Application of the multigrid amplitude function method for time-dependent MOC based on the linear source approximation

ABSTRACT

An efficient numerical scheme for time-dependent MOC calculations is proposed. In the present scheme, one of the most successful factorization method, the multigrid amplitude function (MAF) method, is employed to achieve faster computation with the minimum degradation for the temporal integration of the scalar flux. In addition, the MAF method is re-derived based on the linear source approximation, which is not applied for time-dependent MOC calculations in the past studies as far as the authors’ knowledge, to reduce the spatial discretization error with the coarser flux region separation. The accuracy and computational time of the present scheme are evaluated through the calculation of the TWIGL and the C5G7-TD 2D benchmark problems. The present calculation results show that the present scheme is 6.2 times faster than the conventional method while achieving the same accuracy in the C5G7-TD benchmark problem.     

基于最小二乘的线性源特征线方法研究

特征线方法一般采用平源近似来求解,平源近似需要大量较小的网格才能获得精确的结果,从而会消耗较多内存,影响计算效率。相比平源近似,线性源可在网格较少的情况下得到较精确的数值结果。本文提出一种基于最小二乘的线性源特征线方法,并通过计算压水堆栅元及C5G7基准题等算例,对该方法进行了分析。数值结果表明,基于最小二乘的线性源特征线方法能在网格较少的情况下提供稳定、精确的数值结果。     

一种求解反应堆中子扩散方程和输运方程的方法

结合反应堆中子物理方程的特点和非结构网格技术,提出了一种在任意网格下求解反应堆中子物理方程的方法。以反应堆中子扩散方程和一阶离散纵标的输运方程为例,从空间离散、方程离散和边界条件实施等方面介绍了该方法的实施过程。利用该方法编制的程序计算了BN-600基准题、CFR1000概念堆和BWR栅元3种情况的有效增殖因数,并与其他程序的计算结果进行了对比,初步验证了该方法的合理性。     

基于CPU-GPU异构并行的MOC中子输运计算并行效率优化研究

CPU-GPU异构系统为加速全堆芯特征线方法（MOC）精细计算提供了方法和思路。在实现基于CPU-GPU异构系统的二维MOC异构并行算法基础上,提出了性能分析模型,识别了影响异构并行算法并行效率的主要因素;针对识别到的性能影响因素,实现了输运计算与数据传递相互掩盖,提升了异构并行算法的整体并行效率。数值结果表明：程序具备良好的计算精度;数据传递（MPI通信和CPU与GPU之间的数据拷贝）是影响异构并行算法并行效率的主要因素;实现输运计算与数据传递相互掩盖后,程序性能和强并行效率均有所提升;5异构节点（包含20块GPU）并行时,程序整体效率提升达8%,强并行效率从87%提升到95%;相比CPU节点并行计算,4个CPU-GPU异构节点整体性能优于20个CPU节点。     

Recent activities in the field of reactor physics

ABSTRACT

Reactor Physics that treat the essentials of how fission nuclear reactors work fundamentally has played important roles in safe operations and design studies of various types of nuclear reactors. From the latest activities in the field of reactor physics, this report summarizes some outstanding researches and developments published in scientific journals, including the Journal of Nuclear Science and Technology and others.     

Reduction of the Spatial Discretization Error in the Method of Characteristics using the Diamond-difference Scheme

In this paper, the diamond-difference (DD) scheme, which is commonly used in discrete-ordinate codes, is applied to the method of characteristics (MOC) to reduce the spatial discretization error of the flat flux approximation. Smaller spatial discretization error allows coarser background mesh division, which leads to smaller computational burden. Some theoretical considerations on the DD scheme are discussed to clarify the strength of this method. An absorption cross section weighted DD scheme (AWDD), which utilizes macroscopic absorption cross section to set the weight, is also discussed. The DD and AWDD schemes are implemented to AEGIS, which is a lattice physics code based on MOC. Then the AEGIS code is applied to two different benchmark problems whose spatial discretization errors are large. The calculation results indicate that from the viewpoint of spatial discretization error, the AWDD scheme is superior to the conventional MOC in which the step characteristics approximation is commonly used. Since incorporation of the AWDD scheme to current MOC codes is very simple, it will be a good candidate of spatial discretization method for MOC codes.     

二维MOC的CMFD加速计算模块开发与验证

DRAGON程序中的二维特征线法(MOC)计算模块包含多种加速方法,但加速效率很高的粗网有限差分(CMFD)加速算法并未得到应用。为提高DRAGON程序中现有的二维MOC计算模块的计算效率,开发了CMFD加速计算模块并探究其收敛稳定性。运用C5G7-2D基准题验证所开发的CMFD加速计算模块,验证结果表明,所开发的CMFD加速计算模块与DRAGON程序中原有的加速模块相比具有很高的计算效率,较同类计算程序OpenMOC有更好的收敛稳定性。     

Radially and azimuthally dependent resonance self-shielding treatment for general multi-region geometry based on a unified theory

A unified resonance self-shielding method, which can treat general sub-divided fuel regions, is developed for lattice physics calculations in reactor physics field. In a past study, a hybrid resonance treatment has been developed by theoretically integrating equivalence theory and ultra-fine-group slowing-down calculation. It can be applied to a wide range of neutron spectrum conditions including low moderator density ranges in severe accident states, as long as each fuel region is not sub-divided. In order to extend the method for radially and azimuthally sub-divided multi-region geometry, a new resonance treatment is established by incorporating the essence of sub-group method. The present method is composed of two-step flux calculation, i.e. ‘coarse geometry + fine energy’ (first step) and ‘fine geometry + coarse energy’ (second step) calculations. The first step corresponds to a hybrid model of the equivalence theory and the ultra-fine-group calculation, and the second step corresponds to the sub-group method. From the verification results, effective cross-sections by the new method show good agreement with the continuous energy Monte-Carlo results for various multi-region geometries including non-uniform fuel compositions and temperature distributions. The present method can accurately generate effective cross-sections with short computation time in general lattice physics calculations.     

子群法与特征线法结合的中子共振计算

传统的中子共振自屏计算方法采用了有理近似,局限于处理简单的共振模型,在处理复杂燃料栅元/组件时会引入较大误差。为提高复杂情况下共振计算的精度,将子群法共振模型与特征线方法结合,推导了子群法-特征线法方程。基于WIMSD格式的69群数据库,编制了可用于任意二维几何中子共振计算的SGMOC程序。通过数值验证表明,该程序计算结果与MCNP程序计算结果吻合良好,具有较高的计算精度与几何通用性。     

ARM计算环境下堆芯程序CORTH和KYLIN2的移植

为了论证国产芯片在堆芯数值计算领域的可行性,对子通道计算软件CORTH和堆芯组件程序KYLIN2的串行版本在飞腾处理器的ARM计算环境进行了移植。移植过程在ARM计算环境下通过合理的程序代码修订,去除对商业函数库的依赖,且在特征线循环结构的扫描计算过程引入OpenMP多线程并行。实验参照对象为频率两倍差异的Intel商用处理器。结果表明CORTH程序和KYLIN2均能够成功移植,且与Intel商用处理器的数值稳定性保持一致。计算效率方面CORTH程序移植后的串行效率与Intel计算环境差异较小;KYLIN2移植后的串行效率较低,但通过线程并行后计算效率接近Intel处理器的串行效率。移植结果论证集群系统这种混合国际和国内处理器的资源结构,能够在计算资源紧张的情况下充分利用国产硬件,提升计算环境的整体利用效率。     

GPU加速MOC输运计算性能分析研究

特征线方法(MOC)在求解堆芯规模中子输运方程时面临计算时间长的问题,加速和并行算法是目前研究的热点。基于MOC在特征线和能群层面的并行特性,采用统一计算设备构架(CUDA)编程规范,实现了基于图形处理器(GPU)的并行二维MOC算法。测试了菱形差分和步特征线法分别在双精度、混合精度及单精度浮点运算下的计算精度、效率及GPU加速效果。采用性能分析工具对GPU程序性能进行了分析,识别了程序性能瓶颈。结果表明:菱形差分和步特征线法在不同浮点运算精度下均表现出良好的计算精度;相比于CPU单线程计算,GPU加速效果在双精度和单精度情况下分别达到35倍和100倍以上。     

A methodology to predict a fission gas release ratio of MOX fuel with heterogeneous microstructure

The objective of this study is to formulate a methodology to predict a fission gas release ratio of MIMAS MOX. An irradiated MIMAS MOX fuel with plutonium rich agglomerates was subjected to elemental analyses by electron probe micro analysis and secondary ion mass spectrometry in order to investigate xenon distribution. The results of the elemental analyses showed that the plutonium rich agglomerates at the periphery of the fuel pellet sample retained a high concentration of xenon as gas bubbles. Then, the results were used as reference data for modification of models in a fuel rod analysis code, FEMAXI-7. Using the modified FEMAXI-7, we applied an approach to prediction of fission gas release ratio of MOX fuel with plutonium rich agglomerates. In the approach, two separated analyses using FEMAXI-7 were performed for the plutonium rich agglomerates and the matrix. Fission gas release ratios obtained from the two analyses were processed through weighted-average with burnup ratios of the plutonium rich agglomerates and the matrix. Finally, the fission gas release ratios were compared with results of rod puncture tests. As a result of the comparison, it was confirmed that the proposed approach could well predict fission gas release ratio of MOX fuel with plutonium rich agglomerates.     

Resonance Calculation for Large and Complicated Geometry Using Tone's Method by Incorporating the Method of Characteristics

A new efficient approach for evaluating the background cross section, which is based on Tone's method, is presented. Though the collision probability method is used in the conventional Tone's method, the method of characteristics (MOC) is used in the present method. Since the computation time of MOC is shorter than that of the collision probability method in a large and complicated geometry, the present method will be useful not only for lattice physics calculation, but also for analyses of advanced reactors with complicated geometry. Verification calculations are carried out in two configurations, i.e., a PWR fuel assembly geometry and a multiassembly geometry adjacent to the baffle-reflector region. The validity of the present method has been confirmed through the results of verification calculations.     

Evaluation of gases'molecular abundance ratio by fiber-optic laser-induced breakdown spectroscopy with a metal-assisted method

A metal-assisted method is proposed for the evaluation of gases'molecular abundance ratio in fiber-optic laser-induced breakdown spectroscopy(FO-LIBS).This method can reduce the laser ablation energy and make gas composition identification possible.The principle comes from the collision between the detected gases and the plasma produced by the laser ablation of the metal substrate.The interparticle collision in the plasma plume leads to gas molecules dissociating and sparking,which can be used to determine the gas composition.The quantitative relationship between spectral line intensity and molecular abundance ratio was developed over a large molecular abundance ratio range.The influence of laser ablation energy and substrate material on gas quantitative calibration measurement is also analyzed.The proposed metal-assisted method makes the measurement of gases'molecular abundance ratios possible with an FO-LIBS system.     

垂直加热通道内超临界水流动稳定性参数敏感性分析

给出了无量纲分析法与频域法相结合的稳定性分析方法的详细描述,并定义了影响稳定性的关键无量纲数。针对垂直加热通道内超临界水进行了密度波稳定性分析,并建立了稳定性边界。对系统入口阻力因数、出口阻力因数、摩擦因数、进出口压降和流动方向等进行了参数敏感性分析,结果表明高的入口阻力因数有利于系统的稳定,但高的出口阻力因数和高的摩擦因数不利于系统的稳定,系统进出口压差对系统的稳定性影响较小,向上流动比向下流动更有利于系统的稳定。计算结果对超临界水堆的堆芯和系统设计具有指导性作用。     

Theoretical Analysis on Time-Dependent Energy Spectra of Neutrons in a Small Graphite Assembly

A theoretical study was carried out on the time-dependent neutron spectrum in a small graphite assembly into which the neutron pulses were injected through a pre-moderator layer of polyethylene. Numerical analyses were performed by means of the usual time-step method, as well as by the spatial mode expansion time-step and two-region difference equation methods.

It was verified that addition of the pre-moderator does not substantially affect the space-time-dependent spectral behavior of neutrons in a graphite system of dimensions adopted in current experimental arrangements.

A strong space dependence of the time-dependent spectra was observed in the form of spectral hardening in increasing distance from source, which was termed “propagation hardening”.

The space-time-dependence and neutron trapping at Bragg peak energies appearing on the measured spectra were well reproduced by both the spatial mode expansion time-step and two-region calculations.     

中国先进研究堆堆水池窄量程液位测量方案选择及误差分析

介绍了中国先进研究堆（CARR）水池窄量程液位测量的4种方案：远传隔离法兰差压法、安全级吹气法、绝压变送器测量法、差压变送器测量法，并对这4种测量方案进行比较、分析，最后对选定的测量方案进行了误差分析。结果表明：差压变送器测量法满足测量要求。     

Biased Selection of Particle Flight Directions as a Variance Reduction Technique in Monte Carlo Calculations

As a practical variance reduction technique applicable to Monte Carlo shielding calculations, the present article shows a new simple biased sampling technique on particle flight directions. Scattered particles not directed towards the detector positions are killed if they are not so important, that is, if the particle weights are sufficiently small compared to the source weight. In this way, we can reduce the sample size required for obtaining an accurate estimate for the detector response.

The present technique was incorporated into the multigroup neutron and γ-ray transport code MORSE, and sample calculations were performed on spherical fast neutron systems. The results have shown that this biased technique is effective for dealing with neutron multiplication as well as neutron transmission problems. The neutron flux or the effective multiplication factor of a nuclear reactor is estimated more accurately than from the method of path-length stretching with about the same computation time. In addition, it is shown that the flight-direction biasing can further effectively be used by combining it with other variance reduction techniques.     

Size-resolved source apportionment of aerosol particles using polycapillary X-ray lens with a plateau in its focal spot

A laboratory micro X-ray fluorescence spectrometer based on a special polycapillary X-ray lens (PXRL) was used to carry out the source apportionment of aerosol particles. In the curve of the distribution of the X-ray intensity in the focal spot of the special PXRL, there was a plateau with a diameter of 21.3 μm in which the distribution of the X-ray intensity was homogeneous. The gain in flux density in the plateau of the PXRL is 1490. The uniformity of this plateau was 2.9%. This was helpful for the quantitative X-ray fluorescence analysis of a single aerosol particle with smaller size than that of the plateau of the PXRL. The fingerprint database of aerosol particles with given sizes from various air pollution sources was established with the single particle analysis method. The size-resolved source apportionment of aerosol particles in haze in Beijing city was performed with this fingerprint database.