Jae Man Noh

A New Approach of Analytic Basis Function Expansion to Neutron Diffusion Nodal Calculation

A new nodal method that directly solves the multidimensional diffusion equation without the transverse integration procedure is described. The new method expands the homogeneous flux distributions within a node in nonseparable analytic basic functions satisfying the neutron diffusion equation at any point of the node. Thus, the method accurately models large localized flux gradients in the vicinity of nodal corner points as well as nodal interfaces. To demonstrate its accuracy and applicability to realistic problems, the new method was tested on several well-known benchmark problems, including a mixed-oxide fuel problem, and the initial core of Ulchin Unit 1, which is a Framatome-type pressurized water reactor rated at 2,775 MW (thermal). The results show that the new method significantly improves the accuracy in the nodal flux distribution and the core multiplication factor. The method also facilitates pinwise flux reconstruction since the homogeneous flux distributions obtained from the nodal calculation are very accurate and may be used directly in the reconstruction.

Analytic Function Expansion Nodal Method for Hexagonal Geometry

A new hexagonal nodal method that directly solves the multidimensional diffusion equation without the transverse integrated procedure is described. The new method expands the homogeneous flux distributions within a node in nonseparable analytic basis functions satisfying the neutron diffusion equations at any point of the node. Because the new method does not use the transverse integration, it does not suffer from the need of approximating the transverse leakage shape and the non-physical singular terms occurring in hexagonal nodes. And, because of the use of analytical basis functions and the corner-point flux included in the nodal coupling equations, the method accurately models large localized flux gradients in the vicinity of nodal corner points as well as nodal interfaces. The new method was tested on two hexagonal benchmark problems consisting of uranium-oxide and mixed-oxide fuel assemblies to demonstrate its accuracy and applicability to realistic problems. The results shown that the new method accurately predicts the nodal flux distribution and the core multiplication factor.

The Analytic Function Expansion Nodal Method Refined with Transverse Gradient Basis Functions and Interface Flux Moments

Abstract A refinement of the analytic function expansion nodal (AFEN) method is described. By increasing the number of flux expansion terms in the way that the original basis functions are combined with the transverse-direction linear functions, the refined AFEN method can describe the flux shape in the nodes more accurately, since the added flux expansion terms still satisfy the diffusion equation. The additional nodal unknowns introduced are the interface flux moments, and the additional constraints required are provided by the continuity conditions of the interface flux moments and the interface current moments. Also presented is an algebraically exact method for removing the numerical singularity that can occur in any analytic nodal method when the core contains nearly no-net-leakage nodes. The refined AFEN method was tested on the Organization for Economic Cooperation and Development (OECD)-L336 mixed-oxide benchmark problem in rectangular geometry, and the VVER-440 benchmark problem and a nearly no-net-leakage node embedded core problem, both in hexagonal geometry. The results show that the method improves not only the accuracy in predicting the flux distribution but also the computing time, and that it can replace the corner-point fluxes with the interface flux moments without accuracy degradation, unless the problem consists of strongly dissimilar nodes. The possibility of excluding the corner-point fluxes increases the flexibility in implementing this method into the existing codes that do not have the corner-point flux scheme and may make it fit better for the nonlinear scheme based on two-node problems.

Acceleration of the Analytic Function Expansion Nodal method by two-factor two-node nonlinear iteration

A nonlinear iterative scheme is developed to reduce the computing time of the Analytic Function Expansion Nodal (AFEN) method and is applied to three test problems, including a mixed-oxide fuel problem. The new nonlinear scheme is based on solving two-node problems and using two nonlinear correction factors at every interface instead of one factor, as in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents, which are used as the boundary conditions of the two-node problem. The numerical results show that this new nonlinear scheme reproduces the same solution as that of the original AFEN method and that the computing time is significantly reduced in comparison with the original AFEN method.