Perturbation Theory-Based Whole-Core Eigenvalue Sensitivity and Uncertainty (SU) Analysis via a 2D/1D Transport Code

Abstract

For nuclear reactor physics, uncertainties in the multigroup cross sections inevitably exist, and these uncertainties are considered as the most significant uncertainty source. Based on the home-developed 3D high-fidelity neutron transport code HNET, the perturbation theory was used to directly calculate the sensitivity coefficient of keff to the multigroup cross sections, and a reasonable relative covariance matrix with a specific energy group structure was generated directly from the evaluated covariance data by using the transforming method. Then, the “Sandwich Rule” was applied to quantify the uncertainty of keff. Based on these methods, a new SU module in HNET was developed to directly quantify the keff uncertainty with one-step deterministic transport methods. To verify the accuracy of the sensitivity and uncertainty analysis of HNET, an infinite-medium problem and the 2D pin-cell problem were used to perform SU analysis, and the numerical results demonstrate that acceptable accuracy of sensitivity and uncertainty analysis of the HNET are achievable. Finally, keff SU analysis of a 3D minicore was analyzed by using the HNET, and some important conclusions were also drawn from the numerical results.

Generalized Perturbation Theory Based Total Sensitivity and Uncertainty Analysis for High-Fidelity Neutronics Calculation

“…It is worth noted that the ability of calculation for explicit sensitivity coefficient is verified in our precious work (J. Ma et al, 2020) and verification will not be performed in this paper. For the verification of total sensitivity, the integral sensitivity coefficients (integrating with volume and energy) of selected cross sections of representative isotopes and reaction types in resonance energy groups are summarized in Table 2 for comparison.…”

“…According to the mathematical derivation, the explicit sensitivity coefficient of k eff due to the perturbation of effective resonance cross sections σcan be eventually expressed as (J. Ma et al, 2020),…”

“…The denominator and the derivation term in numerator could be obtained based on the discrete form of neutron transport equation according to our previous research (J. Ma et al, 2020), and the exact form of explicit sensitivity coefficients won't be given in this paper.…”

“…Based on this scheme, explicit sensitivity analysis for LWR with high-fidelity deterministic transport simulation can be performed (Q. Wu, et al, 2018;J. Ma, et al, 2020).…”

Design and optimization of passive residual heat removal system for lead‐bismuth reactorSVBR‐100

“…Therefore, uncertainty analysis was performed to find the key parameters affecting the system performance, research the uncertainty propagation rules, and evaluate the precision of codes. Uncertainty analysis has been widely used in the field of nuclear engineerings, such as system simulation, 23‐25 multidimensional CFD, 21,26‐29 and reactor physics calculation 30,31 …”