Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: IV. Effects of Imprecisely Known Source Parameters

Ruixian Fang,Dan Gabriel Cacuci

doi:10.3390/en13061431

Ruixian Fang, Dan Gabriel Cacuci

Open Access

https://doi.org/10.3390/en13061431

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Journal: Energies	Publication Date: Mar 19, 2020
Citations: 19	License type: CC BY 4.0

Affiliation: University of South Carolina

Abstract

By applying the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to the polyethylene-reflected plutonium (PERP) benchmark, this work presents results for the first- and second-order sensitivities of this benchmark’s leakage response with respect to the spontaneous fission source parameters. The numerical results obtained for these sensitivities indicate that the 1st-order relative sensitivity of the leakage response to the source parameters for the two fissionable isotopes in the benchmark are all positive, signifying that an increase in the source parameters will cause an increase in the total neutron leakage from the PERP sphere. The 1st- and 2nd-order relative sensitivities with respect to the source parameters for 239Pu are very small (10−4 or less). In contradistinction, the 1st-order and several 2nd-order relative sensitivities of the leakage response with respect to the source parameters of 240Pu are large. Large values (e.g., greater than 1.0) are also displayed by several mixed 2nd-order relative sensitivities of the leakage response with respect to parameters involving the source and: (i) the total cross sections; (ii) the average neutrons per fission; and (iii) the isotopic number densities. On the other hand, the values of the mixed 2nd-order relative sensitivities with respect to parameters involving the source and: (iv) the scattering cross sections; and (v) and the fission cross sections are smaller than 1.0. It is also shown that the effects of the 1st- and 2nd-order sensitivities of the PERP benchmark’s leakage response with respect to the benchmark’s source parameters on the moments (expected value, variance and skewness) of the PERP benchmark’s leakage response distribution are negligibly smaller than the corresponding effects (on the response distribution) stemming from uncertainties in the total, fission and scattering cross sections.

Highlights

In previous works [1,2,3], the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM)conceived by Cacuci [4,5,6] has been applied to the subcritical polyethylene-reflected plutonium metal OECD/NEA-benchmark [7], to compute efficiently the exact values of the1st-order and 2nd-order sensitivities of the PERP’s leakage response with respect to the following model parameters: (i) 180 group-averaged total microscopic cross sections [1]; (ii) 21,600 group-averaged scattering microscopic cross sections [2]; and (iii) 120 fission process parameters [3]
The equations needed for deriving the expression of the 2nd-order sensitivities ∂2 L(α)/∂q∂q are obtained by particularizing Equation (208) from Reference [6] to the PERP benchmark, which yields: Z
We present the computation and analysis of the numerical results for the 2nd-order mixed sensitivities ∂2 L(α)/∂q∂σs of the leakage response with respect to the source parameters and group-averaged scattering microscopic cross sections of all isotopes contained in the PERP benchmark

Summary

Introduction

In previous works [1,2,3], the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM). This work is organized, as follows: Section 2 presents the computational results for the 12 first-order sensitivities and 12 × 12 second-order sensitivities of the leakage response with respect to the benchmark’s source parameters.

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Alternative Path

Second-Order Sensitivities