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Open AccessArticle

Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics

Department of Mechanical Engineering, University of South Carolina, 300 Main Street, Columbia, SC 29208, USA
Academic Editor: Patrick Blaise
J. Nucl. Eng. 2021, 2(2), 114-123; https://doi.org/10.3390/jne2020012
Received: 16 November 2020 / Revised: 11 March 2021 / Accepted: 25 March 2021 / Published: 8 April 2021
(This article belongs to the Special Issue Selected Papers from PHYSOR 2020)
This paper illustrates the relative importance of the largest first- and second-order sensitivities of the leakage response of an OECD/NEA reactor physics benchmark (a polyethylene-reflected plutonium sphere) to the benchmark’s underlying total cross sections. It will be shown that numerous 2nd-order sensitivities of the leakage response with respect to the total cross sections are significantly larger than the largest corresponding 1st-order sensitivities. In particular, the contributions of the 2nd-order sensitivities cause the mean (expected) value of the response to differ appreciably from its computed value and also cause the response distribution to be skewed towards positive values relative to the mean. Neglecting these large 2nd-order sensitivities would cause very large non-conservative errors by under-reporting the response’s variance and expected value. The results presented in this paper also underscore the need for obtaining reliable cross section covariance data, which are currently unavailable. Finally, comparing the CPU-times needed for computations, this paper demonstrates that the Second-Order Adjoint Sensitivity Analysis Methodology is the only practical method for computing 2nd-order sensitivities exactly, without introducing methodological errors, for large-scale systems characterized by many uncertain parameters. View Full-Text
Keywords: polyethylene-reflected plutonium sphere (PERP) benchmark; 2nd-order adjoint sensitivity analysis; 1st- and 2nd-order sensitivities; total cross sections; expected value; variance and skewness of PERP response polyethylene-reflected plutonium sphere (PERP) benchmark; 2nd-order adjoint sensitivity analysis; 1st- and 2nd-order sensitivities; total cross sections; expected value; variance and skewness of PERP response
MDPI and ACS Style

Cacuci, D.G. Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics. J. Nucl. Eng. 2021, 2, 114-123. https://doi.org/10.3390/jne2020012

AMA Style

Cacuci DG. Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics. Journal of Nuclear Engineering. 2021; 2(2):114-123. https://doi.org/10.3390/jne2020012

Chicago/Turabian Style

Cacuci, Dan G. 2021. "Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics" J. Nucl. Eng. 2, no. 2: 114-123. https://doi.org/10.3390/jne2020012

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