Analysis of Instabilities, Nonlinear Oscillations and Startup Transients in Advanced Nuclear Reactors

Safety concerns for nuclear reactors necessitate analysis of instabilities that may occur during their startup or normal operation. Such analysis can be done exhaustively through computationally inexpensive reduced-order models using one-dimensional and lumped parameter approaches. While linear stability analysis gives information about the response of a dynamical system to small perturbations about its normal operating condition, analysis of nonlinear dynamics and bifurcations reveals the system behaviour in the presence of large perturbations. Transients occurring during the startup process involve large changes in system variables and have to be analysed accordingly. In this lecture, one-dimensional time-dependent mathematical modelling of boiling systems and supercritical fluid systems will be discussed along with lumped parameter modelling for linear and nonlinear stability analysis. Methods for analysis of linear and nonlinear oscillations and startup transients will be explained. Two advanced nuclear reactors — namely, the natural circulation boiling water reactor and the supercritical water-cooled reactor — will be considered for case studies. Mathematical modelling of these reactors — using the lumped parameter approach and the one-dimensional system code RELAP5/MOD3.4 — will be described. Using these models, the following studies will be discussed: linear stability analysis and parametric effects, nonlinear dynamics and bifurcations, startup transients and their time-series analysis