反應器物理「漫談」反應器物理「漫談」郭文生郭文生

101101年年 33月月 2828日日

什麼是「反應器物理」？什麼是「反應器物理」？• Nuclear reactor physics is the branch of sc

ience that deals with the study and application of chain reaction to induce controlled rate of fission for energy in reactors.

• Also called– Core physics– Neutronics

談什麼？談什麼？• 從 Transport Theory說起• 「古典」與「近代」反應器物理• Lattice Calculation vs. Core Calculation• 反應器物理與數值解法• 反應器物理與安全分析• Kinetics• Monte Carlo法• 應用面

Transport TheoryTransport Theory

• 最基本、最複雜的理論• 7-variable (r, E, W, t) nonlinear partial diffe

rential equation:

• Who is the “Trouble Maker?”

Transport Theory (cont’d)Transport Theory (cont’d)

• How to deal with the ”Trouble Maker?”– Diffusion Theory Approximation– Nodal Method Approximation

• How about the energy part (E)?– Span from ~0eV to 20Mev– Multi-group Approximation

• Multi-group neutron diffusion equation• Multi-group nodal equation

古典古典 vs.vs. 近代反應器物理近代反應器物理• 古典

– 以 Diffusion Theory為主– 計算機效能不強– 核燃料及反應器設計較單純

• 近代– Nodal Theory的時代

• Nodal Transport vs. Nodal Diffusion• Power Reconstruction• 從二群巨觀截面發展至多群微觀截面

– 核燃料及反應器設計愈來愈複雜– 計算機效能大幅提昇

Cell/Lattice Calculation vs. Core Cell/Lattice Calculation vs. Core CalculationCalculation

• Based upon the principle of separation of variables

• Break down the whole 7-variable problem domain into:– Cell/Lattice Calculation

• Confined to smaller scale of geometry: – pin cell (a unique axial segment of fuel rod)– fuel lattice (a unique axial segment of fuel assembly)

• Focus on dealing with energy and angular

– Core Calculation• Focus on larger scale of geometry: whole core or a quadrant• More relaxation on energy and angular

反應器物理與數值解法反應器物理與數值解法• Finite Difference vs. Finite Element

• 傳統的 Power Series已不夠用• 數值解的收斂問題

–複雜的燃料及反應器的設計使 Iteration Matrix不易維持 Diagonal Dominance

–其他實務上碰到的問題，如 Refueling S/D Margin計算

反應器物理與安全分析反應器物理與安全分析• 為安全分析 (Transient)的上游• 提供安全分析重要的輸入參數

– Power Distribution– Cross Sections– Kinetic Parameters

• Must be Weighted by Adjoint Flux

• 某些 Slow Transient可以用 Stead-State Rx Physics Code來分析

KineticsKinetics• 從 Point Kinetics進展至Multi-dimensional

Kinetics– Point Kinetics不一定最保守

• 一般為 System Code (RETRAN, RELAP, etc.)的一部份模組

• 3-D Kinetics一般用於 Core-wise Accident Analysis: Rod Ejection, Rod Drop

• BWR Stability: Time-Domain vs. Frequency Domain

Monte CarloMonte Carlo 法法• Good and Bad

– 除實驗外的最具公信力的方法• 最少近似• Continuous Energy XS

– 複雜的輸入模式，速度慢– 溫度問題– 燃耗問題

• Combinatorial Geometry vs. Boolean Geometry– 堆積木– AND/OR/NOT

應用面應用面• LWR Fuel & Core Design

– UO2+Gd2O3 Fuel , MOX Fuel– 12-month cycle, 18-month cycle, 24-month cycle, …

• Support of Rx Operation– Power Rx: e.g. On-Line Core Monitoring System– Research Rx

• SFP or Dry Storage Cask Criticality Analysis• Gen IV Rx Design

– More on Fast Rx• ADS• Space Rx/Submarine Rx

Thanks for Your Time!Thanks for Your Time!