• 한국수자원학회논문집
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• 제45권2호
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• pp.179-189
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• 2012

오염물질의 이동 현상을 모의하기 위하여, 감쇠항이 있는 3차원 이송-확산 방정식의 수치모형이 개발되었다. 개발된 모형은 유한차분 모형으로서 시간단계의 가중치 ${\alpha}$를 포함하는 음해법(implicit finite difference method)과, 반복법인 Gauss-Seidel SOR(successive over relaxation)이 사용되었다. 모형은 보다 단순화된 가정 하에서 존재하는 두 가지의 해석적인 해와 비교되었다. 그 결과 Peclet number가 5~20 이하에서는 수치 분산의 영향이 크지 않았고 작은 오차범위 내에서 해석적인 해와 동일하였다. 또한 가중치 ${\alpha}$의 변화에 대한 모형의 거동은 Crank-Nicolson 모형(${\alpha}$=0.5)이 fully-implicit 모형(${\alpha}$=1)보다 해석적인 해에 접근함을 보여주었다. 모형의 검증과 실효성 제고를 위하여, mass balance를 검토하였다. 즉, 이송, 확산 및 감쇠항 각각에 대한 질량 이동을 산출하였으며, 그 결과 질량 이동의 계산 오차는 약 3% 이내였다. 본 모형은 감쇠 과정이 수반되는 3차원 이송-확산의 농도분포와 질량이동을 산출할 수 있으며 다양한 경계조건을 설정함으로서 현장조건을 반영할 수 있다. 그러나본 모형은 고정격자를 기반으로하는 유한차분 모형이므로 Peclet number가 비교적 작게 나타날 수 있는 토양 및 지하수계의 오염물질 이동 등의 문제에서 유용하게 적용될 수 있을 것으로 사료된다.

• Bulletin of the Korean Chemical Society
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• 제7권4호
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• pp.283-288
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• 1986

A nonlinear analysis is presented for the treatment of fluctuations near the critical point in the presence of diffusion in the Schlogl models. The two time scaling method is used to obtain an evolution equation for the amplitude of fluctuations. It is shown that the fluctuations decay to zero in the stable region and they are enhanced to a finite value as time goes to infinity in the unstable region.

• Nuclear Engineering and Technology
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• 제49권6호
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• pp.1259-1268
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• 2017

The alpha eigenvalue problem in multigroup neutron diffusion is studied with particular attention to the theoretical analysis of the model. Contrary to previous literature results, the existence of eigenvalue and eigenflux clustering is investigated here without the simplification of a unique fissile isotope or a single emission spectrum. A discussion about the negative decay constants of the neutron precursors concentrations as potential eigenvalues is provided. An in-hour equation is derived by a perturbation approach recurring to the steady state adjoint and direct eigenvalue problems of the effective multiplication factor and is used to suggest proper detection criteria of flux clustering. In spite of the prior work, the in-hour equation results give a necessary and sufficient condition for the existence of the eigenvalue-eigenvector pair. A simplified asymptotic analysis is used to predict bands of accumulation of eigenvalues close to the negative decay constants of the precursors concentrations. The resolution of the problem in one-dimensional heterogeneous problems shows numerical evidence of the predicted clustering occurrences and also confirms previous theoretical analysis and numerical results.

• Nuclear Engineering and Technology
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• 제54권4호
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• pp.1195-1205
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• 2022

Recent developments on spectral diffusion algorithms, i.e., algorithms which exploit the projection of the solution on the eigenfunctions of the Laplacian operator, demonstrated their effective applicability in fast transient conditions. Nevertheless, the numerical error introduced by these algorithms, together with the uncertainties associated with model parameters, may impact the reliability of the predictions on short-lived volatile fission product release from nuclear fuel. In this work, we provide an upper bound on the numerical error introduced by the presented spectral diffusion algorithm, in both constant and time-varying conditions, depending on the number of modes and on the time discretization. The definition of this upper bound allows introducing a methodology to a priori bound the numerical error on short-lived volatile fission product retention.

• 한국수자원학회논문집
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• 제32권6호
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• pp.607-616
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• 1999

비보존성 오염물질의 종확산에 관한 수치모형을 개발하였다. 계산기법으로는 종확산 방정식을 이송, 감쇠 및 확산 방정식으로 분리하고, 이들 방정식을 1/3 시간 간격에 대하여 번갈아 계산하는 단계분리 유한차분기법을 사용하였다. 이송방정식에 대해서는 Holly-Preissmann 기법을, 감쇠방정식에 대해서는 해석적 방법을, 확산방정식에 대해서는 Crank-Nicholson 기법을 각각 사용하였다. 오염물질이 불균일 흐름 내로 연속적으로 유입되는 경우 및 균일 흐름 내로 순간적으로 부하되는 경우에 대한 종확산 문제에 모형을 적용하여 계산결과를 정확해와 비교함으로써 모형을 검증하였다. 또한 감쇠방정식의 수치해법으로써 Euler 방법을 사용하는 기존의 모형에 계산결과를 비교하였다. 감쇠계수가 커질수록 본 모형이 기존의 모형에 비하여 더욱 정확한 계산결과를 나타내었다.

• 한국수소및신에너지학회논문집
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• 제20권6호
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• pp.479-484
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• 2009

The effect of anode gas channel height on gas diffusion and cell performance in a 100 $cm^2$ class molten carbonate single cell is investigated. Single cell separators with three different channel height are used. The effect of the gas channel height on the distribution of the reactive gas concentration is evaluated by the two-dimensional concentration diffusion equation. The overpotential caused by concentration drop with different channel height is estimated by the voltage decay related to diffusion of reactants, well known as concentration polarization, using limiting current density. The estimation could have the possibility to identify the reactant mass transfer polarization in the complicate factors of the overall electrodes.

• Environmental Sciences Bulletin of The Korean Environmental Sciences Society
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• 제10권S_3호
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• pp.97-106
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• 2001

To improve the water quality, particularly for sea bathers, the behaviour of wastewater from sewage outfalls in water adjacent to Swansea, UK, was studied using a mathematical model. The water quality in the sewage receiving basin was determined using factors like the outfall diffuser location(distance from land boundary), sewage treatment scheme, discharge time, and bacteria decay rate, etc. With respect to these factors, an optimal strategy for sewage discharge was then investigated to minimize bacteria levels along the bathing beaches. As water quality criteria, predicted faecal coliform levels were monitored along the coast adjacent to the outfall locations. The resultant values were compared with EC Mandatory(<2000, 95 % of 20 samples) and Guideline Standards(< 100, 80 % of 20 samples). For the advective-diffusion equation, the non linear advective terms were represented using the ULTIMATE algorithm and the third-order accurate QUICKEST scheme to avoid numerical diffusion. Details of the simulation results are then presented as an optimal policy for sewage discharge in the region.

• Nuclear Engineering and Technology
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• 제54권8호
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• pp.2771-2782
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• 2022

When assessing the radiological consequences of postulated accident scenarios, it is of primary interest to determine the amount of radioactive fission gas accumulated in the fuel rod free volume. The state-of-the-art semi-empirical approach (ANS 5.4-2010) is reviewed and compared with a mechanistic approach to evaluate the release of radioactive fission gases. At the intra-granular level, the diffusion-decay equation is handled by a spectral diffusion algorithm. At the inter-granular level, a mechanistic description of the grain boundary is considered: bubble growth and coalescence are treated as interrelated phenomena, resulting in the grain-boundary venting as the onset for the release from the fuel pellets. The outcome is a kinetic description of the release of radioactive fission gases, of interest when assessing normal and off-normal conditions. We implement the model in SCIANTIX and reproduce the release of short-lived fission gases, during the CONTACT 1 experiments. The results show a satisfactory agreement with the measurement and with the state-of-the-art methodology, demonstrating the model soundness. A second work will follow, providing integral fuel rod analysis by coupling the code SCIANTIX with the thermo-mechanical code TRANSURANUS.