SummaryIn this paper, a non‐intrusive stochastic model reduction scheme is developed for polynomial chaos representation using proper orthogonal decomposition. The main idea is to extract the optimal orthogonal basis via inexpensive calculations on a coarse mesh and then use them for the fine‐scale analysis. To validate the developed reduced‐order model, the method is implemented to: (1) the stochastic steady‐state heat diffusion in a square slab; (2) the incompressible, two‐dimensional laminar boundary‐layer over a flat plate with uncertainties in free‐stream velocity and physical properties; and (3) the highly nonlinear Ackley function with uncertain coefficients. For the heat diffusion problem, the thermal conductivity of the slab is assumed to be a stochastic field with known exponential covariance function and approximated via the Karhunen–Loève expansion. In all three test cases, the input random parameters are assumed to be uniformly distributed, and a polynomial chaos expansion is found using the regression method. The Sobol's quasi‐random sequence is used to generate the sample points. The numerical results of the three test cases show that the non‐intrusive model reduction scheme is able to produce satisfactory results for the statistical quantities of interest. It is found that the developed non‐intrusive model reduction scheme is computationally more efficient than the classical polynomial chaos expansion for uncertainty quantification of stochastic problems. The performance of the developed scheme becomes more apparent for the problems with larger stochastic dimensions and those requiring higher polynomial order for the stochastic discretization. Copyright © 2015 John Wiley & Sons, Ltd.

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Civil marine reactors face a unique set of design challenges. These include requirements for a small core size and long core lifetime, a 20% cap on fissile loading, and limitations on using soluble neutron absorbers. In this reactor physics study, we seek to design a core that meets these requirements over a 15 effective full-power-years (EFPY) life at 333 MWth using homogeneously mixed all-UO 2 and micro-heterogeneous ThO 2 -UO 2 duplex fuels. In a companion (Part I) paper, we found assembly designs using 15% and 18% 235 U for UO 2 and duplex fuels, respectively, loaded into 13×13 pin arrays. High thickness (150 μm) ZrB 2 integral fuel burnable absorber (IFBA) pins and boron carbide (B 4 C) control rods are used for reactivity control. Taking advantage of self-shielding effects, these designs maintain low and stable assembly reactivity with little burnup penalty.In this paper (Part II), whole-core design analyses are performed for small modular reactor (SMR) to determine whether the core remains critical for at least 15 EFPY with a reactivity swing of less than 4000 pcm, subject to appropriate constraints. The main challenge is to keep the radial form factor below its limit (1.50). Burnable poison radial-zoning is examined in the quest for a suitable arrangement to control power peaking. Optimized assemblies are loaded into a 3D reactor model in PANTHER. The PANTHER results confirm that the fissile loadings of both fuels are well-designed for the target lifetime: at the end of the ∼15-year cycle, the cores are on the border of criticality. The duplex fuel core can achieve ∼4% longer core life, has a ∼3% lower initial reactivity and ∼30% lower reactivity swing over life than the final UO 2 core design. The duplex core is therefore the more successful design, giving a core life of ∼16 years and a reactivity swing of less than 2500 pcm, while satisfying all the neutronic safety parameters. In particular, one of the major objectives of this study is to offer/explore a thorium-based candidate alternative fuel platform for the proposed marine core. It is proven by literature reviews that the ability of the duplex fuel was never explored in the context of a single-batch, LEU, SBF, long-life SMR core. In this regard, the motivation of this paper is to understand the underlying physics of the duplex fuel and 'open the option' of designing the functional cores with both the duplex and UO 2 fuel cores.

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