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.
Highlights
Recent research and engineering studies of the so‐called traveling wave reactor (TWR) concept carried out by TerraPower LLC
The feasibility of the TWR was presented based on existing sodium cooled fast reactor (SFR) technologies, where depleted or natural uranium is fed in by a radial fuel shuffling scheme and a permanent power shape, i.e., a stationary burning/breeding wave, is formed
The results demonstrate that the inward fuel drifting can achieve a higher keff than the outward one and it is more feasible for application purposes
Summary
Recent research and engineering studies of the so‐called traveling wave reactor (TWR) concept carried out by TerraPower LLC. If one considers the reverse problem, namely instead of a wave traveling through stationary fuel, fuel moving under a stationary neutron flux and power shape, a burning/breeding wave could exist, which is stationary with respect to the fixed coordinate system, but moving relatively to the fuel This is the main issue that we study in this paper. The axial fuel shuffling is not common in convectional reactors, the axial fuel shuffling (motion) can be dealt with theoretically and numerically much more than the radial one This is why one had considered the TWR concept first in the axial or plane direction [6,7,8,9,10,11,12,13,14,15,16]. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor kinf, and the normalized power are presented for showing 2‐D and drifting speed effects
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