Adjoint-Based Sensitivity Analysis of Coupled Criticality Problems

Sensitivity analysis is a technique that is widely used in reactor physics calculations to efficiently obtain first-order changes in responses of interest due to variations of input parameters. This paper presents an extension of the well-known perturbation procedures for the critical eigenvalue and flux functionals. The extended method makes it possible to determine sensitivities in coupled criticality problems with mutual feedback between neutronics and one or more augmenting systems (e.g., thermal hydraulics or fission product poisoning). The technique uses appropriate neutronic and augmenting adjoint functions, which can be obtained by solving a system of coupled adjoint equations.

Three different approaches are presented for considering the effects of perturbations in coupled criticality problems with feedback: The steady-state power level is allowed to adjust to maintain criticality with the perturbed parameters (power perturbation), a change is allowed in the critical eigenvalue while the flux is constrained (eigenvalue perturbation), or simultaneous perturbations are made to ensure criticality at the unperturbed power level (control parameter perturbation). In the case of power and eigenvalue perturbations, sensitivities can be obtained with or without power- and k-reset procedures, respectively, yielding identical results to control parameter perturbation.

The paper presents the theoretical background, an application to a one-dimensional slab problem with thermal and fission product feedback, and a numerical procedure to obtain the necessary adjoint functions. The proposed technique relies on using the neutronics and augmenting codes separately as a preconditioner for Krylov methods employed to the coupled adjoint problem. This makes the development of new codes unnecessary and provides a means of large-scale implementation.