A Modal Expansion Equilibrium Cycle Perturbation Method for Optimizing High Burnup Fast Reactors.

Abstract

This dissertation develops a simulation tool capable of optimizing advanced nuclear reactors considering the multiobjective nature of their design. An Enhanced Equilibrium Cycle (EEC) method based on the classic equilibrium method is developed to evaluate the response of the equilibrium cycle to changes in the core design. Advances are made in the consideration of burnup-dependent cross sections and dynamic fuel performance (fission gas release, fuel growth, and bond squeeze-out) to allow accuracy in high-burnup reactors such as the Traveling Wave Reactor. EEC is accelerated for design changes near a reference state through a new modal expansion perturbation method that expands arbitrary flux perturbations on a basis of lambda-eigenmodes. A code is developed to solve the 3-D, multigroup diffusion equation with an Arnoldi-based solver that determines hundreds of the reference flux harmonics and later uses these harmonics to determine expansion coefficients required to approximate the perturbed flux. The harmonics are only required for the reference state, and many substantial and localized perturbations from this state are shown to be well-approximated with efficient expressions after the reference calculation is performed. The modal expansion method is coupled to EEC to produce the later-in-time response of each design perturbation.

Because the code determines the perturbed flux explicitly, a wide variety of core performance metrics may be monitored by working within a recently-developed data management system called the ARMI. Through ARMI, the response of each design perturbation may be evaluated not only for the flux and reactivity, but also for reactivity coefficients, thermal hydraulics parameters, economics, and transient performance.

Considering the parameters available, an automated optimization framework is designed and implemented. A non-parametric surrogate model using the Alternating Conditional Expectation (ACE) algorithm is trained with many design perturbations and then transformed through the Physical Programming (PP) paradigm to build an aggregate objective function without iteratively determining weights. Finally, the design is optimized with standard gradient-based methods. Through the power of ACE and the transparency of PP, the optimization system allows users to locate designs that best suit their multiobjective preferences with ease.