Abstract
In this study, an analytical solution of the neutron transport equation in an annular reactor is presented with a short and rotating neutron source of the type S(x) {delta} (x- Vt), where V is the speed of annular pulsed reactor. The study is an extension of a previous study by Williams [12] carried out with a pulsed source of the type S(x) {delta} (t). In the new concept of annular pulsed reactor designed to produce continuous high flux, the core consists of a subcritical annular geometry pulsed by a rotating modulator, producing local super prompt critical condition, thereby giving origin to a rotating neutron pulse. An analytical solution is obtained by opening up of the annular geometry and applying one energy group transport theory in one dimension using applied mathematical techniques of Laplace transform and Complex Variables. The general solution for the flux consists of a fundamental mode, a finite number of harmonics and a transient integral. A condition which limits the number of harmonics depending upon the circumference of the annular geometry has been obtained. Inverse Laplace transform technique is used to analyse instability condition in annular reactor core. A regenerator parameter in conjunction with perimeter of the ring
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Citation Formats
Teixeira, Paulo Cleber Mendonca.
Analytical solution of neutron transport equation in an annular reactor with a rotating pulsed source; Resolucao analitica da equacao de transporte de neutrons em um reator anelar com fonte pulsada rotativa.
Brazil: N. p.,
2002.
Web.
Teixeira, Paulo Cleber Mendonca.
Analytical solution of neutron transport equation in an annular reactor with a rotating pulsed source; Resolucao analitica da equacao de transporte de neutrons em um reator anelar com fonte pulsada rotativa.
Brazil.
Teixeira, Paulo Cleber Mendonca.
2002.
"Analytical solution of neutron transport equation in an annular reactor with a rotating pulsed source; Resolucao analitica da equacao de transporte de neutrons em um reator anelar com fonte pulsada rotativa."
Brazil.
@misc{etde_20429754,
title = {Analytical solution of neutron transport equation in an annular reactor with a rotating pulsed source; Resolucao analitica da equacao de transporte de neutrons em um reator anelar com fonte pulsada rotativa}
author = {Teixeira, Paulo Cleber Mendonca}
abstractNote = {In this study, an analytical solution of the neutron transport equation in an annular reactor is presented with a short and rotating neutron source of the type S(x) {delta} (x- Vt), where V is the speed of annular pulsed reactor. The study is an extension of a previous study by Williams [12] carried out with a pulsed source of the type S(x) {delta} (t). In the new concept of annular pulsed reactor designed to produce continuous high flux, the core consists of a subcritical annular geometry pulsed by a rotating modulator, producing local super prompt critical condition, thereby giving origin to a rotating neutron pulse. An analytical solution is obtained by opening up of the annular geometry and applying one energy group transport theory in one dimension using applied mathematical techniques of Laplace transform and Complex Variables. The general solution for the flux consists of a fundamental mode, a finite number of harmonics and a transient integral. A condition which limits the number of harmonics depending upon the circumference of the annular geometry has been obtained. Inverse Laplace transform technique is used to analyse instability condition in annular reactor core. A regenerator parameter in conjunction with perimeter of the ring and nuclear properties is used to obtain stable and unstable harmonics and to verify if these exist. It is found that the solution does not present instability in the conditions stated in the new concept of annular pulsed reactor. (author)}
place = {Brazil}
year = {2002}
month = {Dec}
}
title = {Analytical solution of neutron transport equation in an annular reactor with a rotating pulsed source; Resolucao analitica da equacao de transporte de neutrons em um reator anelar com fonte pulsada rotativa}
author = {Teixeira, Paulo Cleber Mendonca}
abstractNote = {In this study, an analytical solution of the neutron transport equation in an annular reactor is presented with a short and rotating neutron source of the type S(x) {delta} (x- Vt), where V is the speed of annular pulsed reactor. The study is an extension of a previous study by Williams [12] carried out with a pulsed source of the type S(x) {delta} (t). In the new concept of annular pulsed reactor designed to produce continuous high flux, the core consists of a subcritical annular geometry pulsed by a rotating modulator, producing local super prompt critical condition, thereby giving origin to a rotating neutron pulse. An analytical solution is obtained by opening up of the annular geometry and applying one energy group transport theory in one dimension using applied mathematical techniques of Laplace transform and Complex Variables. The general solution for the flux consists of a fundamental mode, a finite number of harmonics and a transient integral. A condition which limits the number of harmonics depending upon the circumference of the annular geometry has been obtained. Inverse Laplace transform technique is used to analyse instability condition in annular reactor core. A regenerator parameter in conjunction with perimeter of the ring and nuclear properties is used to obtain stable and unstable harmonics and to verify if these exist. It is found that the solution does not present instability in the conditions stated in the new concept of annular pulsed reactor. (author)}
place = {Brazil}
year = {2002}
month = {Dec}
}