高温气冷堆控制棒区不连续因子的计算与应用

应用不连续因子理论修正的扩散方程,对高温气冷堆侧反射层中控制棒区域的强吸收体和空洞区的局部均匀化进行处理.解决了均匀化区域不存在裂变中子源、边界存在强中子流所带来的的难题,并以输运计算的解为基准进行验算.结果表明:对控制棒区域可进行局部均匀化以及采用简化的边界条件计算不连续因子;用不连续因子修正的扩散方程可准确地处理控制棒.采用不连续因子修正的扩散方程计算高温气冷堆控制棒在计算精度、计算时间上均有优势.     

不连续因子应用于高温气冷堆三维扩散计算

高温气冷堆的三维燃耗计算、三维控制棒价值计算、堆芯功率重构以及芯外探测器响应分析都必须通过三维计算实现.由于高温气冷堆侧反射层中控制棒与吸收球区均为强吸收体,因此,在该区域无法直接用扩散方法计算,而用输运方法实现三维计算又过于耗时.根据不连续因子理论,利用二维(R,θ)几何下输运-扩散耦合计算,实现控制棒与吸收球区的局部均匀化,求得不连续因子和均匀化截面.在此基础上,实现带不连续因子的三维扩散计算.计算结果表明:常规的扩散计算会带来误差,采用不连续因子修正的扩散计算,不但对中子注量率分布改善明显,对本征值、控制棒价值等的改善也很明显,可逼近精细的输运方程的结果,而计算量明显减少.带不连续因子修正的扩散计算是实现高温气冷堆三维计算的有效途径.     

高温气冷堆控制棒区等效截面方法的改进

等效截面方法以耦合输运计算和扩散计算为基础,只需要对吸收体区的扩散截面系数进行修正,能够方便地求解带有强吸收体的堆芯计算问题。本文以二维输运计算为基准,在二维堆芯模型的条件下尝试了将吸收体区域进行网格划分的可能性,并对几种网格划分的方式及相应的均匀化方案进行了初步探索。计算结果证明,这套方法既能保持扩散计算速度快的优点,又能达到精细化输运模型计算的精度。     

角度相关不连续因子在JRR3M堆芯输运计算中的应用

针对含有强吸收体控制组件的日本研究堆JRR3M,在进行堆芯输运方程计算时,给出了角通量不连续因子(AFDF)的定义,并指出使用角通量不连续因子的必要性,提出使用迭代求解的方法来提高计算精度,并使之满足不连续因子自洽性。针对堆芯设计计算量大的特点,使用了超栅元近似方法。该方法能有效缩短计算时间,且灵活性强。利用组件形状函数,能重构出非均匀模型堆芯通量分布。最后讨论了扩散计算时不连续因子的选取问题,指出根据参考的不同,应选择不同的不连续因子。     

超级均匀化方法用于球床氟盐冷却高温堆扩散计算

球床氟盐冷却高温堆的控制棒位于侧反应射层内,存在无裂变中子源且受堆芯泄漏谱强烈影响的强吸收体区域扩散计算难题。超级均匀化方法(Super Homogenization,SPH)被用于对氟盐球冷却床堆侧反射层中控制棒区域的强吸收体进行等效均匀化处理,同时堆芯除控制棒区域外采用谱修正方法(Spectra Modification,SM),将输运计算的结果作为基准进行验算。结果表明,SM-SPH模型能有效地计算球床氟盐冷却高温堆反射层控制棒价值及通量分布,并且较常规的SPH方法能更好地处理棒间干涉效应。     

氦气氛中氙在石墨球中扩散系数的测定

在核反应堆设计中,氙在石墨中的扩散是计算氙毒的一个重要因素。Salzano等曾在石英玻璃装置中利用不同扩散时间氙气向石墨球内的扩散量来测量高温负压下氙在石墨球中的扩散系数。Decken等简单地介绍了由石墨球中的氪向球外的不稳定扩散过程,测量氪在石墨球中的扩散系数。他把与一定氪分压(含有~(85)Kr)相平衡的石墨球从平衡容器中     

考虑角点不连续因子的精细功率重构及验证

在采用调制法进行组件精细功率重构时,由于改进的格林函数节块法程序引入了组件不连续因子,导致重构时角点中子通量不连续,需引入角点不连续因子进行修正保证其连续性。文中利用改进格林函数节块法程序堆芯扩散计算的结果,采用高阶多项式展开的调制法来进行组件内的精细功率重构,探讨了角点不连续因子在精细功率重构中的重要作用。并通过秦山二期实际堆芯的两种工况对其进行了验证,与SIMULATE-3的计算结果对比表明:考虑角点不连续因子的精细功率重构具有较高的计算精度,能够满足工程计算的要求。     

高温气冷堆控制棒硼燃耗特性分析

控制棒价值及其燃耗规律是核反应堆物理设计关注的要点之一。球床式高温气冷堆控制棒位于侧反射层石墨孔道中,吸收体为圆环形的B₄C,其燃耗特性具有特殊性。采用MCNP耦合燃耗计算模块的方法,对控制棒吸收体进行精细划分,分析了各子区域硼的详细燃耗特性及控制棒价值的变化规律。计算结果表明,由于强烈的空间自屏效应,虽然吸收体外层硼燃耗很多,但吸收体内层硼燃耗很少,因此,反应堆运行寿期末控制棒价值减少很小。     

MC-SN耦合粒子信息转换精度分析

屏蔽计算是核设施屏蔽设计与优化的重要依据,蒙特卡罗(MC)方法与离散纵标(S_N)法的耦合方法可有效解决复杂几何深穿透输运问题。MC-S_N耦合方法将蒙特卡罗程序产生的粒子径迹信息转换为离散纵标法的边界面入射角通量密度,在此过程中需统计每个离散方向对应角度区域的粒子信息,以经纬线划分角度区域的方法在转换过程中会影响粒子平衡。通常角通量密度可采用球谐函数展开,本文针对层对称求积组和勒让德切比雪夫求积组,研究耦合方法对各阶球谐函数的转换精度。分析结果表明,耦合方法的离散角度区域划分对低阶球谐函数的转换精度较高,但对高阶球谐函数的转换精度具有较大影响,其中对二阶球谐函数转换精度的平均偏差在10%以上。由于高阶求积组的角度区域的划分相关性更强,因此转换精度明显高于低阶求积组。     

输运方法求解堆芯均匀化问题

研究不连续因子在输运方法求解堆芯均匀化问题中的应用。选用的计算方法为二维离散纵标法(SN),重点讨论了普通燃料组件和强吸收的控制棒组件的均匀化处理。将不连续因子引入SN方法中、给出了两种不连续因子的求解方法以及修正控制棒组件均匀化吸收截面的修正因子。通过两个典型例题的计算显示改进效果。     

Applicability of angular flux discontinuity factor preserving region-wise leakage for integro-differential transport equation

In the current core analysis, spatial homogenization is utilized to reduce the computational time. The discontinuity factor (DF) is one of the effective correction factors to reduce spatial homogenization error. The DF in diffusion equation is widely used; on the other hand the DF in transport equation has not been put to practical use although several efforts have been carried out. In this paper, the angular flux discontinuity factor (AFDF) as the DF for the integro-differential transport equation (e.g., the discrete-ordinate method, the method of characteristics) is theoretically described and its applicability is discussed. The AFDF is used to preserve the region-wise neutron leakage at each spatial mesh and defined as a ratio of heterogeneous and homogeneous angular fluxes at the homogenized region surface. In a homogeneous calculation with the AFDF, the angular flux is discontinuous at the region surface. In this paper the applicability of the AFDF to fuel pin cell homogenization is verified for one-dimensional slab geometry. As a result of this verification, it is confirmed that the AFDF has the capability to reduce the spatial homogenization error of fuel pin cell homogenization.     

核级石墨微观孔隙有效扩散系数研究

有效扩散系数是描述石墨内部扩散传质的重要参数,传统经验公式中的单一平均孔径假设无法反映石墨内部复杂的孔隙孔径分布规律及其对扩散的影响,现有核级石墨的有效扩散系数计算公式与实验结果相差较大。考虑到受Knudsen扩散影响,并根据核级石墨微观孔隙孔径分布规律及扩散理论将孔径范围分为两类,从而对有效扩散系数计算公式进行了修正。采用压汞仪对IG110核级石墨未氧化及不同温度下等温氧化样品进行了孔径分析,采用本文修正公式计算了有效扩散系数并与实验测量结果进行了比较。同时对失重率、温度和压力对有效扩散系数的影响进行了讨论。结果发现,修正公式计算结果与核级石墨扩散系数的实验结果相符,提高了核级石墨有效扩散系数的计算精度。有效扩散系数随失重率的增加而升高,失重率低于20%时增长明显。有效扩散系数与温度呈0.528次方关系,与压力大致呈-0.33次方关系。     

离散纵标屏蔽计算空间自适应方法研究

离散纵标法是目前国际上通用的核装置辐射屏蔽计算的主要方法之一。空间变量离散误差对离散纵标屏蔽计算的精度至关重要。实际屏蔽计算中存在较强的非均匀性,传统的空间离散方法不能高效地在全局达到较高精度。本文采用线性间断有限元方法进行空间离散,由基于两网格的误差估计和基于残差的误差估计驱动空间网格自适应细化;基于树状结构的六面体网格,对传统的输运扫描进行改进,在粗-细网映射中保持零阶、一阶空间矩守恒。数值结果表明：线性间断有限元方法具有较好的射线传递特性和空间收敛性;自适应算法能较好地对通量密度间断、通量密度梯度大、光学厚度大的区域进行网格细化。在达到相同计算精度时,自适应方法所需的网格数较均匀细分的方法减少约1个数量级,能有效提高屏蔽计算效率。     

Application of the discontinuity factor theory to accelerate routine rod worth calculations for modular HTRs

A modular high temperature gas cooled reactor (HTR) is equipped with strong absorbers and many void areas in the control rod regions which are located in the graphitic side reflector. When using diffusion calculations, a special skill is required to homogenize these ex-core absorber regions. These difficulties arise from the fact that these absorber regions do not contain fission sources while the boundaries of the absorber regions are exposed to very strong neutron currents. This paper shows that a mere conventional homogenization technique is not enough to obtain acceptable results. It is shown that a discontinuity factor-corrected diffusion-solution can be found which yields very good, satisfactory results for fast, whole core diffusion calculations. The verification is done by comparing time-consuming transport calculations [S_N-codes or multi-group MCNP-codes] with a fast running diffusion code, corrected by the newly proposed homogenization technique.     

Applicability of Constant Flux Approximation in Method of Characteristics with Filtering to Tiny Regions

For the method of characteristic (MOC), a system with large-gradient neutron flux caused by a strong absorber or neutron leakage is reported to entail large errors in spatial mesh discretization and require very fine mesh spacing. To apply the MOC to such fine models, the ray-trace path width has to be fine in order to make many paths cross each region. Our new method intends to obtain good accuracy with a coarse path width. With a coarse path width on the MOC, some tiny regions have less ray-tracing paths. The reliability of flux calculation for the regions can be evaluated with the calculation volumes that are estimated in ray tracing. If the discrepancy between the calculation and true volumes becomes large, the accuracy cannot be expected. In this study, the discrepancies were numerically evaluated, and it is found that the discrepancies occur on a very tiny region. To make the flux calculation of such tiny regions more reliable, an approximation, in which the outgoing flux is equal to the incoming neutron, is applied instead of the usual MOC equation. The criteria switching on the approximation, which is called filtering, was numerically evaluated for PWR assemblies. The method is validated with numerical benchmark calculations.     

Development of Numerical Methods for Simulation of Rapid Multi-Phase Interactions

Techniques commonly used in the calculations of multi-phase flow, such as local parameter averaging and continuity phase assumptions, may result in large calculational inaccuracies for phenomena with rapid phase change. For example, with vapor explosions, a large degree of pseudo-diffusion (i.e. numerical diffusion) of components in dispersed states or with discontinuous fronts may occur, and local information, useful for modeling and evaluation of the phenomena, may be lost. Pseudo-diffusion of the components which act as high-temperature heat sources affects component distributions throughout the entire system. Numerical divergence is also often caused by fluctuation of these high-temperature components. In this paper, two treatment methods are proposed to avoid these problems. One method is a dispersed component method, which was developed for dispersed components. This method includes special modeling for some local parameters and some treatments to suppress pseudo-diffusion and numerical divergence. The other is a multi-region scheme, where a calculation domain is divided into an expanding, multi-phase mixture region and the surrounding, single-phase continuum region. The front of the mixture region is tracked using an adaptable grid to accurately follow the interface. By this method, numerical diffusion at the interface can be avoided. The effectiveness of these treatments is demonstrated by numerical simulations.     

The present status of R&D for the muon target at J-PARC: The development of silver-brazing method for graphite

At the J-PARC muon science facility, the muon target was made of an isotropic graphite (IG-43). The energy deposited by the proton beam is estimated to be 3.3 kW on graphite and 600 W on the copper frame. To alleviate the thermal stress, a titanium stress absorber is inserted between the graphite and the copper. Although graphite is known to be difficult to be brazed, the titanium is attached to the graphite through silver-brazing. In this report, we will describe the development of a silver-brazing method for graphite in the fabrication of the J-PARC muon target. A capillary test between the graphite and the titanium was performed to determine the optimal brazing conditions. The test involved bonding graphite and titanium plates while varying the gap between them in order to determine the brazing material and the optimal surface treatment of graphite. Subsequently, a trial muon-production target was fabricated using this optimized brazing method. Specimens were cut from the trial target, and bending test experiments were performed to determine the tensile and shear strength of the interface. As a result, it was confirmed that graphite could be bonded adequately through the silver-brazing.