Fractional divergence for neutron flux profile in nuclear reactors

Das, Shantanu; Biswas, B.B.

doi:10.1504/ijnest.2007.014652

Cited by 23 publications

(8 citation statements)

References 16 publications

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“…The parameters of the controller (2) i.e. N and q may be selected so as to match the N and q of the system under control which has a generic structure like (3). Firstly the maximum order of the controller (Nq) and commensurate order (q) are fixed by making them same as that of the system, so as to precisely move N number of system poles using N number of controller zeros.…”

Section: Contributions Of the Design Approach And Few Discussionmentioning

confidence: 99%

“…System identification which is a well established tool in control engineering to build models for unknown or poorly understood dynamical systems has already been extended using fractional calculus to get a better description of the physical system [2]. Application of fractional calculus has also been done in few nuclear engineering problems as a better description of the neutron diffusion equation in spatial [3] and temporal [4] domain, point reactor kinetics [5], neutron transport equation [6]- [7], compact modeling of nuclear reactor [8] and robust controller design for reactor power regulation [9] etc. Fractional order modeling of physical systems firstly requires the knowledge of the number of FO elements, present in the model i.e.…”

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confidence: 99%

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Continuous order identification of PHWR models under step-back for the design of hyper-damped power tracking controller with enhanced reactor safety

Das

Mukherjee

Das

et al. 2013

Nuclear Engineering and Design

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Abstract:In this paper, discrete time higher integer order linear transfer function models have been identified first for a 500 MWe Pressurized Heavy Water Reactor (PHWR) which has highly nonlinear dynamical nature. Linear discrete time models of the nonlinear nuclear reactor have been identified around eight different operating points (power reduction or step-back conditions) with least square estimator (LSE) and its four variants. From the synthetic frequency domain data of these identified discrete time models, fractional order (FO) models with sampled continuous order distribution are identified for the nuclear reactor. This enables design of continuous order Proportional-Integral-Derivative (PID) like compensators in the complex w-plane for global power tracking at a wide range of operating conditions. Modeling of the PHWR is attempted with various levels of discrete commensurate-orders and the achievable accuracies are also elucidated along with the hidden issues, regarding modeling and controller design. Credible simulation studies are presented to show the effectiveness of the proposed reactor modeling and power level controller design. The controller pushes the reactor poles in higher Riemann sheets and thus makes the closed loop system hyper-damped which ensures safer reactor operation at varying dc-gain while making the power tracking temporal response slightly sluggish; but ensuring greater safety margin.

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Section: Contributions Of the Design Approach And Few Discussionmentioning

confidence: 99%

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confidence: 99%

Continuous order identification of PHWR models under step-back for the design of hyper-damped power tracking controller with enhanced reactor safety

Das

Mukherjee

Das

et al. 2013

Nuclear Engineering and Design

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“…The beauty of this subject is that fractional derivatives (or integrals) are not a local (or point) property (or quantity) (Das and Basudeb, 2007). Therefore, they consider the history and non-local distributed effects.…”

Section: Introductionmentioning

confidence: 99%

Development of a 3D-Multigroup program to simulate anomalous diffusion phenomena in the nuclear reactors

Moghaddam

Afarideh

Espinosa-Paredes

2015

Annals of Nuclear Energy

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“…The beauty of this subject is that fractional derivatives (and integrals) are not a local (or point) property (or quantity) [1]. Therefore, it considers the history and non-local distributed effects.…”

Section: Introductionmentioning

confidence: 99%

Development of a 2D-Multigroup Code (NFDE-2D) based on the neutron spatial-fractional diffusion equation

Moghaddam

Afarideh

Espinosa-Paredes

2015

Applied Mathematical Modelling

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a b s t r a c tThe first aim of this work is the numerical solution of the neutron spatial-fractional diffusion equation in two-dimension for energy multigroups using the shifted Grünwald-Letnikov approximation in the fractional derivatives. The second aim is related to illustrate a real application of fractional derivatives in the nuclear reactors. The novelty of this work is the discretization method of the neutron fractional diffusion equation in multigroup form for high heterogeneous multiplicative media where the effective multiplication factor (K eff ) was rigorously calculated. When the classical Laplacian is converted to fractional Laplacian, the jump length statistics are unrestricted. For neutron population in the nuclear reactors there is a new version of the neutron diffusion equation which is established on the fractional space derivatives, called in this work as neutron fractional diffusion equation (NFDE). We have developed the NFDE-2D as a nuclear reactors core calculation code, which is validated with some numerical experiments where different orders of fractional derivative are considered. The results demonstrate that reactors exhibit the complex behavior against order of fractional derivative which is depended on the competition between neutron absorption and super-diffusion phenomena, which is comparable with the neutron transport theory.

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Fractional divergence for neutron flux profile in nuclear reactors

Cited by 23 publications

References 16 publications

Continuous order identification of PHWR models under step-back for the design of hyper-damped power tracking controller with enhanced reactor safety

Continuous order identification of PHWR models under step-back for the design of hyper-damped power tracking controller with enhanced reactor safety

Development of a 3D-Multigroup program to simulate anomalous diffusion phenomena in the nuclear reactors

Development of a 2D-Multigroup Code (NFDE-2D) based on the neutron spatial-fractional diffusion equation

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