Iterative resonance self-shielding methods using resonance integral table in heterogeneous transport lattice calculations

This paper describes the iteration methods using resonance integral tables to estimate the effective resonance cross sections in heterogeneous transport lattice calculations. Basically, these methods have been devised to reduce an effort to convert resonance integral table into subgroup data to be used in the physical subgroup method. Since these methods do not use subgroup data but only use resonance integral tables directly, these methods do not include an error in converting resonance integral into subgroup data. The effective resonance cross sections are estimated iteratively for each resonance nuclide through the heterogeneous fixed source calculations for the whole problem domain to obtain the background cross sections. These methods have been implemented in the transport lattice code KARMA which uses the method of characteristics (MOC) to solve the transport equation. The computational results show that these iteration methods are quite promising in the practical transport lattice calculations.     

蒙特卡罗方法用于LiFTLD自屏蔽因子的模拟计算

自屏蔽因子是用LiFTLD探测器高精度测量n-γ混合场的重要参数.本文采用MCNP程序对文献中给定尺寸、密度和6Li含量的LiFTLD的自屏蔽因子进行了计算,并与推导的自屏蔽公式、Horowitz等的计算结果进行了比较.同时,对计算结果还专门设计了实验进行验证,证实MCNP计算自屏蔽因子所采用的模型和方法是可靠的.对于文献中没有给出自屏蔽因子的现有的LiFTLD,通过选取合理的模型,用MCNP计算了它们的自屏蔽因子.该研究结果对于n-γ混合场区分测量以及TLD的LET效应的研究都具有重要意义.     

Improvement of moment-based probability table for resonance self-shielding calculation

In the present paper, an improved method has been proposed to produce a probability table needed for the resonance self-shielding calculations with the sub-group method. The proposed method is based on a relation between the effective cross section and the cross section moment, which is obtained from a numerical analysis. Using the proposed method, more accurate probability tables can be obtained with less number of the tabulated steps than the conventional method. This enables us to reduce computation time and computer memory storage for the sub-group calculations.     

Li-Al靶片自屏特性研究

描述对3个总厚度分别为2、4和8mm的Li-Al合金靶片组进行入堆辐照,测量靶片在堆内辐照时内部的中子注量率分布,并计算出其相应的自屏因子的过程。结果表明,3个靶片组的自屏因子分别为0.76、0.55及0.30。     

Advanced resonance self-shielding method for gray resonance treatment in lattice physics code GALAXY

A new resonance self-shielding method based on the equivalence theory is developed for general application to the lattice physics calculations. The present scope includes commercial light water reactor (LWR) design applications which require both calculation accuracy and calculation speed. In order to develop the new method, all the calculation processes from cross-section library preparation to effective cross-section generation are reviewed and reframed by adopting the current enhanced methodologies for lattice calculations. The new method is composed of the following four key methods: (1) cross-section library generation method with a polynomial hyperbolic tangent formulation, (2) resonance self-shielding method based on the multi-term rational approximation for general lattice geometry and gray resonance absorbers, (3) spatially dependent gray resonance self-shielding method for generation of intra-pellet power profile and (4) integrated reaction rate preservation method between the multi-group and the ultra-fine-group calculations. From the various verifications and validations, applicability of the present resonance treatment is totally confirmed. As a result, the new resonance self-shielding method is established, not only by extension of a past concentrated effort in the reactor physics research field, but also by unification of newly developed unique and challenging techniques for practical application to the lattice physics calculations.     

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.     

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.     

An improved fitting method for subgroup parameters based on the heterogeneous cells

An accurate subgroup parameters fitting method, where background cross sections obtained based on heterogeneous cells are used to fit the subgroup level and subgroup weight, is proposed in this paper. Due to the dependence of background cross section on the subgroup level, the calculation of the subgroup parameters is a nonlinear problem, which causes the iteration between fitting subgroup parameters and updating background cross sections. The cubic spline interpolation method is used to update the background cross sections to avoid frequently solving fixed source equations. In the fitting process, the negative subgroup parameters are often obtained, and the accuracy of the subgroup parameters is very sensitive to the iterative initial values of subgroup levels. To avoid these problems, additional constraints ensuring positive subgroup parameters and guaranteeing numerical stability are added to the optimization function. Penalty function method is used to convert the optimization problem with constraints into the one without constraints, making the problem easy to be solved. The proposed method is tested against the problems of pin cell, pressurized water reactor assemblies and plate-type assembly. The numerical results show that the self-shielded cross sections calculated by the proposed method agree well with those by Monte Carlo code.     

Resonance self-shielding method using resonance interference factor library for practical lattice physics computations of LWRs

This paper presents a new method of resonance interference effect treatment using resonance interference factor for high fidelity analysis of light water reactors (LWRs). Although there have been significant improvements in the lattice physics calculations over the several decades, there exist still relatively large errors in the resonance interference treatment, in the order of ～300 pcm in the reactivity prediction of LWRs. In the newly developed method, the impact of resonance interference to the multi-group cross-sections has been quantified and tabulated in a library which can be used in lattice physics calculation as adjustment factors of multi-group cross-sections. The verification of the new method has been performed with Mosteller benchmark, UO₂ and MOX pin-cell depletion problems, and a 17×17 fuel assembly loaded with gadolinia burnable poison, and significant improvements were demonstrated in the accuracy of reactivity and pin power predictions, with reactivity errors down to the order of ～100 pcm.     

Thermal neutron self-shielding correction factors for large sample instrumental neutron activation analysis using the MCNP code

Thermal neutron self-shielding within large samples was studied using the Monte Carlo neutron transport code MCNP. The code enabled a three-dimensional modeling of the actual source and geometry configuration including reactor core, graphite pile and sample. Neutron flux self-shielding correction factors derived for a set of materials of interest for large sample neutron activation analysis are presented and evaluated. Simulations were experimentally verified by measurements performed using activation foils. The results of this study can be applied in order to determine neutron self-shielding factors of unknown samples from the thermal neutron fluxes measured at the surface of the sample.     

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.     

Application of wavelets scaling function expansion method in resonance self-shielding calculation

The wavelets expansion method is widely used in various fields due to its powerful ability to simulate the oscillating functions. This method is applied to discretize the energy variable of neutron angular flux within the resonant energy range. Meanwhile, the conventional multi-group method is applied in fast and thermal energy ranges. This coupled method can obtain the problem-dependent continuous-energy neutron flux spectrum within the resonant energy range. The method of characteristics (MOC) is employed as a space-variable solver in this paper to keep the powerful capability of dealing with the complex geometry problems. A pressurized water reactor (PWR) fuel cell problem with UO2 fuel (UOX) and mixed oxide fuel (MOX), and a cylindrical cluster fuel problem are calculated by utilizing this coupled method. Results of these problems are all in good agreement with the results of the Monte Carlo statistical transport code MCNP. It is concluded that this is a valuable method to solve the resonance self-shielding calculation problems in a complex geometry, and it is promising to be applicable for realistic reactor problems.     

Integration of equivalence theory and ultra-fine-group slowing-down calculation for resonance self-shielding treatment in lattice physics code GALAXY

A new hybrid resonance self-shielding treatment method in reactor physics field is developed by integrating equivalence theory and ultra-fine-group slowing-down calculation from the theoretical point of view. In the conventional equivalence theory, scattering source approximation and taking no account of resonance interference effect cause prediction error of effective cross-section. By reviewing the derivation scheme of neutron flux in the equivalence theory, the essence of the ultra-fine-group treatment is effectively incorporated. A new form of energy-dependent flux is based on multi-term rational equation, but the scattering source can be solved by the way similar to the slowing-down equation. The accurate non-fuel flux is also considered without direct heterogeneous calculation. The new method can also efficiently eliminate the multi-group condensation error by a semi-analytical reaction rate preservation scheme between ultra-fine and multi-group treatments. The present method is implemented in Mitsubishi Heavy Industries, Ltd. lattice physics code GALAXY. From comparisons of neutronics parameters between GALAXY and a continuous energy Monte-Carlo code, applicability of the new method for lattice physics calculations is confirmed. GALAXY achieves high accuracy with short computation time. Therefore, it can be efficiently applied to generation of the nuclear constants used in the nuclear design and safety analysis of commercial light water reactors.     

Extension to cylindrical samples of the universal curve of resonance neutron self-shielding factors

Resonance neutron self-shielding factors for cylindrical samples of nuclides used as activation detectors or as targets for radionuclide production have been calculated using the MCNP code. These factors depend on the sample dimensions, as well as on the physical and nuclear properties of the nuclides. However, defining a dimensionless variable, which includes the relevant characteristics of the samples, it is possible to extend to cylinders a previously deduced universal curve for isolated resonances of any nuclide and samples of other geometries (foils, wires and spheres).