压水堆堆芯pin-by-pin计算环境效应处理模型研究

栅格非均匀计算过程中采用的全反射边界条件近似带来的中子射流效应和中子能谱干涉效应等环境效应对栅元均匀化常数具有较大影响。为在全堆芯pin by pin计算中处理环境效应带来的影响，本文从两个方面进行了计算分析。首先，基于棋盘式多组件问题对栅元均匀化群常数相对误差及各能群栅元不连续因子相对重要性进行了分析，可发现在等效均匀化常数中，热群不连续因子对全堆芯pin by pin计算精度的影响最重要；其次，基于最小二乘法建立了热群栅元不连续因子和堆芯中子学特征量之间的多项式函数关系，利用参数化技术提出了热群常数堆芯在线计算方法，其中堆芯中子学特征量包括扩散系数、移出截面、中子源项、归一化中子通量密度等。采用C5G7基准题和KAIST基准题进行了数值验证，计算结果表明，热群常数堆芯在线计算方法能有效降低全堆芯pin by pin计算特征值和棒功率相对误差，对处于不同燃料组件交界面附近的栅元，计算精度提升尤为显著。

Environmental Effect Treatment Model for PWR pin-by-pin Calculation

With the development of computing technology, an improved scheme named pin-by-pin calculation becomes popular in recent years. Different from the traditional two step calculation, only the heterogeneous structure within each pin is homogenized, leaving the assembly heterogeneous during the three dimensional whole core calculation. Alone with the development of the pin by pin homogenization technology, the reflective boundary condition used in the process of the pin by pin homogenized parameters becomes the main error source. In principle, the homogenized group constants can preserve the neutron leakage and reaction rates only for the boundary conditions at which they are created. However, the exact boundary condition of an assembly in the active core cannot be obtained in advance for the two step scheme. The size of the homogenization region in the pin by pin calculation is almost equal to the averaged neutron free path, making the pin by pin homogenized parameters more dependent on the assembly environment compared with the assembly-homogenized parameters. Focused on the environment effect of the pin by pin homogenization, the errors of the homogenized parameters were analyzed firstly. For a typical checkerboard problem, it can be found that large pin power errors always occur in the pins close to the interface between two assemblies due to the large spectral mismatch between the single assembly and full core conditions in those locations. And the errors of the pin by pin homogenized group constants can be negligible except for the pin cell discontinuity factors (PDF) of thermal group. Secondly, the relative importance of PDF in each group was analyzed. it can be found that the PDF of the thermal group is more important and contribute more to the error than the fast group ones. Finally, the function for the PDF predication was proposed. The least squares method (LSM) for multivariate polynomial was utilized to functionalize the relation of the thermal group PDF and the core parameters. The PDF predication function would be created with heterogeneous solutions obtained from several single-assembly calculations and several spectral geometry calculations. It is expected to predicate PDF with a whole core pin by pin homogeneous solution. In this work, the polynomial order of the PDF predication function was analyzed, and the selected core parameters are based on the physics underlying core neutronics behavior. In order to numerically analyze the performance of the method, C5G7 and KAIST benchmarks were evaluated. Results of the C5G7 and KAIST benchmarks indicate that the PDF predication of the thermal group can get high precision results of eigen value, and work effectively in reducing the relative error of pin cell power, especially for the pins located near the interface between different assemblies.