Abstract
This work applies the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to compute the 1st-order and unmixed 2nd-order sensitivities of a polyethylene-reflected plutonium (PERP) benchmark’s leakage response with respect to the benchmark’s imprecisely known isotopic number densities. The numerical results obtained for these sensitivities indicate that the 1st-order relative sensitivity to the isotopic number densities for the two fissionable isotopes have large values, which are comparable to, or larger than, the corresponding sensitivities for the total cross sections. Furthermore, several 2nd-order unmixed sensitivities for the isotopic number densities are significantly larger than the corresponding 1st-order ones. This work also presents results for the first-order sensitivities of the PERP benchmark’s leakage response with respect to the fission spectrum parameters of the two fissionable isotopes, which have very small values. Finally, this work presents the overall summary and conclusions stemming from the research findings for the total of 21,976 first-order sensitivities and 482,944,576 second-order sensitivities with respect to all model parameters of the PERP benchmark, as presented in the sequence of publications in the Special Issue of Energies dedicated to “Sensitivity Analysis, Uncertainty Quantification and Predictive Modeling of Nuclear Energy Systems”.
Highlights
In Parts I−V [1,2,3,4,5], which are precursors of this work, the Second-Order Adjoint Sensitivity Analysis
The contribution stemming from the source term and macroscopic fission cross sections is obtained by particularizing Equation (206) in [7] for the polyethylene-reflected plutonium (PERP) benchmark, which yields:
We present the overall summary and conclusions based on the comprehensive results that have been detailed in Parts I−V [1,2,3,4,5] and in the present work for the 1st- and 2nd-order sensitivities of the PERP benchmark’s leakage response with respect to the PERP model’s imprecisely known parameters
Summary
In Parts I−V [1,2,3,4,5], which are precursors of this work, the Second-Order Adjoint Sensitivity Analysis. The 1st-order and 2nd-order sensitivities of the leakage response with respect to the isotopic number densities will be computed by specializing the general expressions derived by Cacuci [6,7,8] to the PERP benchmark, and summarizing the respective contributions stemming from the total, scattering and fission macroscopic cross sections, and the sources, respectively. The 2nd-order sensitivity analysis of the PERP benchmark is completed and concluded in this work, which is structured as follows: Section 2 presents the computational results for the six first-order sensitivities of the leakage response with respect to the benchmark’s isotopic number densities. The total been defined in previous workssphere [1,2,3,4,5] and is reproduced, in Appendix
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