China
Africa
Explore chapters and articles related to this topic
An Introduction to Neutron Transport Theory
Published in Robert E. Masterson, Introduction to Nuclear Reactor Physics, 2017
Unlike the neutron diffusion equation, the neutron transport equation is based on the premise that the flow of particles in a material is a function of angle as well as a function of the usual spatial and temporal variables (energy, spatial position, and time). In other words, instead of the neutron flux being a function of just x, y, z, E, and t, it can also be a function of θ and ϕ (see Figure 22.1 to see how this can occur). This means that the particle flow at any point in time is a function of seven independent variables instead of just five. In its most complete form, these two additional angular variables make the neutron transport equation approximately 100 times more difficult to solve either analytically or numerically than the neutron diffusion equation. Basically, this is true because the neutron current J(x, y, z, E, t) can no longer be written as a simple constant (e.g., the diffusion coefficient D) multiplied by the negative gradient of the particle flux along each coordinate direction, for example,In this chapter, we would like to derive the neutron transport equation in its most common form. Sometimes, the neutron transport equation is also called the Boltzmann transport equation. These equations are similar to each other, but the Boltzmann transport equation can be applied to other types of particles such as photons. In other words, it can be applied to any particle that does not have an electric charge. (Only the scattering kernel is different.) We will then present several methods for obtaining approximate solutions to the neutron transport equation. To simplify our discussion, we will limit most of our discussion to just one spatial dimension. This limitation does not alter the basic approach that can be used for more than one dimension. However, geometries with more than one spatial dimension can lead to considerable algebraic complexity, and it is our intention to avoid as much of this complexity as possible in order to focus on the underlying principles that neutron transport theory employs.
Verification and Validation of RAPID Formulations and Algorithms Based on Dosimetry Measurements at the JSI TRIGA Mark-II Reactor
Published in Nuclear Science and Engineering, 2021
Valerio Mascolino, Alireza Haghighat, Luka Snoj
Neutron transport simulations are usually performed utilizing one of two approaches: the deterministic method or the stochastic (Monte Carlo) method. The deterministic method consists of the discretization and solution of the integro-differential linear Boltzmann equation (LBE) for neutrons on a computer and is capable of obtaining detailed three-dimensional (3-D) nuclear quantities for the entirety of the system being modeled and analyzed. However, it requires careful examination of the numerical techniques to be used for treating different variables, such as the differencing scheme for geometry discretization, the multigroup approach for the energy variable, and the identification of a suitable angular quadrature. Often, the simulation of real-world 3-D reactor problems requires a prohibitive amount of memory and time on parallel processors. On the other hand, Monte Carlo methods do not rely on geometrical, energy, or direction discretizations and can be very precise. However, they require significant computation times to obtain precise results in small or low-interaction regions.1 In addition, these methods have been demonstrated to be plagued by unavoidable source convergence issues when utilized for criticality calculations.2–5
Rattlesnake: A MOOSE-Based Multiphysics Multischeme Radiation Transport Application
Published in Nuclear Technology, 2021
Yaqi Wang, Sebastian Schunert, Javier Ortensi, Vincent Laboure, Mark DeHart, Zachary Prince, Fande Kong, Jackson Harter, Paolo Balestra, Frederick Gleicher
Nuclear reactors demonstrate multiple simultaneous physical phenomena that are often tightly coupled in terms of their influence on each other. The behavior of nuclear reactors is governed by many different physics that occur on varying length and time scales. Simulation of such systems by direct representation of the coupling of sets of phenomena is often described as multiphysics. In nuclear reactor systems, these physics include neutron, gamma, and thermal radiation transport, fluid mechanics, solid mechanics, thermal conduction, radiation damage, etc. Among these, neutron transport, or neutronics, is the driving force and is unique to nuclear reactors. The central purpose of neutronics simulations is to determine the distribution of the neutron population in a system, which consequently dictates the power density with various neutron-induced reactions. The power density drives temperature distribution, stress, and displacement fields. Fission products and radiation damage from neutron reactions lead to changes in the thermomechanical properties of nuclear fuel and structural materials. In turn, changes in the multiphysics state variables, such as temperature and density, affect the neutron distribution, instilling a feedback loop for the behavior of multiphysics systems.
Multifunctional Neutronics Calculation Methodology and Program for Nuclear Design and Radiation Safety Evaluation
Published in Fusion Science and Technology, 2018
Neutron transport is the process in which neutrons propagate through the atoms in a physical system. This includes neutron motions and interactions of neutrons with materials. The traditional neutron transport methods can be classified into two categories: MC approach and deterministic approach. The MC approach is adopted as the main approach for fusion analysis due to its high calculation precision and strong geometric adaptability. However, it was indicated that two major challenges exist in the MC simulation of neutron transport13: (1) it is nearly impossible to obtain accurate results with good precision in reasonable time with modern computing resource and (2) the modeling of complex heterogeneous facilities requires enormous efforts. Facing these challenges, the FDS Team has proposed integrated irregular modeling theory and calculation methods for complex nuclear systems. It includes irregular modeling methods concerning the synergistic effect of direction, space, material, and neutron source14–16; MC and deterministic coupling model with self-adaptive transition region; advanced calculation approaches with feature prejudgment17,18; and discrete ordinates nodal transport method with coarse spatial meshes for curvilinear geometries based on source conversion.19 These innovative theories and methods make it realistic to perform the accurate and efficient three-dimensional (3-D) nuclear design and safety evaluation for complex nuclear systems. Short summaries of the theories/methods are present in Secs. II.A, II.B, and II.C.