This paper proposes a flux mapping method directly using the higher order harmonics (HOH) of the neutronics equation of the nominal core. The bi-orthogonality and completeness of the HOH set are studied. and they are ...This paper proposes a flux mapping method directly using the higher order harmonics (HOH) of the neutronics equation of the nominal core. The bi-orthogonality and completeness of the HOH set are studied. and they are the theoretical basis for the flux mapping method. Using the bi-orthogonality of HOH and the strict formula for eigenvalue estimation. the process and formulas for HOH calculation called as the source iteration method with source correction are derived. The analysis can predict any order of harmonics for 2-or 3-dimensional geometries.Preliminary verification of the capability for flux mapping is also given. and other applications of HOH for reactor operation analysis and failure diagnosis are underway.展开更多
Applications using higher orderharmonics (HOH) require knowledge ofthe completeness ofthe HOHfor the diffusion difference equation.This papershowsthatthe set of HOHforthefission sourceis complete ,butthat the setfor...Applications using higher orderharmonics (HOH) require knowledge ofthe completeness ofthe HOHfor the diffusion difference equation.This papershowsthatthe set of HOHforthefission sourceis complete ,butthat the setfortheflux usingthe multi group modelis notcomplete .This paperusesthe assumption thatthe set offlux vectors of HOHfor every group is complete. This assumption can be proven only forthose groups into which noscattering neutrons enter.However,itisalso shownto betrueforseveralpracticalreactor models.Analysisshows thatthe number of HOHwith non zero eigenvaluesis equaltothe numberofdifference meshes withfissile material, and thatthe eigenvalues have positive realvalues.This assumptionis valuablefor HOHapplications,butrequires furthertheoreticalstudyto verify whetheritisuniversally applicable.展开更多
文摘This paper proposes a flux mapping method directly using the higher order harmonics (HOH) of the neutronics equation of the nominal core. The bi-orthogonality and completeness of the HOH set are studied. and they are the theoretical basis for the flux mapping method. Using the bi-orthogonality of HOH and the strict formula for eigenvalue estimation. the process and formulas for HOH calculation called as the source iteration method with source correction are derived. The analysis can predict any order of harmonics for 2-or 3-dimensional geometries.Preliminary verification of the capability for flux mapping is also given. and other applications of HOH for reactor operation analysis and failure diagnosis are underway.
文摘Applications using higher orderharmonics (HOH) require knowledge ofthe completeness ofthe HOHfor the diffusion difference equation.This papershowsthatthe set of HOHforthefission sourceis complete ,butthat the setfortheflux usingthe multi group modelis notcomplete .This paperusesthe assumption thatthe set offlux vectors of HOHfor every group is complete. This assumption can be proven only forthose groups into which noscattering neutrons enter.However,itisalso shownto betrueforseveralpracticalreactor models.Analysisshows thatthe number of HOHwith non zero eigenvaluesis equaltothe numberofdifference meshes withfissile material, and thatthe eigenvalues have positive realvalues.This assumptionis valuablefor HOHapplications,butrequires furthertheoreticalstudyto verify whetheritisuniversally applicable.
