Development of a computer code system for the analysis of prism and pebble type VHTR cores

Korea Atomic Energy Research Institute (KAERI) is developing a new computer code system for an analysis of very high temperature gas-cooled reactor (VHTR) cores based on the existing HELIOS/MASTER code system. Several methodologies were developed in order for the original light water reactor (LWR) code system to treat the unique VHTR characteristics easily such as the so-called double-heterogeneity problem, the effects of a spectrum shift and a thermal up-scattering, a strong fuel/reflector interaction, etc. The method of a reactivity-equivalent physical transformation (RPT) and the equivalent cylindrical fuel (ECF) model are proposed to transform the double-heterogeneous fuel problem into a single-heterogeneous one in a cylindrical coordinate for both a prismatic fuel and a pebble-bed fuel. An eight energy group structure with appropriate group boundaries has been constructed in the MASTER diffusion nodal calculation, within which the issues of a spectrum shift and a thermal up-scattering are resolved. The concern about a strong fuel/reflector interaction can be handled easily by applying the equivalence theory to a simple one-dimensional spectral geometry consisting of the fuel and reflector regions. By combining all the methodologies described above, a well-known two-step core analysis procedure has been established, where HELIOS is used for the transport lattice calculation and MASTER for the 3-D diffusion nodal core calculation. The applicability of our code system was tested against several core benchmark problems. The results of these benchmark tests revealed that our code system is very accurate and practical for an analysis of both the prismatic and pebble-bed reactor cores.     

IAEA GT-MHR benchmark calculations by using the HELIOS/MASTER physics analysis procedure and the MCNP Monte Carlo code

The IAEA's gas-cooled reactor program has coordinated international cooperation for an evaluation of a high temperature gas-cooled reactor's performance, which includes a validation of the physics analysis codes and the performance models for the proposed GT-MHR. This benchmark problem consists of the pin and block calculations and the reactor physics of the control rod worth for the GT-MHR with a weapon grade plutonium fuel. Benchmark analysis has been performed by using the HELIOS/MASTER deterministic code package and the MCNP Monte Carlo code. The deterministic code package adopts a conventional 2-step procedure in which a few group constants are generated by a transport lattice calculation, and the reactor physics analysis is performed by a 3-dimensional diffusion calculation.In order to solve particular modeling issues in GT-MHR, recently developed technologies were utilized and new analysis procedure was devised. Double heterogeneity effect could be covered by using the reactivity-equivalent physical transformation (RPT) method. Strong core–reflector interaction could be resolved by applying an equivalence theory to the generation of the reflector cross sections. In order to accurately handle with very large control rods which are asymmetrically located in a fuel and a reflector block, the surface dependent discontinuity factors (SDFs) were considered in applying an equivalence theory. A new method has been devised to consider SDFs without any modification of the nodal solver in MASTER.All computational results of the HELIOS/MASTER code package were compared with those of MCNP. The multiplication factors of HELIOS for the pin cells are in very good agreement with those of MCNP to within a maximum error of 693 pcm Δρ. The maximum differences of the multiplication factors for the fuel blocks are about 457 pcm Δρ and the control rod worths of HELIOS are consistent with those of MCNP to within a maximum error of 3.09%. On considering a SDF in the core calculations, the maximum differences of the control rod worths are significantly decreased to be 7.7% from 21.5%. It is showed that there are good consistencies between the deterministic code package and the Monte Carlo code from the results of these benchmark calculations. Therefore, the HELIOS/MASTER 2-step procedure can be used as a standard reactor physics analysis tool for a prismatic VHTR.     

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。      

基于OpenMC的多群截面库制作及有效性验证

OpenMC是麻省理工大学计算反应堆物理组开发的开源蒙特卡罗程序,能够方便地制作适用于特定堆芯中子能谱分布的多群反应截面及高阶勒让德散射截面以用于离散坐标输运程序ANISN的计算。本文基于ENDF/B-Ⅶ.1和CENDL-3.1评价数据库,利用OpenMC计算制作了ANSIN格式的多群截面并通过基准题的计算验证计算结果的准确性。通过截面转换程序的编写,将OpenMC给出的堆芯各阶勒让德散射分量,堆芯中子能谱分布,散射、吸收反应率以及裂变中子产生速率等信息转换为ANISN程序可读取的截面库格式。采用制作的截面库利用ANINS计算有效中子增殖因子及堆芯中子通量分布。结果表明,ANISN确定论的计算结果与OpenMC给出的蒙特卡罗计算结果相吻合,验证了这种方法可有效地为ANISN提供截面数据,将来可推广应用于二维、三维确定论中子输运计算。     

Analysis of Heavy-Water-Moderated,Cluster-Type Fuel Lattices by Cluster Physics Code ‘MESSIAH’

This paper presents a comprehensive analysis performed by a new cluster analysis code ‘MESSIAH’ on reactor physics constants measured in the critical facility for a pressure-tube-type, heavy-water-moderated reactor. The MESSIAH code system utilizes the method of the collision probability to solve the neutron transport equation. The effective space dependent cross sections are calculated in the thermal and resonance energy range before the eigenvalue calculation for the whole energy range. With use of these cross sections, the multi-group, space dependent transport equation is solved, and the flux distribution, spectrum and k _eff are obtained to the input bucking. In the above three steps the method of the collision probability is used consistently and extensively. The treatment of leakage neutrons from lattices in MESSIAH is also confirmed by an independent method using a Monte Carlo calculation. The calculated reactor physics constants, especially the micro-parameters and the activation traverse of Dy, agreed fairly well with the experiment. The diffusion calculation with use of the group constants calculated by MESSIAH predicts the reactivity of 0% void core excellently (<0.12%). However, for a 100% void core, the calculated reactivity was slightly lower than the experiment (~0.74%), which was attributed to over prediction of the diffusion constants.     

基于CITATION-ORIGEN2球床堆平衡态计算程序的实现

基于确定论中子扩散软件CITATION和点燃耗软件ORIGEN2,编写了球床堆分析程序COBBLE,以实现指定燃料球加载策略下的球床堆平衡态燃耗计算。COBBLE程序采用谱区能谱修正方法,通过迭代求解得到球床堆堆芯平衡态参数。本文选取简化的球床模块高温气冷堆(PBMR)堆芯进行建模,计算其功率分布及燃耗分布,并使用基于蒙特卡罗方法的球床堆燃耗计算程序PBRE进行了验证与分析。结果表明,COBBLE程序适用于球床堆的平衡态燃耗计算。     

反应堆堆芯先进中子学模拟软件SCAP-N研发

堆芯中子学计算是反应堆设计分析的基础,为提高堆芯中子学计算的模拟分辨率与计算精度,开发了反应堆堆芯先进中子学模拟软件（SCAP-N）。该程序首先根据轴向特征对堆芯进行分层,并逐层进行二维堆芯非均匀输运计算,再采用超级均匀化方法（SPH）获得栅元等效均匀化截面,最后进行三维堆芯逐棒（pin-by-pin）输运计算,获得堆芯有效增殖因子与精细棒功率分布。为提高程序计算效率,采用分布式/共享式（MPI/OPENMP）混合并行方式对程序进行了并行化开发。利用虚拟反应堆（VERA）系列基准例题及美国先进非能动压水堆（AP1000）启动物理试验实测数据对程序进行了测试验证。结果表明,相比于商用核设计程序系统,SCAP-N程序采用的逐棒输运技术能够提高堆芯中子学的计算精度。与同类型高精度中子学程序相比,SCAP-N具有更高的计算效率,可进一步提高核电厂的经济性及运行灵活性。      

“Used fuel” vectors and waste minimization strategies for VHTRS operating without refueling

Generation IV Very High Temperature Reactors (VHTRs) are well-known for their flexibility with respect to feasible fuel cycle options. In this paper, the LEU- and TRU-fueled VHTR configurations are analyzed accounting for their capabilities to attain an extended single-batch OTTO (Once-Through-Then-Out) mode of operation without intermediate refueling. The requirement of waste minimization is imposed as one of the design constraints defining possible system configurations and deployment strategies. The resulting “used fuel” vectors are examined considering anticipated disposal options as well as viability of fuel reprocessing. A Monte Carlo-deterministic analysis methodology has been implemented for coupled design studies of VHTRs with TRUs using the ORNL SCALE 5.1 code system. The developed modeling approach provides an exact-geometry 3D representation of the VHTR core details properly capturing VHTR physics. The presented analysis is focused on prismatic block core concepts for VHTRs. It is being performed within the scope of the U.S. DOE NERI project on utilization of higher actinides (TRUs and partitioned MAs) as a fuel component for extended-life VHTR configurations.     

Use of the surface harmonics method forcalculation of 2D C5G7 MOX benchmark

The C5G7 MOX benchmark specifying a sixteen-assembly core with asurrounding water reflector was proposed as a basis to measure current transport code abilities in the treatment of reactor core problems without spatial homogenization. Seven-group cross sections for all materials were used as initial information. Just that fact allows to test an accuracy of solving the neutron transport equation excluding additional errors connected with preparing the group cross sections. In this paper, Surface Harmonics Method (SHM) is applied to calculation of the two-dimensional configuration of this benchmark. Different approximations of SHM were applied, both with and without spatial homogenization. Additionally, this fact allowed evaluating the effect of spatial homogenization of cells. Comparisons were carried out for k_eff and pin powers both with the reference results and between the results calculated by different SHM approximations.     

Implications of the differences in neutron spectra predicted for reactor pressure vessel walls by transport and the P1MG codes

Neutron-energy spectra were calculated for the interface between the vessel wall and cladding of the Army SM-1A Reactor pressure vessel using the transport theory code Program S and the diffusion code P1MG. Different sets of basic nuclear data and microscopic cross sections were used for the two calculations. Spectra were normalized to the same amount of activation in an iron, neutron flux detector. The transport code predicted a higher flux of neutrons in the energy groups between 6 and 10 MeV resulting in a lower overall intensity for the transport theory spectrum versus the P1MG spectrum. This was found to be consistent with the predictions of two transport codes versus the P1MG code for the PM-2A reactor vessel wall and for a simulated reactor vessel wall experiment. Such divergence of results for a given reactor using two different code analysis techniques raises important questions as to their usually unqualified acceptance and use for projecting the lifetime fluence for a reactor pressure vessel. Strong support is thus generated for establishment of one “standard” set of basic nuclear data from which all reactor physics analysts can draw to generate specific cross sections for reactor physics calculations, and for the writing of a new reactor physics spectrum code specifically for deep penetration analysis of reactor pressure vessel walls.     

基于抽样方法的特征值不确定度分析

核数据是反应堆物理计算的基础数据,研究其不确定度对反应堆物理计算引入的不确定度,对提高反应堆的安全性和经济性具有重要意义。本文基于抽样理论研究了反应堆物理计算不确定度分析的方法,研发了不确定度分析程序UNICORN。基于ENDF/B-Ⅶ.1评价数据库,使用NJOY程序开发了多群协方差数据库。采用UNICORN程序和多群协方差数据库对三哩岛燃料棒和基准题RB31的k∞进行了不确定度分析,得到核数据库中各分反应道截面的不确定度对k∞造成的不确定度。结果表明:238 U(n,γ)截面对三哩岛燃料棒k∞造成的不确定度最大,相对不确定度达0.4%左右;协方差数据库的不同来源会对不确定度分析结果造成一定影响。     

NAPTH: Neutronics analysis code system for the fusion–fission hybrid reactor with pressure tube type blanket

The fusion–fission hybrid reactor is considered as a potential path to the early application of fusion energy. A new concept with pressure tube type blanket has recently been proposed for a feasible hybrid reactor. In this paper, a code system for the neutronics analysis of the pressure tube type hybrid reactor is developed based on the two-step calculation scheme: the few-group homogeneous constant calculation and the full blanket calculation. The few-group homogeneous constants are calculated using the lattice code DRAGON4. The blanket transport calculation is performed by the multigroup Monte Carlo code. A link procedure for fitting the cross sections is developed between these two steps. An additional procedure is developed to calculate the burnup, power distribution, energy multiplication factor, tritium breeding ratio and neutron multiplication factor. From some numerical results, it is found that the code system NAPTH is reliable and exhibits good calculation efficiency. It can be used for the conceptual design of the pressure tube type hybrid reactor with precise geometry.     

核数据处理程序NECP-Atlas的开发与验证

本文开发了自主化的核数据处理程序NECP-Atlas，该程序将不同的核数据处理功能封装为不同的程序模块，可将评价核数据经过共振重构及线性化、多普勒展宽计算、不可分辨共振区处理、热中子散射计算、多群截面计算等过程，处理为WIMS-D/E格式多群数据库。采用WLUP（WIMSD library update project）基准题、国际临界安全基准题ICSBEP（international criticality safety benchmark evaluation project）等对NECP-Atlas加工产生的核数据进行验证，结果显示NECP-Atlas和NJOY-2016程序精度相当。     

Simplified two and three dimensional HTTR benchmark problems

To assess the accuracy of diffusion or transport methods for reactor calculations, it is desirable to create heterogeneous benchmark problems that are typical of whole core configurations. In this paper we have created two and three dimensional numerical benchmark problems typical of high temperature gas cooled prismatic cores. Additionally, a single cell and single block benchmark problems are also included. These problems were derived from the HTTR start-up experiment. Since the primary utility of the benchmark problems is in code-to-code verification, minor details regarding geometry and material specification of the original experiment have been simplified while retaining the heterogeneity and the major physics properties of the core from a neutronics viewpoint. A six-group material (macroscopic) cross section library has been generated for the benchmark problems using the lattice depletion code HELIOS. Using this library, Monte Carlo solutions are presented for three configurations (all-rods-in, partially-controlled and all-rods-out) for both the 2D and 3D problems. These solutions include the core eigenvalues, the block (assembly) averaged fission densities, local peaking factors, the absorption densities in the burnable poison and control rods, and pin fission density distribution for selected blocks. Also included are the solutions for the single cell and single block problems.     

Anomalous Isotope Fractionation in Uranium Enrichment Process

A benchmark calculation for a deep penetration problem of 14 MeV neutrons through a 3m thick iron slab was carried out by using a vectorized continuous energy Monte Carlo code MVP with the JENDL-3 and ENDF/B-IV cross sections. Reference solutions for neutron spectra and averaged cross sections were obtained at various locations through the iron slab with good statistics owing to a high computation speed of the code. The accuracy of multigroup calculations with the JSSTDL/J3 library was investigated by comparison with the obtained reference solutions.

Both calculations with JENDL-3 and ENDF/B-IV showed a similar attenuation of total fluxes from thermal to 14 MeV through the slab, while differences of one order at the maximum were observed in the calculated fluxes in the resonance energy region. The multigroup calculations with the JSSTDL/J3 295- and 125-group libraries underestimate the streaming effect through the cross section minima above the well-known 24 keV window, which resulted in the underestimation of fluxes above this window by more than two decades at 3 m penetration compared with the continuous energy method. Taking into account the spatial dependence of averaged cross sections, the underestimation was reduced to about one decade. It was found, however, that an accurate prediction of streaming effect is fairly difficult by the multigroup method.     

Scaling analysis for the high temperature Gas Reactor Test Section (GRTS)

This paper presents an overview of a scaling analysis for a reduced scale Gas Reactor Test Section capable of modeling a variety of important phenomena in a Very High Temperature Gas Reactor. This research effort is being conducted at Oregon State University in support of an Idaho National Laboratory Lab Directed Research and Development project titled, Developing Core Flow Analysis Methods for the VHTR and GFR Designs. The INL point design for a prismatic core VHTR was selected for this scaling analysis, although the project maintains its secondary objective of co-generating Gas-Cooled Fast Reactor GFR-relevant thermal hydraulics data. The specific goal of the scaling analysis was to support the design of a test facility that can be used to produce benchmark data for depressurized conduction cool-down conditions. The scaling analysis determined that the GRTS will be capable of simulating core conduction and radiation heat transfer, vessel radiation heat transfer, core temperature profiles, air-ingress by lock-exchange, air-ingress by molecular diffusion, and single-phase air natural circulation. This paper shall focus on two aspects of the GRTS scaling analysis; air-ingress scaling analysis and scaling of the core heat transfer behavior for a DCC event.     

Thermal-fluid assessment of the design options for reactor vessel cooling in a prismatic core VHTR

The design of the reactor pressure vessel is an important issue in the VHTR design due to its high operating temperature. The extensive experience base in Light Water Reactor makes SA508/533 steel emerge as a strong candidate for the VHTR reactor vessel but requires maintaining the vessel temperature below the ASME code limit. To meet the temperature requirement, three types of vessel cooling options for a prismatic core VHTR are considered: an internal vessel cooling, an external vessel cooling, and an internal insulation. The performances of the vessel cooling options are evaluated by using a system thermo-fluid analysis code and a commercial computational fluid dynamics code during normal operation and accidents. The results suggested that the internal vessel cooling with the modified inlet flow path will be a promising option. The external cooling option does not ensure an effective cooling of the RPV. The insulation option provides an effective reduction of the RPV temperature in the normal and accident conditions but reduces the fuel safety margin during the accidents, requiring careful consideration before the implementation.     

SARAX-FXS程序针对非均匀快堆堆芯计算中的改进及应用

SARAX-FXS程序是基于确定论方法,适用于快谱堆芯组件能谱、均匀化参数计算的程序。由于快堆中组件空间自屏的非均匀效应不可忽视,本文将基于一维圆柱、平板几何的碰撞概率方法加入SARAX-FXS模块,并以等效一维模型计算组件的均匀化参数。为保证能群归并前后的核反应率守恒,在组件计算中引入超级均匀化(SPH)因子修正截面。采用快堆基准题MET-1000对程序的计算结果进行验证,结果表明,与参考解相比,SARAX-FXS的一维计算模块具有较高的精度,特征值计算相对偏差在100~200pcm之间。堆芯计算结果显示,引入SPH因子可提高特征值计算的精度约300pcm,功率分布的均方根误差可从约3%下降至约1%。     

Decay heat analysis of VHTR cores by Monte Carlo core depletion calculation

In this study, a decay heat analysis was performed for prism type VHTR cores by combining Monte Carlo depletion calculation with McCARD code and the decay cooling calculation with ORIGEN-2 code. In the Monte Carlo depletion approach, the McCARD multi-cycle core depletion calculation was performed up to an equilibrium cycle, involving a great details of core geometry and material inventory. ORIGEN-2 performs only the decay cooling calculation with the full scope of ORIGEN-2 nuclides inventory provided by the McCARD depletion calculation. The accuracy of the decay heat analysis procedure developed in the previous work by using HELIOS and ORIGEN-2 codes was also verified. The HELIOS/ORIGEN-2 procedure showed a good accuracy for a short period of cooling time. However, a relatively large discrepancy between the two was observed for a long period of cooling time. As expected, the decay heat of a TRU fueled DB-MHR core was much higher than that of uranium fueled PMR200 core due to the fuel composition difference, which means that more attention for effective removal of the decay heat should be paid in designing the TRU fueled deep burn cores to ensure the safety of the deep burn core during the conduction cooling events.     

Evaluation of the influence of bypass flow gap distribution on the core hot spot in a prismatic VHTR core

Core bypass flow in VHTR is one of the key issues for core thermal margins and efficiency. The bypass flow in the prismatic core varies during core cycles due to the irradiation shrinkage/swelling and thermal expansion of the graphite blocks. A procedure to evaluate the local gap size variation between graphite blocks was developed and applied to a prismatic core VHTR. The influence of the core restraint mechanism on the bypass flow gap was evaluated. The predicted gap size is as much as 8 mm when the graphite block is exposed to its allowable limit of fast neutron fluence. The analysis for the core bypass flow and hot spot was carried out based on the calculated gap distributions. The results indicate that the bypass gap and flow distributions are closely related to the local hot spot and its location and the core restraint mechanism preventing outward movement of the graphite block by a fastening device reduces the bypass gap size, which results in the decrease of maximum fuel temperature not less than 100 °C, when compared to the case without it.