核反应堆堆芯物理计算的核心任务之一是求解中子输运方程，但全堆芯直接中子输运计算面临着极高的计算复杂度，使得直接计算极为困难，因此基于均匀化理论的两步法技术应运而生，目前仍然是核反应堆堆芯物理分析的主流方法。
均匀化是针对总体跨度大、精细分布复杂的介质的一种处理方法，其本质是在不显著影响宏观整体计算精度的前提下，分步考虑微观局部特征，从而降低算力要求。均匀化理论可以用于空间、能量、角度、核素等多种相空间维度，也可以应用到多个尺度上。
均匀化并非简单地打混平均，需要保证特定物理量在均匀化前后的守恒性，比如核反应率、中子泄漏率、有效增殖因子、缓发中子产生率、衰变热释放率等。这些守恒要求使得均匀化参数不仅与被替代的非均匀介质本身相关，还与其所处的环境紧密相关，也与均匀化前后采用的计算方法直接相关。
近年来，NECP团队面向压水堆、快堆、高温气冷堆等多种不同类型反应堆开展了大量的均匀化理论研究和相应的软件研发工作。
l压水堆堆芯均匀化技术创新研究
压水堆是当前应用最广泛的核电站反应堆类型，为全球提供了大量稳定的电力，对世界能源供应和经济发展意义重大。压水堆堆芯内的中子学特点是局部非均匀、整体均匀，均匀化计算中一般先进行局部组件尺度的非均匀计算，再进行堆芯尺度的三维计算。
NECP团队自主研发了压水堆堆芯物理分析软件NECP-Bamboo[1][2][3][4][5]，在该软件的研发过程中自主创新了一系列均匀化技术，主要包括基于非均匀组件一步法计算的组件均匀化计算方法[1]、面向小型堆或重反射层结构或六角形几何的二维反射层均匀化计算方法[6][7]、处理环境效应的子网格均匀化方法[8]、面向各向同性和各向异性SP3理论的光薄栅元均匀化方法[9][10][11][12]、考虑中子泄漏对中子能谱影响的非均匀泄漏修正理论[13]、能量维度上从子群到能群的归并均匀化方法[14]、核素维度上基于定量重要性分析的燃耗链压缩方法[15][16]等。
现有的压水堆堆芯物理计算主要是基于扩散理论或者SP3理论，大都采用输运修正后的各向同性散射近似，面临计算精度不足的问题。NECP团队创新性地提出了基于P1理论的压水堆堆芯物理计算方法，包括粗网计算和Pin-by-pin计算[17]，目前正在开展针对P1理论的均匀化方法研究。
图1（左） 传统的组件扩散计算棒功率误差
图2（右） NECP-Bamboo栅元SP3计算棒功率误差
l快堆堆芯均匀化技术创新研究
快中子反应堆是我HN发展“三步走”战略承上启下的关键环节，在HN可持续发展方面具有至关重要的作用。快堆具有中子能谱硬、中子平均自由程长、燃料组分复杂、共振效应剧烈等特点，给均匀化少群截面的产生带来诸多挑战。
NECP团队自主研发了先进反应堆堆芯计算分析软件NECP-SARAX[18][19]，在该软件的研发过程中自主创新了一系列均匀化技术，主要包括面向改进TONE方法的能群并行与加速技术[20]、考虑截面角度相关性的均匀化参数计算技术[21]、自适应能群结构产生技术[22]、基于等效堆芯的能群等效压缩技术[23]以及中子、光子释热计算的参数产生技术[24]等。
面向多场景应用，例如ADS反应堆，其中子能量上限通常将突破20MeV，而现有确定论的计算手段仅考虑了20MeV以下的中子反应；又如微小型快堆，堆芯能谱的复杂特性以及能谱干涉导致截面具有强烈的堆芯位置相关性。针对以上问题，NECP团队进一步开展了含高能数据的均匀化参数计算技术以及基于平均宏观泄漏截面的在线均匀化技术的研究，拓宽了NECP-SARAX的能量适用范围[25][26]。
表1 含高能数据的堆芯计算分析技术应用效果
图3 在线均匀化技术的实施效果
l高温气冷堆堆芯均匀化技术创新研究
球床式高温气冷堆是具备第四代核电特征的堆型，具备固有安全性好、发电效率高、模块化建造等特点，在我国核电事业发展中具有巨大潜力。然而，与传统的压水堆相比，球床式高温气冷堆的燃料双重非均匀性、连续在线换料、球床堆芯结构等独有特点，给数值模拟计算带来巨大挑战。
我国现有高温气冷堆的设计软件仍采用德国的VSOP软件，自主化软件研发和应用与国外有一定差距。为了进一步提升球床式高温气冷堆堆芯物理计算精度，在华HN技术研究院的支持下，NECP团队在充分吸收已有程序的理论方法和研发经验的基础上，进一步改进和创新，形成了一套优化的高温气冷堆堆芯物理计算方法，自主开发了NECP-Panda软件[27][28][29][30]。相比于现有方法，其在均匀化截面计算、控制棒区域中子流效应修正等理论方法上进行了改进。
球床式高温气冷堆具有瘦长几何、超热能谱的特点，活性区中子泄漏对堆芯能谱影响显著。然而，组件均匀化计算通常采用的是无限（全反射边界）模型，未准确考虑各材料之间的中子泄漏，因此，NECP实验室采用了基于蒙特卡罗精细建模的在线中子泄漏修正方法获得精确少群常数[28]，实现了高精度堆芯物理计算。目前该计算方法及软件正在基于HTR-PM实际运行数据开展全面验证确认工作。
图4 在线中子泄漏修正均匀化模型
代表论文
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[2]Wen Yang, Hongchun Wu, Yunzhao Li, Jiewei Yang and Liangzhi Cao. Development and verification of PWR-core fuel management calculation code system NECP-Bamboo: Part II Bamboo-Core. Nuclear Engineering and Design, 337:279-290, 2018.
[3]Yunzhao Li, Tao He, Boning Liang, Hongchun Wu, Jiewei Yang. Development and verification of PWR-core nuclear design code system NECP-Bamboo: Part III: Bamboo-Transient. Nuclear Engineering and Design, 359, 2020.
[4]Yunzhao Li, Wen Yang, Sicheng Wang, Hongchun Wu, Liangzhi Cao. A Three-dimensional PWR-core pin-by-pin analysis code NECP-Bamboo2.0. Annals of Nuclear Energy, 144, 2020.
[5]Yuancheng Zhou, et al. Automatic modeling of PWR-core in the two-step reactor-core physics analysis code NECP-Bamboo. Nuclear Engineering and Design, 2023, 414:112546.
[6]Cheng Zhang, LiangzhiCao, YunzhaoLi, et al. Hexagonal PWR-core modeling and simulation with application of NECP-Bamboo[C]. Physor 2020, Cambridge, UK, 2020.
[7]ChengZhang, ChenghuiWan, LiangzhiCao, et al. Method research and engineering validation of the improved homogenization for the heavy reflector in VVER. Annals of Nuclear Energy, 2022 173(April): 109119.
[8]JunweiQin ,Yunzhao Li, Shuhao Pan , Weiguo Wang. An improved submesh method to treat the environmental effect in PWR-core two-step analysis. Nuclear Engineering and Technology, 2024, 103429.
[9]Yunzhao Li, Bin Zhang, Hongchun Wu, Liangzhi Cao.Improvements to the SP3 Discontinuity Factors in PWR Pin-by-pin Calculation [J].Trans. Am. Nucl. Soc.,2014,111:1409-1411.
[10]Bin Zhang, Hongchun Wu, Yunzhao Li,Liangzhi Cao and Wei Shen.Evaluation of Pin-Cell Homogenization Techniques for PWR Pin-by-Pin Calculation. Nuclear Science and Engineering, 186:134-146, 2017.
[11]Sicheng Wang, Liangzhi Cao, Yunzhao Li, Hongchun Wu. An energy-group structure optimization from seven to four for PWR-core pin-by-pin calculation. Nuclear Engineering and Design, 402, February 2023, 112115
[12]Yunzhao Li, Junwei Qin, Fan Xia, Hongchun Wu. Fine-mesh homogenization and anisotropic SP3 calculation for PWR cores with plate-type fuel and strong absorbers. Annals of Nuclear Energy, 198, April 2024, 110283
[13]Yunzhao Li, Bin Zhang, Hongchun Wu, Wei Shen. Heterogeneous neutron-leakage model for PWR pin-by-pin calculation. Annals of Nuclear Energy, 110:443-452, 2017.
[14]Muhammad Asim Shahzad, Liangzhi Cao, Qingming He, Fan Xia, Yunzhao Li. Multi-group equivalence in subgroup method based on generalized equivalence theory. Annals of Nuclear Energy, 2020, 149:107770.
[15]Yunzhao Li, Kai Huang, Hongchun Wu, Liangzhi Cao. A depletion system compression method based on quantitative significance analysis. Nuclear Science and Engineering. 187(1):49-69, 2017.
[16]Kai Huang, Hongchun Wu, Yunzhao Li, Liangzhi Cao. Depletion system compression method with treatment of decay heat. Progress in Nuclear Energy. 101:476-485, 2017.
[17]Junwei Qin, Yunzhao Li, Liangzhi Cao, Hongchun Wu. P1 Generalized Equivalence Theory for PWR-core pin-by-pin neutronics calculation. Annals of Nuclear Energy, 2025, 213:111147.
[18]Zheng YQ, Du XN, Xu ZT, Zhou SC, Liu Y, Wan CH, Xu LF. SARAX: A new code for fast reactor analysis part I: Methods. Nuclear Engineering and Design. 2018, 340: 421-310.
[19]Zheng YQ, Qiao L, Zhai ZA, Du XN, Xu ZT. SARAX: A new code for fast reactor analysis part II: Verification, validation and uncertainty quantification. Nuclear Engineering and Design. 2018, 331: 41-53.
[20]Du XN, Yang YC, Zheng YQ, Wang YP, Wu HC. The acceleration of improved Tone's method in advanced reactor lattice neutron spectrum calculation. Progress in Nuclear Energy, 2023, 162, 104771.
[21]Du XN, Wu XW, Zheng YQ, Wang YP. Reactivity Effect Evaluation of Fast Reactor Based on Angular-Dependent Few-Group Cross Sections Generation. Energies, 2021; 14(13): 4042.
[22]Yang YC, Zheng YQ, Du XN, Wu HC, Adaptive energy group division in the few-group cross-section generation for full spectrum reactor modeling with deterministic method. uclear Engineering and Technology, 2024, 56(6):2019-2028.
[23]Xiao BW, Wei LF, Zheng YQ, Zheng B, Wu HC, On the equivalence of reaction rate in energy collapsing of fast reactor code SARAX. Nuclear Engineering and Technology, 2021, 53(5):732-740.
[24]陈建达,郑友琦,杜夏楠,吴宏春.基于SARAX-LAVENDER的快堆光子释热行为分析.现代应用物理,2021,12(01):75-80.
[25]Chen WJ, Du XN, Zhang XC, Zheng YQ, Wu HC, Development and Validation of NECP-SARAX: An Advanced Neutron Analysis Code System for Accelerator-Driven Subcritical Systems. Submitted to Annals of Nuclear Energy, Under review.
[26]陈文杰, 杜夏楠, 郑友琦, 吴宏春, SARAX 程序堆用高能中子数据库加工与验证. 第二十届反应堆数值计算与粒子输运学术会议CORPHY暨2024年反应堆物理会议, 中国, 哈尔滨, 08.27-08.30, 2024.
[27]Yuxuan Wu, Yongping Wang, Shuai Qin, et al. NECP-panda: A neutronics and thermal-hydraulic analysis code for pebble-bed high temperature gas-cooled reactor. Annals of Nuclear Eenergy, 208, 2024.
[28]吴宇轩，王永平，秦帅，等. 球床式高温气冷堆物理热工计算程序NECP-Panda中子学计算模块研发进展[J]. 核技术，2025.
[29]Yuxuan Wu, Yongping Wang, Shuai Qin, et al. Development progress of neutronics and thermal-hydraulics calculation program NECP-Panda for pebble-bed high temperature gas-cooled reactor. 31st International Conference on Nuclear Engineering (ICONE31), Prague, Czech Republic, August 4-8, 2024.
[30]Dongyu Xu, Yongping Wang, Hongchun Wu, et al. Thermal-hydraulics and neutronics coupling calculation and validation of NECP-Panda a computational code for pebble-bed high temperature gas-cooled reactors. 31st International Conference on Nuclear Engineering (ICONE31), Prague, Czech Republic, August 4-8, 2024.
