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Title: A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors

Abstract

A two-dimensional/one-dimensional (2D/1D) variational nodal approach is presented for pressurized water reactor core calculations without fuel-moderator homogenization. A 2D/1D approximation to the within-group neutron transport equation is derived and converted to an even-parity form. The corresponding nodal functional is presented and discretized to obtain response matrix equations. Within the nodes, finite elements in the x-y plane and orthogonal functions in z are used to approximate the spatial flux distribution. On the radial interfaces, orthogonal polynomials are employed; on the axial interfaces, piecewise constants corresponding to the finite elements eliminate the interface homogenization that has been a challenge for method of characteristics (MOC)-based 2D/1D approximations. The angular discretization utilizes an even-parity integral method within the nodes, and low-order spherical harmonics (P N) on the axial interfaces. The x-y surfaces are treated with high-order P N combined with quasi-reflected interface conditions. Furthermore, the method is applied to the C5G7 benchmark problems and compared to Monte Carlo reference calculations.

Authors:
 [1];  [2];  [3];  [4];  [1]
  1. Xi'an Jiaotong Univ., Xi'an, Shannxi (China)
  2. Northwestern Univ., Evanston, IL (United States)
  3. Argonne National Lab. (ANL), Lemont, IL (United States)
  4. Purdue Univ., West Lafayette, IN (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Natural Science Foundation of China (NNSFC)
OSTI Identifier:
1374150
Grant/Contract Number:
AC02-06CH11357
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Nuclear Science and Engineering
Additional Journal Information:
Journal Volume: 186; Journal Issue: 2; Journal ID: ISSN 0029-5639
Publisher:
American Nuclear Society - Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS; 2D/1D variational nodal method; eliminating the interface homogenization

Citation Formats

Zhang, Tengfei, Lewis, E. E., Smith, M. A., Yang, W. S., and Wu, Hongchun. A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors. United States: N. p., 2017. Web. doi:10.1080/00295639.2016.1273023.
Zhang, Tengfei, Lewis, E. E., Smith, M. A., Yang, W. S., & Wu, Hongchun. A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors. United States. doi:10.1080/00295639.2016.1273023.
Zhang, Tengfei, Lewis, E. E., Smith, M. A., Yang, W. S., and Wu, Hongchun. Tue . "A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors". United States. doi:10.1080/00295639.2016.1273023. https://www.osti.gov/servlets/purl/1374150.
@article{osti_1374150,
title = {A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors},
author = {Zhang, Tengfei and Lewis, E. E. and Smith, M. A. and Yang, W. S. and Wu, Hongchun},
abstractNote = {A two-dimensional/one-dimensional (2D/1D) variational nodal approach is presented for pressurized water reactor core calculations without fuel-moderator homogenization. A 2D/1D approximation to the within-group neutron transport equation is derived and converted to an even-parity form. The corresponding nodal functional is presented and discretized to obtain response matrix equations. Within the nodes, finite elements in the x-y plane and orthogonal functions in z are used to approximate the spatial flux distribution. On the radial interfaces, orthogonal polynomials are employed; on the axial interfaces, piecewise constants corresponding to the finite elements eliminate the interface homogenization that has been a challenge for method of characteristics (MOC)-based 2D/1D approximations. The angular discretization utilizes an even-parity integral method within the nodes, and low-order spherical harmonics (PN) on the axial interfaces. The x-y surfaces are treated with high-order PN combined with quasi-reflected interface conditions. Furthermore, the method is applied to the C5G7 benchmark problems and compared to Monte Carlo reference calculations.},
doi = {10.1080/00295639.2016.1273023},
journal = {Nuclear Science and Engineering},
number = 2,
volume = 186,
place = {United States},
year = {Tue Apr 18 00:00:00 EDT 2017},
month = {Tue Apr 18 00:00:00 EDT 2017}
}

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  • It has been proposed that the fluctuations of the neutron current, called the current noise, can be used in addition to the scalar noise in reactor diagnostic problems. The possibility of the localization of a vibrating control rod pin in a pressurized water reactor control assembly is investigated by using the scalar neutron noise and the two-dimensional radial current noise as measured at one central point in the assembly. An explicit localization technique is elaborated in which the searched position is determined as the absolute minimum of a minimization function. The technique is investigated in numerical simulations. The results ofmore » the simulation tests show the potential applicability of the method.« less
  • A consistent “2D/1D” neutron transport method is derived from the 3D Boltzmann transport equation, to calculate fuel-pin-resolved neutron fluxes for realistic full-core Pressurized Water Reactor (PWR) problems. The 2D/1D method employs the Method of Characteristics to discretize the radial variables and a lower order transport solution to discretize the axial variable. This paper describes the theory of the 2D/1D method and its implementation in the MPACT code, which has become the whole-core deterministic neutron transport solver for the Consortium for Advanced Simulations of Light Water Reactors (CASL) core simulator VERA-CS. Several applications have been performed on both leadership-class and industry-classmore » computing clusters. Results are presented for whole-core solutions of the Watts Bar Nuclear Power Station Unit 1 and compared to both continuous-energy Monte Carlo results and plant data.« less