Mathematical Methods in Nuclear Reactor Physics

This paper deals with an alternative numerical method for calculating depletion and production chains of the main isotopes found in a pressurized water reactor. It is based on the use of the exponentiation procedure coupled to orthogonal polynomial expansion to compute the transition matrix associated with the solution of the differential equations describing isotope concentrations in the nuclear reactor. Actually, the method was implemented in an automated nuclear reactor core design system that uses a quick and accurate 3D nodal method, the Nodal Expansion Method (NEM), aiming at solving the diffusion equation describing the spatial neutron distribution in the reactor. This computational system, besides solving the diffusion equation, also solves the depletion equations governing the gradual changes in material compositions of the core due to fuel depletion. The depletion calculation is the most time-consuming aspect of the nuclear reactor design code, and has to be done in a very precise way in order to obtain a correct evaluation of the economic performance of the nuclear reactor. In this sense, the proposed method was applied to estimate the critical boron concentration at the end of the cycle. Results were compared to measured values and confirm the effectiveness of the method for practical purposes.

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Nuclear Reactor Physics 3e

10.1002/9783527812318 ◽

2018 ◽

Cited By ~ 5

Author(s):

Weston M. Stacey

Keyword(s):

Nuclear Reactor ◽

Reactor Physics

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Advances in Monte-Carlo code TRIPOLI-4®’s treatment of the electromagnetic cascade

EPJ Web of Conferences ◽

10.1051/epjconf/201817001008 ◽

2018 ◽

Vol 170 ◽

pp. 01008

Author(s):

Davide Mancusi ◽

Alice Bonin ◽

François-Xavier Hugot ◽

Fadhel Malouch

Keyword(s):

Monte Carlo ◽

Nuclear Reactor ◽

Thick Target ◽

Monte Carlo Code ◽

Reactor Physics ◽

Validation And Verification ◽

Electron Positron ◽

A Charge ◽

Charge Deposition ◽

Nuclear Instrumentation

TRIPOLI-4® is a Monte-Carlo particle-transport code developed at CEA-Saclay (France) that is employed in the domains of nuclear-reactor physics, criticality-safety, shielding/radiation protection and nuclear instrumentation. The goal of this paper is to report on current developments, validation and verification made in TRIPOLI-4 in the electron/positron/photon sector. The new capabilities and improvements concern refinements to the electron transport algorithm, the introduction of a charge-deposition score, the new thick-target bremsstrahlung option, the upgrade of the bremsstrahlung model and the improvement of electron angular straggling at low energy. The importance of each of the developments above is illustrated by comparisons with calculations performed with other codes and with experimental data.

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Virtual Nuclear Reactor for Education of Nuclear Reactor Physics

Journal of the Visualization Society of Japan ◽

10.3154/jvs.28.1191 ◽

2008 ◽

Vol 28-1 (2) ◽

pp. 1191-1191

Author(s):

Masashi TSUJI ◽

Takashi NARABAYASHI ◽

Youichiro SHIMAZU

Keyword(s):

Nuclear Reactor ◽

Reactor Physics

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Towards Development of Uncertainty Library for Nuclear Reactor Core Simulation

Volume 3: Nuclear Fuel and Material, Reactor Physics, and Transport Theory ◽

10.1115/icone26-82385 ◽

2018 ◽

Author(s):

Hany S. Abdel-Khalik ◽

Dongli Huang ◽

Ondrej Chvala ◽

G. Ivan Maldonado

Keyword(s):

Cross Sections ◽

Degrees Of Freedom ◽

Nuclear Reactor ◽

Reactor Core ◽

Sensitivity Study ◽

Reactor Physics ◽

Rigorous Approach ◽

Uncertainty Space ◽

Core Simulation

Uncertainty quantification is an indispensable analysis for nuclear reactor simulation as it provides a rigorous approach by which the credibility of the predictions can be assessed. Focusing on propagation of multi-group cross-sections, the major challenge lies in the enormous size of the uncertainty space. Earlier work has explored the use of the physics-guided coverage mapping (PCM) methodology to assess the quality of the assumptions typically employed to reduce the size of the uncertainty space. A reduced order modeling (ROM) approach has been further developed to identify the active degrees of freedom (DOFs) of the uncertainty space, comprising all the cross-section few-group parameters required in core-wide simulation. In the current work, a sensitivity study, based on the PCM and ROM results, is applied to identify a suitable compressed representation of the uncertainty space to render feasible the quantification and prioritization of the various sources of uncertainties. While the proposed developments are general to any reactor physics computational sequence, the proposed approach is customized to the TRITON-NESTLE computational sequence, simulating the BWR lattice model and the core model, which will serve as a demonstrative tool for the implementation of the algorithms.

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