Methodology for Discontinuity Factors Generation for Simplified P<sub>3</sub> Solver Based on Nodal Expansion Formulation
The Simplified Spherical Harmonic (SP<sub>N</sub>) approximation was first introduced as a three-dimensional (3D) extension of the plane-geometry Spherical Harmonic (P<sub>N</sub>) equations. A third order SP<sub>N</sub> (SP<sub>3</sub>) solver, recent...
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MDPI AG
2021-10-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/14/20/6478 |
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| author | Yuchao Xu Jason Hou Kostadin Ivanov |
| author_facet | Yuchao Xu Jason Hou Kostadin Ivanov |
| author_sort | Yuchao Xu |
| collection | DOAJ |
| description | The Simplified Spherical Harmonic (SP<sub>N</sub>) approximation was first introduced as a three-dimensional (3D) extension of the plane-geometry Spherical Harmonic (P<sub>N</sub>) equations. A third order SP<sub>N</sub> (SP<sub>3</sub>) solver, recently implemented in the Nodal Expansion Method (NEM), has shown promising performance in the reactor core neutronics simulations. This work is focused on the development and implementation of the transport-corrected interface and boundary conditions in an NEM SP<sub>3</sub> solver, following recent published work on the rigorous SP<sub>N</sub> theory for piecewise homogeneous regions. A streamlined procedure has been developed to generate the flux zero and second order/moment discontinuity factors (DFs) of the generalized equivalence theory to minimize the error introduced by pin-wise homogenization. Moreover, several colorset models with varying sizes and configurations are later explored for their capability of generating DFs that can produce results equivalent to that using the whole-core homogenization model for more practical implementations. The new developments are tested and demonstrated on the C5G7 benchmark. The results show that the transport-corrected SP<sub>3</sub> solver shows general improvements to power distribution prediction compared to the basic SP<sub>3</sub> solver with no DFs or with only the zeroth moment DF. The complete equivalent calculations using the DFs can almost reproduce transport solutions with high accuracy. The use of equivalent parameters from larger size colorset models show a slightly reduced prediction error than that using smaller colorset models in the whole-core calculations. |
| first_indexed | 2024-03-10T06:36:56Z |
| format | Article |
| id | doaj.art-b624724c7c824df8867d12b5d0cfd37c |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T06:36:56Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-b624724c7c824df8867d12b5d0cfd37c2023-11-22T18:03:45ZengMDPI AGEnergies1996-10732021-10-011420647810.3390/en14206478Methodology for Discontinuity Factors Generation for Simplified P<sub>3</sub> Solver Based on Nodal Expansion FormulationYuchao Xu0Jason Hou1Kostadin Ivanov2Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695, USADepartment of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695, USADepartment of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695, USAThe Simplified Spherical Harmonic (SP<sub>N</sub>) approximation was first introduced as a three-dimensional (3D) extension of the plane-geometry Spherical Harmonic (P<sub>N</sub>) equations. A third order SP<sub>N</sub> (SP<sub>3</sub>) solver, recently implemented in the Nodal Expansion Method (NEM), has shown promising performance in the reactor core neutronics simulations. This work is focused on the development and implementation of the transport-corrected interface and boundary conditions in an NEM SP<sub>3</sub> solver, following recent published work on the rigorous SP<sub>N</sub> theory for piecewise homogeneous regions. A streamlined procedure has been developed to generate the flux zero and second order/moment discontinuity factors (DFs) of the generalized equivalence theory to minimize the error introduced by pin-wise homogenization. Moreover, several colorset models with varying sizes and configurations are later explored for their capability of generating DFs that can produce results equivalent to that using the whole-core homogenization model for more practical implementations. The new developments are tested and demonstrated on the C5G7 benchmark. The results show that the transport-corrected SP<sub>3</sub> solver shows general improvements to power distribution prediction compared to the basic SP<sub>3</sub> solver with no DFs or with only the zeroth moment DF. The complete equivalent calculations using the DFs can almost reproduce transport solutions with high accuracy. The use of equivalent parameters from larger size colorset models show a slightly reduced prediction error than that using smaller colorset models in the whole-core calculations.https://www.mdpi.com/1996-1073/14/20/6478transport-corrected SP<sub>3</sub>nodal expansion methodgeneralized equivalence theorydiscontinuity factors |
| spellingShingle | Yuchao Xu Jason Hou Kostadin Ivanov Methodology for Discontinuity Factors Generation for Simplified P<sub>3</sub> Solver Based on Nodal Expansion Formulation Energies transport-corrected SP<sub>3</sub> nodal expansion method generalized equivalence theory discontinuity factors |
| title | Methodology for Discontinuity Factors Generation for Simplified P<sub>3</sub> Solver Based on Nodal Expansion Formulation |
| title_full | Methodology for Discontinuity Factors Generation for Simplified P<sub>3</sub> Solver Based on Nodal Expansion Formulation |
| title_fullStr | Methodology for Discontinuity Factors Generation for Simplified P<sub>3</sub> Solver Based on Nodal Expansion Formulation |
| title_full_unstemmed | Methodology for Discontinuity Factors Generation for Simplified P<sub>3</sub> Solver Based on Nodal Expansion Formulation |
| title_short | Methodology for Discontinuity Factors Generation for Simplified P<sub>3</sub> Solver Based on Nodal Expansion Formulation |
| title_sort | methodology for discontinuity factors generation for simplified p sub 3 sub solver based on nodal expansion formulation |
| topic | transport-corrected SP<sub>3</sub> nodal expansion method generalized equivalence theory discontinuity factors |
| url | https://www.mdpi.com/1996-1073/14/20/6478 |
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