Generalization of the analytical exponential model to solve the point kinetics equations of Be- and D2O-moderated reactors

A new mathematical formula of the period–reactivity relation for beryllium and heavy-water-moderated reactors has been presented. This formula is represented in a polynomial form with a degree I+J+1I+J+1 for II-group of delayed neutrons and JJ-group of photoneutrons. A sample form for the coefficients of such a polynomial is presented which have a linear dependence on the step reactivity insertion. The analytical exponential model (AEM) is developed and generalized. The generalization of the analytical exponential model (GAEM) is analyzed and applied to solve point kinetics equations of the U235-fuelled, Be- and D2O-moderated reactors. The generalized method provides a fast and accurate computational technique for the point reactor kinetics equations of photoneutrons and delayed neutrons with step, ramp, sinusoidal and temperature feedback reactivity. Results of this method are presented for different types of reactivity and compared with other referenced methods.