Measurement and analysis of integral fusion neutronics data on simulated experimental lithium-lead module at the LOTUS facility

In-system foil activation rates and tritium production rates were measured in an experimental lithium-lead module (EL²M)- major component being a 62-cm thick pseudo-cylindrical region containing lithium and lead pellets so arranged as to simulate Li₁₇Pb_8.3 eutectic—at fusion blanket neutronics facility LOTUS. Sets of two foils each—Zr and In—were irradiated at multiple locations in the central rod to measure⁹⁰Zr(n,2n)^89m+gZr and¹¹⁵In(n,n)^115mIn reaction rates. Tritium measurements were done using two techniques: off-line liquid scintillation technique of Dierck and online lithium glass scintillation technique, the latter technique providing only T₆ (tritium from⁶Li). These measurements have been analyzed both by two-dimensional and three-dimensional transport codes DORT and MCNP, respectively. Though computed results broadly reproduce spatial profiles (along the central rod) of the measured quantities, differences as large as 50% are found.     

等效天然铀入堆辐照试验中子学性能分析

本文基于重水堆堆芯核设计程序系统,计算分析了装入等效天然铀（NUE）燃料的试验堆芯的中子学性能。对选择两个燃料通道进行入堆试验的方案进行了论证分析,通过与相应的设计限值以及全天然铀（NU）燃料堆芯中子学性能的比较,检验了实际入堆NUE燃料的中子学等效性。研究表明,实际入堆NUE燃料满足燃料的等效性要求,两个NUE燃料通道入堆试验方案从核设计角度是可行的,堆芯安全性不受影响。     

Experimental and Theoretical Studies of Heavy-Water Homogeneous Two-Region System

A series of critical experiments and theoretical analyses has been made on two-region systems in which a heavy water solution of uranyl sulfate with ²³⁵U enrichment of about 20% is surrounded by heavy water, poisoned with B or mixed with ThO₂. D-to-²³⁵U atomic ratios in the core solutions ranged 4,500–1,000, depending on the core diameter and the blanket concentration.

The theoretical effective multiplication factor is decreased by treating the leakage of fast neutrons from the core rigorously, and is increased by using spatial-dependent effective cross sections. These treatments are justified by the agreement found between the calculated and measured values for the Cd ratio and the thermal flux distribution. The disagreement seen in the effective multiplication factor between the theoretical and experimental values may be attributed to uncertainty in the resonance integral of ²³⁵U. The discrepancy in the effective multiplication factors does not exceed 1%, when the accepted value of νI _f -I _a is reduced to a smaller value.     

Prediction Uncertainty Analysis of Neutronic Properties of Fast Breeder Reactor by Use of Sensitivity-Based Methodology

The prediction accuracies of key neutronic characteristics including burnup properties evaluated with use of the sensitivity-based methodology have been reviewed for a fast breeder reactor. The bias factor method, the cross section adjustment method and the combined method are used to evaluate the prediction accuracies. The calculation method of sensitivity coefficients used in the uncertainty analysis is discussed. The three methods are compared from the theoretical and numerical points. For the numerical comparison, they are applied to a 1,000 MWe fast breeder reactor. The prediction uncertainties are within the range of 0.7~1.0% for k_eff , 3~5% for control rod worth, 1~2% for ²³⁹Pu fission rate distribution, 12% for burnup reactivity loss and 1.5% for breeding ratio. These values are much smaller than those predicted without any integral data.     

气冷微堆燃料设计的中子学特性影响研究

为分析气冷微堆燃料设计的中子学特性影响,基于方形燃料组件模型,利用蒙特卡罗程序RMC研究了TRISO颗粒、燃料芯块在燃料设计中的主要参量对组件中子学特性的影响。研究结果表明,燃料颗粒体积占比和包覆层厚度不变时,组件寿期随燃料核芯直径的增大先显著增大,而后趋于平稳;燃料颗粒体积占比和燃料核芯直径不变时,组件寿期随包覆层厚度的增大而减小;燃料装载量不变时,芯块直径增大,组件寿期显著增大,而芯块高度影响较小;无燃料区厚度的增加对组件中子学特性有明显的负面影响,基体材料密度、基体杂质硼当量对组件中子学特性的影响较小。研究结果将为后续气冷微堆包覆颗粒弥散燃料的设计优化提供指导。     

Theoretical Study on New Bias Factor Methods to Effectively Use Critical Experiments for Improvement of Prediction Accuracy of Neutronic Characteristics

Extended bias factor methods are proposed with two new concepts, the LC method and the PE method, in order to effectively use critical experiments and to enhance the applicability of the bias factor method for the improvement of the prediction accuracy of neutronic characteristics of a target core. Both methods utilize a number of critical experimental results and produce a semifictitious experimental value with them. The LC and PE methods define the semifictitious experimental values by a linear combination of experimental values and the product of exponentiated experimental values, respectively, and the corresponding semifictitious calculation values by those of calculation values. A bias factor is defined by the ratio of the semifictitious experimental value to the semifictitious calculation value in both methods. We formulate how to determine weights for the LC method and exponents for the PE method in order to minimize the variance of the design prediction value obtained by multiplying the design calculation value by the bias factor. From a theoretical comparison of these new methods with the conventional method which utilizes a single experimental result and the generalized bias factor method which was previously proposed to utilize a number of experimental results, it is concluded that the PE method is the most useful method for improving the prediction accuracy. The main advantages of the PE method are summarized as follows. The prediction accuracy is necessarily improved compared with the design calculation value even when experimental results include large experimental errors. This is a special feature that the other methods do not have. The prediction accuracy is most effectively improved by utilizing all the experimental results. From these facts, it can be said that the PE method effectively utilizes all the experimental results and has a possibility to make a full-scale-mockup experiment unnecessary with the use of existing and future benchmark experiments.     

托卡马克聚变中子源的数值模型研究

托卡马克(Tokamak)聚变装置中子学分析中,聚变中子源描述是重要的输入参数,其准确性直接影响分析结果的可靠性。通过分析ITER和欧洲聚变示范堆(EU DEMO)中子学分析中所采用的聚变中子源模型,提出了一种完整描述Tokamak中L-mode、H-mode等离子体的D-D、D-T聚变中子源的数值模型。在中国聚变工程实验堆(CFETR)的工程集成设计平台上,编写了基于蒙特卡罗算法的程序SCG求解该数值模型,实现了读取(零维)等离子体参数、输出可供典型中子学软件MCNP直接读取的中子源定义文件的功能。以CFETR氦冷球床包层的中子学分析模型为基准,在相同的L-mode等离子体D-T聚变工况下,相较于采用EU DEMO源子程序,采用本模型计算得到的中子壁负载差异最大值为2.02%,包层氚增殖率差异为0.18%,全堆能量增益因子的差异为0.23%。结果表明,本模型与其他源描述的差异较小,可应用于CFETR的中子学分析。     

溶液堆气泡及瞬态中子学模型

溶液堆的燃料（UO₂(NO₃)₂水溶液）具有液体形态，兼作核燃料和慢化剂，裂变碎片与水分子碰撞产生辐照裂解气体气泡，气泡在燃料中存在和运动使得溶液堆的瞬态中子学模拟十分困难。本研究首先基于稳态的物理热工耦合方法对溶液堆进行模拟，对模拟结果体现的气泡行为特征进行提炼，建立溶液堆气泡数值模型，再将该气泡模型应用于溶液堆瞬态中子学分析程序中，使用该程序对瞬态试验进行模拟并与测量结果进行比较，发现气泡行为特征与耦合方法的模拟结果一致。     

Estimation of sensitivity coefficient based on lasso-type penalized linear regression

We proposed the penalized regression ‘adaptive smooth-lasso’ for the estimation of sensitivity coefficients of the neutronics parameters. The proposed method utilizes the variation of the microscopic cross-sections and the neutronics parameters obtained by random sampling. The weighted penalty term of the proposed method is more appropriate for the estimation of the sensitivity of neutronics parameters to the microscopic cross-section than that of the conventional methods. In a numerical verification calculation, sensitivity coefficients of k_eff of an accelerator-driven system are estimated using the proposed method, the conventional penalized regression, and the direct method. Comparison of these results indicates that the proposed method is superior to the conventional penalized linear regression from the viewpoint of reproduction of the reference sensitivity coefficients obtained by the direct method. Through the verification calculations, the proposed method can be a candidate for a practical method to estimate the sensitivity coefficients with low calculation cost.     

Neutronics analysis of the power flattening and minor actinides burning in a thorium-based fusion–fission hybrid reactor blanket

A neutronics analysis has been performed for a thorium fusion breeder with a special task of burning minor actinide ²³⁷Np, ²⁴¹Am, ²⁴³Am, and ²⁴⁴Cm, and production of ²³³U for the future PWR application. Under a first wall fusion neutron wall loading of 0.1 MW/m² by a plant factor of 100%, preliminary neutronics calculations have been performed using the one-dimensional transport and burnup calculation code BISONC and the Monte Carlo transport code MCNP. To obtain a quasi-constant nuclear heat production density, 11 fuel rods containing the mixture of ThO₂ and minor actinides are placed in a radial direction in the fissile zone where ThO₂ is mixed with variable amounts of minor actinides. Calculation results show that the tritium breeding ratio is greater than 1.05 for both investigated Cases A and B, and the hybrid reactor is self-sufficient in the tritium required for the (DT) fusion driver in those models during the operation period. The blanket energy multiplication factor M, varies between 13.8 and 29.6 depending on the fuel types at the end of the operation period. The peak-to-average fission power density ratio (Γ) is less than 1.66 and 1.68 for both Cases A and B, respectively during the operation time. After 720 days of plant operation, the accumulated ²³³U is 1277 and 1725 kg in the blanket for the Cases A and B, respectively.     

Investigation of the packing structure of pebble beds by DEM for CFETR WCCB

Li₂TiO₃/Be₁₂Ti mixed pebble beds with multi-sized particles are one of the potential candidates for the WCCB (water-cooled ceramic breeder blanket) of the CFETR (China Fusion Engineering Test Reactor). To meet the neutronics requirements of a WCCB, a study of the packing structure of the concerned pebble bed is necessary. In this paper, the discrete element method (DEM) is applied to produce a prototypical blanket pebble bed by directly simulating the contact state of each individual particle using basic interaction laws. According to the current simulation, the packing factor of a mono-sized pebble bed is 0.62–0.64, while the value will become more than 0.75 for Li₂TiO₃/Be₁₂Ti mixed breeding pebble bed with a diameter ratio of not less than 5 as well as an appropriate mixed volume ratio, and thus can meet the neutronics requirements.     

Lowering the enrichment of the Syrian miniature neutron source reactor

An investigation of lowering the fuel enrichment of MNSR was realized. A 3-D neutronic model was developed for the analysis of the reactor. It was found that lower number of fuel elements is needed when UO₂ is used with 5.45 g of ²³⁵U content in each fuel rod. Sensitivity of the reactor to the purity of the beryllium reflector proved to be an important factor in determining the reactor neutronics as well as the weight of loaded fuel in the core. Inherent safety features of low excess reactivity and shutdown margins are preserved and enhanced. Average thermal fluxes over different zones of the core are kept very much unchanged. ©     

The TFTR Lithium Blanket Module program

The Lithium Blanket Module (LBM) is an approximately 80×80×80 cm cubic module, representative of a helium-cooled lithium oxide fusion reactor blanket module, that will be installed on the TFTR (Tokamak Fusion Test Reactor) in late 1986. The principal objective of the LBM Program is to perform a series of neutron transport and tritium-breeding measurements throughout the LBM when it is exposed to the TFTR toroidal fusion neutron source, and to compare these data with the predictions of Monte Carlo (MCNP) neutronics codes. The LBM consists of 920 2.5-cm diameter breeder rods constructed of lithium oxide (Li₂O) pellets housed in thin-walled stainless steel tubes. Procedures for mass-producing 25,000 Li₂O pellets with satisfactory reproducibility were developed using purified Li₂O powder, and fabrication of all the breeder rods was completed in early 1985. Tritium assay methods were investigated experimentally using both small lithium metal samples and LBM-type pellets. This work demonstrated that the thermal extraction method will be satisfactory for accurate evaluation of the minute concentrations of tritium expected in the LBM pellets (0.1–1 nCi/g).     

Approximate Treatment of Thermal Expansion Effect in Lattice Transport Calculations

In this paper, thermal expansion effect on neutronics characteristics is approximately taken into account by a correction on cross sections. Dimensions of reactor core components depend on their temperatures due to the thermal expansion phenomena. However, the variation of calculation geometry requires considerable computational load for trajectory based lattice transport calculations such as the characteristics method since ray tracing must be re-executed. Therefore, if a correction on cross sections can accurately capture the effect of geometrical variation due to the thermal expansion, computation time of a lattice transport calculation that treat temperature variation can be reduced. Three different corrections on cross sections were tested in PWR fuel assembly geometry using UO₂ and MOX fuels. It was found that the correction of cross sections that preserves neutron attenuation in a region almost reproduce the reference calculation that explicitly considers geometrical variation due to the thermal expansion. The result of this paper will be useful for lattice calculations in production analysis since material temperatures are frequently changed in such analysis to cover various reactor conditions.     

超临界水冷堆环形燃料组件核热耦合分析

在超临界水冷堆预概念设计中,组件设计是十分重要的,将影响堆芯性能。超临界水冷堆中水密度变化剧烈的特性要求必须进行核热耦合分析。从中子学及热工性能角度,使用三维核热耦合程序对环形燃料组件进行了优化设计。应用中子学计算程序FENNEL-N对环形燃料组件进行三维扩散计算,可得到组件内单棒功率分布,应用热工计算程序SUBSC对组件进行子通道分析。在计算过程中,分析了燃料棒间距及燃料棒与组件壁盒之间的间隙对组件性能的影响。计算结果显示,增大棒间距和棒壁间隙能提高组件k_inf,但会增大组件内功率峰因子;子通道受热不均匀性对组件热工性能影响较大,通过加入定位格架的方式能展平冷却剂出口温度,降低最大包壳温度。对环形燃料组件的安全分析表明,从中子学角度该组件是安全的。     

中国氦冷固态实验包层2×6模块中子学计算分析

为了满足ITER对波纹度的要求,核工业西南物理研究院提出了新的减少低活化铁素体钢的氦冷固态（HCSB）实验包层模块（TBM）设计方案。采用MCNP程序及ITER全堆MCNP模型,对新设计的2×6HCSB-TBM进行三维中子学计算分析,给出了模块产氚率、核热沉积和功率密度分布等结果。在ITER运行因子为22%时,HCSB-TBM的产氚率为12.68mg/d。TBM内总核热沉积为522.5kW,最高功率密度为11.8W/cm³,出现在氚增殖区Li₄SiO₄中。计算结果可为TBM进一步的结构、热工水力学优化及其他系统设计提供中子学数据。     

堆芯在线监测系统SOMPAS中子学计算核心测试验证

SOMPAS是上海核工程研究设计院有限公司（SNERDI）开发的堆芯在线监测系统，其中子学计算核心为SNERDI最新开发的堆芯核设计系统SCAP。SCAP在SOMPAS中应用前必须进行全面的测试，特别是与电厂实测值比较，以验证确认其精度、可靠性和适用性等。测试验证对象为我国自主开发的300 MWe级核电站，涵盖秦山一期和恰希玛1、2号机组总共32个循环的电厂实测数据。数值计算结果表明，SCAP具有很高的计算精度和可靠性，满足作为中子学计算核心在SOMPAS中应用的要求。     

中国聚变工程试验堆包层的核热耦合效应研究

本文以中国聚变工程试验堆（CFETR）的氦冷固态包层和水冷固态包层为研究对象,基于蒙特卡罗程序MCNP和计算流体力学程序FLUENT,利用3D-1D-2D耦合方法和伪材料方法,分别对200 MW的氦冷固态包层和水冷固态包层及1.5 GW的水冷固态包层方案进行了核热耦合计算分析。研究结果表明,金属铍的热散射效应和轻水密度是聚变包层核热耦合效应的主要来源,核热耦合效应对氦冷固态包层的影响可忽略,对水冷固态包层的氚增殖比和温度分布有一定程度的影响。     

A small long-cycle PWR core design concept using fully ceramic micro-encapsulated (FCM) and UO2–ThO2 fuels for burning of TRU

In this paper, a new small pressurized water reactor (PWR) core design concept using fully ceramic micro-encapsulated (FCM) particle fuels and UO₂–ThO₂ fuels was studied for effective burning of transuranics from a view point of core neutronics. The core of this concept rate is 100 MWe. The core designs use the current PWR-proven technologies except for a mixed use of the FCM and UO₂–ThO₂ fuel pins of low-enriched uranium. The significant burning of TRU is achieved with tri-isotropic particle fuels of FCM fuel pins, and the ThO₂–UO₂ fuel pins are employed to achieve long-cycle length of ～4 EFPYs (effective full-power year). Also, the effects of several candidate materials for reflector are analyzed in terms of core neutronics because the small core size leads to high sensitivity of reflector material on the cycle length. The final cores having 10 w/o SS303 and 90 w/o graphite reflector are shown to have high TRU burning rates of 33%–35% in FCM pins and significant net burning rates of 24%–25% in the total core with negative reactivity coefficients, low power peaking factors, and sufficient shutdown margins of control rods.     

cosRMC复杂曲面开发及在聚变中子学的应用

中国聚变工程实验堆（CFETR）是我国自主设计和研制的重大科学工程，CFETR旨在与ITER相衔接和补充，为研制DEMO级别聚变堆电站提供必要的技术。蒙特卡罗方法在聚变中子学与屏蔽设计等方面具有重要作用。本文基于自主化蒙特卡罗程序cosRMC，研究了蒙特卡罗复杂曲面建模的数学模型和计算方法，开发了复杂曲面建模功能，并通过PPCS（power plant conceptual study）模型验证了该功能实现的正确性。然后构建了CFETR的三维精细化模型，并利用该模型对CFETR包层设计中的关键中子学参数进行计算分析。结果表明，cosRMC对中子学参数氚增殖比、中子壁载荷和核热沉积的计算结果与MCNP的计算值吻合良好，相对偏差均小于5%，满足工程设计需求。研究证明了cosRMC应用于聚变堆包层中子学分析的正确性和有效性。CFETR中子学参数的计算分析，也为其设计和优化提供了参考。