Constitutive laws for the neutron density current

Espinosa-Paredes, Gilberto; Morales-Sandoval, Jaime B.; Vázquez-Rodríguez, R.; Espinosa-Martínez, É.-G.

doi:10.1016/j.anucene.2008.05.002

Cited by 79 publications

(6 citation statements)

References 16 publications

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“…The B factor is the geometric buckling factor in reactor physics. Taking into consideration that Σ a =1/λ a , and D = λ tr /3 where λ a is the absorption mean-free path and λ tr is the transport scattering diffusion length given by the more advanced transport theory in terms of transport and absorption cross-sections equation as [73,74];…”

Section: Discussionmentioning

confidence: 99%

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

W.¹,

Elmaghraby²,

Salama³

et al. 2022

Preprint

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The complexity of the neutron transport phenomenon throws its shadows on every physical system wherever neutron is produced or used. In the current study, an ab initio derivation of the neutron self-shielding factor, the problem of the decrease of the neutron flux as it penetrates into a material placed in an isotropic neutron field, has been attempted employing the theory of steady-state neutron transport, starting from Stuart's formula. Simple formulae were derived based on the integral cross-section parameters, which can be adopted by the user according to various variables, such as the neutron flux distribution and geometry of the simulation at hand. The concluded formulae of the self-shielding factors comprise an inverted sigmoid function normalized a weight representing the ratio between the total and scattering macroscopic cross-sections of the medium. The general convex volume geometries are reduced to a set of chord lengths, while the neutron interactions probabilities within the volume are parameterized to the epithermal and thermal neutron energies. The arguments of the inverted-sigmoid function were derived from a simplified version of neutron transport formulation. Accordingly, the obtained general formulae were successful in giving the experimental values of the neutron self-shielding factor for different elements and different geometries. The results were validated by comparing them to the experimental data as well as a variety of data extracted from the literature.

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Section: Discussionmentioning

confidence: 99%

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

W.¹,

Elmaghraby²,

Salama³

et al. 2022

Preprint

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“…Several researchers have contributed to the development of a variety of FO models along with the necessary satisfactory motivation and analysis for the same. The FO neutron diffusion equation models were proposed in [ 7 , 8 , 49 ]. The FO models used in the work are proposed in [ 5 ].…”

Section: Fractional-order Models Of Nuclear Reactormentioning

confidence: 99%

“…The model of a nuclear reactor is derived from the model of neutron chain reaction. All the FO models of nuclear reactor developed in the literature are fundamentally based on the assumption that movement of neutrons in the reactor core is a subdiffusive process [ 7 , 8 ]. This work deals with the development of artificial neural network (ANN)-based models for the FO point reactor kinetics model with reactivity feedback and other FO models derived from the same.…”

Section: Introductionmentioning

confidence: 99%

Modeling nonlinear fractional-order subdiffusive dynamics in nuclear reactor with artificial neural networks

Bhusari¹,

Patil²,

Jadhav³

et al. 2022

Int. J. Dynam. Control

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This paper presents the development and analysis of artificial neural network (ANN) models for the nonlinear fractional-order (FO) point reactor kinetics model, FO Nordheim–Fuchs model, inverse FO point reactor kinetics model and FO constant delayed neutron production rate approximation model. These models represent the dynamics of a nuclear reactor with neutron transport modeled as subdiffusion. These FO models are nonlinear in nature, are comprised of a system of coupled fractional differential equations and integral equations, and are considered to be difficult for solving both analytically and numerically. The ANN models were developed using the data generated from these models. The work involves the iterative process of ANN learning with different combinations of layers and neurons. It is shown through extensive simulation studies that the developed ANN models faithfully capture the transient and steady-state dynamics of these FO models, thereby providing a satisfactory representation for the nonlinear subdiffusive process of neutron transport in a nuclear reactor.

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“…Coefficient N 1 is obtained by substituting α = 1 in M 1 and N 2 = M 2 . Fractional-order models for the neutron transport have also been proposed in [9] and [10].…”

Section: Introductionmentioning

confidence: 99%

Analysis of fractional-order telegraph model for neutron transport in nuclear reactor with slab geometry

Vyawahare

Nataraj

2013

2013 European Control Conference (ECC)

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This paper deals with the analysis of fractionalorder (FO) telegraph equation which models the transport of thermal neutrons inside a nuclear reactor with slab geometry. The FO model, previously developed by the authors, models the neutron transport as anomalous diffusion, precisely a subdiffusion. This model removes the lacunae of the conventional integer-order model of neutron movements. Here, the FO model is solved using the well known technique of separation of variables and the spatial distribution and time evolution of the neutron flux in the slab reactor are computed. This exercise is probably being performed for the first time for the fractionalorder model of neutron transport. It clearly depicts the wavelike nature of the neutron flux. Also, the convergence of neutron flux for FO telegraph and subdiffusion models for asymptotic time establishes the long-time subdiffusive behaviour of the FO telegraph equation. The analysis carried out in this paper is thus forms a crucial step in the process of development of fractional-order model for a nuclear reactor.

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Constitutive laws for the neutron density current

Cited by 79 publications

References 16 publications

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

Modeling nonlinear fractional-order subdiffusive dynamics in nuclear reactor with artificial neural networks

Analysis of fractional-order telegraph model for neutron transport in nuclear reactor with slab geometry

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