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An Implicit Correlation Method for COMET Core Eigenvalue Uncertainty Analysis

Dingkang Zhang, Farzad Rahnema

Nuclear Science and Engineering / Volume 182 / Number 3 / March 2016 / Pages 369-376

Technical Paper /

First Online Publication:February 23, 2016
Updated:March 10, 2016

The coupled stochastic deterministic COarse MEsh radiation Transport (COMET) method requires a library of incident flux response expansion coefficients for its whole-core calculations. These coefficients are calculated using a stochastic method because of its high accuracy and robustness in modeling geometric complexity. However, the stochastic uncertainty inherent in response coefficients is unavoidably propagated into the whole-core calculations, and consequently, its effects must be quantitatively evaluated. The current method in COMET based on the error propagation significantly overpredicts uncertainty since the correlations among response coefficients are ignored. In this paper, a new adjoint-based method is developed to take into account the uncertainty and correlations of response coefficients. In this approach, forward calculations are first performed to obtain whole-core solutions such as the core eigenvalue and forward partial currents crossing mesh surfaces. Low-order adjoint calculations are then performed to determine the sensitivity of response coefficients. The core eigenvalue uncertainty is finally computed by taking into account the variances of surface-to-surface response coefficients, response fission production, and absorption rates as well as their correlations. The eigenvalue uncertainty predicated by the new method agrees very well with the reference solution, with a discrepancy <3 pcm, while the original error propagation method significantly overestimates the uncertainty. It is also found that the new method’s computational efficiency is comparable to that of the current error propagation method in COMET since the computation time spent on the adjoint calculations is negligible. As an additional benefit, since the covariances among response coefficients are absorbed into the variance of the response net gain rates and the variance of the effective leakage terms, no extra computer memory is needed to store these covariances.