Ser Gi Hong

Fourier Convergence Analysis of the Rebalance Methods for Discrete Ordinates Transport Equations in Eigenvalue Problems

Abstract This paper analyzes the convergence of the rebalance iteration methods for accelerating the power iteration method of the discrete ordinates transport equation in the eigenvalue problem. The rebalance iteration methods include the coarse mesh rebalance (CMR), the coarse mesh finite difference (CMFD), and the partial current-based CMFD methods. The convergence analysis is performed with the well-known Fourier analysis through linearization. In the linearized form, these rebalance methods are formulated in a unified way where the rebalance methods are different only in a parameter. The analyses are applied for both one- and two-group problems in a homogeneous infinite medium and a finite medium having periodic boundary conditions. The theoretical analysis shows that the convergences of the rebalance methods for the eigenvalue problems are closely related with the ones for the fixed source problems and that the convergences for the eigenvalue problems can be analyzed with the formula for the fixed source problem after transforming the scattering cross sections into a different cross-section set. The numerical tests show that the Fourier convergence analysis provides a reasonable estimate for the numerical spectral radii for the model problems.

Resonance self-shielding methodology of new neutron transport code STREAM

This paper reports on the development and verification of three new resonance self-shielding methods. The verifications were performed using the new neutron transport code, STREAM. The new methodologies encompass the extension of energy range for resonance treatment, the development of optimum rational approximation, and the application of resonance treatment to isotopes in the cladding region. (1) The extended resonance energy range treatment has been developed to treat the resonances below 4 eV of three resonance isotopes and shows significant improvements in the accuracy of effective cross sections (XSs) in that energy range. (2) The optimum rational approximation can eliminate the geometric limitations of the conventional approach of equivalence theory and can also improve the accuracy of fuel escape probability. (3) The cladding resonance treatment method makes it possible to treat resonances in cladding material which have not been treated explicitly in the conventional methods. These three new methods have been implemented in the new lattice physics code STREAM and the improvement in the accuracy of effective XSs is demonstrated through detailed verification calculations.

A small long-cycle PWR core design concept using fully ceramic micro-encapsulated (FCM) and UO2–ThO2 fuels for burning of TRU

In this paper, a new small pressurized water reactor (PWR) core design concept using fully ceramic micro-encapsulated (FCM) particle fuels and UO2–ThO2 fuels was studied for effective burning of transuranics from a view point of core neutronics. The core of this concept rate is 100 MWe. The core designs use the current PWR-proven technologies except for a mixed use of the FCM and UO2–ThO2 fuel pins of low-enriched uranium. The significant burning of TRU is achieved with tri-isotropic particle fuels of FCM fuel pins, and the ThO2–UO2 fuel pins are employed to achieve long-cycle length of ∼4 EFPYs (effective full-power year). Also, the effects of several candidate materials for reflector are analyzed in terms of core neutronics because the small core size leads to high sensitivity of reflector material on the cycle length. The final cores having 10 w/o SS303 and 90 w/o graphite reflector are shown to have high TRU burning rates of 33%–35% in FCM pins and significant net burning rates of 24%–25% in the total core with negative reactivity coefficients, low power peaking factors, and sufficient shutdown margins of control rods.

A Core Physics Study of Advanced Sodium-Cooled TRU Burners with Thorium- and Uranium-Based Metallic Fuels

Abstract In this work, 400-MW(electric) sodium-cooled fast reactor cores using thorium- and uranium-based metallic fuels for high burning rates of light water reactor spent-fuel transuranics (TRUs) are neutronically designed and analyzed based on equilibrium cycles with a focus on consistent comparative analysis of the differences in performance between thorium- and uranium-based fueled cores. Axial uranium and thorium blankets are introduced in thorium- and uranium-based driver fueled burner cores to improve TRU burning rates without considerable increases of burnup reactivity swing. For this core configuration, it was shown that cores using thorium and depleted uranium blankets can be designed to have a high TRU burning rate, a low sodium void reactivity (SVR) worth, and a low burnup reactivity swing. In particular, the use of uranium or thorium blankets without recycling in the thorium-based driver fueled cores led to significant reductions of burnup reactivity swing with considerable increases of the TRU burning rate and small increases of SVR. In addition, the core configuration having central nonfuel regions was considered to show the effects of the thorium-based driver metallic fuel versus the uranium-based metallic fuel coupled with moderator rods. The core configuration with thorium-based fuel led to a negative SVR without moderator rods, and the use of moderator rods further improved the Doppler coefficient and reduced SVR. Also, a decomposition analysis of SVR was performed to better understand the differences in the contributing factors between the uranium- and thorium-based fueled cores, and a quasi-static reactivity balance analysis was performed to show the inherent safety of the cores in terms of self-controllability.

Sub-cell balanced nodal expansion methods using S4 eigenfunctions for multi-group SN transport problems in slab geometry

A highly accurate S4 eigenfunction-based nodal method has been developed to solve multi-group discrete ordinate neutral particle transport problems with a linearly anisotropic scattering in slab geometry. The new method solves the even-parity form of discrete ordinates transport equation with an arbitrary SN order angular quadrature using two sub-cell balance equations and the S4 eigenfunctions of within-group transport equation. The four eigenfunctions from S4 approximation have been chosen as basis functions for the spatial expansion of the angular flux in each mesh. The constant and cubic polynomial approximations are adopted for the scattering source terms from other energy groups and fission source. A nodal method using the conventional polynomial expansion and the sub-cell balances was also developed to be used for demonstrating the high accuracy of the new methods. Using the new methods, a multi-group eigenvalue problem has been solved as well as fixed source problems. The numerical test results of one-group problem show that the new method has third-order accuracy as mesh size is finely refined and it has much higher accuracies for large meshes than the diamond differencing method and the nodal method using sub-cell balances and polynomial expansion of angular flux. For multi-group problems including eigenvalue problem, it was demonstrated that the new method using the cubic polynomial approximation of the sources could produce very accurate solutions even with large mesh sizes.