Browsing by Subject "Neutron transport theory"
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Item Development and implementation of a finite element solution of the coupled neutron transport and thermoelastic equations governing the behavior of small nuclear assemblies(2006) Wilson, Stephen Christian; Biegalski, Steven R.Small, highly enriched reactors designed for weapons effects simulations undergo extreme thermal transients during pulsed operations. The primary shutdown mechanism of these reactors -- thermal expansion of fuel material -- experiences an inertial delay resulting in a different value for the fuel temperature coefficient of reactivity during pulse operation as compared to the value appropriate for steady-state operation. The value appropriate for pulsed operation may further vary as a function of initial reactivity addition. Here we design and implement a finite element numerical method to predict the pulse operation behavior of Sandia Pulsed Reactor (SPR) II, SPR III, and a hypothetical spherical assembly with identical fuel properties without using operationally observed data in our model. These numerical results are compared to available SPR II and SPR III operational data. The numerical methods employed herein may be modified and expanded in functionality to provide both accurate characterization of the behavior of fast burst reactors of any common geometry or isotropic fuel material in the design phase, as well as a computational tool for general coupled thermomechanical-neutronics behavior in the solid state for any reactor type.Item Development and implementation of stochastic neutron transport equations and development and analysis of finite difference and Galerkin methods for approximate solution to Volterra's population equation with diffusion and noise(Texas Tech University, 1999-05) Sharp, Wyatt D.Many systems in this world are influenced by stochastic (random) processes either from within the system or from external agents. When modeling these systems, these processes and their derivatives arise naturally in a field of study called stochastic differential equations (SDEs). SDEs find application in diverse areas of engineering, chemistry, physics, economics and finance, population dynamics, pharmacology and medicine, and social sciences, to name a few. This research is divided into two parts, the common thread being SDEs. In the second chapter, a new system of SDEs for modeling the random behavior of neutron travel is derived. Numerical methods are developed to solve this system and shown to be accurate when compared with the Monte Carlo method. In the third chapter, two independent numerical methods are developed to solve Volterra's population equation with diffusion and noise. Error analyses are performed on the two methods which prove convergence of the approximations to the exact solution. Three numerical examples are given which confirm the results of the error analyses.Item Interface problems in neutron transport by a new set of quadratures(Texas Tech University, 1990-05) Coskun, ErhanIn this study, we consider the monoenergetic neutron transport equation in plane geometry. Using some exact properties of the neutron angular flux, we compute new quadrature sets and compare the numerical results on some physical problems involving interfaces with those of the Gauss-Legendre set. The numerical results show that the new quadrature sets perform better than the Gauss-Legendre set. We are presently investigating the convergence analysis of the interface problem.Item Neutron transport calculations with a new set of quadratures(Texas Tech University, 1990-05) Nielsen, Stuart ScottNot availableItem Richardson extrapolation of a positive method for numerically solving the transport equation in spherical geometry(Texas Tech University, 1989-05) Abbott, William ErvinThis thesis presents a positive method for numerically solving the neutron transport equation in spherical geometry. The method is shown to have an asymptotic error expansion allowing the use of Richardson extrapolation to improve the numerical results. Numerical results for the method are presented for several spherical models. These results are compared to exact solutions where possible and to numerical results from standard nonpositive difference methods. In addition, a convergence analysis is presented for the method.Item Simulation of reactor pulses in fast burst and externally driven nuclear assemblies(2008-05) Green, Taylor Caldwell, 1981-; Biegalski, Steven R.; Schneider, Erich A.The following research contributes original concepts to the fields of deterministic neutron transport modeling and reactor power excursion simulation. A deterministic neutron transport code was created to assess the value of new methods of determining neutron current, fluence, and flux values through the use of view factor and average path length calculations. The neutron transport code is also capable of modeling the highly anisotropic neutron transport of deuterium-tritium fusion external source neutrons using diffusion theory with the aid of a modified first collision source term. The neutron transport code was benchmarked with MCNP, an industry standard stochastic neutron transport code. Deterministic neutron transport methods allow users to model large quantities of neutrons without simulating their interactions individually. Subsequently, deterministic methods allow users to more easily couple neutron transport simulations with other physics simulations. Heat transfer and thermoelastic mechanics physics simulation modules were each developed and benchmarked using COMSOL, a commercial heat transfer and mechanics simulation software. The physics simulation modules were then coupled and used to simulate reactor pulses in fast burst and externally driven nuclear assemblies. The coupled system of equations represents a new method of simulating reactor pulses that allows users to more fully characterize pulsed assemblies. Unlike older methods of reactor pulse simulation, the method presented in this research does not require data from the operational reactor in order to simulate its behavior. The ability to simulate the coupled neutron transport and thermo-mechanical feedback present in pulsed reactors prior their construction would significantly enhance the quality of pulsed reactor pre-construction safety analysis. Additionally, a graphical user interface is created to allow users to run simulations and visualize the results using the coupled physics simulation modules.Item Stability of the diamond difference approximation in energy to the Spencer-Lewis equation of electron transport(Texas Tech University, 1987-12) Seth, Daniel L.Consider the Spencer-Lewis equation (S-L) of electron transport in an azimuthally symmetric slab geometry setting with energy restricted to a finite interval. Further, S-L is subject to boundary conditions in the form of known incident particle fluxes at the slab faces. The one-dimensional diamond difference approximation is applied in the energy variable to the continuous slowing down term (i.e., the energy derivative) of S-L, This results in a semi-discrete system of integro-differential equations in the spatial and angular variables (D.E.S-L). The numerical stability of D,E.S-L as an approximation to S-L is demonstrated for solutions of D.E,S-L that belong to an L2 function space. The system of integro-differential equations may be rewritten as a system of integral equations. Under certain reasonable conditions on the data, the existence-uniqueness of solutions of the integral equations in a Banach space of square integrable functions with weighted norms is established. This implies the existence of L2 solutions of the integral equations. Under further assumptions on the data, the solutions of the integral equations are shown to be the required solutions of the integro-differential equations as well. Moreover, if the data are all bounded, the solutions are bounded.