A Three-Dimensional Variational Nodal Method for Pin-Resolved Neutron Transport Analysis of Pressurized Water Reactors. (2nd November 2017)

• Record Type: Journal Article
• Authors: Zhang, Tengfei; Wang, Yongping; Lewis, E. E.; Smith, M. A.; Yang, W. S.; Wu, Hongchun
• Is Part Of: Nuclear science and engineering. Volume 188:Number 2(2017)
• Page Start: 160
• Page End: 174
• Publication Date: 2017-11-02
• Subjects: Three-dimensional variational nodal method -- eliminating the fuel-moderator homogenization; Nuclear energy -- Periodicals; Nuclear engineering -- Periodicals; Nuclear energy; Nuclear engineering; Periodicals; 539.705
• DOI: 10.1080/00295639.2017.1350002
• Languages: English
• ISSNs: 0029-5639

Abstract

Abstract: A three-dimensional variational nodal method (VNM) is presented for pressurized water reactor core calculations without fuel-moderator homogenization. The nodal functional is presented and discretized to obtain response matrix equations. Within the nodes, finite elements in the x-y plane and orthogonal polynomials in z are used to approximate the spatial flux distribution. On the lateral interfaces, orthogonal polynomials are employed. On the axial interfaces, the finite elements facilitate a spatially accurate current representation that has proven to be a challenge for the method of characteristics–based two-dimensional/one-dimensional approximations which typically rely on spatial homogenization. The angular discretization utilizes an even-parity integral method within the nodes, with the integrals evaluated using high-order Chebyshev-Legendre cubature. On the lateral and axial interfaces, low-order spherical harmonics (Pn ) are augmented by high-order Pn expansions to which quasi-reflected conditions are applied. With quasi-reflected conditions, the solution converges to the high-order Pn solution for an infinite lattice of identical cells with no gradient, while the low-order Pn expansions handle global gradients in both the radial and axial directions. The method is implemented in the PANX code and applied first to a number of model problems to study convergence of the space-angle approximations and then to the C5G7 benchmark problems. Multigroup Monte Carlo solutions provide reference values for eigenvalues and pin-power distributions.