Power series solution method for solving point kinetics equations with lumped model temperature and feedback

Point kinetics equations are stiff differential equations, and their solution by the conventional explicit methods will give a stable consistent result only for very small time steps. Since the neutron lifetime in a LMFBR is very short, the point kinetics equations for LMFBRs become even stiffer. In this study the power series solution (PWS) method is applied for solving the point kinetics equations for a typical LMFBR. A Fortran program is developed for accident analysis of LMFBRs with the PWS method for solving the point kinetics and a lumped model for solving the heat transfer equations. A new technique is developed with fixing factor to find out the average temperature at the peak power node (PPN) without performing temperature calculations at all axial nodes in a reactor fuel pin. The temperature at PPN also decides whether the reactor is within the design safety limit (DSL) or it has entered a serious transient that may lead to an accident. The coupled heat transfer and point kinetics models for a peak power node give the average fuel, clad and coolant temperatures. For the transient over power accidents (TOPA), this is the best way for calculating the temperature, with minimum amount of computations. TOPA analyses are carried out with PWS method. It is found that the PWS methodology uses a small number of numerical operations, while the computational time and the accuracy are comparable with the available fast computational tools. This methodology can be used in nuclear reactor simulation studies and accident analysis.