On the stability of the point reactor kinetics equations

Theler, Germán; Bonetto, F.

doi:10.1016/j.nucengdes.2010.03.007

Cited by 16 publications

(2 citation statements)

References 9 publications

(9 reference statements)

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“…That is to say, in general, the rate of absorptions and leakages will not exactly overcome the neutrons born by fissions sources, and some kind of feedback-either through an external control system or by means of an inherent stability mechanism of the core [4]is needed to keep the reactor power within a certain interval. Mathematically, this means that the transport-and thus the diffusion-equation does not have a steady-state solution.…”

Section: Introductionmentioning

confidence: 99%

Unstructured Grids and the Multigroup Neutron Diffusion Equation

Theler¹

2013

Science and Technology of Nuclear Installations

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The neutron diffusion equation is often used to perform core-level neutronic calculations. It consists of a set of second-order partial differential equations over the spatial coordinates that are, both in the academia and in the industry, usually solved by discretizing the neutron leakage term using a structured grid. This work introduces the alternatives that unstructured grids can provide to aid the engineers to solve the neutron diffusion problem and gives a brief overview of the variety of possibilities they offer. It is by understanding the basic mathematics that lie beneath the equations that model real physical systems; better technical decisions can be made. It is in this spirit that this paper is written, giving a first introduction to the basic concepts which can be incorporated into core-level neutron flux computations. A simple two-dimensional homogeneous circular reactor is solved using a coarse unstructured grid in order to illustrate some basic differences between the finite volumes and the finite elements method. Also, the classic 2D IAEA PWR benchmark problem is solved for eighty combinations of symmetries, meshing algorithms, basic geometric entities, discretization schemes, and characteristic grid lengths, giving even more insight into the peculiarities that arise when solving the neutron diffusion equation using unstructured grids.

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Section: Introductionmentioning

confidence: 99%

Unstructured Grids and the Multigroup Neutron Diffusion Equation

Theler¹

2013

Science and Technology of Nuclear Installations

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“…Point re ac tor ki net ics has been con ven tion ally used for the sta bil ity anal y sis of re ac tors [1,2]. In the pres ent work, a gen eral meth od ol ogy has been de veloped for the lin ear sta bil ity anal y sis of nu clear re ac -tors, where in ad di tion to the fuel and cool ant tem per ature re ac tiv ity feed backs, the xe non re ac tiv ity feed back has also been in cluded.…”

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confidence: 99%

Linear stability analysis of a nuclear reactor using the lumped model

et al. 2016

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The sta bil ity anal y sis of a nu clear re ac tor is an im por tant as pect in the de sign and op er a tion of the re ac tor. A sta ble neutronic re sponse to per tur ba tions is es sen tial from the safety point of view. In this pa per, a gen eral meth od ol ogy has been de vel oped for the lin ear sta bil ity anal y sis of nu clear re ac tors us ing the lumped re ac tor model. The re ac tor ki net ics has been mod elled us ing the point ki net ics equa tions and the re ac tiv ity feed backs from fuel, cool ant and xe non have been mod elled through the ap pro pri ate time de pend ent equa tions. These gov ern ing equa tions are linearized con sid er ing small per tur ba tions in the re ac tor state around a steady op er at ing point. The char ac ter is tic equa tion of the sys tem is used to es tab lish the sta bil ity zone of the re ac tor con sid er ing the re ac tiv ity co ef fi cients as pa ram e ters. This meth od ol ogy has been used to iden tify the sta bil ity re gion of a typ i cal pres sur ized heavy wa ter re ac tor. It is shown that the pos i tive re ac tiv ity feed back from xe non nar rows down the sta bil ity re gion. Fur ther, it is ob served that the neu tron ki net ics pa ram e ters (such as the num ber of de layed neu tron pre cur sor groups con sid ered, the neu tron gen er a tion time, the de layed neu tron fractions, etc.) do not have a sig nif i cant in flu ence on the lo ca tion of the sta bil ity bound ary. The sta bil ity bound ary is largely in flu enced by the pa ram e ters gov ern ing the evo lu tion of the fuel and cool ant tem per a ture and xe non con cen tra tion.

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