A Transfer Function-Equivalent-Diffusion-based Approach for Monoenergetic Flux Prediction

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Painter, Bailey Christopher
Kotlyar, Dan
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Coupled Monte Carlo (MC) and thermal hydraulic (TH) analysis is valuable as a design or reference tool but can be slow especially when implemented in a Picard iteration. Previous work has developed a novel prediction block to achieve convergence with fewer MC simulations. The prediction works in two stages: (1) a surrogate-like model predicts macroscopic cross sections on-the-fly and (2) a first order perturbation (FOP) solver predicts the flux response to the updated cross sections. The main challenge with the prediction block is that the FOP model requires a fission matrix. This fission matrix is impractical to generate for most problems, particularly fine-mesh problems. This work investigates replacing the FOP solution with a monoenergetic diffusion solution. For a simple 1D boiling water reactor (BWR) pincell, the proposed prediction block produces a monoenergetic flux that is within good agreement of the MC flux. A realistic 3D pressurized water reactor (PWR) core is then introduced to demonstrate that 3D, coarse mesh problems require the application of equivalence parameters such as assembly discontinuity factors (ADFs) and superhomogenization (SPH) factors to produce accurate 1-group nodal diffusion solutions. This work investigates the implementation of the well-established Jacobian-free Newton Krylov (JFNK) method to produce these equivalence parameters in a time-efficient manner. In this case, only tens of one-group nodal diffusion solutions are required to produce converged equivalence parameters. The results obtained in this work show that the converged equivalence parameters are very successful in reproducing the heterogenous solution (up to 2.5% error for SPH and 0.3% error for ADFs), without needing to modify the nodal diffusion solution. In addition, the results show that ADFs yield the best agreement and are also stable (i.e., not varying) when thermal hydraulic fields are perturbed. These results suggest that the proposed prediction block methodology is rigorous.
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