An analytical approach to bifurcations and stability in nuclear reactors Summarized and modified version (original) (raw)
2019, Progress in Nuclear Energy
Asymptotic analytical methods are applied to study some problems related with bifurcations (both local and global) and stability in three simple mathematical models of nuclear reactors. The first case is a reactor which is subcritical at rest and driven by a distributed external neutron source. Under suitable conditions in the temperature feedback reactivity, the mathematical model predicts a static global bifurcation with three critical states, two stable and one unstable, with the possibility of a runaway. The dynamics of this system is studied, in a framework of slow manifold theory, by methods of restricted nonlinear modal analysis, and the results of a digital simulation are summarized. The model could be modified and extended to study the space time dynamics of sub-critical multiplying systems driven by external neutron sources (neutron beams produced by accelerators). The second case is related with in phase and out of phase xenon oscillations in large thermal reactors. The known subcritical Hopf bifurcation that appears in the context of global mode oscillations is revisited. After applying a nonlinear modal analysis to the mathematical model, a normal form is derived by an averaging method. Approximate analytical formulae for the radii of the unstable limit cycles and for the trajectories of the state variables in a neighborhood of the bifurcation point are obtained. The third case is a non-trivial modification and development of a simple mathematical model intended to describe certain mechanical kinetic effects stemming from a possible coupling of nuclear, thermal and mechanical vibration processes. We show that, under suitable conditions, a dynamic supercritical Hopf bifurcation in the reactor power appears in the framework of our modified model. A normal form is derived by an averaging method. Analytical formulae for the radii of the stable limit cycles and the trajectories of the state variables in a neighborhood of the bifurcation are given.
Related papers
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.