Three-Dimensional Nodal Diffusion and Transport Theory Methods for Hexagonal-<i>z</i>Geometry

Wagner, M.

doi:10.13182/nse89-a23690

Cited by 59 publications

(10 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Work by M. R. Wagner ignored these discontinuity terms in his solution and used low order polynomials to approximate the averaged 1-D source of the transverseintegrated diffusion equation. 2 The numerical accuracy obtained for the flux was comparable to the results achieved by Lawrence, but the neutron balance condition was not being fully achieved, and thus fidelity and accuracy suffered. The code HEXPEDITE is an improvement over the work developed by Wagner.…”

Section: Introductionmentioning

confidence: 82%

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

Bingham¹,

Ferrer²,

Ougouag³

2009

View full text Add to dashboard Cite

An accurate and computationally efficient two-or three-dimensional (2-D or 3-D) neutron diffusion model will be needed to develop, compute safety parameters, and analyze the fuel cycle of a prismatic very high temperature reactor design under the Next Generation Nuclear Plant. To meet this need, an analytical Nodal Green's function method for the transverse integrated neutron diffusion equation was developed in 2-D and 3-D hexagonal geometry. This scheme is incorporated into the algorithm of the HEXPEDITE, a code first developed by Fitzpatrick and Ougouag. HEXPEDITE neglects discontinuous terms that arise in the transverse leakage because of the transverse integration procedure application to hexagonal geometry, and cannot account for the localized effects of burnable poisons across nodal boundaries. The test code being developed for this document accounts for these terms by maintaining a strict 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 and fidelity of the code by adding the effect of the discontinuous terms to the transverse integrated flux solution. This is achieved through the use of the Nodal Green's function method to the complete equation resulting from the transverse integration procedure. The result is a rigorous semi-analytical solution. The new treatment of the burnable applies a similar approach, but with singular terms of pre-computed strength, based on blackness theory. vi vii ACKNOWLEDGEMENTS

show abstract

Section: Introductionmentioning

confidence: 82%

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

Bingham¹,

Ferrer²,

Ougouag³

2009

View full text Add to dashboard Cite

show abstract

“…[1][2][3] In the NEACRP 3-D neutron transport benchmarks, these codes were applied to the smallsize FBR core with hexagonal geometry (the KNK-II core), and the numerical results of these codes were summarized by comparing with the reference Monte Carlo solutions. 4) From the comparisons, it was found that the accuracy of these codes was not satisfactory.…”

Section: Introductionmentioning

confidence: 99%

Effect of Polynomial Expansion Order of Intranode Flux Treatment in Nodal S_NTransport Calculation Code NSHEX for Large-Size Fast Power Reactor Core Analysis

Sugino¹,

Kugo²

2011

Journal of Nuclear Science and Technology

View full text Add to dashboard Cite

The nodal discrete ordinates (S N ) transport calculation code for three-dimensional hexagonal geometry NSHEX treats intranode flux distribution using a polynomial series and considers the angular dependence of flux by the S N method. For the improvement of calculation accuracy of NSHEX for practical use to large-size fast reactor plants, the maximum order of the polynomial series is extended from two to six. In order to check the effect of the polynomial expansion order, NSHEX is applied to the intermediate-size fast power reactor core ''Monju'' and the large-size one ''Super Phenix,'' including various control rod insertion conditions. From the application, it is found that extension of the polynomial expansion order is effective especially for the large-size core ''Super Phenix'' under the control-rod-inserted condition.

show abstract

“…Some of them, such as the NEM , use a transverse integration procedure over the hexagonal nodes taking advantage of the superior calculation efficiency of the transverse-integrated nodal methods. However, when applied to a hexagon, the transverse-integrated nodal diffusion equation contains non-physical singular terms, as is explained in (Lawrence, 1986) and (Wagner, 1989); then, some kind of approximation has to be introduced. These approximations significantly degrade the accuracy of the method.…”

Section: Introductionmentioning

confidence: 99%

Extension of the analytic nodal diffusion solver ANDES to triangular-Z geometry and coupling with COBRA-IIIc for hexagonal core analysis

Lozano¹,

Jiménez²,

García-Herranz³

et al. 2010

Annals of Nuclear Energy

View full text Add to dashboard Cite

In this paper the extensión of the multigroup nodal diffusion code ANDES, based on the Analytic Coarse Mesh Finite Difference (ACMFD) method, from Cartesian to hexagonal geometry is presented, as well as its coupling with the thermal-hydraulic (TH) code COBRA-IIIc for hexagonal core analysis.In extending the ACMFD method to hexagonal assemblies, triangular-Z nodes are used. In the radial plañe, a direct transverse integration procedure is applied along the three directions that are orthogonal to the triangle interfaces. The triangular nodalization avoids the singularities, that appear when applying transverse integration to hexagonal nodes, and allows the advantage of the mesh subdivisión capabilities implicit within that geometry. As for the thermal-hydraulics, the extensión of the coupling scheme to hexagonal geometry has been performed with the capability to model the core using either assemblywise channels (hexagonal mesh) or a higher refinement with six channels per fuel assembly (triangular mesh). Achieving this level of TH mesh refinement with COBRA-IIIc code provides a better estimation of the in-core 3D flow distribution, improving the TH core modelling.The neutronics and thermal-hydraulics coupled code, ANDES/COBRA-IIIc, previously verified in Cartesian geometry core analysis, can also be applied now to full three-dimensional VVER core problems, as well as to other thermal and fast hexagonal core designs. Verification results are provided, corresponding to the different cases of the OECD/NEA-NSC VVER-1000 Coolant Transient Benchmarks.

show abstract

Three-Dimensional Nodal Diffusion and Transport Theory Methods for Hexagonal-zGeometry

Cited by 59 publications

References 6 publications

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

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

Effect of Polynomial Expansion Order of Intranode Flux Treatment in Nodal S_NTransport Calculation Code NSHEX for Large-Size Fast Power Reactor Core Analysis

Extension of the analytic nodal diffusion solver ANDES to triangular-Z geometry and coupling with COBRA-IIIc for hexagonal core analysis

Contact Info

Product

Resources

About

Three-Dimensional Nodal Diffusion and Transport Theory Methods for Hexagonal-zGeometry

Cited by 59 publications

References 6 publications

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

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

Effect of Polynomial Expansion Order of Intranode Flux Treatment in Nodal SNTransport Calculation Code NSHEX for Large-Size Fast Power Reactor Core Analysis

Extension of the analytic nodal diffusion solver ANDES to triangular-Z geometry and coupling with COBRA-IIIc for hexagonal core analysis

Contact Info

Product

Resources

About

Effect of Polynomial Expansion Order of Intranode Flux Treatment in Nodal S_NTransport Calculation Code NSHEX for Large-Size Fast Power Reactor Core Analysis