Quantification of control rod worth uncertainties propagated from nuclear data via a hybrid high-order perturbation and efficient sampling method

Abstract

Based on the high order perturbation theory and few-group neutron diffusion equation, the formula to evaluate control rod worth is derived for various core state, which is equivalent to establish a function between CRW and eigenvalue, few-group homogenized cross sections, flux and adjoint flux. Then, an effective hybrid high order perturbation and efficient sampling (HOPES) method to quantify the uncertainty of control rod worth propagated from uncertainties in input parameters is proposed. To verify the validity of the HOPES method, a three dimensional mini core model with typical AP1000 fuel assemblies in a 3 × 3 checkerboard pattern is built and uncertainty in nuclear data is chosen as the main uncertainty source. Numerical results indicate that the HOPES method is much more effective to directly propagate uncertainties in input parameters to the final control rod worth and can quantify the uncertainty of either differential or integral control rod worth more accurately. Finally, the uncertainty of differential and integral CRW propagated from nuclear cross sections was quantified for the first time by using the HOPES method.