Application of Backward Differentiation Formula to Spatial Reactor Kinetics Calculation With Adaptive Time Step Control

Shim, Cheon Bo; Jung, Yeon Sang; Yoon, Jong Il; Joo, Han Gyu

doi:10.5516/net.2011.43.6.531

Cited by 18 publications

(6 citation statements)

References 11 publications

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“…This is necessary to ensure a null reactivity from the initial conditions. Various time-discretization methods may be used for solving the time-dependent neutron transport equation, including the θ-method, the backward differentiation formula (BDF) method [42], and so on. A detailed discussion of these methods can be found in [68].…”

Section: D Time-dependent Neutron Transport Equationsmentioning

confidence: 99%

MPACT Theory Manual (V.4.3)

Larsen

Collins²,

Kochunas

et al. 2022

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This manual presents the theory underlying the three-dimensional (3D) whole-core, pin-resolved neutron transport calculation methodologies employed in the MPACT code. MPACT's primary goal is to provide accurate sub-pin power distributions in a computationally efficient manner. To accomplish this, MPACT offers several different transport method options. The 2D/1D method, in which 3D problems are decomposed into an axial stack of radial "slices," is currently the most commonly used. In this option, two-dimensional (2D) planar solutions are provided by the method of characteristics (MOC), and axial solutions are provided via one-dimensional (1D) approximate diffusion, or P 3 solutions. The radial and axial solutions are coupled by (i) axial and radial transverse leakages, and (ii) a global 3D coarse mesh finite difference (CMFD) solve, which provides both acceleration and stability to the solution iteration scheme.The subsequent chapters of this manual present a range of topics, including MOC, CMFD, axial nodal transport solvers, 2D/1D, self-shielding, depletion, thermal-hydraulics, and transient methods. Development of the underlying theory of the 2D/1D method is presented, diagrams are included to highlight important algorithmic flow, and important concepts are discussed as appropriate. This manual is intended to be selfsufficient, but references to published articles and other materials are included for further reading.MPACT is a relatively new code, with new capabilities and many computational methods that did not exist until recently. This manual is an even newer document, with chapters written by several different code contributors working under time constraints. For these reasons, the manual is not yet complete and finalized.

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Section: D Time-dependent Neutron Transport Equationsmentioning

confidence: 99%

MPACT Theory Manual (V.4.3)

Larsen

Collins²,

Kochunas

et al. 2022

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“…The Backward Euler method is the most popular for dealing with the time derivative term in Equations (1) and (2) due to its numerical stability. The finite difference method was employed for the spatial variables in Equation (2), and a small mesh size (~1 cm) was adopted to guarantee accuracy.…”

Section: Theoretical and Mathematic Modelmentioning

confidence: 99%

Transient analysis for liquid-fuel molten salt reactor based on MOREL2.0 code

et al. 2017

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SummaryA molten salt reactor (MSR) is characterized by simultaneously using liquid fuel salt as both the nuclear fuel and coolant. The redistribution of delayed neutron precursors (DNPs) makes the transient behavior of MSRs different from traditional solid-fuel reactors. In this study, a 3D coupled neutronics/thermal hydraulics code, MOREL2.0, was employed to analyze a liquid-fuel Thorium Molten Salt Reactor (TMSR-LF) under perturbations of fuel pump start-up and coast-down and by overheating and overcooling the inlet fuel temperature. Some transient processes were simulated to provide guidance for the future design and optimization of TMSR-LFs. In response to the perturbations, reactivity was lost and gained in the pump start-up and coast-down, respectively.Overheating the inlet fuel temperature introduced negative reactivity, and TMSR-LF maintained a safety state, while overcooling the inlet fuel temperature resulted in positive reactivity. Overcooling by 70 K produced a supercritical transient condition and a rapid increase in power within a short period, which was followed by a decrease in power due to negative temperature feedback. The transient results demonstrate that the negative temperature feedback coefficients guarantee TMSR-LF inherent safety and the variation range of temperature stay within the safety margin.

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“…It is a linear multistep method with one step. The BDE or Petzold–Gear method is the more used for the solution of DAEs and is an implicit multipoint method that uses known solution data determined at several previous time points as well as the unknown solution at the current point because of the following: − …”

Section: Kinetic Modeling Of Hydrocracking Reactionsmentioning

confidence: 99%

Experimental Methods for Developing Kinetic Models for Hydrocracking Reactions with Slurry-Phase Catalyst Using Batch Reactors

Quitian

Ancheyta

2016

Energy Fuels

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Experimental methods for studying the chemical kinetics of hydrocracking reactions with disperse catalysts in batch operation are reviewed. Batch operating conditions and description of modes of operation of the reactors are discussed. The experimental procedures used to produce, analyze, and interpret the experimental data required for determining the chemical kinetics of hydrocracking reactions with catalyst in dispersed phase are also reviewed. Two possible batch operation modes used for the study of such reactions are described: isothermal and temperature scanning operation. The typical kinetic models for hydrocracking are discussed in detail and step-by-step procedures to calculate the stoichiometric coefficients, mass transfer coefficients, rate constants, and activation energies from experimental data are provided.

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Application of Backward Differentiation Formula to Spatial Reactor Kinetics Calculation With Adaptive Time Step Control

Cited by 18 publications

References 11 publications

MPACT Theory Manual (V.4.3)

MPACT Theory Manual (V.4.3)

Transient analysis for liquid-fuel molten salt reactor based on MOREL2.0 code

Experimental Methods for Developing Kinetic Models for Hydrocracking Reactions with Slurry-Phase Catalyst Using Batch Reactors

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