• Nuclear Engineering and Technology
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• v.55 no.2
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• pp.749-755
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• 2023

A new approximation method was proposed for treating the non-resonant spatial self-shielding effects of double heterogeneous region such as the double heterogeneous effect of VHTR fuel compact in the thermal energy range and that of BP compact with BISO. The method was developed based on the effective homogenization method and a spherical unit cell model with explicit coated layers and a matrix layer. The self-shielding factor was derived from the relation between the collision probabilities for a double heterogeneous compact and the effective cross section for the homogenized compact. First, the collision probabilities and transmission probabilities for all layers of the spherical model were calculated using conventional collision probability solver. Then, the effective cross section for the homogenized sphere cell representing the homogenized compact was obtained from the transmission probability calculated using the probability density function of a chord length. The verification calculations revealed that the proposed method can predict the self-shielding factor with a maximum error of 2.3% and the double heterogeneous effect with a maximum error of 200 pcm in the typical VHTR problems with various packing fractions and BP compact sizes.

• Proceedings of the Korean Nuclear Society Conference
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• 1995.10a
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• pp.73-78
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• 1995

이중 또는 삼중으로 탄소 피막된 핵연료 입자를 Graphite 소결체에 채워넣은 핵연료를 설계하고, 이에 대한 핵적 타당성을 검토하고자 하였다. 핵계산 체계로서 CASMO-3가 갖는 Spatial Self-shielding 효과의 문제, 코드의 계산 방식 문제, 핵자료 결손 문제를 검토한 후 보정 계수를 산출하려 하였다. CASMO-3의 정확도는 MCNP-4A를 통해 검증하였는데, 비균질한 소결체 내부를 균질화 함으로서 야기되는 Spatial Self-Shielding 효과는 임계도의 차이가 거의 없는 것으로 확인되어졌고, 계산 코드의 차이로 인한 효과 또한 무시할 수 있었다. 그러나 CASMO-3의 핵자료에서 탄소와 실리콘의 자료 부족은 임계도 차이가 0.06184정도로 다소 차이가 나기 때문에 보정이 필요함을 확인하였으나 CASMO-3 자체의 유용성에는 문제가 없었다.

• Nuclear Engineering and Technology
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• v.54 no.4
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• pp.1464-1470
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• 2022

This paper presents a high performance burnable absorber named as CIMBA (Cylindrically Inserted and Mechanically Separated Burnable Absorber) for the soluble-boron-free SMR. The CIMBA is the cylindrical gadolinia inserted into the annular fuel pellets. Although the CIMBA utilizes the spatial self-shielding effect of the fuel material, a large reactivity upswing occurs when the gadolinia is depleted. To minimize the reactivity swing of the CIMBA-loaded FA, two approaches were investigated. One is controlling the spatial self-shielding effect of the CIMBA as burnup proceeds by a multi-layered structure of the CIMBA (ML-CIMBA) and the other is the mixed-loading of two different types of CIMBA (MIX-CIMBA). Both approaches show promising performances to minimize the reactivity swing, where the MIX-CIMBA is more preferable due to its simpler fabrication process. In conclusion, the MIX-CIMBA is expected to accelerate the commercialization of the CIMBA and can be used to achieve an optimal soluble-boron-free SMR core design.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1287-1300
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• 2017

Based on the observation that ignoring the angle dependency of multigroup resonance cross sections within a fuel pellet would result in nontrivial underestimation of the spatial self-shielding of flux, a parametrized spectral superhomogenization (SPH) factor library (PSSL) method is developed as a practical means of resolving the problem. Region-wise spectral SPH factors are calculated by the normal and transport corrected SPH iterations after ultrafine group slowing down calculations over various light water reactor pin-cell configurations. The parametrization is done with fuel temperature, U-238 number density, fuel radius, moderator source represented by ${\Sigma}_{mod}V_{mod}$, and the number density ratio of resonance nuclides to that of U-238 in a form of resonance interference correction factors. The parametrization is successful in that the root mean square errors of the interpolated SPH factors over the fuel regions of various pin-cells are within 0.1%. The improvement in reactivity error of the PSSL method is shown to be superior to that by the original SPH method in that the reactivity bias of -200 pcm to -300 pcm vanishes almost completely. It is demonstrated that the environment effect takes only about 4% in the reactivity improvement so that the pin-cell based PSSL method is effective in the assembly problems.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1269-1286
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• 2017

This paper presents a newly developed resonance self-shielding method based on Tone's method in $APOLLO3^{(R)}$ for fast and thermal reactor calculations. The new method is based on simplified models, the narrow resonance approximation for the slowing down source and Tone's approximation for group collision probability matrix. It utilizes mathematical probability tables as quadrature formulas in calculating effective cross-sections. Numerical results for the ZPPR drawer calculations in 1,968 groups show that, in the case of the double-column fuel drawer, Tone's method gives equivalent precision to the subgroup method while markedly reducing the total number of collision probability matrix calculations and hence the central processing unit time. In the case of a single-column fuel drawer with the presence of a uranium metal material, Tone's method obtains less precise results than those of the subgroup method due to less precise heterogeneous-homogeneous equivalence. The same options are also applied to PWR UOX, MOX, and Gd cells using the SHEM 361-group library, with the objective of analyzing whether this energy mesh might be suitable for the application of this methodology to thermal systems. The numerical results show that comparable precision is reached with both Tone's and the subgroup methods, with the satisfactory representation of intrapellet spatial effects.