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Multigroup Methods for Neutron Diffusion Problems

Description: Abstract: "The age-diffusion is adequate to describe the neutron behavior of a very large class of nonthermal reactors (all except those whose dimensions are comparable to the neutron mean free path). Thus, a convenient means of obtaining an accurate solution to this equation is very useful for general reactor calculations. Methods for reducing the age-diffusion equation to a finite set of coupled ordinary differential equations, called multigroup equations, are described. The relative merits of several alternate schemes are discussed. The multigroup equations may be solved by iterative procedures based on an assumed spatial distribution of the fission source neutrons. In practice the initially assumed source shape is accurate enough so that additional iterations are unnecessary. Analytical and numerical methods for solving the multigroup equations with the assumed source are discussed. The adjoint equations are also reduced to multigroup form, and examples of the adjoint function in obtaining improved reactivity values are given."
Date: August 20, 1953
Creator: Hurwitz, H. & Ehrlich, R.
Partner: UNT Libraries Government Documents Department

Nodal Green’s Function Method Singular Source Term and Burnable Poison Treatment in Hexagonal Geometry

Description: An accurate and computationally efficient two or three-dimensional neutron diffusion model will be necessary for the development, safety parameters computation, and fuel cycle analysis of a prismatic Very High Temperature Reactor (VHTR) design under Next Generation Nuclear Plant Project (NGNP). For this purpose, an analytical nodal Green’s function solution for the transverse integrated neutron diffusion equation is developed in two and three-dimensional hexagonal geometry. This scheme is incorporated into HEXPEDITE, a code first developed by Fitzpatrick and Ougouag. HEXPEDITE neglects non-physical discontinuity terms that arise in the transverse leakage due to the transverse integration procedure application to hexagonal geometry and cannot account for the effects of burnable poisons across nodal boundaries. The test code being developed for this document accounts for these terms by maintaining an inventory of neutrons by using the nodal balance equation as a constraint of the neutron flux equation. The method developed in this report is intended to restore neutron conservation and increase the accuracy of the code by adding these terms to the transverse integrated flux solution and applying the nodal Green’s function solution to the resulting equation to derive a semi-analytical solution.
Date: September 1, 2009
Creator: Bingham, A.A.; Ferrer, R.M. & ougouag, A.M.
Partner: UNT Libraries Government Documents Department

The use of active learning strategies in the instruction of Reactor Physics concepts

Description: Each of the Active Learning strategies employed to teach Reactor Physics material has been or promises to be instructionally successful. The Cooperative Group strategy has demonstrated a statistically significant increase in student performance on the unit exam in teaching conceptually difficult, transport and diffusion theory material. However, this result was achieved at the expense of a modest increase in class time. The Tutorial CBI programs have enabled learning equally as well as classroom lectures without the direct intervention of an instructor. Thus, the Tutorials have been successful as homework assignments, releasing classroom time for other instruction. However, the time required for development of these tools was large, on the order of two hundred hours per hour of instruction. The initial introduction of the Case-Based strategy was roughly as effective as the traditional classroom instruction. Case-Based learning could well, after important modifications, perform better than traditional instruction. A larger percentage of the students prefer active learning strategies than prefer traditional lecture presentations. Student preferences for the active strategies were particularly strong when they believed that the strategies helped them learn the material better than they would have by using a lecture format. In some cases, students also preferred the active strategies because they were different from traditional instruction, a change of pace. Some students preferred lectures to CBI instruction, primarily because the CBI did not afford them the opportunity to question the instructor during the presentation.
Date: January 1, 2000
Creator: Robinson, Michael A.
Partner: UNT Libraries Government Documents Department

Analysis and Numerical Solution for Multi-Physics Coupling of Neutron Diffusion and Thermomechanics in Spherical Fast Burst Reactors

Description: Coupling neutronics to thermomechanics is important for the analysis of fast burst reactors, because the criticality and safety study of fast burst reactors heavily depends on the thermomechanical behavior of fuel materials. For instance, the shut down mechanism or the transition between super and sub-critical states are driven by the fuel material expansion or contraction. The material expansion or contraction is due to temperature gradient which results from fission power. In this paper, we introduce a numerical model for coupling of neutron diffusion and thermomechanics in fast burst reactors. We also provide some analysis of the coupled system. We studied material behaviors corresponding to different levels of power pulses.
Date: May 1, 2009
Creator: Kadioglu, Samet Y.; Knoll, Dana A. & Oliveira, Cassiano de
Partner: UNT Libraries Government Documents Department

Asymptotic Analysis of Time-Dependent Neutron Transport Coupled with Isotopic Depletion and Radioactive Decay

Description: We describe an asymptotic analysis of the coupled nonlinear system of equations describing time-dependent three-dimensional monoenergetic neutron transport and isotopic depletion and radioactive decay. The classic asymptotic diffusion scaling of Larsen and Keller [1], along with a consistent small scaling of the terms describing the radioactive decay of isotopes, is applied to this coupled nonlinear system of equations in a medium of specified initial isotopic composition. The analysis demonstrates that to leading order the neutron transport equation limits to the standard time-dependent neutron diffusion equation with macroscopic cross sections whose number densities are determined by the standard system of ordinary differential equations, the so-called Bateman equations, describing the temporal evolution of the nuclide number densities.
Date: September 27, 2006
Creator: Brantley, P S
Partner: UNT Libraries Government Documents Department

The use of particle tracks in problem analysis

Description: The visualization of the microscopic phenomena in a Monte Carlo simulation can improve the understanding of the problem and provide an important check on the model definition and execution. The paths, or tracks, of a sample of the Monte Carlo particles show how fission source neutrons migrate from one generation to another. The location of fission source neutrons and interactions can be shown by event markers. This new visualization is available for the Monte Carlo n-particle code MCNP due to the addition of fission source neutrons, tagged by cycle number, to the particle track (PTRAC) data. We report here on the use of this and similar information for the analysis and illustration of criticality calculations.
Date: June 1, 1995
Creator: Van Riper, K.A.; McKinney, G.W. & Urbatsch, T.
Partner: UNT Libraries Government Documents Department

Finite difference solution of the time dependent neutron group diffusion equations

Description: In this thesis two unrelated topics of reactor physics are examined: the prompt jump approximation and alternating direction checkerboard methods. In the prompt jump approximation it is assumed that the prompt and delayed neutrons in a nuclear reactor may be described mathematically as being instantaneously in equilibrium with each other. This approximation is applied to the spatially dependent neutron diffusion theory reactor kinetics model. Alternating direction checkerboard methods are a family of finite difference alternating direction methods which may be used to solve the multigroup, multidimension, time-dependent neutron diffusion equations. The reactor mesh grid is not swept line by line or point by point as in implicit or explicit alternating direction methods; instead, the reactor mesh grid may be thought of as a checkerboard in which all the ''red squares'' and '' black squares'' are treated successively. Two members of this family of methods, the ADC and NSADC methods, are at least as good as other alternating direction methods. It has been found that the accuracy of implicit and explicit alternating direction methods can be greatly improved by the application of an exponential transformation. This transformation is incompatible with checkerboard methods. Therefore, a new formulation of the exponential transformation has been developed which is compatible with checkerboard methods and at least as good as the former transformation for other alternating direction methods. (auth)
Date: August 1, 1975
Creator: Hendricks, J.S. & Henry, A.F.
Partner: UNT Libraries Government Documents Department

A Numerical Model for Coupling of Neutron Diffusion and Thermomechanics in Fast Burst Reactors

Description: We develop a numerical model for coupling of neutron diffusion adn termomechanics in order to stimulate transient behavior of a fast burst reactor. The problem involves solving a set of non-linear different equations which approximate neutron diffusion, temperature change, and material behavior. With this equation set we will model the transition from a supercritical to subcritical state and possible mechanical vibration.
Date: November 1, 2008
Creator: Kadioglu, Samet Y.; Knoll, Dana A. & Oliveira, Cassiano De
Partner: UNT Libraries Government Documents Department

Final report [on solving the multigroup diffusion equations]

Description: Progress achieved in the development of variational methods for solving the multigroup neutron diffusion equations is described. An appraisal is made of the extent to which improved variational methods could advantageously replace difference methods currently used. (DG)
Date: January 1, 1975
Creator: Birkhoff, G.
Partner: UNT Libraries Government Documents Department

Determination of diffusion parameters using response matrix theory

Description: A method is presented which provides the accuracy of the response matrix method, but without requiring the development of a response matrix reactor code. The method is used to determine diffusion parameters which, when used in conventional reactor diffusion codes, provide the same results as a response matrix reactor code. (auth)
Date: November 1, 1975
Creator: Pryor, R.J. & Sicilian, J.M.
Partner: UNT Libraries Government Documents Department

Differencing the diffusion equation on unstructured meshes in 2-D

Description: During the last few years, there has been an increased effort to devise robust transport differencings for unstructured meshes, specifically arbitrarily connected grids of polygons. Adams has investigated unstructured mesh discretization techniques for the even- and odd-parity forms of the transport equation, and for the more traditional first-order form. Conversely, development of unstructured mesh diffusion methods has been lacking. While Morel, Kershaw, Shestakov and others have done a great deal of work on diffusion schemes for logically-rectangular grids, to the author`s knowledge there has been no work on discretizations of the diffusion equation on unstructured meshes of polygons. In this paper, the authors introduce a point-centered diffusion differencing for two-dimensional unstructured meshes. They have designed the method to have the following attractive properties: (1) the scheme is equivalent to the standard five-point point-centered scheme on an orthogonal mesh; (2) the method preserves the homogeneous linear solution; (3) the method gives second-order accuracy; (4) they have strict conservation within the control volume surrounding each point; and (5) the numerical solution converges to the exact result as the mesh is refined, regardless of the smoothness of the mesh. A potential disadvantage of the method is that the diffusion matrix is asymmetric, in general.
Date: October 24, 1994
Creator: Palmer, T.S.
Partner: UNT Libraries Government Documents Department

A bibliography on finite element and related methods analysis in reactor physics computations (1971--1997)

Description: This bibliography provides a list of references on finite element and related methods analysis in reactor physics computations. These references have been published in scientific journals, conference proceedings, technical reports, thesis/dissertations and as chapters in reference books from 1971 to the present. Both English and non-English references are included. All references contained in the bibliography are sorted alphabetically by the first author`s name and a subsort by date of publication. The majority of the references relate to reactor physics analysis using the finite element method. Related topics include the boundary element method, the boundary integral method, and the global element method. All aspects of reactor physics computations relating to these methods are included: diffusion theory, deterministic radiation and neutron transport theory, kinetics, fusion research, particle tracking in finite element grids, and applications. For user convenience, many of the listed references have been categorized. The list of references is not all inclusive. In general, nodal methods were purposely excluded, although a few references do demonstrate characteristics of finite element methodology using nodal methods (usually as a non-conforming element basis). This area could be expanded. The author is aware of several other references (conferences, thesis/dissertations, etc.) that were not able to be independently tracked using available resources and thus were not included in this listing.
Date: January 1, 1998
Creator: Carpenter, D.C.
Partner: UNT Libraries Government Documents Department