale core unlike the small-scale core.     

Burn up calculations for the Iranian miniature reactor: A reliable and safe research reactor

Presenting neutronic calculations pertaining to the Iranian miniature research reactor is the main goal of this article. This is a key to maintaining safe and reliable core operation. The following reactor core neutronic parameters were calculated: clean cold core excess reactivity (ρ_ex), control rod and shim worth, shut down margin (SDM), neutron flux distribution of the reactor core components, and reactivity feedback coefficients. Calculations for the fuel burnup and radionuclide inventory of the Iranian miniature neutron source reactor (MNSR), after 13 years of operational time, are carried out. Moreover, the amount of uranium burnup and produced plutonium, the concentrations and activities of the most important fission products, the actinide radionuclides accumulated, and the total radioactivity of the core are estimated. Flux distribution for both water and fuel temperature increases are calculated and changes of the central control rod position are investigated as well. Standard neutronic simulation codes WIMS-D4 and CITATION are employed for these studies. The input model was validated by the experimental data according to the final safety analysis report (FSAR) of the reactor. The total activity of the MNSR core is calculated including all radionuclides at the end of the core life and it is found to be equal to 1.3 × 10³Ci. Our investigation shows that the reactor is operating under safe and reliable conditions.     

Applications of the multidimensional equations to complex fuel assembly problems

For the analysis of reactors with complex fuel assemblies or fine mesh applications as pin by pin neutron flux reconstruction, the usual approximation of the neutron transport equation by the multigroup diffusion equation does not provide good results. A classical approach to solve the neutron transport equation is to apply the spherical harmonics method obtaining a finite approximation known as the P_L equations. In this line, a nodal collocation method for the discretization of these equations on a rectangular mesh is used in this paper to analyse reactors with MOX fuel assemblies. Although the 3D P_L nodal collocation method becomes feasible due to the improvements in computer hardware, a complete treatment of the detailed structure of the fuel assemblies in actual three-dimensional geometry is still prohibitive, thus, an assembly homogenization method is necessary. A homogenization method compatible with our multidimensional P_L code is proposed and tested performing heterogeneous and homogenized calculations. In this work, we apply the method to 2D complex fuel assembly configurations.     

Thermal neutron self-shielding correction factors for large sample instrumental neutron activation analysis using the MCNP code

Thermal neutron self-shielding within large samples was studied using the Monte Carlo neutron transport code MCNP. The code enabled a three-dimensional modeling of the actual source and geometry configuration including reactor core, graphite pile and sample. Neutron flux self-shielding correction factors derived for a set of materials of interest for large sample neutron activation analysis are presented and evaluated. Simulations were experimentally verified by measurements performed using activation foils. The results of this study can be applied in order to determine neutron self-shielding factors of unknown samples from the thermal neutron fluxes measured at the surface of the sample.