http://li.mit.edu/Stuff/CNSE/Paper/Lawrence86PNE.pdf

Progress in nodal methods for the solution of the neutron diffusion and transport equations

This investigation is to review advanced technologies for modeling and control of reactor cores in nuclear power plants for electricity generation. A reactor core in a nuclear power plant is the key part as the hot source with radioactivity nuclear fuel, which possesses security risks and economic potential. Incapacity of a nuclear power plant to carry out desired control of its core can result in either higher operating costs or a reduction in system security and reliability, and the implementation of desirable control for the core can improve security and effectiveness of the nuclear power plant. Generally speaking, the reactor core control contains the power (or coolant temperature) control and axial power difference (namely power distribution) control of the core. The core power control is to regulate the core power, and the core load following control is to regulate the core power and axial power difference simultaneously. Modeling reactor cores is the inevitable preliminary work for research of reactor core control. Over the decades, continuous work has been devoted to the research of including modeling, power and load following control for reactor cores. In this paper, the review on advanced technologies for modeling, power and load following control of reactor cores is presented. Modeling approaches for reactor cores are reviewed such as the point reactor core modeling. Power control methods for reactor cores are reviewed such as the feedback control with a state observer. Load following control techniques for reactor cores are reviewed such as Mode A, Mode G, Mode T, Mechanical Shim and advanced control methods of containing multivariable frequency control, etc. The review in this paper can contribute to comprehend the past work with respective advantages, and then exploit novel research directions for development of nuclear power plants.

Modeling and control of nuclear reactor cores for electricity generation: A review of advanced technologies

As an effort to establish a fast, yet accurate multigroup nodal solution method that is crucial in repeated static and transient calculations for advanced reactors, the source expansion form of the semi-analytic nodal method (SANM) is introduced within the framework of the coarse mesh finite difference (CMFD) formulation. The source expansion is to expand the analytic form of the source appearing in the groupwise neutron diffusion equation with a set of orthogonal polynomials in order to obtain a group decoupled analytic solution. Both one- and two-node formulations are examined to determine the best nodal kernel. For the acceleration, a two-level CMFD scheme is established employing a multigroup and two-group CMFD. In addition, an alternative two-node direct SANM formulation with a quartic polynomial is examined to assess the direct vs. iterative resolution of the group coupling. The performance of the CMFD formulation with three different multigroup SANM nodal kernels is examined for a wide variety of multigroup benchmark problems including several MOX-loaded LWR cores and large FBR cores. It is demonstrated that superior accuracy is achievable with all the SANM kernels while the iterative two-node SANM kernel outperforms the others in the multigroup calculations employing more than two groups, and the two-level CMFD formulation is quite efficient in the acceleration of the outer iteration.

https://s-space.snu.ac.kr/bitstream/10371/8784/1/jnst45-668.pdf

Two-level coarse mesh finite difference formulation with multigroup source expansion nodal kernels

The equations of the high-order linear-nodal numerical scheme are cast in an augmented weighted-difference form for three-dimensional Cartesian nodes. The coupling exhibited by these equations indicates that this new algorithm is simpler and, hence, faster than previous nodal schemes of this degree of accuracy. A well-logging problem and a fast reactor problem are examined. The new scheme developed is compared with the classical linear-linear nodal scheme and the diamond-difference scheme. For the well-logging problem, it is found that the new scheme is both faster and simpler than the classical linear-linear nodal scheme while sacrificing little in accuracy. Even though the new scheme is more accurate than the diamond-difference scheme for the reactor problem, the results indicate that state-of-the-art acceleration methods are needed for nodal schemes.

/pdf/augmented-weighted-diamond-form-of-the-linear-nodal-scheme-39t2xk46rk.pdf

Augmented weighted-diamond form of the linear-nodal scheme for Cartesian coordinate systems

Finite element methods for problems of neutron transport have been an academic field of activity for over a decade. Reviews of the state of the art have been given by Williams and Goddard (1) and Lewis (2) and a short history of the finite element method in various fields given by Ackroyd (3).

Some Recent Developments in Finite Element Methods for Neutron Transport

This investigation concentrates on the numerical solution of the multigroup neutron diffusion equations by computer codes. For a realistic model liquid-metal fast breeder reactor, several benchmark problems in two and three space dimensions were derived and calculations were performed by eight different computer programs. The effect on k/sub eff/ and the neutron fluxes of the refinement of the discretization mesh is studied. Very good agreement (approximately 0.05%) of the results was found in those cases where the computer programs use the same discretization scheme of mesh-edged discretization formulas, although the codes employ different methods of solution. On the other hand, minor discrepancies remain between results obtained by codes using mesh-edged and mesh-centered discretization formulas, even for fine-mesh grids. The reasons are not understood in every detail. Fortunately, these discrepancies are very small and more of theoretical than practical interest. The effect of a simple group condensation scheme of k/sub eff/ was also investigated by considering several different energy group structures. Spatial mesh refinements and resolution of the energy range were found to be well decoupled. As the main result, one may take the fact that spatial and energetic mesh refinements may influence the results rather strongly, unless the mesh stepmore » is comparable to the minimum diffusion length and unless enough energy groups are used.« less

G. Buckel

Papers

Benchmark Calculations for a Sodium-Cooled Breeder Reactor by Two- and Three-Dimensional Diffusion Methods