Effectiveness of Control Rods Partially Inserted into a Reflected Reactor

Abstract

This paper describes a method of evaluating the effectiveness of cylindrical control rods for the general case where multiple control rods of various effective lengths affecting epithermal and thermal neutrons are arbitrarily distributed and partially inserted to mutually independent positions in a reflected reactor. This method is a generalization of the technique introduced by Nordheim & Scalettar (N-S method), employing the two-group, three-dimensional diffusion theory with modified application of the boundary condition imposed on the surface of control rods. Either the multiplication constant or the prompt neutron decay constant can be designated as eigen-value of the system. Moreover, vector-matrix notations are employed to faciliate the treatment of the problems and the subsequent derivation of the critical determinant. The general problem based on the asymmetrical arrangement of control rods can be reduced to a number of special cases to find out the order of the critical determinant. We discuss the imitations of the modified N-S method. Finally, we perform numerical studies and compare the calculated results with experimental data based upon the pulsed neutron source method.