• Nuclear Engineering and Technology
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• v.56 no.3
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• pp.772-784
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• 2024

The hexagonal nodal code RENUS has been enhanced to handle irregularly deformed hexagonal assemblies. The underlying RENUS methods involving triangle-based polynomial expansion nodal (T-PEN) and corner point balance (CPB) were extended in a way to use line and surface integrals of polynomials in a deformed hexagonal geometry. The nodal calculation is accelerated by the coarse mesh finite difference (CMFD) formulation extended to unstructured geometry. The accuracy of the unstructured nodal solution was evaluated for a group of 2D SFR core problems in which the assembly corner points are arbitrarily displaced. The RENUS results for the change in nuclear characteristics resulting from fuel deformation were compared with those of the reference McCARD Monte Carlo code. It turned out that the two solutions agree within 18 pcm in reactivity change and 0.46% in assembly power distribution change. These results demonstrate that the proposed unstructured nodal method can accurately model heterogeneous thermal expansion in hexagonal fueled cores.

• Proceedings of the Korea Society for Energy Engineering kosee Conference
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• 1993.11a
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• pp.99-102
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• 1993

A consistent general order nodal method for solving the three-dimensional neutron diffusion equation in (x-y-z) geometry has been derived by using a weighted integral technique and expanding the spatial variable by the Legendre orthogonal series function. The equation set derived can be converted into any order nodal schemes. It forms a compact system for general order of nodal moments. The method utilizes fewer unknown variables in the schemes for iterative-convergence solution than other nodal methods listed in the literatures, and because the method utilizes the analytic solutions of the transverse-integrated one dimensional equations and a consistent approximation for a given spatial variable through all the solution procedures, which renders the use of an approximation for the transverse leakages no longer necessary, we can expect extremely accurate solutions and the solution would converge exactly when the mesh width is decreased or the approximation order is increased.

• Nuclear Engineering and Technology
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• v.32 no.6
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• pp.605-617
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• 2000

Nodal transport methods are studied for the solution of two dimensional discrete-ordinates, simplified even-parity transport equation(SEP) which is known to be an approximation to the true transport equation. The polynomial expansion nodal method(PEN) and the analytic function expansion nodal method(AFEN）which have been developed for the diffusion theory are used for the solution of the discrete-ordinates form of SEP equation. Our study shows that while the PEN method in diffusion theory can directly be converted without complication, the AFEN method requires a theoretical modification due to the nonhomogeneous property of the transport equation. The numerical results show that the proposed two methods work well with the SEP transport equation with higher accuracies compared with the conventional finite difference method.

• Nuclear Engineering and Technology
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• v.54 no.5
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• pp.1789-1803
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• 2022

RAST-F is a new full-core analysis code based on the two-step approach that couples a multi-group cross-section generation Monte-Carlo code MCS and a multi-group nodal diffusion solver. To demonstrate the feasibility of using MCS/RAST-F for fast reactor analysis, this paper presents the coupled nodal code verification results for the MET-1000 and CAR-3600 benchmark cores. Three different multi-group cross-section calculation schemes are employed to improve the agreement between the nodal and reference solutions. The reference solution is obtained by the MCS code using continuous-energy nuclear data. Additionally, the MCS/RAST-F nodal solution is verified with results based on cross-section generated by collision probability code TULIP. A good agreement between MCS/RAST-F and reference solution is observed with less than 120 pcm discrepancy in k_eff and less than 1.2% root-mean-square error in power distribution. This study confirms the two-step approach MCS/RAST-F as a reliable tool for the three-dimensional simulation of reactor cores with fast spectrum.

• Nuclear Engineering and Technology
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• v.16 no.4
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• pp.202-216
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• 1984

The success of coarse-mesh nodal solution methods provides strong motivation for finding homogenized parameters which, when used in global nodal calculation, will reproduce exactly all average nodal reaction rates for large nodes. Two approximate theories for finding these ideal parameters, namely, simplified equivalence theory and approximate node equivalence theory, are described herein and then applied to the PWR benchmark problem. Nodal code, ANM, is used for the global calculation as well as for the homogenization calculation. From the comparative analysis, it is recommended that homogenization be carried out only for the unique type of fuel assemblies and for core boundary color-sets. The use of approximate homogenized cross-sections and approximate discontinuity factors predicts nodal powers with maximum error of 0.8% and criticality within 0.1% error relative to the fine-mesh KIDD calculations.

• Nuclear Engineering and Technology
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• v.54 no.8
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• pp.3059-3072
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• 2022

A Jacobian-Free Newton Krylov Two-Nodal Coarse Mesh Finite Difference algorithm based on Nodal Expansion Method (NEM_TNCMFD_JFNK) is successfully developed and proposed to solve the three-dimensional (3D) and multi-group reactor physics models. In the NEM_TNCMFD_JFNK method, the efficient JFNK method with the Modified Incomplete LU (MILU) preconditioner is integrated and applied into the discrete systems of the NEM-based two-node CMFD method by constructing the residual functions of only the nodal average fluxes and the eigenvalue. All the nonlinear corrective nodal coupling coefficients are updated on the basis of two-nodal NEM formulation including the discontinuity factor in every few newton steps. All the expansion coefficients and interface currents of the two-node NEM need not be chosen as the solution variables to evaluate the residual functions of the NEM_TNCMFD_JFNK method, therefore, the NEM_TNCMFD_JFNK method can greatly reduce the number of solution variables and the computational cost compared with the JFNK based on the conventional NEM. Finally the NEM_TNCMFD_JFNK code is developed and then analyzed by simulating the representative PWR MOX/UO₂ core benchmark, the popular NEACRP 3D core benchmark and the complicated full-core pin-by-pin homogenous core model. Numerical solutions show that the proposed NEM_TNCMFD_JFNK method with the MILU preconditioner has the good numerical accuracy and can obtain higher computational efficiency than the NEM-based two-node CMFD algorithm with the power method in the outer iteration and the Krylov method using the MILU preconditioner in the inner iteration, which indicates the NEM_TNCMFD_JFNK method can serve as a potential and efficient numerical tool for reactor neutron diffusion analysis module in the JFNK-based multiphysics coupling application.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05a
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• pp.79-86
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• 1998

The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized. In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of applications to the NEACRP PWR rod ejection benchmark problem.

• Nuclear Engineering and Technology
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• v.53 no.9
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• pp.2788-2802
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• 2021

Multigroup cross section (MG XS) generation by the UNIST in-house Monte Carlo (MC) code MCS for fast reactor analysis using nodal diffusion codes is reported. The feasibility of the approach is quantified for two sodium fast reactors (SFRs) specified in the OECD/NEA SFR benchmark: a 1000 MW_th metal-fueled SFR (MET-1000) and a 3600 MW_th oxide-fueled SFR (MOX-3600). The accuracy of a few-group XSs generated by MCS is verified using another MC code, Serpent 2. The neutronic steady-state whole-core problem is analyzed using MCS/RAST-K with a 24-group XS set. Various core parameters of interest (core k_eff, power profiles, and reactivity feedback coefficients) are obtained using both MCS/RAST-K and MCS. A code-to-code comparison indicates excellent agreement between the nodal diffusion solution and stochastic solution; the error in the core k_eff is less than 110 pcm, the root-mean-square error of the power profiles is within 1.0%, and the error of the reactivity feedback coefficients is within three standard deviations. Furthermore, using the super-homogenization-corrected XSs improves the prediction accuracy of the control rod worth and power profiles with all rods in. Therefore, the results demonstrate that employing the MCS MG XSs for the nodal diffusion code is feasible for high-fidelity analyses of fast reactors.

• Nuclear Engineering and Technology
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• v.53 no.5
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• pp.1391-1402
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• 2021

The aim of this work is to prepare a neutron noise calculator based on the second order of average current nodal expansion method (ACNEM). Generally, nodal methods have the ability to fulfill the neutronic analysis with adequate precision using coarse meshes as large as a fuel assembly size. But, for the zeroth order of ACNEM, the accuracy of neutronic simulations may not be sufficient when coarse meshes are employed in the reactor core modeling. In this work, the capability of second order ACNEM is extended for solving the neutron diffusion equation in the frequency domain using coarse meshes. For this purpose, two problems are modeled and checked including a slab reactor and 2D BIBLIS PWR. For validating of results, a semi-analytical solution is utilized for 1D test case, and for 2D problem, the results of both forward and adjoint neutron noise calculations are exploited. Numerical results indicate that by increasing the order of method, the errors of frequency dependent coarse mesh solutions are considerably decreased in comparison to the reference. Accordingly, the accuracy of second order ACNEM can be acceptable for the neutron noise calculations by using coarse meshes in the nuclear reactor core.

• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.203-216
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• 1999

A previously proposed finite element formulation method is refined and modified to generate a new type of elements. The method is based on selecting a set of general solution modes for element formulation. The constant strain modes and higher order modes are selected and the formulation method is designed to ensure that the element will pass the basic single element test, which in turn ensures the passage of the basic patch test. If the element is to pass the higher order patch test also, the element stiffness matrix is in general asymmetric. The element stiffness matrix depends only on a nodal displacement matrix and a nodal force matrix. A symmetric stiffness matrix can be obtained by either modifying the nodal displacement matrix or the nodal force matrix. It is shown that both modifications lead to the same new element, which is demonstrated through numerical examples to be more robust than an assumed stress hybrid element in plane stress application. The method of formulation can also be used to arrive at the conforming displacement and hybrid stress formulations. The convergence of the latter two is explained from the point of view of the proposed method.