In this paper, we formulate a new flux reconstruction method based on the High Dimensional Model Representation (HDMR) of the nodal flux shape. The method requires the conventional nodal parameters obtained as a result of the transverse-integration nodal solution procedure as well as corner values calculated by a combination of finite-volume and finite-difference approximations. The proposed flux reconstruction procedure is applicable to rectangular nodes and more than two energy groups. The flux reconstruction method is applied to a number of homogeneous and heterogeneous test problems in order to evaluate its accuracy.

This work addresses the problem of propagating uncertainty from group-wise neutron cross-sections to the results of neutronics diffusion calculations. Automatic differentiation based on dual number arithmetic was applied to uncertainty propagation in the framework of local sensitivity analysis. As an illustration, we consider a two-group diffusion problem in an infinite medium, which has a solution in a closed form. We employ automatic differentiation in conjunction with the sandwich formula for uncertainty propagation in three ways. Firstly, by evaluating the analytical expression for the multiplication factor using dual number arithmetic. Then, by solving the diffusion problem with the power iteration algorithm and the algebra of dual matrices. Finally, automatic differentiation is used to calculate the partial derivatives of the production and loss operators in the perturbation formula from the adjoint-weighted technique. The numerical solution of the diffusion problem is verified against the analytical formulas and the results of the uncertainty calculations are compared with those from the global sensitivity analysis approach. The uncertainty values obtained in this work differ from values given in the literature by less than 1?10?5.

The OSCAR-4 code suite is a nodal diffusion based calculational system, which has been used over many years for research reactor support. It is primarily used to support the operation of the SAFARI-1 research reactor at Necsa, South Africa, but is also applied at various other international research reactors (such as HOR, HFR and MNR). Recently, the next generation OSCAR system (termed OSCAR-5) has been under development, with specific focus on the challenges which highly heterogeneous research reactor core designs pose – in particular with regard to core design and core-follow type analyses. The main aim of the new development is the seamless integration between high fidelity and standard core analysis methods. A detailed heterogeneous model is constructed in a code-independent front-end system, which is then capable of deploying the model to all codes connected to it. In particular, automatic input generation is available for Monte Carlo codes like MCNP and Serpent, as well as the nodal diffusion solver in OSCAR-4. The deployment to a nodal diffusion code uses advanced homogenization and nodal equivalence methods to ensure a theoretically minimized discrepancy between the heterogeneous and homogeneous solutions. The nodal model is developed in a staged process, allowing tight monitoring and control of the model error as compared to the reference heterogeneous Monte Carlo model. In particular, all non-fuel homogenized multi-group cross-sections are generated from a set of fullcore heterogeneous calculations, while fuel models are generated from typical, often infinite lattice, environments. The use of infinite lattice models results in the so-called environmental error on the nodal equivalence parameters, which in the new system may be remedied via various correction schemes in the nodal diffusion solver. The numerical impact of these approaches is illustrated on the SAFARI-1, OPAL and IPEN reactor benchmarks as they appear in the ongoing IAEA CRP T12029 on multi-cycle depletion and activation analysis.

Nodal diffusion methods are often used for full core neutronic analysis. They require few-group homogenised neutron cross sections for every heterogeneous sub-region of the core. The homogenised cross sections are pre-calculated at various reactor states and represented in a way that facilitates the reconstruction of cross sections at other possible states. In this study hierarchical Lagrange interpolation on Clenshaw-Curtis sparse grids was used to represent the homogenised cross sections of a MOX (mixed oxide) fuel assembly. Representations were produced for the homogenised cross sections of a number of individual isotopes, as well as the effective (lumped) cross section of all the materials in the assembly. The impact of increasing the number of neutron energy groups from two to six, as well as using different state parameter intervals, on both the representation accuracy and the way in which the cross sections depend on the state parameters, was investigated. The two sets of state parameter intervals were designed to be applicable to the simulation of standard reactor operations and transient analysis, respectively. The anisotropy feature of the representation procedure, which allows more samples to be taken for state parameters that are known to be more important to the representation accuracy than others, was applied, and the effect this refinement to the method has on the representation accuracy was studied. Results of this study show that the sparse grid method is capable of constructing efficient representations to an accuracy that is considered acceptable in practical applications, if the anisotropy feature is used. (C) 2016 Elsevier Ltd. All rights reserved.

The purpose of this study was to develop a coupled accurate multi-physics model of the SAFARI-1 Material Testing Reactor (MTR), a facility that is used for both research and the production of medical isotopes. The model was developed as part of the SAFARI-1 benchmarking project as a cooperative effort between the Pennsylvania State University (PSU) and the South African Nuclear Energy Corporation (Necsa). It was created using a multi-physics coupling of state of the art nuclear reactor simulation tools, consisting of a neutronics code and a thermal hydraulics code.The neutronics tool used was the PSU code NEM, and the results from this component were verified using the Necsa neutronics code OSCAR-4, which is utilized for SAFARI-1 core design and fuel management. On average, the multiplication factors of the neutronics models agreed to within 5 pcm and the radial assembly-averaged powers agreed to within 0.2%.The thermal hydraulics tool used was the PSU version of COBRA-TF (CTF) sub-channel code, and the results of this component were verified against another thermal hydraulics code, the RELAP5-3D system code, used at Necsa for thermal hydraulics analysis of SAFARI-1. Although only assembly-averaged results from RELAP5-3D were available, they fell within the range of values for the corresponding assemblies in the comprehensive CTF solution. This comparison allows for the first time to perform a quantification of steady-state errors for a low-powered MTR with an advanced thermal hydraulic code such as CTF on a per-channel basis as compared to simpler and coarser-mesh RELAP5-3D modeling. Additionally, a new cross section representation was used to ensure that the thermal hydraulic feedback effects on the core neutronics were captured as accurately as possible. This cross section representation was applied to SAFARI-1 core calculations for the first time in this work. Such implementation helps to quantify the effect of detailed modeling of thermal hydraulics feedback effects on neutronics results in multi-physics simulations.The outcome of the study is the intended coupled neutronics/thermal hydraulics model of the SAFARI-1 reactor. (C) 2014 Elsevier Ltd. All rights reserved.

Nodal diffusion methods are often used to calculate the distribution of neutrons in a nuclear reactor core. They require few-group homogenized neutron cross sections for every heterogeneous sub-region of the core. The homogenized cross sections are pre-calculated at various reactor states and represented in a way that facilitates the reconstruction of cross sections at other possible states. In this study a number of such representations were built for the cross sections of a MOX (mixed oxide) fuel assembly via hierarchical Lagrange interpolation on Clenshaw-Curtis sparse grids. Traditionally, nodal reactor core simulators have employed cross sections with two energy groups, but there is evidence that more energy groups are needed to simulate reactor cores that contain MOX. Representations were therefore constructed for both the traditional two energy groups and a six energy group structure. Both the rate at which the representation accuracy improves with the number of samples and the complexity of the cross section dependence on individual state parameters were examined. The anisotropy feature of the representation procedure, which allows more samples to be taken for state parameters that are known to be more important to the representation accuracy than others, was applied throughout. The results show that the representation method allows both two-group and six-group cross sections to be represented in a computationally efficient manner to an industrially acceptable level of accuracy, despite additional complexity in the dependence of six-group cross sections on the state parameters.

Few group, homogenized neutron cross sections are represented as a function of various state parameters through multidimensional Lagrange interpolation. The interpolation is built on a Clenshaw-Curtis sparse grid by applying the method of mean weighted residuals. Unlike traditional approaches, which use either the Smolyak construction or the combinatorial formula for interpolation on a sparse grid, our approach is based on the properties of multidimensional cardinal functions, built as a tensor product of one-dimensional basis functions. The interpolation technique combines the efficiency of Chebyshev interpolation with low calculation and storage requirements of sparse grid methods, which makes it scalable in dimensionality. In addition, the method provides a way to optimize the size of the library, while still keeping control of the accuracy of the representation. The representation method was applied to the few group homogenized cross sections of diverse light water reactors: PWR and MTR fuel assemblies and a VVER fuel pin. These examples differ in terms of intervals of state parameters, number of energy groups, the number of microscopic cross sections treated explicitly, and transport codes used for calculations. The analysis of the results obtained allows one to conclude that the method is capable of providing cross section representation with an accuracy that is sufficient for use in practical applications with reasonable calculational resources. (C) 2013 Elsevier Ltd. All rights reserved.

This paper presents a pseudo spectral method for representing few-group homogenised cross sections, based on hierarchical polynomial interpolation. The interpolation is performed on a multi-dimensional sparse grid built from Chebyshev nodes. The representation is assembled directly from the samples using basis functions that are constructed as tensor products of the classical one-dimensional Lagrangian interpolation functions. The advantage of this representation is that it combines the accuracy of Chebyshev interpolation with the efficiency of sparse grid methods. As an initial test, this interpolation method was used to construct a representation for the two-group macroscopic cross sections of a VVER pin cell. (authors)

The problem considered in this paper involves the representation of few group, homogenized neutron cross sections. The method for cross section representation proposed and studied in this paper utilizes a hierarchical multilinear interpolation based on sparse grid nodes. Besides interpolation itself, the method includes a built-in means of estimating the interpolation error and a procedure for optimizing the representation with the goal to reduce its footprint and the cross section reconstruction time. The method was tested on the capture cross sections of a standard Material Test Reactor fuel element for different isotopes and the results were compared to a multilinear interpolation on a tensor product grid. It is demonstrated that cross sections can be interpolated with the necessary accuracy on a sparse grid, which requires a significantly smaller number of sample points than the corresponding tensor product (full) grid. The built-in means of estimating the interpolation error is shown to be conservative by comparison with the error estimated on independent samples. The representation optimization procedure allows the discarding of most of the terms in the tensor product interpolation, as well as many terms in the sparse grid interpolation with a minimal impact on the interpolation error.

Thesis (MSc Engineering Sciences (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.