Monte Carlo Perturbation Theory Estimates of Sensitivities to System Dimensions

Burke, Timothy P.; Kiedrowski, Brian C.

doi:10.1080/00295639.2017.1388093

Title: Monte Carlo Perturbation Theory Estimates of Sensitivities to System Dimensions

Journal Article · Mon Dec 11 00:00:00 EST 2017 · Nuclear Science and Engineering

DOI:https://doi.org/10.1080/00295639.2017.1388093· OSTI ID:1438024

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Univ. of Michigan, Ann Arbor, MI (United States)

Here, Monte Carlo methods are developed using adjoint-based perturbation theory and the differential operator method to compute the sensitivities of the k-eigenvalue, linear functions of the flux (reaction rates), and bilinear functions of the forward and adjoint flux (kinetics parameters) to system dimensions for uniform expansions or contractions. The calculation of sensitivities to system dimensions requires computing scattering and fission sources at material interfaces using collisions occurring at the interface—which is a set of events with infinitesimal probability. Kernel density estimators are used to estimate the source at interfaces using collisions occurring near the interface. The methods for computing sensitivities of linear and bilinear ratios are derived using the differential operator method and adjoint-based perturbation theory and are shown to be equivalent to methods previously developed using a collision history–based approach. The methods for determining sensitivities to system dimensions are tested on a series of fast, intermediate, and thermal critical benchmarks as well as a pressurized water reactor benchmark problem with iterated fission probability used for adjoint-weighting. The estimators are shown to agree within 5% and 3σ of reference solutions obtained using direct perturbations with central differences for the majority of test problems.

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Research Organization:: Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA), Office of Defense Nuclear Nonproliferation; US Nuclear Regulatory Commission (NRC), Rockville, MD (United States)

Grant/Contract Number:: NA0002576; NRC-HQ-13-G-38- 0007

OSTI ID:: 1438024

Journal Information:: Nuclear Science and Engineering, Vol. 189, Issue 3; ISSN 0029-5639

Publisher:: American Nuclear Society - Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 10 works

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References (20)

SCALE Continuous-Energy Eigenvalue Sensitivity Coefficient Calculations Perfetti, Christopher M.; Rearden, Bradley T.; Martin, William R. Nuclear Science and Engineering, Vol. 182, Issue 3 https://doi.org/10.13182/NSE15-12	journal	March 2016
Development of a Generalized Perturbation Theory Method for Sensitivity Analysis Using Continuous-Energy Monte Carlo Methods Perfetti, Christopher M.; Rearden, Bradley T. Nuclear Science and Engineering, Vol. 182, Issue 3 https://doi.org/10.13182/NSE15-13	journal	March 2016
Non-Parametric Estimation of a Multivariate Probability Density Epanechnikov, V. A. Theory of Probability & Its Applications, Vol. 14, Issue 1 https://doi.org/10.1137/1114019	journal	January 1969
An Improvement of the Monte Carlo Generalized Differential Operator Method by Taking into Account First- and Second-Order Perturbations of Fission Source Raskach, Kirill Fedorovich Nuclear Science and Engineering, Vol. 162, Issue 2 https://doi.org/10.13182/NSE162-158	journal	June 2009
Impact of Perturbed Fission Source on the Effective Multiplication Factor in Monte Carlo Perturbation Calculations Nagaya, Yasunobu; Mori, Takamasa Journal of Nuclear Science and Technology, Vol. 42, Issue 5 https://doi.org/10.1080/18811248.2005.9726411	journal	May 2005
Development of Calculation Technique for Iterated Fission Probability and Reactor Kinetic Parameters Using Continuous-Energy Monte Carlo Method Nauchi, Yasushi; Kameyama, Takanori Journal of Nuclear Science and Technology, Vol. 47, Issue 11 https://doi.org/10.1080/18811248.2010.9711662	journal	November 2010
Surface Perturbation Theory Lewins, Jeffery Nuclear Science and Engineering, Vol. 7, Issue 6 https://doi.org/10.13182/NSE60-A25754	journal	June 1960
The OpenMC Monte Carlo particle transport code Romano, Paul K.; Forget, Benoit Annals of Nuclear Energy, Vol. 51 https://doi.org/10.1016/j.anucene.2012.06.040	journal	January 2013
Monte Carlo Method for Geometrical Perturbation and its Application to the Pulsed Fast Reactor Takahashi, Hiroshi Nuclear Science and Engineering, Vol. 41, Issue 2 https://doi.org/10.13182/NSE70-A20712	journal	August 1970
XGPT: Extending Monte Carlo Generalized Perturbation Theory capabilities to continuous-energy sensitivity functions Aufiero, Manuele; Martin, Michael; Fratoni, Massimiliano Annals of Nuclear Energy, Vol. 96 https://doi.org/10.1016/j.anucene.2016.06.012	journal	October 2016
Kernel Density Estimation of Reaction Rates in Neutron Transport Simulations of Nuclear Reactors Burke, Timothy P.; Kiedrowski, Brian C.; Martin, William R. Nuclear Science and Engineering, Vol. 188, Issue 2 https://doi.org/10.1080/00295639.2017.1350000	journal	August 2017
Stochastic Perturbation Analysis Applied to Neutral Particle Transport Rief, Herbert Advances in Nuclear Science and Technology https://doi.org/10.1007/0-306-47810-2_2	book	January 2002
Adjoint-Weighted Tallies for k -Eigenvalue Calculations with Continuous-Energy Monte Carlo Kiedrowski, Brian C.; Brown, Forrest B.; Wilson, Paul P. H. Nuclear Science and Engineering, Vol. 168, Issue 3 https://doi.org/10.13182/NSE10-22	journal	July 2011
Calculation of effective point kinetics parameters in the Serpent 2 Monte Carlo code Leppänen, Jaakko; Aufiero, Manuele; Fridman, Emil Annals of Nuclear Energy, Vol. 65 https://doi.org/10.1016/j.anucene.2013.10.032	journal	March 2014
Kernel Density Estimation Method for Monte Carlo Global Flux Tallies Banerjee, Kaushik; Martin, William R. Nuclear Science and Engineering, Vol. 170, Issue 3 https://doi.org/10.13182/NSE10-77	journal	March 2012
Adjoint-Based k -Eigenvalue Sensitivity Coefficients to Nuclear Data Using Continuous-Energy Monte Carlo Kiedrowski, Brian C.; Brown, Forrest B. Nuclear Science and Engineering, Vol. 174, Issue 3 https://doi.org/10.13182/NSE12-46	journal	July 2013
ENDF/B-VII.1 Nuclear Data for Science and Technology: Cross Sections, Covariances, Fission Product Yields and Decay Data Chadwick, M. B.; Herman, M.; Obložinský, P. Nuclear Data Sheets, Vol. 112, Issue 12 https://doi.org/10.1016/j.nds.2011.11.002	journal	December 2011
Internal Interface Perturbations in Neutron Transport Theory Rahnema, F. Nuclear Science and Engineering, Vol. 86, Issue 1 https://doi.org/10.13182/NSE84-A17971	journal	January 1984
Application of the virtual density theory in fast reactor analysis based on the neutron transport calculation Zheng, Youqi; Xiao, Yunlong; Wu, Hongchun Nuclear Engineering and Design, Vol. 320 https://doi.org/10.1016/j.nucengdes.2017.05.020	journal	August 2017
Eigenvalue sensitivity to system dimensions Favorite, Jeffrey A.; Bledsoe, Keith C. Annals of Nuclear Energy, Vol. 37, Issue 4 https://doi.org/10.1016/j.anucene.2010.01.004	journal	April 2010

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Calculating the k -Eigenvalue Sensitivity to Typical Geometric Perturbations with the Adjoint-Weighted Method in the Continuous-Energy Reactor Monte Carlo Code RMC Li, Hao; Yu, Ganglin; Huang, Shanfang Nuclear Science and Engineering, Vol. 193, Issue 11 https://doi.org/10.1080/00295639.2019.1614800	journal	June 2019

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