Super-Nodal Methods for Space Time Kinetics

transverse leakage;analytical nodal methods;homogenization;reactor analysis;nodal;super nodal;neutronics;reactor simulator

Mertyurek, Ugur ; Robert E. Funderlic, Committee Member,Robert E. White, Committee Member,Paul J. Turinsky, Committee Chair,KuruvillaVerghese, Committee Member,Dmitriy Y. Anistratov, Committee Member,Mertyurek, Ugur ; Robert E. Funderlic ; Committee Member ; Robert E. White ; Committee Member ; Paul J. Turinsky ; Committee Chair ; KuruvillaVerghese ; Committee Member ; Dmitriy Y. Anistratov ; Committee Member

University:North Carolina State University

关键词: transverse leakage;    analytical nodal methods;    homogenization;    reactor analysis;    nodal;    super nodal;    neutronics;    reactor simulator;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/5909/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 摘 要 】

The purpose of this research has been to develop an advanced Super-Nodal method to reduce the run time of 3-D core neutronics models, such as in the NESTLE reactor core simulator and FORMOSA nuclear fuel management optimization codes. Computational performance of the neutronics model is increased by reducing the number of spatial nodes used in the core modeling. However, as the number of spatial nodes decreases, the error in the solution increases. The Super-Nodal method reduces the error associated with the use of coarse nodes in the analyses by providing a new set of cross sections and ADFs (Assembly Discontinuity Factors) for the new nodalization. These so called homogenization parameters are obtained by employing consistent collapsing technique.During this research a new type of singularity, namely "fundamental mode singularity", is addressed in the ANM (Analytical Nodal Method) solution. The "Coordinate Shifting" approach is developed as a method to address this singularity. Also, the "Buckling Shifting" approach is developed as an alternative and more accurate method to address the zero buckling singularity, which is a more common and well known singularity problem in the ANM solution. In the course of addressing the treatment of these singularities, an effort was made to provide better and more robust results from the Super-Nodal method by developing several new methods for determining the transverse leakage and collapsed diffusion coefficient, which generally are the two main approximations in the ANM methodology. Unfortunately, the proposed new transverse leakage and diffusion coefficient approximations failed to provide a consistent improvement to the current methodology. However, improvement in the Super-Nodal solution is achieved by updating the homogenization parameters at several time points during a transient. The update is achieved by employing a refinement technique similar to pin-power reconstruction. A simple error analysis based on the relative residual in the 3-D few group diffusion equation at the fine mesh level is also introduced in this work.The proposed Super-Nodal method was tested for PWR cores with large heterogeneities and under severe reactor accident conditions. Two nodalizations, SN1 and SN2, have been used with three types of collapsing schemes, namely SN1, SN2, and SN1-r. The core is axially collapsed from 18 nodes to 12 and 8 nodes in the SN1 and SN2 nodalizations, respectively. While the SN1 and SN2 schemes refer to SN1 and SN2 nodalizations, SN1-r refers to SN1 nodalization with multiple refining steps. The first test case is the steady state analysis of a core. The general core geometry is modified to introduce a strong heterogeneity by introducing partial length BP rods in the four central fuel assemblies. Even though the Super-Nodal method agrees well with the fine i.e. reference, solution for the axial and radial power distributions, it fails to represent the intra-nodal flux shape for the BP loaded assemblies. For the second test case the core is depleted and a control rod bank is inserted and withdrawn in 40 seconds. A computer CPU time speedup of 1.53 and 1.64 are achieved for the SN1 and SN2 schemes, respectively. Both schemes represent the core power level with a small error; however, both schemes fail to accurately represent the peak node power during the transient. The SN1-r scheme with two additional refining steps removes this discrepancy with a decreased speedup of 1.24. Test Case 3 is a rod ejection accident. Similar to Test Case 2, all three schemes predict accurately the core power level; however, only the SN1-r scheme shows good accuracies for the peak node power. The SN1, SN2 and SN1-r schemes give speedups of 1.53, 2.08 and 1.26, respectively. Test Case 4 is a large steam line break accident. The SN2 and SN1 schemes fail to converge beyond the point that the prompt criticality is reached. The SN1-r scheme agrees well with the reference solution?s axial and radial power distributions. It also provides an accurate prediction of peak node power except at the time of prompt criticality where the peak node power error reaches 10% of full rated power. The speedup is also small for this case, 1.15, due to the need for frequent refine-collapse steps in order to achieve adequate accuracy.