Abstract
The main objective of this work is to solve the neutron transport equation in one and two dimensions (slab geometry and X Y geometry, respectively), with no time dependence, for BWR assemblies using nodal methods. In slab geometry, the nodal methods here used are the polynomial continuous (CMPk) and discontinuous (DMPk) families but only the Linear Continuous (also known as Diamond Difference), the Quadratic Continuous (QC), the Cubic Continuous (CC), the Step Discontinuous (also known as Backward Euler), the Linear Discontinuous (LD) and the Quadratic Discontinuous (QD) were considered. In all these schemes the unknown function, the angular neutron flux, is approximated as a sum of basis functions in terms of Legendre polynomials, associated to the values of the neutron flux in the edges (left, right, or both) and the Legendre moments in the cell, depending on the nodal scheme used. All these schemes were implemented in a computer program developed in previous thesis works and known with the name TNX. This program was modified for the purposes of this work. The program discreetizes the domain of concern in one dimension and determines numerically the angular neutron flux for each point of the discretization when the number of energy groups
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Citation Formats
Xolocostli M, J V.
Solution of the transport equation in stationary state, in one and two dimensions, for BWR assemblies using nodal methods; Solucion de la ecuacion de transporte en estado estacionario, en 1 y 2 dimensiones, para ensambles tipo BWR usando metodos nodales.
Mexico: N. p.,
2002.
Web.
Xolocostli M, J V.
Solution of the transport equation in stationary state, in one and two dimensions, for BWR assemblies using nodal methods; Solucion de la ecuacion de transporte en estado estacionario, en 1 y 2 dimensiones, para ensambles tipo BWR usando metodos nodales.
Mexico.
Xolocostli M, J V.
2002.
"Solution of the transport equation in stationary state, in one and two dimensions, for BWR assemblies using nodal methods; Solucion de la ecuacion de transporte en estado estacionario, en 1 y 2 dimensiones, para ensambles tipo BWR usando metodos nodales."
Mexico.
@misc{etde_20453813,
title = {Solution of the transport equation in stationary state, in one and two dimensions, for BWR assemblies using nodal methods; Solucion de la ecuacion de transporte en estado estacionario, en 1 y 2 dimensiones, para ensambles tipo BWR usando metodos nodales}
author = {Xolocostli M, J V}
abstractNote = {The main objective of this work is to solve the neutron transport equation in one and two dimensions (slab geometry and X Y geometry, respectively), with no time dependence, for BWR assemblies using nodal methods. In slab geometry, the nodal methods here used are the polynomial continuous (CMPk) and discontinuous (DMPk) families but only the Linear Continuous (also known as Diamond Difference), the Quadratic Continuous (QC), the Cubic Continuous (CC), the Step Discontinuous (also known as Backward Euler), the Linear Discontinuous (LD) and the Quadratic Discontinuous (QD) were considered. In all these schemes the unknown function, the angular neutron flux, is approximated as a sum of basis functions in terms of Legendre polynomials, associated to the values of the neutron flux in the edges (left, right, or both) and the Legendre moments in the cell, depending on the nodal scheme used. All these schemes were implemented in a computer program developed in previous thesis works and known with the name TNX. This program was modified for the purposes of this work. The program discreetizes the domain of concern in one dimension and determines numerically the angular neutron flux for each point of the discretization when the number of energy groups and regions are known starting from an initial approximation for the angular neutron flux being consistent with the boundary condition imposed for a given problem. Although only problems with two-energy groups were studied the computer program does not have limitations regarding the number of energy groups and the number of regions. The two problems analyzed with the program TNX have practically the same characteristics (fuel and water), with the difference that one of them has a control rod. In the part corresponding to two-dimensional problems, the implemented nodal methods were those designated as hybrids that consider not only the edge and cell Legendre moments, but also the values of the neutron flux in the corner points. In this geometry nodal, continuous and discontinuous schemes were used. For the continuos schemes, only the Bi Quadratic (BiQ) and the Bi Cubic (BiC) were considered. In the case of the discontinuous ones two nodal schemes were considered, namely the Discontinuous Bi Linear (DBiL) and Discontinuous Bi Quadratic (DBiQ). The nodal schemes applied use from 4 up to 16 interpolation parameters per cell. These schemes are-defined for a set D{sub c} of interpolation parameters and a polynomial space S{sub h} corresponding to each one of the nodal schemes considered. All these four nodal hybrid schemes were implemented in a computer program called TNHXY starting from the computer program TNXY developed in previous thesis works. Several subroutines wae added to calculate the average neutron flux for each cell and for each energy group, generating two versions, one for the continuous schemes and one for the discontinuous schemes. For this geometry, two benchmark problems of the ANL-7416 document were analyzed. They are 7x7 BWR fuel assemblies, one without control rod and the other one with control rod. The computer program was also applied to a MOX assembly proposed by the Nuclear Energy Agency and it is considered as a reference problem. The results obtained for the one-dimensional problems using TNX for the effective multiplication factor were compared with the ones obtained with the code ANISN/PC. TNX code shows a faster convergence within four significant figures for the case with no control rod and three significant figures for the case with control rod (using double precision). These results suggest TNX is a very useful tool for this kind of calculations. For X Y geometry, the results obtained with TNHXY were compared with those calculated with the code TWOTRAN. To get these results, several spatial (1x1, 2x2, 4x4 per cell) and angular meshes (S{sub 2}, S{sub 4}, S{sub 6}, and S{sub 8}) were used. The results for the problem with no control rod were practically the same as those obtained with TWOTRAN using the scheme DBiL that is the simplest one. The results for the other three schemes are practically the same, except for differences in the fourth or fifth significant figure. For the MOX assembly, the results obtained for k{sub eff} with TNHXY were compared with the values obtained with the codes HELIOS, MCNP4B/ENDF-VI and CPM-3. The results obtained with TNHXY are comparable with those reported with the other codes. Particularly, when k{sub eff} values obtained with TNHXY are compared with those obtained with MCNP-4B/ENDF-VI the error was less than 0.5%. Finally, the cross sections used in TNHXY were obtained with the code HELIOS. (Author)}
place = {Mexico}
year = {2002}
month = {Jul}
}
title = {Solution of the transport equation in stationary state, in one and two dimensions, for BWR assemblies using nodal methods; Solucion de la ecuacion de transporte en estado estacionario, en 1 y 2 dimensiones, para ensambles tipo BWR usando metodos nodales}
author = {Xolocostli M, J V}
abstractNote = {The main objective of this work is to solve the neutron transport equation in one and two dimensions (slab geometry and X Y geometry, respectively), with no time dependence, for BWR assemblies using nodal methods. In slab geometry, the nodal methods here used are the polynomial continuous (CMPk) and discontinuous (DMPk) families but only the Linear Continuous (also known as Diamond Difference), the Quadratic Continuous (QC), the Cubic Continuous (CC), the Step Discontinuous (also known as Backward Euler), the Linear Discontinuous (LD) and the Quadratic Discontinuous (QD) were considered. In all these schemes the unknown function, the angular neutron flux, is approximated as a sum of basis functions in terms of Legendre polynomials, associated to the values of the neutron flux in the edges (left, right, or both) and the Legendre moments in the cell, depending on the nodal scheme used. All these schemes were implemented in a computer program developed in previous thesis works and known with the name TNX. This program was modified for the purposes of this work. The program discreetizes the domain of concern in one dimension and determines numerically the angular neutron flux for each point of the discretization when the number of energy groups and regions are known starting from an initial approximation for the angular neutron flux being consistent with the boundary condition imposed for a given problem. Although only problems with two-energy groups were studied the computer program does not have limitations regarding the number of energy groups and the number of regions. The two problems analyzed with the program TNX have practically the same characteristics (fuel and water), with the difference that one of them has a control rod. In the part corresponding to two-dimensional problems, the implemented nodal methods were those designated as hybrids that consider not only the edge and cell Legendre moments, but also the values of the neutron flux in the corner points. In this geometry nodal, continuous and discontinuous schemes were used. For the continuos schemes, only the Bi Quadratic (BiQ) and the Bi Cubic (BiC) were considered. In the case of the discontinuous ones two nodal schemes were considered, namely the Discontinuous Bi Linear (DBiL) and Discontinuous Bi Quadratic (DBiQ). The nodal schemes applied use from 4 up to 16 interpolation parameters per cell. These schemes are-defined for a set D{sub c} of interpolation parameters and a polynomial space S{sub h} corresponding to each one of the nodal schemes considered. All these four nodal hybrid schemes were implemented in a computer program called TNHXY starting from the computer program TNXY developed in previous thesis works. Several subroutines wae added to calculate the average neutron flux for each cell and for each energy group, generating two versions, one for the continuous schemes and one for the discontinuous schemes. For this geometry, two benchmark problems of the ANL-7416 document were analyzed. They are 7x7 BWR fuel assemblies, one without control rod and the other one with control rod. The computer program was also applied to a MOX assembly proposed by the Nuclear Energy Agency and it is considered as a reference problem. The results obtained for the one-dimensional problems using TNX for the effective multiplication factor were compared with the ones obtained with the code ANISN/PC. TNX code shows a faster convergence within four significant figures for the case with no control rod and three significant figures for the case with control rod (using double precision). These results suggest TNX is a very useful tool for this kind of calculations. For X Y geometry, the results obtained with TNHXY were compared with those calculated with the code TWOTRAN. To get these results, several spatial (1x1, 2x2, 4x4 per cell) and angular meshes (S{sub 2}, S{sub 4}, S{sub 6}, and S{sub 8}) were used. The results for the problem with no control rod were practically the same as those obtained with TWOTRAN using the scheme DBiL that is the simplest one. The results for the other three schemes are practically the same, except for differences in the fourth or fifth significant figure. For the MOX assembly, the results obtained for k{sub eff} with TNHXY were compared with the values obtained with the codes HELIOS, MCNP4B/ENDF-VI and CPM-3. The results obtained with TNHXY are comparable with those reported with the other codes. Particularly, when k{sub eff} values obtained with TNHXY are compared with those obtained with MCNP-4B/ENDF-VI the error was less than 0.5%. Finally, the cross sections used in TNHXY were obtained with the code HELIOS. (Author)}
place = {Mexico}
year = {2002}
month = {Jul}
}