Next >

Neutron diffusion : concepts and uncertainty analysis for engineers and scientists

Preface Basic Reactor Principles Anatomic structure Binding Energy Calculation of 1 u Nuclear Reactions Nuclear Fusion Radioactivity Rate of Radioactive Decay Radioactive Equilibrium Radioactive Disintegration Series Artificial Radioactivity Nuclear Fission Basic Reactor Principles Principles, Production, and Interaction of Neutrons with Matter Production of Neutrons Neutron Reactions and Radiation Properties of a Ray Properties of в Ray Properties of y Ray Inelastic and Elastic Scattering of Neutrons Elastic Scattering Maxwell-Boltzmann Distribution Bibliography Neutron Diffusion Theory Cross Section of Neutron Reactions Transport Cross Section Rates of Neutron Reactions Neutron Diffusion Equation Helmholtz Equation Bibliography Fundamentals of Uncertainty Probabilistic Uncertainty Elementary Properties of Probability Conditional Probability Random Variables Distributions Binomial Distribution Poisson Distribution Normal or Gaussian Distribution Stochastic Differential Equations Euler-Maruyama and Milstein Methods Euler-Maruyama Method Milstein Method Interval Uncertainty Degenerate Intervals Intersection, Union and Interval Hull Width, Absolute Value and Midpoint Interval Arithmetic Fuzzy Uncertainty Definitions Fuzzy Set Support of a Fuzzy Set a-Level Set of a Fuzzy Set Convexity of a Fuzzy Set Height of a Fuzzy Set Fuzzy Numbers Triangular Fuzzy Number Trapezoidal Fuzzy Number Fuzzy Arithmetic Interval and Fuzzy Systems of Equations Linear System of Equations with Triangular Fuzzy Numbers Linear System of Equations with Trapezoidal Fuzzy Numbers Fuzzy Eigenvalue Problems Bibliography Uncertain Neutron Diffusion Uncertain Factors Involved in Neutron Diffusion Theory Diffusion Coefficient and Absorption Coefficient Fuzzy Finite Element Method Uncertainty Caused by the Stochastic Process Hybrid Uncertainties Modelling of the Uncertain Neutron Diffusion Equation Bibliography One-Group Model Analytical Method Separation of Variable Method One-Dimensional Wave Equation Boundary Conditions Numerical Methods Finite Difference Method Taylor Series Expansion Finite Difference by Polynomials Finite Difference Equations Finite Element Method Finite Elements for Ordinary Differential Equations Bibliography Uncertain One-Group Model Background Formulation of the Problem Case Study 1 Discussion Case Study 2 Discussion Bibliography Multigroup Model Background Group Diffusion Equation Formulation Multigroup Neutron Diffusion Equation Bibliography Uncertain Multigroup Model Fuzzy Finite Element for Coupled Differential Equations Fuzzy Multigroup Neutron Diffusion Equation Case Study Results and Discussion Thermal-Group Neutron Fluxes Fast-Group Neutron Fluxes Bibliography Point Kinetic Diffusion Reactivity Prompt and Delayed Neutrons Delayed Neutron Parameters Point Reactor Kinetic Equations for a Non-Stationary One-Group Bare Reactor with Delayed Neutrons Bibliography Stochastic Point Kinetic Diffusion Birth-Death Processes Pure Death Process Pure Birth Process Stochastic Point Kinetic Model Bibliography Hybridized Uncertainty in Point Kinetic Diffusion Black-Scholes Stochastic Differential Equation Preliminary Analytical Solution of Stochastic Differential Equations Solution of Fuzzy Stochastic Differential Equations Example Problems Langevin Stochastic Differential Equation Solution of Fuzzy Stochastic Differential Equations Example Problem Point Kinetic Neutron Diffusion Equation Stochastic Point Kinetic Model with Fuzzy Parameters Case Study Bibliography

Next >

Uncertainty Analysis
Uncertainty analysis provides a measure of the error associated with a calculated value. The devices listed in Table 5.1 directly measure physical parameters against Fig. 5.6 Photographs of a 0.2-2 L min 1 Parker liquid flow indicator, b desiccant solution density meter, and c...
(A Novel SOFC Tri-generation System for Building Applications)
Uncertainty Analysis
Uncertainty due to methodological choices (e.g. when defining the system boundaries, allocation vs. system expansion) has not been addressed in this study, because it is considered to be beyond the scope. However, the uncertainty in the estimation of environmental impacts associated with LCI raw input...
(Development of Recycled Polypropylene Plastic Fibres to Reinforce Concrete)
Analysis of Engineering Skills and Competencies
Stakeholders were asked to evaluate a set of 22 engineering skills on three main levels: • Skills importance currently. • Satisfaction level of engineering talent passion of these skills, as an outcome of existing undergraduate engineering education system. • Skills importance in 2030. The set...
(Engineering and Technology Talent for Innovation and Knowledge-Based Economies: Competencies, Leadership, and a Roadmap for Implementation)
Neutron Diffusion Theory
Neutron diffusion theory is the backbone of a nuclear reactor. It gives scientific insights to study various nuclear design problems. The neutrons are characterized by a single energy or speed in one-group diffusion theory and the model allows preliminary design estimates (Keepen 1964). Multigroup diffusion...
(Neutron diffusion : concepts and uncertainty analysis for engineers and scientists)
Neutron Diffusion Equation
To derive the neutron diffusion equation, we have to consider the following assumptions: 1. Use a one-speed or one-group approximation where the neutrons can be characterized by a single average kinetic energy. 2. Characterize the neutron distribution in the reactor by the particle density n(r,...
(Neutron diffusion : concepts and uncertainty analysis for engineers and scientists)
Uncertain Neutron Diffusion
Generally, every system possesses uncertainties caused by measurement errors, vague data and boundary conditions. Accordingly, the involved coefficients, parameters and constants become uncertain. Neutron diffusion is the backbone of a nuclear reactor. The scattering of a neutron occurs when it undergoes...
(Neutron diffusion : concepts and uncertainty analysis for engineers and scientists)
Uncertain Factors Involved in Neutron Diffusion Theory
The neutron collision inside a reactor depends upon the geometry of the reactor, diffusion coefficient, absorption coefficient, etc. In general, these parameters are not crisp and hence we get an uncertain neutron diffusion equation. Here, these uncertain parameters are taken as fuzzy. To investigate...
(Neutron diffusion : concepts and uncertainty analysis for engineers and scientists)
Modelling of the Uncertain Neutron Diffusion Equation
As discussed earlier, because of the uncertainties caused by diffusion and absorption coefficients, the one- and multigroup neutron diffusion equation becomes uncertain. If the uncertainties are in terms of interval, then these equations are called interval one- or multigroup neutron diffusion equations....
(Neutron diffusion : concepts and uncertainty analysis for engineers and scientists)
Multigroup Neutron Diffusion Equation
Let us consider a 1D reactor core which is divided into various energy groups and different regions having constant material properties. The discretization of the reactor core into various groups is shown in Figure 7.1. Using the previous procedure, the shape functions are multiplied with Equation 7.6,...
(Neutron diffusion : concepts and uncertainty analysis for engineers and scientists)
Fuzzy Multigroup Neutron Diffusion Equation
Let us consider the 1D reactor core, which is divided into various energy groups and different regions having constant material properties. The discretization of the reactor core into various groups is shown in Figure 7.1. The general form of the fuzzy neutron diffusion equation may be written as (Glasstone...
(Neutron diffusion : concepts and uncertainty analysis for engineers and scientists)