Development of two-group, two-dimensional, frequency-dependent detector adjoint function based on the nodal method

A concept of local/global components, based on the frequency-dependent detector adjoint function, and a nodalization technique was utilized in development of one- and two-dimensional computer codes to calculate the response of a detector to a vibrating absorber in reactor cores. The frequency-dependent detector adjoint functions presented by complex equations were expanded into real and imaginary parts. In the nodalization technique, the flux is expanded into polynomials about the center point of each node. The phase angles and the magnitudes of the two-energy group detector adjoint functions were calculated for a neutron detector located in the middle of the south core tank of the Iowa State University UTR-10 reactor using a one-dimensional computer code. Results were compared with the exact analytical solution and were found to be within 2% of the values obtained from the analytical solution. Using a two-dimensional computer code, the phase angle and the magnitude of the one-energy group detector adjoint function was calculated for a detector located in the center of a 200 cm x 200 cm reactor. Results were within 3% of the values obtained from the analytical solution and the computer code EXTERMINATOR