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

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
• /
• v.16 no.2
• /
• pp.211-221
• /
• 2018

Nodal transport methods are proposed for solving the simplified even-parity neutron transport (SEP) equation. These new methods are attributed to the success of existing nodal diffusion methods such as the Polynomial Expansion Nodal and the Analytic Function Expansion Nodal Methods, which are known to be very effective for solving the neutron diffusion equation. Numerical results show that the simplified even-parity transport equation is a valid approximation to the transport equation and that the two nodal methods developed in this study also work for the SEP transport equation, without conflict. Since accuracy of methods is easily increased by adding node unknowns, the proposed methods will be effective for coarse mesh calculation and this will also lead to computation efficiency.

• Nuclear Engineering and Technology
• /
• v.54 no.9
• /
• pp.3494-3515
• /
• 2022

This paper presents the development of a nodal diffusion code, RAST-V, and its verification and validation for VVER (vodo-vodyanoi energetichesky reactor) analysis. A VVER analytic solver has been implemented in an in-house nodal diffusion code, RAST-K. The new RAST-K version, RAST-V, uses the triangle-based polynomial expansion nodal method. The RAST-K code provides stand-alone and two-step computation modes for steady-state and transient calculations. An in-house lattice code (STREAM) with updated features for VVER analysis is also utilized in the two-step method for cross-section generation. To assess the calculation capability of the formulated analysis module, various verification and validation studies have been performed with Rostov-II, and X2 multicycles, Novovoronezh-4, and the Atomic Energy Research benchmarks. In comparing the multicycle operation, rod worth, and integrated temperature coefficients, RAST-V is found to agree with measurements with high accuracy which RMS differences of each cycle are within ±47 ppm in multicycle operations, and ±81 pcm of the rod worth of the X2 reactor. Transient calculations were also performed considering two different rod ejection scenarios. The accuracy of RAST-V was observed to be comparable to that of conventional nodal diffusion codes (DYN3D, BIPR8, and PARCS).

• Proceedings of the Korean Nuclear Society Conference
• /
• 1996.05a
• /
• pp.157-162
• /
• 1996

A novel nodal method is developed for the two-dimensional multi-group diffusion equations based on the Spectral-Galerkin approach. In this study, the nodal diffusion equations with Robin boundary condition are reformulated in a weak (variational) form, which is then approximated spatially by choosing appropriate basis functions. For the nodal coupling relations between the neighbouring nodes, the continuity conditions of partial currents are utilized. The resulting discrete systems with sparse structured matrices are solved by the Preconditioned Conjugate Gradient Method (PCG) and sweeping technique. The method is validated on two test problems.

• Proceedings of the Korean Nuclear Society Conference
• /
• 1995.10a
• /
• pp.29-34
• /
• 1995

The good features of the analytic function expansion nodal (AFEN) method are utilized to develop a practical scheme jot the multigroup diffusion problems, in combination with the polynomial expansion nodal (PEN) method. The thermal group fluxes exhibiting strong gradients are solved by the AFEN method[1-6], while the fast group fluxes that are smoother than the thermal group fuzes are solved by the PEN method[7-9]. The scheme is applied to a MOX-fuel loaded core with good results.

• Proceedings of the Korea Society for Energy Engineering kosee Conference
• /
• 2000.11a
• /
• pp.115-120
• /
• 2000

The analysis of flux distribution under stead-state in large power reactors with assymetry reactivity insertions requires the use of three-dimensional diffusion calculations. For the purpose, consistently formulated modern nodal methods based on higher order interface techniques have become popular tools for flux distributions in large commercial nuclear reactors. Among the earlier developments, the nodal Green's function method obtains its nodal interface equation from the transverse-integrated integral diffusion equation using a finite-medium Green's function. In this method, the outgoing current from a node surface is formulated as a response of the incoming currents and the spatially integrated neutron source within the same node. The well-known nodal expansion method is also based on an interface partial current formulation. Nodal methods high-level interface variables, i.e., interface net current and flux, may be more computationally efficient than the nodal Green's function method because they have one fewer unknown per interface. The Analytic Nodal Method(ANM), which can be classified as an interface net current technique and, was faster in solving some standard benchmark problems than the other two methods.(omitted)

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

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

• Proceedings of the Korean Nuclear Society Conference
• /
• 1996.05a
• /
• pp.131-136
• /
• 1996

An analytic nodal expansion method has been derived for the multigroup neutron diffusion equation in 2-D cylindrical(R-Z) coordinate. In this method we used the second order Legendre polynomials for source, and transverse leakage, and then the diffusion eqaution was solved analytically. This formalism has been applied to 2-D LWR model. $textsc{k}$$_{eff}$, power distribution, and computing time have been compared with those of ADEP code(finite difference method). The benchmark showed that the analytic nodal expansion method in R-Z coordinate has good accuracy and quite faster than the finite difference method. This is another merit of using R-Z coordinate in that the transverse integration over surfaces is better than the linear integration over length. This makes the discontinuity factor useless.s.

• Proceedings of the Korean Nuclear Society Conference
• /
• 1996.05a
• /
• pp.34-39
• /
• 1996

A consistent general order nodal method for solving the 3-D neutron diffusion equation in (x-y-z) geometry has ben derived by using a weighted integral technique and expanding the spatial variables 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 the analytic solutions of the transverse-integrated quasi -one dimensional equations and a consistent expansion for the spatial variables so that it renders the use of an approximation for the transverse leakages no necessary. Thus, we can expect extremely accurate solutions and the solution would converge exactly when the mesh width is decreased or the approximation order is increased since the equation set is consistent mathematically.