Chaotic Analysis And Prediction On Flow Instability Of Natural Circulation Under Rolling Motion Condition

Natural circulation is important to nuclear power system. However, naturalcirculation system itself is a nonlinear system and has a relatively poor stability. When thenuclear power plant runs under ocean condition, the additional acceleration caused byrolling motion changes the nonlinear characteristics of the system. On the basis of earlyexperimental study, the method of chaotic time series analysis is used to analyze thenonlinear characteristics of natural circulation flow instability under rolling condition andchaotic oscillation is forecasted.Many chaotic time series analysis methods are used in this paper to analyze thenonlinear characteristics of natural circulation flow instability under rolling condition.After the experimental data are subject to de-noised preliminarily, the spectrumcharacteristics of time series are analyzed with spectrum analysis. The attractor structureis depicted in the phase space through phase space reconstruction base on the result of thetime delay and embedding dimension. The system bifurcation diagram is createdaccording to Poincaré section and geometric invariants such as correlation dimension,Kolmogorov entropy and the largest Lyapunov exponent are calculated. Finally, theirregular compound oscillation is subject to chaotic predict.The nonlinear phenomena and evolution mechanism of natural circulation flowinstability are analyzed from two aspects in this paper. From the aspects of interaction ofsystem dissipative force and driving force, the coupling and feedback degree among theadditional forces caused by rolling motion, thermal driving force and flow resistancedecide the chaos degree of flow instability. Besides, the natural circulation system underrolling motion is the nonlinear system under the action of periodic external force, whichcan be viewed as a coupling system of linear oscillator and non-linear oscillator, thedegree of coupling between the two oscillators decides the nonlinear behavior of thesystem. The above two analysis aspects have different emphases but can be mutuallyconfirmed, the former can explain the evolution process of flow instability of system,while the latter can well explain the evolution mechanism of complex flow oscillation,especially synchronization. According to the result of nonlinear analysis, the mechanism of nonlinear phenomenasuch as chaos, synchronization and bifurcation in the system is proved and explained. First,the results of spectrum analysis, attraction structure, Poincaré section and geometricinvariants shows the irregular complex flow oscillations are typical chaotic oscillations.When irregular complex flow oscillations occur, various influencing factors of the naturalcirculation system will not dominate independently, with small differences and complexinteraction and feedback between them. The influence of rolling parameters on the systemchaos is also discussed in this paper. It is found that the severer the rolling is, the larger thedimensionless frequency required for chaos will be. Besides, there are regular complexflow oscillations both after and before the chaos, the spectrum analysis result shows that anew common period occurs to regular complex flow oscillations, which is a typicalsynchronization. The mechanism for synchronization can be well explained from theaspect of oscillator coupling. When one of linear oscillator or non-linear oscillatordominates separately, the frequency of disadvantageous oscillator is locked on thefrequency of advantageous oscillator. The common period of the synchronization beingthe common multiple of the period of trough-type instability and density wave oscillation.Finally, after chaos and synchronization are discovered, the evolved route fromsynchronization to chaos is analyzed. A new frequency is found in spectrum analysis andPoincare Section, showing that period doubling bifurcation occurs in the naturalcirculation system under rolling motion. Period doubling bifurcation is a commonbifurcation method of nonlinear system under the action of periodic external force, whichis an important route to lead to chaos.The characteristics and mechanism of the nonlinear evolution of natural circulationflow instability under rolling motion are analyzed from the variation trend of spectralevolution, attractor structure and geometric invariants calculation results. It is found thatwith the increasing of non-dimensional power, the system changed from limit cycle tochaotic oscillations via period doubling bifurcation, and finally returned to steady flow. Inthis process, the nonlinear characteristics of the system first enhance and then weaken.When non-dimensional power is small or large, some influencing factor of the systemdominates separately and periodic pulsation or steady flow occurs in the system undertheir independent action. When the non-dimensional power reaches the specific value, all factors under the process of shifting cannot play the leading role and there exist feedbackand coupling between each other. So, the nonlinear characteristic of system is the strongest.The nonlinear evolution analysis demonstrates the evolution “routine diagram” of naturalcirculation flow instability under rolling motion, from which we can find variousnonlinear phenomena and the evolution relations among them.Finally, on the basis of proving that irregular complex flow oscillations are chaos,chaotic forecasting is performed. Comparisons of the prediction results and experimentaldata indicated that the chaos forecasting is effective. But the maximum length ofpredictable time equals to the reciprocal of the largest Lyapunov exponent, which isdecided by the extreme sensitivity of chaos to the initial value. In order to improve thepracticability of the forecast, the method of optimizing reconstructing phase spaceparameter and dynamic prediction is proposed in this paper, which can improve theforecasting prevision and realize sustainable forecasting. The forecast can provide areference for the safe operation of nuclear power plant.The results of related research provided the scientific basis for natural circulationflow instability under rolling condition and provided the foundation for deep research.