Calculating Space-Dependent Reactor Transfer Functions Using Statics Techniques

Abstract

A method has been developed by which statics techniques can be used to calculate source transfer functions in the multigroup, multidimensional approximation. With the flux resolved into steady and fluctuating components, the time-dependent neutron balance equations are satisfied by the fluctuating part alone. Assuming that the external source and the flux response are sinusoidal, the original time-dependent equations transform into a set of complex equations dependent on space and frequency but independent of time. Separating the equations into real and imaginary parts yields coupled, inhomogeneous differential equations (two for each group). These can be solved by well-known statics techniques for the real and imaginary components φR and φI of the complex amplitudes of the fluxes, in turn yielding the gain and phase shift for each frequency of interest.This method was applied to the NORA reactor for which the space-dependent transfer function had been determined experimentally. The two-group telegrapher's equations were programmed for one-dimensional cylindrical geometry and the difference equations solved by direct matrix inversion and also by interative techniques. Results of the calculations closely reproduce the reported experimental results for gain and phase shift.