Patent Number: 052672760
Section: summary

Field of the Invention This invention relates generally to considerations in the design and control of nuclear reactors and is particularly directed to neutron transport analysis in the general geometry of a nuclear reactor. BACKGROUND OF THE INVENTION GTRAN2 is a two dimension (2D) general geometry multigroup neutron transport code which combines the geometric flexibility of Monte Carlo (MC) codes with the computational efficiency of deterministic codes. Due to its geometrical flexibility, this code can be used for calculations of reactors with complex geometrical features. This code is based on the exact collision probability (CP) formalism for the solution of the integral form of the neutron transport equation. This method is considered to be very accurate, but several major limitations have prevented its broader utilization over the past three decades. Some of these limitations are briefly summarized in the following paragraphs. Computer memory limitation. The spatial coupling of all regions in the global domain results in large and dense CP matrices. Very fine meshing is required for some problems, since the CP method gains accuracy with increasing subdivision of the regions. The number of meshes that can be treated is severely limited by the available computer memory, since the number of CP matrix elements increases as N.sub.r.sup.2 x N.sub.g, with N.sub.r being the total number of meshes, and N.sub.g being the total number of energy groups. As an example, consider a domain divided into 500 meshes. For a 12-group problem, the CP matrix will consist of 500.times.500.times.12=3.times.10.sup.6 double precision elements, requiring 24 Mbytes of memory. Computational cost limitation. Calculation of the CP matrix is the most time-consuming part of the entire calculation in the lattice codes based on this method. Moreover, the CPU time increases rapidly with the increased mesh refinement needed to achieve high accuracy in the CP calculations. The calculation of the CP matrices can sometimes require more than 95% of the total CPU time. Isotropic scattering limitation. With the assumption of isotropic neutron scattering and isotropic sources, integration over the angular variable in the integral transport equation can be carried out easily, and a simplified equation for the scalar flux is obtained. If linearly anisotropic scattering is assumed, the number of eigenvalue equations in 2D is increased to three and the number of large CP matrices to nine, to account for higher order flux moments. This is prohibitively expensive and no code has been developed which accounts for linearly anisotropic neutron scattering in two-dimensional geometries. Geometry limitation. The geometrical portion of the CP calculation includes determination of the intersection points between straight lines and region boundaries, i.e., surfaces. The usual procedure was to write a different algorithm for each different geometry, resulting in lattice codes with limited applicability. In order to remedy some of the above mentioned limitations, several related methods were developed in the early seventies, based on the so called interface-current formalism. In order to replace large and dense CP matrices with sparse matrices, regions were decoupled, usually on the pin cell level, and coupled only to the neighboring regions through interface currents. In these methods some accuracy had to be sacrificed, because some additional approximations on the pin cell interfaces had to be made. The present invention overcomes the aforementioned limitations of the prior art by providing a method for determining neutron transport in a nuclear reactor which is more accurate than previous methods and which can be used for virtually any advanced reactor design, thus saving man-years of effort. The inventive method is also faster than the prior approaches, and thus more cost efficient, and allows for highly precise analysis of complicated and irregular nuclear reactor assemblies in one, two or three dimensions. OBJECTS AND SUMMARY OF THE INVENTION Accordingly, it is an object of the present invention to provide a better understanding of the behavior and transport of neutrons in a nuclear reactor. It is another object of the present invention to provide high computation efficiency of neutron cross-sections, reaction rates and other constants for any region of an assembly in a nuclear reactor for use in overall reactor calculations. Yet another object of the present invention is to facilitate solving problems in the area of nuclear reactor physics more accurately and quickly by modifying a collision probability method (CPM) code by certain geometrical aspects of a geometric Monte Carlo (GMC) code. A further object of the present invention is to provide a better understanding of neutron cross-section, reaction rates and other nuclear reactor parameters in newer, more complex reactor assemblies. A still further object of the present invention is to provide a tool for the analysis and design of existing light water reactors (LWR) as well as any future reactor assembly designs including MHTGR. Another object of the present invention is to provide a method for accurately and quickly determining multigroup, steady-state neutron integral transport characteristics in arbitrary two-dimensional geometries for use in analyzing and designing virtually any type and configuration of nuclear reactor. These objects of the present invention are achieved and the disadvantages of the prior art are eliminated by a new transport theory method utilized in GTRAN2 based on a modified collision probability (CP) method. The novel method consists of replacing the geometry independent ray tracing (the most serious limitation in the CP method) by ray tracing based on the combinatorial geometry used in Monte Carlo codes, which permits an exact description of complicated and irregular nuclear reactor assemblies in one, two or three-dimensions. The advantage over the Monte Carlo ray tracing is that the geometric part is decoupled from the rest of the calculations, i.e., the geometrical pre-processing is done only once, and the calculated data are repeatedly used for all energies and all time steps. As a consequence, GTRAN2 is several orders of magnitude faster than Monte Carlo codes and provides more accurate results than heretofore available.