Pin-based Pointwise Energy Slowing-down Method for Resonance Self-shielding Calculation

Abstract

A new resonance self-shielding method using a pointwise energy solution has been developed to overcome the drawbacks in the equivalence theory. In reactor physics, the equivalence theory has been widely used in calculating the effective multi-group cross sections for the neutron transport analyses. The neutron transport codes adopting the equivalence theory give reasonable solutions within short computation time. However, there are still a lot of limitations in the equivalence theory even though many modified and improved equivalence theories have been published over the past several decades. The significant drawbacks in the equivalence theory are newly figured out in this work, and the new method is proposed to overcome the problems. The equivalence theory uses the intermediate resonance approximation on the resonance scattering source and the multi-term rational approximation to represent the fuel escape probability. With these approximations, the effective multi-group cross section is derived with the asymptotic equations. However, there is a gap between the derivation and the practical usage in the lattice physics code. In addition, the equivalence theory assumes that the constant distribution of the scattering sources in the fuel pellet even though the source distribution is quite important in view point of the fuel escape probability. These methods and approximations cause significant errors, in that they overestimate the effective multi-group cross sections, especially for 238U. The new resonance self-shielding method solves pointwise energy slowing-down equations which are derived for a sub-divided fuel pellet and a non-fuel region. A two-step method is developed to efficiently calculate the collision probabilities of the sub-divided fuel pin-cell. In the first step, the collision probabilities of the sub-divided fuel pellet are calculated assuming that the fuel pellet is isolated. In the second step, a shadowing effect correction factor is derived based on the equivalence theory to consider the global self-shielding effect. In addition, a fictitious moderator material is generated to model realistic scattering source from the moderator. The slowing-down solutions are used to generate the multi-group cross sections of the sub-divided fuel pellet. Various techniques and assumptions are incorporated to maximize calculation efficiency in solving the pointwise energy slowing-down equations. Especially, the new method significantly reduces the number of MOC fixed-source calculations which is one of major time consuming calculations in the resonance self-shielding calculation. Although the new method performs the pointwise energy slowing-down calculations, the computational cost is not expensive even compared to that with conventional equivalence theory. With various light water reactor problems, it is demonstrated that the new resonance self-shielding method successfully overcomes the limitations of the equivalence theory and shows great accuracy in calculating the multiplication factor, the multi-group cross section, the reaction rate, and the power distribution with no compromise in computation time.