• Nuclear Engineering and Technology
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• 제28권3호
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• pp.311-319
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• 1996

We reconstruct the assembly pinwise flux using several types of boundary conditions and confirm that the reconstructed fluxes are the same with the reference flux if the boundary condition is exact. We test EPRI-9R benchmark problem with four boundary conditions, such as Dirichlet boundary condition, Neumann boundary condition, homogeneous mixed boundary condition (albedo type), and inhomogeneous mixed boundary condition. We also test reconstruction of the pinwise flux from nodal values, specifically from the AFEN [1, 2] results. From the nodal flux distribution we obtain surface flux and surface current distributions, which can be used to construct various types of boundary conditions. The result show that the Neumann boundary condition cannot be used for iterative schemes because of its ill-conditioning problem and that the other three boundary conditions give similar accuracy. The Dirichlet boundary condition requires the shortest computing time. The inhomogeneous mixed boundary condition requires only slightly longer computing time than the Dirichlet boundary condition, so that it could also be an alternative. In contrast to the fixed-source type problem resulting from the Dirichlet, Neumann, inhomogeneous mixed boundary conditions, the homogeneous mixed boundary condition constitutes an eigenvalue problem and requires longest computing time among the three (Dirichlet, inhomogeneous mixed, homogeneous mixed) boundary condition problems.

• Nuclear Engineering and Technology
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• 제20권3호
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• pp.145-154
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• 1988

현대 nodal code는 원자로의 출력분포와 임계도를 정확하면서도 매우 효율적으로 계산해낸다. 그러나 이 경우 핵연료 집합체내의 세세한 출력분포는 알 수가 없게 되는데 본 논문에서는 이러한 것을 nodal 계산결과로부터 재생하는 방법에 대해서 연구해 보았다. 본 연구에서는 핵연료 집합체의 표면부근에서 열중성자속의 분포가 급격히 변하는 현상을 고려한 개선된 form function 방법을 개발하였다. 새 방법을 몇 개의 가압경수로 benchmark problem에 응용해본 결과 기존의 방법에서 초래되었던 열 중성자속의 큰 재생오차가 속 중성자 속의 재생오차와 비슷하게 줄었으며 따라서 출력분포의 재생오차도 크게 감소하였다. 또한 중성자속의 분포변화가 매우 큰 baffle과 인접한 집합체에서의 출력분포 재생오차도 크게 줄일 수 있었다.

• Nuclear Engineering and Technology
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• 제45권4호
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• pp.529-538
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• 2013

Scattered photons cause blurring and distortions in flash radiography, reducing the accuracy of image reconstruction significantly. The effect of the scattered photons is taken into account and an iterative deduction of the scattered photons is proposed to amend the scattering effect for image restoration. In order to deduct the scattering contribution, the flux of scattered photons is estimated as the sum of two components. The single scattered component is calculated accurately together with the uncollided flux along the characteristic ray, while the multiple scattered component is evaluated using correction coefficients pre-obtained from Monte Carlo simulations.The arbitrary geometry pretreatment and ray tracing are carried out based on the customization of AutoCAD. With the above model, an Iterative Procedure for image restORation code, IPOR, is developed. Numerical results demonstrate that the IPOR code is much more accurate than the direct reconstruction solution without scattering correction and it has a very high computational efficiency.

• Nuclear Engineering and Technology
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• 제21권3호
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• pp.193-204
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• 1989

본 논문에서는 정보 이론의 maximum entropy Principle을 이용하여 중성자속 분포를 재생하는 새로운 방법을 시도하였다. 어떤 대상에 대한 부분적인 정보가 있을 때, 이 정보의 한도 내에서 entropy를 최대화시키는 확률 분포는 가장 객관적인 것이 된다. Nodal method계산결과인 평균 중성자속과 current의 값을 prior information으로 삼고, 핵 연료 집합체의 경계에서의 중성자속 분포를 확률의 형태로 변환해서 확률로써 다룬다. Prior information의 한도 내에서 entropy를 최대화시키는 경계에서의 확률 분포를 구하면 핵연료 집합체의 경계에서의 중성자속 분포가 구해지는데, 이것을 경계조건으로 heterogeneous assembly calculation을 행하여 세부적인 중성자속 분포를 구한다. 이 새로운 방법을 몇 개의 benchmark problem assembly에 응용해 본 결과, 노심의 안쪽 부분에서는 이 방법이 form function method에 의한 것과 비슷한 정확도를 보였고 바깥 부분에서는 다소 큰 오차를 보였다. 본 논문에서는 surface-averaged neutron current를 prior in-formation에 포함시키지 못했는데, 이것을 포함시키면 결과가 훨씬 개선 될 것으로 보인다.

• Nuclear Engineering and Technology
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• 제53권7호
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• pp.2348-2356
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• 2021

As a relatively new radiation imaging method, the cosmic-ray muon scattering imaging technology can be used to prevent nuclear smuggling and is of considerable significance to nuclear safety. Proposed in this paper is a new reconstruction algorithm based on density clustering, aiming to improve inspection quality with better performance. Firstly, this new algorithm is introduced in detail. Then in order to eliminate the inequity of the density threshold caused by the heterogeneity of the muon flux in different positions, a new flux correction method is proposed. Finally, three groups of simulation experiments are carried out with the help of Geant4 toolkit to optimize the algorithm parameters, verify the correction method and test the inspection quality under shielded condition, and compare this algorithm with another common inspection algorithm under different conditions. The results show that this algorithm can effectively identify and locate nuclear material with low misjudging and missing rates even when there is shielding and momentum precision is low, and the threshold correcting method is universally effective for density clustering algorithms.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 2003년도 춘계학술발표대회 요약집
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• pp.102.2-102.2
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• 2003

• Nuclear Engineering and Technology
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• 제31권3호
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• pp.303-313
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• 1999

Various interpolation methods have been compared for reconstruction of LMR pin power distributions in hexagonal geometry. Interpolation functions are derived for several combinations of nodal quantities and various sets of basis functions, and tested against fine mesh calculations. The test results indicate that the interpolation functions based on the sixth degree polynomial are quite accurate, yielding maximum interpolation errors in power densities less than 0.5%, and maximum reconstruction errors less than 2% for driver assemblies and less than 4% for blanket assemblies. The main contribution to the total reconstruction error is made tv the nodal solution errors and the comer point flux errors. For the polynomial interpolations, the basis monomial set needs to be selected such that the highest powers of x and y are as close as possible. It is also found that polynomials higher than the seventh degree are not adequate because of the oscillatory behavior.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1996년도 춘계학술발표회논문집(1)
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• pp.282-287
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• 1996

We. develop in this study a wavelet transform method to apply to the flux reconstruction problem in reactor analysis. When we reconstruct pinwise heterogeneous flux by iterative methods, a difficulty arises due to the near singularity of the matrix as the mesh size becomes finer. Here we suggest a wavelet transform to tower the spectral radius of the near singular matrix and thus to converge by a standard iterative scheme. We find that the spectral radios becomes smatter than one after the wavelet transform is performed on sample problems.

• Nuclear Engineering and Technology
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• 제42권5호
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• pp.474-499
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• 2010

This paper presents the mostortant developments implemented in the APOLLO2 spectral code since its last general presentation at the 1999 M&C conference in Madrid. APOLLO2 has been provided with new capabilities in the domain of cross section self-shielding, including mixture effects and transfer matrix self-shielding, new or improved flux solvers (CPM for RZ geometry, heterogeneous cells for short MOC and the linear-surface scheme for long MOC), improved acceleration techniques ($DP_1$), that are also applied to thermal and external iterations, and a number of sophisticated modules and tools to help user calculations. The method of characteristics, which took over the collision probability method as the main flux solver of the code, allows for whole core two-dimensional heterogeneous calculations. A flux reconstruction technique leads to fast albeit accurate solutions used for industrial applications. The APOLLO2 code has been integrated (APOLLO2-A) within the $ARCADIA^{(R)}$ reactor code system of AREVA as cross section generator for PWR and BWR fuel assemblies. APOLLO2 is also extensively used by Electricite de France within its reactor calculation chain. A number of numerical examples are presented to illustrate APOLLO2 accuracy by comparison to Monte Carlo reference calculations. Results of the validation program are compared to the measured values on power plants and critical experiments.

• 한국전산유체공학회지
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• 제11권4호
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• pp.39-47
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• 2006

In this paper, the authors developed a multidimensional interpolation method inside a finite volume cell in the computation of high-order accurate numerical flux such as the fifth order WEND (weighted essentially non-oscillatory) scheme. This numerical method starts from a simple Taylor series expansion in a proper spatial order of accuracy, and the WEND filter is used for the reconstruction of sharp nonlinear waves like shocks in the compressible flow. Two kinds of interpolations are developed: one is for the cell-averaged values of conservative variables divided in one mother cell (Type 1), and the other is for the vertex values in the individual cells (Type 2). The result of the present study can be directly used to the cell refinement as well as the convective flux between finer and coarser cells in the Cartesian adaptive grid system (Type 1) and to the post-processing as well as the viscous flux in the Navier-Stokes equations on any types of structured and unstructured grids (Type 2).