• Nuclear Engineering and Technology
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• v.28 no.3
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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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• v.20 no.3
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• pp.145-154
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• 1988

This paper is a study on an accurate and computationally efficient method for reconstructing pointwise power distributions from coarse-mesh nodal calculations. The modern nodal codes can calculate global reactor power shapes and criticality very efficiently and accurately. But inherent in the nodal procedures, there is inevitable loss of information on local heterogeneous quantities. In this study, an improved form function method which reflects the exponential transition of the thermal flux near the assembly surface is developed for the reconstruction of the heterogeneous fluxes. Use of the new form function method in several pressurized water reactor (PWR) benchmark problems reduces the maximum errors in the reconstructed thermal flux to those in the reconstructed fast flux. Even for assemblies adjacent to the steel baffle in realistic PWR cores, use of this method also results in improved pointwise power reconstruction.

• Nuclear Engineering and Technology
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• v.45 no.4
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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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• v.21 no.3
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• pp.193-204
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• 1989

This paper develops a new method for reconstructing neutron flux distribution, that is based on the maximum entropy Principle in information theory. The Probability distribution that maximizes the entropy Provides the most unbiased objective Probability distribution within the known partial information. The partial information are the assembly volume-averaged neutron flux, the surface-averaged neutron fluxes and the surface-averaged neutron currents, that are the results of the nodal calculation. The flux distribution on the boundary of a fuel assembly, which is the boundary condition for the neutron diffusion equation, is transformed into the probability distribution in the entropy expression. The most objective boundary flux distribution is deduced using the results of the nodal calculation by the maximum entropy method. This boundary flux distribution is then used as the boundary condition in a procedure of the imbedded heterogeneous assembly calculation to provide detailed flux distribution. The results of the new method applied to several PWR benchmark problem assemblies show that the reconstruction errors are comparable with those of the form function methods in inner region of the assembly while they are relatively large near the boundary of the assembly. The incorporation of the surface-averaged neutron currents in the constraint information (that is not done in the present study) should provide better results.

• Nuclear Engineering and Technology
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• v.53 no.7
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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.

• Proceedings of the Korean Nuclear Society Conference
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• 2003.05a
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• pp.102.2-102.2
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• 2003

• Nuclear Engineering and Technology
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• v.31 no.3
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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.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05a
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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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• v.42 no.5
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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.

• Journal of computational fluids engineering
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• v.11 no.4 s.35
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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).