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in subjects: "Neutron Diffusion Equation"

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Neutron and gamma transport effects by heterogeneous core designs. [LMFBR]

The use of diffusion theory for the prediction of power production near a reactor core-blanket interface and the assumption that gammas are absorbed in situ can lead to substantial errors. This is primarily due to the breakdown of Fick's law for neutron diffusion near the core-blanket boundary, and the gamma leakage from the core into the blanket. These considerations are more pronounced in a situation where a large number of internal blanket assemblies are present, such as in the large heterog… more

Date: January 1, 1977

Creator: Lam, S.K.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

An optimized algorithm for solving the nodal diffusion method on shared memory multiprocessors

Nodal methods play a special role in reactor physics calculations. In recent papers the high computational efficiency of nodal methods has been established and the development of more efficient algorithms tailored to the advanced architectures of modern day computers proposed. The rapidly changing architectures of today's computer influence the way codes have to be programmed so that reasonable speed up and efficiency are attained. We have applied these concepts in solving the one-group neutron… more

Date: January 1, 1990

Creator: Kirk, B.L. & Azmy, Y.Y.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Variational methods in steady state diffusion problems

Classical variational techniques are used to obtain accurate solutions to the multigroup multiregion one dimensional steady state neutron diffusion equation. Analytic solutions are constructed for benchmark verification. Functionals with cubic trial functions and conservational lagrangian constraints are exhibited and compared with nonconservational functionals with respect to neutron balance and to relative flux and current at interfaces. Excellent agreement of the conservational functionals u… more

Date: January 1, 1983

Creator: Lee, C.E.; Fan, W.C.P. & Bratton, R.L.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Solving the uncommon reactor core neutronics problems

The common reactor core neutronics problems have fundamental neutron space, energy spectrum solutions. Typically the most positive eigenvalue is associated with an all-positive flux for the pseudo-steady-state condition (k/sub eff/), or the critical state is to be effected by selective adjustment of some variable such as the fuel concentration. With sophistication in reactor analysis has come the demand for solutions of other, uncommon neutronics problems. Importance functionss are needed for s… more

Date: January 1, 1980

Creator: Vondy, D.R. & Fowler, T.B.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Transport-diffusion comparisons for small core LMFBR disruptive accidents

A number of numerical experiments were performed to assess the validity of diffusion theory for calculating the reactivity state of various small core LMFBR disrupted geometries. The disrupted configurations correspond, in general, to various configurations predicted by SAS3A for transient undercooling (TUC) and transient overpower (TOP) accidents for homogeneous cores and to the ZPPR-7 configurations for heterogeneous core. In all TUC cases diffusion theory was shown to be inadequate for the c… more

Date: November 1, 1977

Creator: Tomlinson, E.T.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Validation and verification summary report for GRIMHX and TRIMHX

As part of the code Certification process, codes used by Reactor Physics to calculate values in Technical Specifications or Safety Analyses must undergo formal Validation and Verification. GRIMHX and TRIMHX are codes used in such a manner. This report summarizes and consolidates the work done to date on the Validation and Verification of these two codes. GRIMHX is a 3-D static reactor code which uses finite difference algorithms to solve the neutron diffusion equation in hex-z geometry. TRIMHX … more

Date: December 1, 1990

Creator: Trumble, E.F.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

VENTURE/PC Manual: A Multidimensional Multigroup Neutron Diffusion Code System

VENTURE/PC is a recompilation of part of the Oak Ridge BOLD VENTURE code system, which will operate on an IBM PC or compatible computer. Neutron diffusion theory solutions are obtained for multidimensional, multigroup problems. This manual contains information associated with operating the code system. The purpose of the various modules used in the code system, and the input for these modules are discussed. The PC code structure is also given. Version 2 included several enhancements not given i… more

Date: December 1, 1991

Creator: Shapiro, A.; Huria, H. C. & Cho, K. W.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport, version II. [LMFBR]

The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P/sub 1/) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several… more

Date: November 1, 1977

Creator: Vondy, D. R.; Fowler, T. B. & Cunningham, G. W.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Model for incorporating fuel swelling and clad shrinkage effects in diffusion theory calculations

A model has been devised for incorporating into the thermal feedback procedure of the PDQ few-group diffusion theory computer program the explicit calculation of depletion and temperature dependent fuel-rod shrinkage and swelling at each mesh point. The model determines the effect on reactivity of the change in hydrogen concentration caused by the variation in coolant channel area as the rods contract and expand. The calculation of fuel temperature, and hence of Doppler-broadened cross sections… more

Date: March 1, 1980

Creator: Schick, W.C. Jr.; Milani, S. & Duncombe, E.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

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

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 demonstr… more

Date: September 27, 2006

Creator: Brantley, P S

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Spin correlations in Au/sub 0. 85/Fe/sub 0. 15/

Neutron diffuse scattering measurements were used to study the spin correlations in Au-15 at. % Fe. Single-crystal data were obtained in the first Brillouin zone for an (001) orientation at temperatures of 10 K and 295 K. The results indicate free-spins at 295 K with the development of spin correlations below about 200 K. The cross section at 10 K is similar to that observed by x-rays with diffuse streaks in (210) directions and diffuse peaks both at (000) and (1 1/2 0). Intercomparison of the … more

Date: January 1, 1987

Creator: Cable, J.W.; Parette, G. & Tsunoda, Y.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Differencing asymptotic diffusion theory

A diffusion theory is presented which extends asymptotic diffusion to non-uniform material properties. Finite difference methods for the diffusion theory naturally result in jump conditions on interfaces when appropriate.

Date: June 7, 1979

Creator: Zimmerman, G.B.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Nodal method for fast reactor analysis

In this paper, a nodal method applicable to fast reactor diffusion theory analysis has been developed. This method has been shown to be accurate and efficient in comparison to highly optimized finite difference techniques. The use of an analytic solution to the diffusion equation as a means of determining accurate coupling relationships between nodes has been shown to be highly accurate and efficient in specific two-group applications, as well as in the current multigroup method.

Date: January 1, 1979

Creator: Shober, R.A.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Neutronics code VALE for two-dimensional triagonal (hexagonal) and three-dimensional geometries

This report documents the computer code VALE designed to solve multigroup neutronics problems with the diffusion theory approximation to neutron transport for a triagonal arrangement of mesh points on planes in two- and three-dimensional geometry. This code parallels the VENTURE neutronics code in the local computation system, making exposure and fuel management capabilities available. It uses and generates interface data files adopted in the cooperative effort sponsored by Reactor Physics RRT … more

Date: August 1, 1981

Creator: Vondy, D.R. & Fowler, T.B.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Alternate differencing technique for the synthetic method

Larsen and coworkers have shown that the effectiveness of the synthetic method is often determined by the techniques used to difference the diffusion equation, the equation taken, in current forms of the synthetic method, as the low-order approximation. They have also developed their own differencing technique. On the other hand, the Los Alamos (LA) approach generates point-centered diffusion difference equations, a feature which is inconvenient for the many people now using box-centered codes.… more

Date: January 1, 1983

Creator: Gelbard, E.M. & Khalil, H.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

A semi-experimental nodal synthesis method for the on-line reconstruction of three-dimensional neutron flux-shapes and reactivity

The safety and optimal performance of large, commercial, light-water reactors require the knowledge at all time of the neutron-flux distribution in the core. In principle, this information can be obtained by solving the time-dependent neutron diffusion equations. However, this approach is complicated and very expensive. Sufficiently accurate, real-time calculations (time scale of approximately one second) are not yet possible on desktop computers, even with fast-running, nodal kinetics codes. A… more

Date: December 10, 1991

Creator: Jacqmin, R. P.

Item Type: Report

Partner: UNT Libraries Government Documents Department

open access

Gain from a mixed finite-difference formulation for three-dimensional diffusion-theory neutronics

The advantage of a mixed differencing scheme for representing the diffusion theory approximation to neutron transport in three-dimensional triangular-Z geometry is demonstrated for a fast reactor. Most of the early codes employed the mesh edge difference formulation as is used in the German D3E code. A mesh centered formulation was chosen for use on a routine basis with mesh points located at the centers of the finite difference elements instead of at the corners where the internal material int… more

Date: January 1, 1981

Creator: Vondy, D.R. & Fowler, T.B.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Geometry-independent approach to coarse-mesh neutron diffusion calculations

This summary describes the development of a boundary coarse-mesh nodal method applicable to arbitrary geometries using the boundary integral technique coupled with nodal source expansion. (JDB)

Date: January 1, 1986

Creator: Kohut, P.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Blackness coefficients, effective diffusion parameters, and control rod worths for thermal reactors - methods

Simple diffusion theory cannot be used to evaluate control rod worths in thermal neutron reactors because of the strongly absorbing character of the control material. However, reliable control rod worths can be obtained within the framework of diffusion theory if the control material is characterized by a set of mesh-dependent effective diffusion parameters. For thin slab absorbers the effective diffusion parameters can be expressed as functions of a suitably-defined pair of blackness coefficie… more

Date: January 1, 1984

Creator: Bretscher, M.M.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Geometry-independent approach to coarse-mesh neutron diffusion calculations

Powerful coarse-mesh and nodal methods have been recently developed to calculate accurate node-average fluxes and eigenvalues. The nodal methods solve for the node-average flux by reducing the multidimensional diffusion problem to a coupled system of 1-D equations. These schemes are mainly limited to rectangular (xyz) nodes and cannot easily be extended to other geometries. The polynomial-based coarse-mesh methods have been applied to thetaRZ and HEXZ geometries. This summary describes the deve… more

Date: June 1, 1985

Creator: Kohut, P.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

An improved quasistatic option for the DIF3D nodal kinetics code

An improved quasistatic scheme is formulated for solution of the time-dependent DIF3D nodal equations in hexagonal-z geometry. This scheme has been implemented, along with adiabatic and point kinetics solution options, in the DIF3D hexagonal-z nodal kinetics code. The improved quasistatic method is shown to permit significant reduction in computing time, even for transients involving pronounced changes in flux shape. The achievable computing time reduction, in addition to being problem dependen… more

Date: January 1, 1991

Creator: Taiwo, T. A. & Khalil, H. S.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Performance of a parallel algorithm for solving the neutron diffusion equation on the hypercube

The one-group, steady state neutron diffusion equation in two- dimensional Cartesian geometry is solved using the nodal method technique. By decoupling sets of equations representing the neutron current continuity along the length of rows and columns of computational cells a new iterative algorithm is derived that is more suitable to solving large practical problems. This algorithm is highly parallelizable and is implemented on the Intel iPSC/2 hypercube in three versions which differ essential… more

Date: January 1, 1989

Creator: Kirk, B.L. & Azmy, Y.Y.

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Finite difference solution of the diffusion equation on coupled Eulerian and Lagrangian grids. [Improvement to CEL and CHAMP codes]

A diffusion equation modeling the flow of radiation was added to the hydrodynamic equations of two coupled Eulerian and Lagrangian finite-difference computer codes. This addition permits the extension of the range of problems to which these codes may be applied to include those in which temperatures on the order of a thousand electron volts are attained. The coupled codes are first-order-accurate shock hydrodynamics programs designed to calculate transient effects resulting from concentrations … more

Date: May 1, 1978

Creator: Hickman, R.B.

Item Type: Report

Partner: UNT Libraries Government Documents Department

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Collocation method for the solution of the neutron transport equation with both symmetric and asymmetric scattering

A collocation method is developed for the solution of the one-dimensional neutron transport equation in slab geometry with both symmetric and polarly asymmetric scattering. For the symmetric scattering case, it is found that the collocation method offers a combination of some of the best characteristics of the finite-element and discrete-ordinates methods. For the asymmetric scattering case, it is found that the computational cost of cross-section data processing under the collocation approach … more

Date: January 1, 1981

Creator: Morel, J.E.

Item Type: Report

Partner: UNT Libraries Government Documents Department