Calculation of reactivity worth of a control rod array

Abstract

The reactivity worth of a linear array of B 4C control rods with stainless steel cladding can be accurately calculated by a new method presented here, which is based on a combination procedure of the collision probability method applied to the control rod region and its vicinity and the diffusion theory used in the region far from the control rod region. A GE-635 code ALAx has been made by use of the above method and an elaborate machine language programming, i.e. the gmap language, and then its computing time is very short; for instance, the processor time of the machine per one case of the four group calculation is only about 1·5 min. First, on the basis of the monoenergetic neutron model, the neutron absorption rates, which are calculated by the slab approximation of the actual rods array with the transport and diffusion theory, are compared with the one by the exact method, and consequently it is concluded that such slab approximations lead to a significant error. After an equivalent logarithmic derivative boundary condition at the surface of the control rod region for each energy group is derived so that the total neutron generating rate by fisson in the system with the boundary condition may be equal to the one by the exact method, the various calculating methods of the previous model are extended to the few group calculation. The multiplication factor and the neutron absorption rates in each group for the same system are calculated by the above various methods together with the ordinary diffusion calculating method, where the boundary condition is used, and the results are compared with the exact ones. Then, for the cruciform control rod system used in the actual BWR core, we can suggest the two-dimensional diffusion calculation with the equivalent boundary conditions for each group which are derived from the above-mentioned procedure.