Stochastic perturbation and stability analysis of a reduced order model of natural circulation loops

Natural circulation is commonly accounted for and designed into thermal fluid systems such as nuclear reactors and concentrated solar thermal plants as part of safety systems and normal operation. This work presents the development of a Fourier-based model of single-phase natural circulation loops with application-relevant boundary conditions to study their performance, stability, and response to geometry-induced turbulence fluctuations. This results in a reduced order model consisting of eight ordinary differential equations that reproduces the phenomena observed in experiments and numerical simulations. This model enables a robust study of the stability and dynamics of the system. The model results compare well against past experiments for steady-state conditions and instability predictions. Supercritical and subcritical Hopf bifurcations are obtained, and a chaotic attractor is observed in line with previous predictions and studies. The effect of transient fluctuations arising from complex geometry in the system is modeled using a data-driven statistical emulator with the help of a modified minor loss coefficient or form friction parameter. The effect of the stochastic friction parameter or stochastic forcing on the model predictions was analyzed. Under certain conditions, the stochastic forcing considerably shrinks the region of stability as the system is perturbed from a metastable state. The stochastic forcing is also found to accelerate the transition to chaos. For cases that do not escape to the chaotic attractor, the reaction of the system to the stochastic parameter depends on the response time of the attractor and its limiting behavior.