Comparison of efficiency of different tests of stability of spatial neutron distribution

Abstract

Two basic approaches are known to the solution of the problem of the stability of the spatial distribution of neutrons in high-capacity power reactors. The first approach is based on the use of harmonics and consists essentially of seeking the solution in the form of an expansion in spatial harmonics. This approach was adopted in the investigations [1-4] together with certain assumptions, and fairly simple engineering stability criteria were obtained. The other approach is based on Lyapunov's second method. There is more justification for this approach since the stability tests obtained using Lyapunov's second method are sufficient, i.e., in contrast to the use of harmonics the sign of the error is known in this case. Among the investigations made in this direction one should mention [5-8]. The most simple sufficient stability criteria suitable for engineering purposes were obtainedin [7, 8]. Since the stability criteria obtained by means of the method of harmonics are approximate and the criteria obtained by means of Lyapunov's method are merely sufficient, one may ask to what extent the above stability criteria are constructive [9]. In the present paper the example of a one-dimensional model of a reactor is used to establish the applicability of the method of D-partition [10] for calculations of stability; this method is used to obtain an exact solution of the problem for various specific values of the parameters. These results are then used to compare different approximate stability criteria. Investigation of Stability by the D-Partition Method Let us consider a thermal neutron power reactor without reflector with a negligibly small reactivity coefficient relative to the coolant. We assume that the neutron distribution along the radius of the reactor does not differ from the steady-state distribution during transient processes. Under the assumption that the neutron balance satisfies the equations of the single-group diffusion approximation, the problem of stability with respect to small perturbations of the steady-state conditions of operations of a reactor with a xenon poison feedback reduces to an investigation of the stability of the solution with null boundary conditions of the following system of equations [1-3]: O~q0 ]_ I O~cl)* H2 0~ -~-~" -~ ~ + ~-~ [a~(I)*~ + ~x] = O, ~ ~ (0, l); Oi ~, ~ .