Abstract
In perturbation calculations, obtaining accurate neutron flux distribution of a reactor core is not an easy task. In early days, the first-order perturbation theory was developed to compute the reactivity change induced by a small perturbation, and no calculation of perturbed neutron flux was involved. Nowadays, most of the applications of perturbation method in in-core fuel management for saving computation time, such as the analysis of fuel misloading, the computation of non-symmetric exposure distribution, and the shuffling of fuel bundles in a core design, more accurate evaluation of neutron flux distribution is highly demanded. This kind of work involves complicated computations of large matrices. The use of high-order eigenvectors in perturbation calculations is always accompanied by high computational cost. Besides, as the dimension of the problem increases from one-dimensional to two-dimensional and even to three-dimensional, the problem becomes more and more difficult to be solved.In this study, Davidson algorithm coupled with shifted form-function vector method has been successfully implemented and shown to be very efficient in the calculation of 1-D, 2-D and 3-D perturbations. Davidson algorithm used in the perturbation calculation is superior to those perturbation methods used in early days. It is neither necessary to evaluate the high-order eigenvectors for perturbation computation, nor necessary to reduce the size of a perturbed problem by assuming the perturbation outside the defined-region is negligible. Davidson algorithm is at first used in the calculation of the unperturbed problem. The bases generated during the iterations are retained for the perturbed calculations. By adding the shifted form-function vector to the basis, the large perturbed problem can be projected into a smaller eigenvalue problem and be solved easily to obtain the perturbed eigenvalue and neutron flux distribution.From the results of the benchmark problems it can be easily seen that the method is not only very accurate but also very efficient. The use of the Symmetric Successive Over-Relaxation iteration procedure is necessary to reduce the dimension of the basis and the cost of orthogonalization in the perturbed and restart calculation. For small perturbations such as fuel-misloading, acceptable results can be obtained in almost no time by using the basis constructed from the unperturbed calculation for the perturbed calculation. For large perturbations such as control rod movement, the use of shifted form-function vector applied to 2-D problem and each axial plane of 3-D problem involving perturbation can effectively improve the accuracy of the perturbation calculations. Acceptable results can be obtained in the consequent restart calculation with one iteration. The method provides an efficient means for surveying calculation such as the evaluation of shutdown margin. To obtain results of comparable accuracy with existing CITATION code, the use of this method for perturbation computation saves 70%~90% of the computation time. These benchmark results demonstrate the potential use of this method to various practical problems.