Reduced Two-Dimensional Critical Problem of Finite Cylindrical Reactor

Abstract

The critical problem is considered for finite cylindrical reactors. By applying the concept embodied in the asymptotic solution of the mono-energetic transport equation, it is possible to reduce the two-dimensional transport equation to an axially and radially reduced one-dimensional form. In essence, the idea is to approximate one of the two space dimensions by the assumption of the asymptotic distribution, and to extend the reactor medium and the asymptotic distribution toward infinity. The resulting reduced equation is solved by making use of the singular eigenfunction expansion method introduced by Case. It is found that the two-dimensional flux distribution can be obtained with high accuracy from the reduced equation, excluding exceptional cases of extremely poor conditions. Numerical results are presented for a wide range of reactor multiplication factor, and are compared with the results obtained by the variational method. It is found that there is only a small contribution of the boundary transien...