燃料棒边缘效应下的子群共振计算方法研究

共振伪核素子群方法可用于处理燃料棒内部空间相关的共振干涉效应,然而该方法只能计算径向均匀核子密度的燃料棒问题,无法处理因边缘效应造成的径向核子密度非均匀分布的问题。针对此问题,基于改进的伪核素理论,提出了一种新的伪核素方法。计算结果表明,该方法解决了原始共振伪核素子群方法无法处理的边缘效应问题,相比于Bondarenko迭代法和干涉因子法,具有更高的精度。     

基于子群方法的双重非均匀性共振计算方法研究

为计算双重非均匀性条件下的共振截面,提出了耦合Sanchez Pomraning方法的改进的子群方法(ISSP)。ISSP采用精细化共振能群结构来规避共振干涉处理,通过求解双重非均匀性条件下的子群固定源方程和慢化方程得到颗粒和基体等各材料的有效共振截面,最后进行双重非均匀性条件下的输运计算。数值结果表明,与连续能量蒙特卡罗程序及超细群计算结果相比,ISSP可精确高效地计算双重非均匀性条件下的共振截面。     

提高子群法共振自屏计算精度研究

基于自行研制的子群法与特征线法相结合的中子共振自屏计算程序SGMOC,研究提高子群法计算精度的2种方法.数值验证表明,2种方法都能提高共振自屏计算精度.其中,采用随机干涉近似求解条件概率的共振干涉效应处理的修正效果约为(0.02％～0.23％)△k/k;考虑共振散射的修正效果约为0.1％△k/k;综合运用2种方法的修正效果约为(0.03％ ～0.27％)△k/k.     

复杂几何燃料组件的共振自屏计算

共振参数计算是反应堆堆芯设计计算中的重要内容,传统的共振计算模型只适应于简单几何计算。本工作应用A.Hebert提出的子群共振自屏计算模型研制了复杂几何燃料组件的共振自屏计算程序。该程序能处理含有两种共振核素的复杂几何下的共振自屏。对一系列问题的数值校验计算表明,该模型在低富集度时具有较好的计算精度。     

基于子群共振自屏方法的特征值隐式敏感性分析

采用经典微扰理论,高效地得到问题相关的多群截面的扰动对特征值的直接影响,即显式敏感性。应用广义微扰理论,推导了在子群共振自屏方法中,多群共振自屏截面对非共振核素截面的灵敏度系数的计算方法。结合前两项内容,得到非共振核素通过共振自屏过程对特征值的间接影响,即隐式敏感性。根据与显式灵敏度系数的比较,分析了隐式敏感性相对于显式敏感性的重要性。     

二维任意几何子群共振计算及加速优化

共振计算是反应堆组件堆芯设计和燃料管理的基础.子群共振计算方法基于共振能群子群截面,调用输运程序作为求解器,对子群中子注量率进行求解并且归并得到有效共振自屏截面,实现任意二维复杂几何的共振计算.由于子群方法在每个共振能群内部需要反复调用输运求解器,因此和等价理论相比速度较慢及本文基于子群方法的理论模型和自主开发的子群共振计算程序,提出并且完成了多群数据库、输运计算源项及多共振核素迭代的优化方案.通过基准题的验证可知,该方案在保持精度的同时提高了子群程序的计算效率,保证了该程序在工程上的实用性.     

NECP软件包中NECL子群数据与任意几何共振模块研制

本文基于子群方法对NECP软件包开发了多群数据库模块和子群共振计算模块。采用本实验室开发的二维任意几何输运程序矩阵MOC作为子群共振模块的求解器。使用MCNP与子群程序计算一系列的共振基准题,并比较了两者所计算的无限增殖因数k_inf和²³⁵U与²³⁸U的微观截面。结果表明,子群程序对任意几何有良好的适应性和精度,可适用于二维任意几何的共振计算。     

复杂燃料成分的多核素共振干涉计算方法研究

共振干涉现象广泛存在于反应堆系统中,是影响共振计算精度的重要因素之一。当前提出的干涉因子方法,其计算效率难以适用于燃耗过程中的复杂燃料成分。基于改进的伪核素理论与超细群慢化方程求解程序,提出了一种针对实际压水堆燃耗过程的快速共振干涉计算方法。对于燃耗过程中的复杂燃料成分,在均匀问题和压水堆栅元几何下进行了共振自屏分析。结果表明,该方法的计算精度与严格的超细群计算及蒙特卡罗方法相当,效率上优于干涉因子方法,适用于压水堆燃耗过程中的快速共振计算。     

确定论方法中共振弹性散射的修正方法研究

截面加工软件(NJOY)程序求解无限均匀慢化方程时采用渐进散射核,忽略了共振弹性散射的影响,给特征值和多普勒系数的计算带来较大的误差。为在确定论程序中考虑这种效应,本文采用多普勒展宽舍弃修正(DBRC)方法修改了蒙特卡罗程序(MCNP)的自由气体模型,利用MCNP代替NJOY制作共振积分表。基于子群共振方法分析了轻水堆燃料棒的无限介质增殖因数和温度系数,并与MCNP的结果进行对比。数值结果表明,由于考虑了共振弹性散射效应,本文提出的修正方法提高了确定论方法的计算精度。     

基于NECP-X的全局-局部耦合共振自屏计算方法研究

为应对高保真共振自屏计算所遇到的挑战,提出了全局-局部耦合共振自屏计算方法。将所有共振自屏效应及相关效应分为全局的效应和局部的效应2类,其中全局的效应较弱或者与能量无关,而局部的效应较为强烈。因此将共振自屏计算分为全局计算、耦合计算和局部计算3个步骤:全局计算建立粗糙模型,采用中子流方法计算丹可夫修正因子,处理全局的效应;耦合计算根据丹可夫修正因子守恒将待求解问题中的燃料棒等效成一维模型;局部计算采用较为精确的共振伪核素子群方法,处理局部的效应。基于NECP-X实现了该方法,数值结果表明,该方法在效率方面比传统方法提高至少一个量级,无限介质增殖因数的计算精度也提高了100~300 pcm。     

A new procedure to generate resonance integral table with an explicit resonance interference for transport lattice codes

Resonance interference could not be considered explicitly in the conventional resonance treatment employing subgroup and direct resonance integral methods when using coarse energy group structure. This problem comes from the lack of information for the resonance shapes of resonant nuclides in the resonance interference formulas. As energy group boundaries get coarser, inaccuracy in estimating self-shielded cross sections with resonance interference gets bigger. A new method has been proposed to conserve the self-shielded cross sections for each group through an explicit consideration of resonance interference effect, which results in a good accuracy in predicting the multiplication factor. This method can be applicable to various mixing combinations of constituent resonant nuclides with resonance interference and can cover wide dilution range. The MERIT code has been used to generate resonance integral tables and to estimate resonance interference effects. And the 2-D transport lattice code KARMA has been used to perform sample calculations to see the effectiveness of the newly developed method. Sample calculations have been performed for single pins with various temperatures, ²³⁵U enrichments and dilution levels with the 47 and 190 energy group structures. The computational results show that this method is able to estimate self-shielded cross sections in each coarse energy group accurately for various temperatures and various geometry and composition configurations.     

基于等效几何理论的复杂几何燃料共振计算方法研究

针对各种研究堆、实验堆以及新型反应堆中广泛应用的复杂几何燃料的共振计算难题,本文基于全局 局部耦合策略开展了可处理复杂几何燃料的等效几何共振计算方法研究。针对复杂几何燃料的孤立问题,基于燃料的逃脱概率守恒,建立了复杂几何燃料模型的等效一维圆柱（或平板）燃料模型;基于燃料到外围结构材料区的碰撞概率守恒,获得了燃料外围结构材料的等效尺寸;根据复杂几何燃料的丹可夫因子守恒,建立了等效一维圆柱（或平板）燃料外围的慢化剂尺寸;针对等效一维圆柱（或平板）燃料模型,采用伪核素子群方法进行了有效自屏截面计算。将该方法应用于非棒状几何燃料的共振计算,结果表明,该方法具有很强的几何处理能力,且具有较高的计算精度和计算效率。     

An advanced approach to calculation of neutron resonance self-shielding

Based on the combination of subgroup method and characteristics method, a resonance self-shielding calculation code SGMOC is programmed. SGMOC code can handle the complex (both in geometry and resonant components) resonance problems. The numerical results are in good agreement with those of MCNP. In order to improve the SGMOC calculation accuracy, two techniques are utilized, i.e., the resonance interference effects between resonant nuclides are considered, and on the other hand, the elastic scattering resonance is taken into account. These two techniques can enhance the accuracy remarkably.     

The treatment of resonance interference effects in the subgroup method

This paper describes the development of a method to treat resonance interference effects within the framework of the subgroup method. The new procedure provides for the treatment of multiple resonance absorbers in which the subgroup weights are determined using a least squares technique and based on the cross sections generated from a mixture of multiple resonance isotopes and a suitably wide range of background cross sections. The method was implemented in the Method of Characteristics code DeCART and validated using MCNP. In order to implement the new method, the NJOY code was used for the calculation of neutron spectra and resonance parameters in for each representative LWR mixture. The resonance parameters, lambda, of the scattering isotopes are computed not just with U-238 as the resonance isotope as in previous applications of the subgroup method, but also with U-235 as resonance isotope for the energy groups in which U-238 has no significant resonances. After developing a procedure for generating lambda factors for scattering isotopes, a method is then described for generating subgroup parameters in a homogeneous system. Again NJOY is used for resonance calculations of a set of mixtures for each resonance isotope at each selected temperature. The group average cross sections instead of the resonance integrals of these mixtures are used to generate subgroup parameters using an optimization algorithm. The generated library is then verified by comparing the solution from DeCART with the solution from MCNP. The method is then extended to a heterogeneous system. The code RMET21 is used for transport calculations for the heterogeneous system. The interference effect from the most important resonance isotopes is treated by generating subgroup weights with resonance cross sections for the cases with two resonance isotopes. The results indicate that the subgroup method can accurately represent resonance interference effects within the framework of the subgroup method.     

双重非均匀子群参数制作研究

弥散颗粒燃料元件中燃料颗粒以随机形式弥散在基体中,难以获得确定几何。同时由于共振自屏现象的存在,呈现出一种双重非均匀系统。当前均匀系统产生的共振积分在双重非均匀系统中使用时,会在较低的共振能群产生一定的共振计算误差。为满足现有组件计算程序直接进行双重非均匀性共振计算的需求。基于Sanchez-Pomraning模型下的特征线固定源计算方法,建立一套双重非均匀共振积分表,最后结合子群方法实现随机介质燃料元件的共振计算。数值结果表明,考虑双重非均匀性产生的积分表,在相同的输运条件下和积分表的适用范围内,由子群共振部分对keff计算带来的绝对偏差能保持在200 pcm内。该工作的意义是对于一些不宜改动的传统组件程序,如HELIOS,通过在线修改共振积分表和子群参数,从而使其直接进行弥散颗粒燃料问题的计算成为可能。     

Effects of Mutual Shielding on Resonance Integrals of 235U, 238U, 239Pu and 240pu below 150 eV

The results of some quantitative studies on resonance interference are presented. The calculations were performed on a FORTRAN IV program RICM2, which solves numerically the slowing down of neutrons over many resonance levels in a two region lattice, and gives reaction rates, average cross sections and effective resonance integrals of the nuclides concerned.

Three combinations of resonant nuclides, ²³⁵U-²³⁸U, ²³⁰Pu-²³⁸U and ²³⁹Pu-²¹⁰Pu, were considered, in conjunction with three oxide fuel rod radii, 0.2, 0.5 and 2.0 cm, the moderator (light water) to fuel volume ratio being maintained constant at 2.0. An energy range below 150eV has been covered by the present calculations. The effects of resonance interference have been found to be appreciable in this energy range.     

Resonance self-shielding calculation using subgroup method and ABC algorithm

In this study, we propose a new method to optimize subgroup parameters for resonance self-shielding calculation. Our approach integrates the merits of both the subgroup method and ABC optimization technique to effectively evaluate self-shielded resonance cross-sections. The ABC algorithm is used to obtain subgroup level in a way that guarantees reproduction of shielded effective cross sections in the subgroup formulation. The temperature dependency of the cross-section is included in both subgroup level and subgroup weight. We used the conjugate gradient method based on the normal equations (CGNR) to evaluate the subgroup weights. An iteration technique is also used to consider the resonance interference. The proposed method is verified by analyzing Rowlands benchmark problems and Mosteller benchmark problems and comparing the obtained results with corresponding Monte Carlo solutions. The multiplication factor results show small errors and also good agreement.