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

One-energy group, two-dimensional computer code was developed to calculate the response of a detector to a vibrating absorber in a reactor core. A concept of local/global components, based on the frequency dependent detector adjoint function, and a nodalization technique were utilized. The frequency dependent detector adjoint functions presented by complex equations were expanded into real and imaginary parts. In the nodalization technique, the ¯ux is expan- ded into polynomials about the center point of each node. The phase angle and the magnitude of the one-energy group detector adjoint function were calculated for a detector located in the center of a 200 200 cm reactor using a two-dimensional nodalization technique, the computer code EXTERMINATOR, and the analytical solution. The purpose of this research was to investigate the applicability of a polynomial nodal model technique to the calculations of the real and the imaginary parts of the detector adjoint function for one-energy group two-dimen- sional polynomial nodal model technique. From the results as discussed earlier, it is concluded that the nodal model technique can be used to calculate the detector adjoint function and the phase angle. Using the computer code developed for nodal model technique, the magnitude of one energy group frequency dependent detector adjoint function and the phase angle were cal- culated for the detector located in the center of a 200 200 cm homogenous reactor. The real part of the detector adjoint function was compared with the results obtained from the EXTERMINATOR computer code as well as the analytical solution based on a double sine series expansion using the classical Greenʹs Function solution. The values were found to be less than 1% greater at 20 cm away from the source region and about 3% greater closer to the source compared to the values obtained from the analytical solution and the EXTERMI- NATOR code. The currents at the node interface matched within 1% of the average value at the interface. The phase angle varied from 0.1 to 0.4 compared to 0.2 calculated using the point reactor zero power transfer function.