Non-Linear Time Series Analysis On Flow Instability Of Natural Circulation Under Rolling Motion Condition

Non-linear time series analysis of natural circulation flow instabilities under rolling motion conditions was studied.Natural circulation flow instability under ocean conditions showed abundant nonlinear characteristics. With the increase of heating power, flow states such as single-phase flow fluctuation, trough-type flow oscillation, irregular complex flow oscillation, regular complex flow oscillation and high volumetric quality flow with slight amplitude were observed in nature circulation system under rolling motion.In this paper, experimental data were analyzed with nonlinear time series analysis methods. Frequency characteristic of time series was analyzed through the analysis of frequency spectrum. The trajectories of attractors were described with the reconstructed phase space, the embedding dimension, correlation dimension and Kolmogorov entropy (K entropy) were determined based on phase space reconstruction theory and G-P method. The maximal Lyapunov exponent (MLE) was calculated with the methods of small data sets.The nonlinear features of the two phase flow instability under rolling motion were analyzed with the results of geometric invariants. Irregular complex flow oscillations was a typical chaotic oscillation caused by the interacted and feedback of bubbles behavior, thermal driving force, flow resistance and additional forces induced by rolling motion.According to the result of geometric invariants, the influences of heating power, inlet sub-cooling degree and rolling motion on the flow instabilities were analyzed. The results indicated that rolling motion strengthened the nonlinear characteristics of two phase flow instability. The higher heating power is. the stronger the nonlinear characteristic becomes. Chaos oscillation was found when the irregular complex flow oscillations turned up, nonlinear characteristics was weakened again when the heating power increased continuously. The flow was destabilized in high inlet sub-cooling degree.The paper analyzes nonlinear evolution mechanism of natural circulation flow instability from the aspects of frequency spectrum, complexity of attraction and variation trend of geometric invariants. It is found that the interaction of hot driving force, frictional resistance and additional forces caused by rolling motion is the basic reason to nonlinear evolution; period doubling bifurcation will occur at trough-type flow oscillation and chaos oscillation will appear at irregular complex flow oscillation; attractor in the phase space from limit cycles to strange attractor via quasi-periodic and then from quasi-periodic to steady state with slight amplitude; the tendencies of correlation dimension, Kolmogorov entropy and maximal Lyapunov exponent show that the complexity of the system first enhances and then weak from single-phase flow fluctuation to high volumetric quality flow with slight amplitude.