Asymptotic Solutions of Serial Radial Fuel Shuffling

Xue-Nong Chen and Edgar Kiefhaber
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Xue-Nong Chen: Institute for Nuclear and Energy Technologies (IKET), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen D-76344, Germany
Edgar Kiefhaber: Institute for Nuclear and Energy Technologies (IKET), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen D-76344, Germany

Energies, 2015, vol. 8, issue 12, 1-17

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 k eff , 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 k eff . Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher k eff 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 k eff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor k inf and the normalized power are presented for two different drifting speeds.

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 (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2015
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