Farzad Rahnema

The Incident Flux Response Expansion Method for Heterogeneous Coarse Mesh Transport Problems

A generalization of the response expansion previously used to develop a variational heterogeneous coarse mesh transport method has been accomplished. This allows a broad class of response functions to be employed within the framework of the original variational principle. New finite element equations were derived based on the general expansion, along with an additional assumption that seemingly breaks the tight coupling that created numerical difficulties in previous work. In addition, the nonvariational method was developed in a new and more thorough manner by considering the implications of the fission source treatment imposed by the response expansion. Results are presented for several heterogeneous light water reactor benchmark problems in the one‐dimensional, multigroup, discrete ordinates approximation. An efficient set of response functions was constructed using the discrete Legendre polynomials as boundary conditions. It was found that the expansion could be truncated at a low order without a significant loss of accuracy. In addition, the expansion order was found to have a much greater impact on the results than the type of method.

Leakage corrected spatial (assembly) homogenization technique

Abstract A homogenization technique is developed to account for the interassembly neutron leakage effect on the homogenized parameters within generalized equivalence theory. To assess its accuracy, the method is implemented into a two-group nodal diffusion model. Both one and two dimensional Boiling Water Reactor benchmark problems are considered. Comparisons to fine-mesh results show an average of 30% accuracy improvement in the nodal power for the most heterogeneous case.

Boundary Condition Perturbation Theory for Use in Spatial Homogenization Methods

An expression is developed in diffusion theory for estimating the first-order change in a ratio of linear functionals due to a perturbation in the current-to-flux ratio boundary condition of a system. One numerical example is given. Additionally, it is shown that the perturbation formalism may be used in the spatial homogenization process to account for interassembly effects such as gross flux tilts and spectral effects caused by neighboring assemblies in the reactor core.

A Heterogeneous Coarse Mesh Transport Method

Abstract A method to solve the neutron transport equation on a grid with arbitrarily large spatial coarse meshes (elements) is developed. The method, which is based on a variational principle, uses discontinuous trial functions to derive a set of integral equations. The trial functions are constructed from surface Greens functions for each unique coarse mesh (e.g., fuel assembly) in the system. The theoretical approach is validated numerically for three multigroup, slab geometry problems, with the angular dependence treated by the discrete ordinates (SN) method. In this case, the fine-mesh results are reproduced by the coarse-mesh method. #Current address: Dan Ilas, Ph.D., Nuclear Science Center, Louisiana State University, Baton Rouge, Louisiana, USA

Generalized Energy Condensation Theory

Abstract A generalization of multigroup energy condensation theory has been developed. The new method generates a solution within the few-group framework that exhibits the energy spectrum characteristic of a many-group transport solution, without the computational time usually associated with such solutions. This is accomplished by expanding the energy dependence of the angular flux in a set of general orthogonal functions. The expansion leads to a set of equations for the angular flux moments in the few-group framework. The zeroth moment generates the standard few-group equation while the higher-moment equations generate the detailed spectral resolution within the few-group structure. It is shown that by carefully choosing the orthogonal function set (e.g., Legendre polynomials), the higher-moment equations are only coupled to the zeroth-order equation and not to each other. The decoupling makes the new method highly competitive with the standard few-group method since the computation time associated with determining the higher moments becomes negligible as a result of the decoupling. The method is verified in several one-dimensional benchmark problems typical of boiling water reactor configurations with mild to high heterogeneity.

A Monte Carlo based nodal diffusion model for criticality analysis of spent fuel storage lattices

Abstract A computational method is presented as an alternative to the Monte Carlo and transport theory models presently used for the criticality analysis of regular lattices for spent fuel storage. The method is developed in the framework of nodal diffusion theory, with nodal parameters obtained from continuous energy Monte Carlo computations. The applicability and the accuracy of the method are assessed in two-dimensional geometry through several benchmark problems.

Higher-Order Boundary Condition Perturbation Theory for the Diffusion Approximation

Abstract A perturbation method is developed for estimating the change in the solution of a reactive system to any order for a perturbation in the boundary condition in diffusion theory. The method derived gives formalisms for the eigenvalue, normalized flux, and homogenized parameters. Five examples are provided to verify the method as well as analyze the errors associated with it. The first example is very simple and solves the state of the system up to eighth order and gives a simple numerical analysis of a large perturbation. The next example gives an analytical solution up to second order. A two-region example is also given, which is partially numerical and partially analytical. An albedo test example shows that the higher-order terms all appear to be present in the formalism. The final example presents a simplified one-dimensional boiling water reactor core analyzed up to third order numerically. Applications of this method, error propagation, and future work are also discussed.

High-order cross-section homogenization method

Abstract A high-order cross-section homogenization method based on boundary condition perturbation theory is developed to improve the accuracy of nodal methods for coarse-mesh eigenvalue calculations. The method expands the homogenized parameters such as the cross-sections and the neutron flux discontinuity factor in terms of the node surface current-to-flux ratio. The expansion coefficients are evaluated during the nodal calculations using additional precomputed homogenization parameters. As a result, it is possible to correct (update) the homogenized parameters to arbitrary order of accuracy for the effect of reactor core environment (fuel assembly neutron leakage) with very little computational effort in the core calculation. The reconstructed fine-mesh flux (fuel-pin power) is a natural byproduct of the new method. A benchmark problem typical of a BWR core is analyzed in one dimension, monoenergetic diffusion theory by modifying a nodal method based on a bilinear, flat as well as a fine-mesh intranodal flux shape. The homogenized parameters are first computed using exact (fine-mesh) albedos and compared to those determined from a fine-mesh core calculation. Two nodal (coarse-mesh) examples are given to show how well this approach works as a higher-order perturbation method is utilized. The paper concludes by showing that this method succeeds in giving excellent results for cores that may be difficult to model using standard nodal methods.

A heterogeneous finite element method in diffusion theory

Abstract A new Heterogeneous Finite Element Method (HFEM) is presented, which does not require prior assembly-level homogenization and which accounts for the leakage effect. The HFEM is developed in diffusion theory. The method is a Lagrange Finite Element Method, that uses basis functions that include fine mesh detail. The elementary basis functions are generated from fixed-boundary-flux fine mesh heterogeneous assembly calculations. The FEM equations are generated using a Galerkin scheme derived from a variational principle. The method is tested on three two-dimensional configurations typical of Boiling Water Reactors, and is shown to be as accurate as the combination Assembly Homogenization—Nodal Method for low-leakage cores and significantly more accurate than the mentioned combination for high-leakage cores

Boundary condition perturbations in transport theory

Expressions are derived for the first-order change in the fundamental eigenvalue of the neutron transport equation due to a perturbation in the boundary condition of the system. The perturbation formula is derived in the context of the energy-dependent transport theory and its diffusion approximation. Numerical examples are given in both transport and diffusion theory.