Resonance Self-Shielding Calculation Methods in Nuclear Reactors (Woodhead Publishing Series in Energy)

✍ Scribed by Liangzhi Cao, Hongchun Wu, Qian Zhang, Qingming He, Tiejun Zu

• Publisher: Woodhead Publishing
• Year: 2022
• Tongue: English
• Leaves: 412
• Edition: 1
• Category: Library

✦ Synopsis

Resonance Self-Shielding Calculation Methods in Nuclear Reactors presents the latest progress in resonance self-shielding methods for both deterministic and Mote Carlo methods, including key advances over the last decade such as high-fidelity resonance treatment, resonance interference effect and multi-group equivalence. As the demand for high-fidelity resonance self-shielding treatment is increasing due to the rapid development of advanced nuclear reactor concepts and progression in high performance computational technologies, this practical book guides students and professionals in nuclear engineering and technology through various methods with proven high precision and efficiency.

✦ Table of Contents

Front Cover
RESONANCE SELF-SHIELDING CALCULATION METHODS IN NUCLEAR REACTORS
RESONANCE SELF-SHIELDING CALCULATION METHODS IN NUCLEAR REACTORS
Copyright
Contents
Foreword
Preface
1 - Introduction
1.1 Background
1.2 Some elements for resonance self-shielding calculation
1.3 Development of resonance self-shielding calculation methods
1.3.1 Equivalence theory method
1.3.2 Ultrafine-group method
1.3.3 Subgroup method
1.4 Layout of this book
References
2 - Resonance cross-section processing
2.1 Evaluated nuclear data library
2.2 Resonance reconstruction
2.2.1 Single-level Breit-Wigner formula
2.2.2 Multilevel Breit-Wigner formula
2.2.3 Reich-Moore formula
2.2.4 R-matrix limited formula
2.2.5 Linearization of resonance cross-sections
2.3 Doppler broadening
2.3.1 Introduction of Doppler broadening
2.3.2 The Doppler-broadening equation
2.3.3 Kernel broadening method
2.4 Unresolved resonance treatment
2.4.1 The model of ladder sampling
2.4.2 Calculation of effective cross-section
2.5 Resonance integral table
2.6 Resonance elastic scattering
2.6.1 The model for RESK
2.6.2 Method to solve the slowing-down equation with neutron upscattering
2.6.3 Generation of S (α, β, T) tables
2.7 Goldstein-Cohen factor
References
3 - Equivalence theory method
3.1 Approximate spectrum of homogeneous systems
3.2 Approximate spectrum of heterogeneous systems
3.3 The establishment of classical equivalence theory
3.4 The calculation of the effective cross-section
3.4.1 The resonance cross-section table
3.4.2 The resonance integral table
3.5 Equivalence theory of lattice systems
3.6 Discrepancy analysis
3.6.1 Rational approximation of neutron collision probability
3.6.2 Two region fuel-moderator heterogeneous system approximation
3.6.3 Narrow resonance (NR) approximation
3.6.4 Multiplication factors calculation
References
4 - Subgroup method
4.1 Introduction
4.2 Methodology of subgroup method
4.2.1 Concept of subgroup
4.2.2 Probability table
4.2.3 Fitting method
4.2.3.1 Padé approximation approach
4.2.3.2 Direct least-square fitting approach
4.2.3.3 An improved fitting approach based on the heterogeneous cells
4.2.4 Moment method
4.2.5 Subgroup transport equation
4.3 Practical application of subgroup method
4.3.1 Application of subgroup method in SUGAR
4.3.2 Categorical subgroup method
4.4 Improvements of subgroup method
4.4.1 Subgroup parameter generation based on heterogeneous geometry
4.4.2 Treatment for the resonance interference effect
4.4.3 Treatment for uniform temperature distribution
References
5 - Ultrafine group method
5.1 Introduction
5.2 Neutron slowing-down equation
5.3 Collision probability calculation and acceleration
5.4 Coupling with method of characteristic (MOC)
References
6 - Wavelet expansion method
6.1 Introduction
6.2 Theoretical method
6.2.1 Brief introduction of wavelets theory
6.2.2 Fundamental idea of wavelets scaling function expansion method
6.2.3 Scattering source calculation
6.2.4 Fission source calculation
6.3 Numerical results
6.3.1 Selecting orders of wavelets scaling expansion
6.3.2 PWR fuel cell problem
6.3.3 Cylindrical cluster geometry problem
6.4 A coupling method of subgroup and wavelet expansion
6.5 Numerical results for the coupling method
6.6 Conclusions
References
7 - Resonance treatment in Monte Carlo method
7.1 Overview
7.2 The Monte Carlo method
7.2.1 Nuclear-data library
7.2.2 Neutron physics
7.2.3 Photon physics
7.2.4 Particle-transport calculation
7.2.5 Tallies
7.2.6 Variance-reduction techniques
7.3 Overview of the Monte Carlo codes
7.3.1 Monte Carlo codes
7.3.2 MCNP
7.3.3 Serpent
7.3.4 OpenMC
7.3.5 MONK
7.3.6 TRIPOLI-4
7.3.7 MVP/GMVP II
7.3.8 McCARD
7.3.9 RMC
7.3.10 JMCT
7.3.11 NECP-MCX
7.4 Temperature treatment of the resolved resonance
7.4.1 On-the-fly temperature interpolation with small temperature intervals
7.4.2 Pseudomaterial method
7.4.3 On-the-fly Doppler method based on the regression model
7.4.4 Explicit treatment of thermal motion
7.4.5 Direct Doppler-broadening based on the multipole representation
7.5 Temperature treatment of the unresolved resonance
7.6 Treatment of the resonance elastic scattering effect
7.6.1 Free gas model
7.6.2 The DBRC method
7.6.3 The WCM
7.6.4 Numerical results
References
8 - High-fidelity resonance self-shielding calculation
8.1 Overview
8.2 Continuous-energy quasi-one-dimensional slowing-down based method
8.2.1 The continuous-energy quasi-1D slowing-down model
8.2.2 The correction method for the subregion self-shielded cross-sections
8.2.3 Numerical results
8.3 Pin-based pointwise energy slowing-down method
8.3.1 The pointwise energy slowing-down equation
8.3.2 The shadowing effect correction factor
8.3.3 Numerical results
8.4 Global-local self-shielding calculation scheme
8.4.1 Global calculation
8.4.2 Establishment of the equivalent 1D model
8.4.3 Local calculation
8.4.3.1 Generation of the cross-section table
8.4.3.2 Generation of the physical probability table
8.4.3.3 Solving the subgroup fixed-source equation
8.4.3.4 Solving the subgroup fixed-source equation
8.4.4 Resonance calculation based on deep-learning method
8.4.4.1 Output shape A
8.4.4.2 Output shape B
8.4.4.3 Output shape C
8.4.4.4 Output shape D
8.4.4.5 Output shape E
8.4.4.6 Output shape F
8.4.5 Numerical results
8.4.5.1 UO2 pin cell problem
8.4.5.2 3 × 3 assemblies problem
References
9 - Resonance treatment for double heterogeneity
9.1 Chord length sampling for stochastic media
9.1.1 Markovian distribution
9.1.2 Chord length sampling scheme
9.2 The analytical dancoff factor approach
9.3 The disadvantage factor approach
9.3.1 Treatment of self-shielding effect of TRISO particles
9.3.2 Calculation of disadvantage factor in resonance-energy range
9.3.3 Calculation of disadvantage factor in thermal-energy range
9.3.4 Treatment of self-shielding effect of fuel rods in the lattice system
9.3.5 Application of the disadvantage factor to subgroup method
9.3.5.1 The hyperfine energy group XS correction scheme
9.3.5.2 The subgroup XS correction scheme
9.3.5.3 Numerical results
9.4 The Sanchez-Pomraning approach
9.4.1 Renewal equation
9.4.2 The equivalent homogenization scheme
9.4.3 The sweeping process of Sanchez-MOC
9.4.4 The recovery of interior flux inside the particle
9.4.5 Improved subgroup method for DH problem
9.4.6 Extension of the Sanchez-Pomraning model to ultrafine group method
9.4.7 Numerical verification
9.4.7.1 Typical FCM single cell problem
9.4.7.1.1 FCM with different packing fractions
9.4.7.1.2 FCM with different TRISO size
9.4.7.2 Different FCM fuel geometry and composition
9.4.7.3 Plutonium spots problem
9.4.7.4 FCM fuel with burnable poison
9.4.7.5 FCM fuel with depletion
References
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
R
S
T
U
V
W
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