On the Application of Eigenfunction Expansions to Problems in Nonlinear Space-Time Reactor Dynamics

Several nonlinear space-time reactor models are studied by employing modal analysis. Eigenfunction modes resulting from the solution of Sturm-Liouville equations satisfying the appropriate linear portion of the neutron diffusion equation are chosen. These modes form a complete, orthogonal set and are convenient to calculate numerically. Examples where coefficients and time constants are representative of present reactor design are studied. The work is focused on space-dependent feedback and local step and ramp reactivity insertions. The large difference in the neutronic and thermal-hydraulic time constants gives rise to computational difficulties. This difficulty, characteristic of “stiff systems” was minimized by use of a rational extrapolation technique to solve the resultant equations.