Development Of R-Z Dimensional Neutron Transport Code Based On Discrete Ordinates Method

The neutron transport codes under R-Z geometry are widely used inreactor engineering, such as, determining the neutron flux distribution.The technology of irradiation damage monitoring of the pressure vessel inWestinghouse, combining the dosimeters outside of the reactor andneutron transport calculation, do well in determining the neutron fluxdistribution within the pressure vessel. And the critical correction factor isobtained by the neutron transport calculation through the dynamic rodworth measurement (DRWM) technology in Westinghouse. In addition,the transient neutron transport program under R-Z geometry can alsoapply to safety analysis of the molten salt reactor.Through extensive research and the theoretical derivation in thispaper, a program, PINE, based on the discrete ordinate method, wasdeveloped to solve the steady-state and transient neutron transportcalculation in2D R-Z coordinate system.First, the paper made a basic introduction to the theory of neutrontransport, given the specific form of the neutron transport equation. Andthen the paper proposed theoretical model based on the discrete ordinatemethod for solving steady-state neutron transport equation intwo-dimensional R-Z geometry. In the numerical solution of the process,based on the discrete ordinate method in the R-Z geometry, use method ofgroup-dividing for energy variables, finite difference approximate forspace variables, and direct discretization for direction variables. Inaddition, discrete ordinate method was applied to solve time-dependent kinetic equations. A fully implicit backward difference was extended fortime discretization and then the resulted fixed-source equation was solvedby the discrete ordinate method.Finally, in this paper, the program was tested by self-designbenchmarks and Takeda benchmarks. The results prove that the PINEprogram numerical algorithms and procedures for the preparation of iscorrect. The codes can solve theK effproblem and the fixed-sourceproblem, giving successfully the value of and the neutron fluxdensity distribution. For transient problems, the codes successfully givethe variation of the neutron flux density distribution at each time pointand show the variation of neutron density in the entire period.To improve the computing speed, the calculation accuracy andversatility of the program, there are several aspects listed to improve theprogram at the end of the paper.