A new three-dimensional neutron diffusion code named TRIVAC was set up using advanced discretizat... more A new three-dimensional neutron diffusion code named TRIVAC was set up using advanced discretization algorithms and improved iteration strategies. The two variable order discretization algorithms used in TRIVAC will be presented. These are based, respectively, on the variational and nodal collocation techniques. These algorithms will be shown to produce reconstructible solutions which are upper and lower limits of the exact solution. The eigenvalue matrix system is solved using an ADI preconditioning of the power method in conjunction with a symmetric variational acceleration technique. Validation results are reported for the IAEA twoand three-dimensional benchmarks, and for a two-dimensional
ABSTRACT In order to better optimize the fuel energy efficiency in PWRs, the burnup distribution ... more ABSTRACT In order to better optimize the fuel energy efficiency in PWRs, the burnup distribution has to be known as accurately as possible, ideally in each pin. However, this level of detail is lost when core calculations are performed with homogenized cross-sections. The pin power reconstruction (PPR) method can be used to get back those levels of details as accurately as possible in a small additional computing time frame compared to classical core calculations. Such a de-homogenization technique for core calculations using arbitrarily homogenized fuel assembly geometries was presented originally by Fliscounakis et al. In our work, the same methodology was implemented in the open-source neutronic codes DRAGON5 and DONJON5. The new type of Selengut homogenization, called macro-calculation water gap, also proposed by Fliscounakis et al. was implemented. Some important details on the methodology were emphasized in order to get precise results.
Calculations based on the characteristics method and different self-shielding models are presente... more Calculations based on the characteristics method and different self-shielding models are presented for 9 × 9 BWR assemblies fully loaded with MOX fuel. The geometry of these assemblies was recovered from the BASALA experimental program. We have focused our study on three configurations simulating the different voiding conditions that an assembly can undergo in a BWR pressure vessel.
ABSTRACT Analytic reductions are used to simplify evaluation of the transmission probabilities in... more ABSTRACT Analytic reductions are used to simplify evaluation of the transmission probabilities in a hexahedron and of the five independent probabilities (two transmission and three leakage probabilities) that are required for a finite tube. The four- and five-dimensional numerical integrations required for transmission and leakage probabilities are reduced to one and two dimensions, respectively.
... Creator/Author, Hebert, A. ; Benoist, P. (Commissariat a l'Energie Atomique, DRN/DEMT-CE... more ... Creator/Author, Hebert, A. ; Benoist, P. (Commissariat a l'Energie Atomique, DRN/DEMT-CEN/ Saclay, 91191 Gif-sur ... Subject, 21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS; PWR TYPE REACTORS; DESIGN; OPERATION; CONTROL ROD WORTHS; CROSS ...
A practical collision probability model is presented for the description of geometries with many ... more A practical collision probability model is presented for the description of geometries with many levels of heterogeneity. Regular regions of the macrogeometry are assumed to contain a stochastic mixture of spherical grains or cylindrical tubes. Simple expressions for the collision probabilities in the global geometry are obtained as a function of the collision probabilities in the macro- and microgeometries. This model was successfully implemented in the collision probability kernel of the APOLLO-1, APOLLO-2, and DRAGON lattice codes for the description of a broad range of reactor physics problems. Resonance self-shielding and depletion calculations in the microgeometries are possible because each microregion is explicitly represented.
ABSTRACT The interface current method is generally used in supercell codes to accelerate computat... more ABSTRACT The interface current method is generally used in supercell codes to accelerate computation of the collision probabilities needed for resolution of the integral neutron transport equation. This method was used to compute all the collision probabilities for a cluster geometry. The resulting complete collision probabilities were then compared with those computed using a direct method. The interface current method was much faster than the direct method for computing collision probabilities, with a loss in precision within the limits of error acceptable for reactor design calculations.
Transactions of the American Nuclear Society, Dec 30, 1995
ABSTRACT Most lattice codes initially designed for pressurized water reactor (PWR) or boiling wat... more ABSTRACT Most lattice codes initially designed for pressurized water reactor (PWR) or boiling water reactor (BWR) assembly analysis can only treat approximately two-dimensional (2-D) Canadian deuterium uranium (CANDU) reactor cluster geometries. Moreover, they generally lack the three-dimensional (3-D) supercell option required for CANDU control device analysis. The lattice code DRAGON has all the features that are necessary for a combined CANDU cell and supercell calculations as well as for PWR or BWR lattice analysis.
A new ray-tracing method for the calculation of collision probabilities within arbitrary three-di... more A new ray-tracing method for the calculation of collision probabilities within arbitrary three-dimensional geometries has been developed. This method is used to discretize the neutron transport equation for the heterogenous rectangular cells containing zones of mixed cylindrical and rectangular geometry. For multicell applications, the interface current (IC) method provides the coupling between cells. The solution to the IC equations over multicell domains consisting of rectangular three-dimensional cells is improved by using an alternative direction implicit scheme with variational acceleration. Results indicate comparisons of this technique with SHETAN for simple geometries and the analysis of a three-dimensional extension of a two-dimensional 15 x 15 pressurized water reactor benchmark problem.
Nuclear Science and Engineering the Journal of the American Nuclear Society, Sep 30, 1993
ABSTRACT The integral transport equation is solved in periodic slab lattices in the case where a ... more ABSTRACT The integral transport equation is solved in periodic slab lattices in the case where a critical buckling search is performed. First, the angular flux is factorized into two parts: a periodic microscopic flux and a macroscopic form with no angular dependence. The macroscopic form only depends on a buckling vector with a given orientation. The critical buckling norm along with the corresponding microscopic flux are obtained using anisotropic collision probability calculations that are repeated until criticality is achieved. This procedure allows the periodic boundary conditions of slab lattices to be taken into account using closed-form contributions obtained from the cyclic-tracking technique, without resorting to infinite series of exponential-integral evaluations. Numerical results are presented for one-group heterogeneous problems with isotropic and anisotropic scattering kernels, some of which include void slit regions.
In the context of the ACRä (Advanced CANDU Reactor), 3D transport calculations are required in or... more In the context of the ACRä (Advanced CANDU Reactor), 3D transport calculations are required in order to simulate the reactivity devices located perpendicularly to the fuel channels. The computational scheme that is usually used for CANDU-6 and ACR reactors is based on a simplified supercell geometry in which the fuel clusters and devices are replaced by annuli. Recently, an exact modeling of 3D supercell configurations was introduced within the framework of the ACR calculations. However, with such a model, fine meshing requirements lead to problems that are very demanding in terms of computational resources.
A new three-dimensional neutron diffusion code named TRIVAC was set up using advanced discretizat... more A new three-dimensional neutron diffusion code named TRIVAC was set up using advanced discretization algorithms and improved iteration strategies. The two variable order discretization algorithms used in TRIVAC will be presented. These are based, respectively, on the variational and nodal collocation techniques. These algorithms will be shown to produce reconstructible solutions which are upper and lower limits of the exact solution. The eigenvalue matrix system is solved using an ADI preconditioning of the power method in conjunction with a symmetric variational acceleration technique. Validation results are reported for the IAEA twoand three-dimensional benchmarks, and for a two-dimensional
ABSTRACT In order to better optimize the fuel energy efficiency in PWRs, the burnup distribution ... more ABSTRACT In order to better optimize the fuel energy efficiency in PWRs, the burnup distribution has to be known as accurately as possible, ideally in each pin. However, this level of detail is lost when core calculations are performed with homogenized cross-sections. The pin power reconstruction (PPR) method can be used to get back those levels of details as accurately as possible in a small additional computing time frame compared to classical core calculations. Such a de-homogenization technique for core calculations using arbitrarily homogenized fuel assembly geometries was presented originally by Fliscounakis et al. In our work, the same methodology was implemented in the open-source neutronic codes DRAGON5 and DONJON5. The new type of Selengut homogenization, called macro-calculation water gap, also proposed by Fliscounakis et al. was implemented. Some important details on the methodology were emphasized in order to get precise results.
Calculations based on the characteristics method and different self-shielding models are presente... more Calculations based on the characteristics method and different self-shielding models are presented for 9 × 9 BWR assemblies fully loaded with MOX fuel. The geometry of these assemblies was recovered from the BASALA experimental program. We have focused our study on three configurations simulating the different voiding conditions that an assembly can undergo in a BWR pressure vessel.
ABSTRACT Analytic reductions are used to simplify evaluation of the transmission probabilities in... more ABSTRACT Analytic reductions are used to simplify evaluation of the transmission probabilities in a hexahedron and of the five independent probabilities (two transmission and three leakage probabilities) that are required for a finite tube. The four- and five-dimensional numerical integrations required for transmission and leakage probabilities are reduced to one and two dimensions, respectively.
... Creator/Author, Hebert, A. ; Benoist, P. (Commissariat a l'Energie Atomique, DRN/DEMT-CE... more ... Creator/Author, Hebert, A. ; Benoist, P. (Commissariat a l'Energie Atomique, DRN/DEMT-CEN/ Saclay, 91191 Gif-sur ... Subject, 21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS; PWR TYPE REACTORS; DESIGN; OPERATION; CONTROL ROD WORTHS; CROSS ...
A practical collision probability model is presented for the description of geometries with many ... more A practical collision probability model is presented for the description of geometries with many levels of heterogeneity. Regular regions of the macrogeometry are assumed to contain a stochastic mixture of spherical grains or cylindrical tubes. Simple expressions for the collision probabilities in the global geometry are obtained as a function of the collision probabilities in the macro- and microgeometries. This model was successfully implemented in the collision probability kernel of the APOLLO-1, APOLLO-2, and DRAGON lattice codes for the description of a broad range of reactor physics problems. Resonance self-shielding and depletion calculations in the microgeometries are possible because each microregion is explicitly represented.
ABSTRACT The interface current method is generally used in supercell codes to accelerate computat... more ABSTRACT The interface current method is generally used in supercell codes to accelerate computation of the collision probabilities needed for resolution of the integral neutron transport equation. This method was used to compute all the collision probabilities for a cluster geometry. The resulting complete collision probabilities were then compared with those computed using a direct method. The interface current method was much faster than the direct method for computing collision probabilities, with a loss in precision within the limits of error acceptable for reactor design calculations.
Transactions of the American Nuclear Society, Dec 30, 1995
ABSTRACT Most lattice codes initially designed for pressurized water reactor (PWR) or boiling wat... more ABSTRACT Most lattice codes initially designed for pressurized water reactor (PWR) or boiling water reactor (BWR) assembly analysis can only treat approximately two-dimensional (2-D) Canadian deuterium uranium (CANDU) reactor cluster geometries. Moreover, they generally lack the three-dimensional (3-D) supercell option required for CANDU control device analysis. The lattice code DRAGON has all the features that are necessary for a combined CANDU cell and supercell calculations as well as for PWR or BWR lattice analysis.
A new ray-tracing method for the calculation of collision probabilities within arbitrary three-di... more A new ray-tracing method for the calculation of collision probabilities within arbitrary three-dimensional geometries has been developed. This method is used to discretize the neutron transport equation for the heterogenous rectangular cells containing zones of mixed cylindrical and rectangular geometry. For multicell applications, the interface current (IC) method provides the coupling between cells. The solution to the IC equations over multicell domains consisting of rectangular three-dimensional cells is improved by using an alternative direction implicit scheme with variational acceleration. Results indicate comparisons of this technique with SHETAN for simple geometries and the analysis of a three-dimensional extension of a two-dimensional 15 x 15 pressurized water reactor benchmark problem.
Nuclear Science and Engineering the Journal of the American Nuclear Society, Sep 30, 1993
ABSTRACT The integral transport equation is solved in periodic slab lattices in the case where a ... more ABSTRACT The integral transport equation is solved in periodic slab lattices in the case where a critical buckling search is performed. First, the angular flux is factorized into two parts: a periodic microscopic flux and a macroscopic form with no angular dependence. The macroscopic form only depends on a buckling vector with a given orientation. The critical buckling norm along with the corresponding microscopic flux are obtained using anisotropic collision probability calculations that are repeated until criticality is achieved. This procedure allows the periodic boundary conditions of slab lattices to be taken into account using closed-form contributions obtained from the cyclic-tracking technique, without resorting to infinite series of exponential-integral evaluations. Numerical results are presented for one-group heterogeneous problems with isotropic and anisotropic scattering kernels, some of which include void slit regions.
In the context of the ACRä (Advanced CANDU Reactor), 3D transport calculations are required in or... more In the context of the ACRä (Advanced CANDU Reactor), 3D transport calculations are required in order to simulate the reactivity devices located perpendicularly to the fuel channels. The computational scheme that is usually used for CANDU-6 and ACR reactors is based on a simplified supercell geometry in which the fuel clusters and devices are replaced by annuli. Recently, an exact modeling of 3D supercell configurations was introduced within the framework of the ACR calculations. However, with such a model, fine meshing requirements lead to problems that are very demanding in terms of computational resources.
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Papers by Alain Hebert