Fast Shutdown Margin Calculation Using Perturbation Theory with Regionwise Flux Expansion

Abstract

A two-dimensional perturbation method with regionwise flux expansion is developed and tested for the boiling water reactor fast shutdown margin calculation. The ways of generating the two-dimensional parameters for the unrodded bundles are tested to find the one that results in the most accurate eigenvalue of the single-rod-out condition. The use of the one-bundle-per-region flux expansion method gives more accurate results than the ring-regionwise flux expansion method. The first four strongest control rods chosen by this method using one-bundle-per-region flux expansion always contain the top four strongest rods predicted by SIMULATE-3 three-dimensional calculations. The strongest rod is always correctly predicted, and the differences in shutdown margin predictions are <1 mk for all the cases tested. The time saved by using the two-dimensional perturbation method rather than the direct three-dimensional full-core calculation is a factor of ∼10 and even more for larger core loadings. By using correct two-dimensional parameters, the accuracies of the perturbation method itself in the calculations of the eigenvalue and the neutron flux distribution are also tested. It is found that the errors are very small even for such a strong perturbation in the shutdown margin calculation.