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Energies 2015, 8(12), 13829-13845; doi:10.3390/en81212398

Asymptotic Solutions of Serial Radial Fuel Shuffling

Institute for Nuclear and Energy Technologies (IKET), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen D-76344, Germany
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Academic Editor: Hiroshi Sekimoto
Received: 16 October 2015 / Revised: 20 November 2015 / Accepted: 24 November 2015 / Published: 4 December 2015
(This article belongs to the Special Issue Sustainable Future of Nuclear Power)
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Abstract

In this paper, the mechanism of traveling wave reactors (TWRs) is investigated from the mathematical physics point of view, in which a stationary fission wave is formed by radial fuel drifting. A two dimensional cylindrically symmetric core is considered and the fuel is assumed to drift radially according to a continuous fuel shuffling scheme. A one-group diffusion equation with burn-up dependent macroscopic coefficients is set up. The burn-up dependent macroscopic coefficients were assumed to be known as functions of neutron fluence. By introducing the effective multiplication factor keff, a nonlinear eigenvalue problem is formulated. The 1-D stationary cylindrical coordinate problem can be solved successively by analytical and numerical integrations for associated eigenvalues keff. Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher keff than the outward one. The 2-D eigenvalue problem has to be solved by a more complicated method, namely a pseudo time stepping iteration scheme. Its 2-D asymptotic solutions are obtained together with certain eigenvalues keff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor kinf and the normalized power are presented for two different drifting speeds. View Full-Text
Keywords: traveling wave reactor (TWR); one-group diffusion model; burn-up equations; radial fuel shuffling; 1-D and 2-D asymptotic solutions; U-Pu conversion cycle traveling wave reactor (TWR); one-group diffusion model; burn-up equations; radial fuel shuffling; 1-D and 2-D asymptotic solutions; U-Pu conversion cycle
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Chen, X.-N.; Kiefhaber, E. Asymptotic Solutions of Serial Radial Fuel Shuffling. Energies 2015, 8, 13829-13845.

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