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

A nodalization technique has been demonstrated to calculate the response of a detector to a vibrating absorber in a reactor core using a concept of local/global components, based on the frequency dependent detector adjoint function. The technique was developed for two-energy group one-dimensional or one-energy group two-dimensional reactor core geometry. The purpose of this research was to expand the applicability of a nodalization model technique to calculate the real and the imaginary parts of the detector adjoint function for two-energy group two-dimensional reactor geometry. The frequency dependent detector adjoint functions presented by complex equations were expanded into real and imaginary parts. In the nodalization technique, the flux or detector adjoint function is expanded into polynomials about the center point of each node. A computer code was developed to calculate static flux for two-energy group, two-dimensional reactor geometry. The eigen value (keff) and static flux were calculated for the Iowa State University UTR-10 reactor and the results were compared against the values calculated using the computer code Image . The eigen values were within less than 0.1% agreement. The phase angle and the detector adjoint function for the frequency of 10 rad/s were calculated for a detector located in the center of a 60×60 cm reactor. The phase angle calculated by the nodalization model technique varied from 0.2° near the source to 0.4° away from the source. These values are well within the range of the phase angle value of 0.2° calculated using the zero power transfer function. The thermal detector adjoint function peaked in the center as expected. The discontinuity in the current of the real thermal detector adjoint function at the detector position was observed as expected. The average current based on the polynomials on the left node of the interface and the right node of the interface matched within 1% of the average value at the interface. The current of the imaginary fast and thermal detector adjoint function on both sides of the interface varied ±2% from the average value at the interface. No discontinuity in the current was observed in the case of the fast real and imaginary and thermal imaginary components of the detector adjoint function at the detector location.