摇摆条件下自然循环流动不稳定性混沌特性分析及预测
|
摘要
自然循环对于船用核动力系统的安全性具有重要意义，但自然循环系统本身是非线性系统且稳定性较差，海洋条件下船舶运动引入的附加加速度会改变系统的非线性特性，本文在前期实验研究的基础上，应用混沌时间序列分析方法研究了摇摆条件下自然循环系统流动不稳定性的非线性特征并对复杂混沌脉动行为进行了预测。
本文用多种混沌时序分析方法从不同角度分析了摇摆运动条件下自然循环系统流量脉动的非线性特征。在对实验数据进行初步降噪后，通过谱分析讨论了时间序列的频谱特性，计算时间延迟和最佳嵌入维数，在此基础上通过相空间重构在相空间中刻画吸引子结构，根据庞加莱截面图构建系统分岔图，计算关联维、Kolmogorov熵和最大Lyapunov指数值等几何不变量，最后对不规则复合型脉动进行了混沌预测。
本文从两个角度分析流动不稳定性的非线性现象与演化机理。首先，从系统耗散力与驱动力的相互作用的角度看，摇摆引起的附加外力、热驱动力与流动阻力这三个因素之间的耦合与反馈程度决定着流动不稳定性的混沌程度。其次，从振子耦合的角度看，摇摆条件下自然循环系统是周期性外力驱迫下的非线性系统，可以看作线性振子与非线性振子的耦合系统，两者的耦合程度决定了系统的非线性行为。以上两个分析角度侧重点有所不同但可以相互印证，前者可以解释系统流动不稳定性的整个演化过程的机理，后者可以很好的解释复合型脉动的演化机理，特别是同步化现象。
根据混沌时序分析计算结果，证明所研究系统中存在混沌、同步化与分岔等典型非线性现象并解释其机理。首先，谱分析、吸引子重构、庞加莱截面图和几何不变量计算结果表明，不规则复合型脉动是典型的混沌振荡，这是因为发生不规则复合型脉动时，自然循环系统的各项影响因素都不能单独起主导作用，他们之间大小相差不大且存在着复杂的相互作用和反馈。本文还讨论了摇摆参数对系统混沌脉动的影响，通过分析发现，摇摆越剧烈，出现混沌时需要的无量纲功率越大。同时在分析中发现，在混沌脉动之前和之后都会出现规则复合型脉动，谱分析结果表明规则复合型脉动出现了新的公共周期，这是典型的同步化现象。从振子耦合的角度可以很好的说明同步化现象产生的机理，当线性振子或非线性振子其中之一单独起主要作用时，不占优的振子锁频到占优的振子频率之上，形成同步化现象，其公共周期是波谷型脉动与密度波型脉动周期的公倍数。最后，在发现了混沌脉动和同步化现象之后，分析了系统由同步化现象演变为混沌的道路，在谱分析图以及庞加莱截面图中发现了新的频率，说明摇摆条件下的自然循环系统出现了倍周期分岔现象。倍周期分岔是周期驱迫下的非线性系统通常出现的分岔方式，是通向混沌的一条重要路径。
通过频率谱演化、吸引子结构和几何不变量计算结果变化趋势等方面分析了摇摆条件下自然循环不稳定性的非线性演化特征与机理。通过分析发现：随着无量纲功率的增加，摇摆条件下自然循环系统经历周期性脉动→混沌脉动→周期性脉动→稳定流动的过程，在这个过程中，流量脉动的非线性特征先增强后减弱，这是因为当无量纲功率较小或者较大时，系统的某个影响因素单独起主要作用，系统在它们的单独作用下发生周期性脉动或稳态流动；当无量功率达到特定值时，力量处于此消彼长过程中的各因素都不能单独起主要作用且相互之间存在相互反馈与耦合，系统出现非线性特征最为强烈的混沌脉动。非线性演化特性分析展示了摇摆条件下自然循环系统流动不稳定性演化的“路线图”，从中可以发现各种非线性现象和他们之间的演变关系。
最后在证明不规则复合型脉动是混沌脉动的基础上，对其进行了混沌预测，预测效果较好，但可预测时间长度受最大Lyapunov指数的限制，这是由混沌脉动对初值的极端敏感性决定的。为了提高预测的实用性，本文提出了优化相空间重构参数和动态预测的方法，此方法可以提高预测精度并且可以实现持续预测，预测结果可以为核动力装置的安全运行提供参考。
本文相关研究成果可以为摇摆条件下自然循环系统流动不稳定性的现象分析和机理研究提供依据，为进一步深入研究提供基础。
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.
本文用多种混沌时序分析方法从不同角度分析了摇摆运动条件下自然循环系统流量脉动的非线性特征。在对实验数据进行初步降噪后，通过谱分析讨论了时间序列的频谱特性，计算时间延迟和最佳嵌入维数，在此基础上通过相空间重构在相空间中刻画吸引子结构，根据庞加莱截面图构建系统分岔图，计算关联维、Kolmogorov熵和最大Lyapunov指数值等几何不变量，最后对不规则复合型脉动进行了混沌预测。
本文从两个角度分析流动不稳定性的非线性现象与演化机理。首先，从系统耗散力与驱动力的相互作用的角度看，摇摆引起的附加外力、热驱动力与流动阻力这三个因素之间的耦合与反馈程度决定着流动不稳定性的混沌程度。其次，从振子耦合的角度看，摇摆条件下自然循环系统是周期性外力驱迫下的非线性系统，可以看作线性振子与非线性振子的耦合系统，两者的耦合程度决定了系统的非线性行为。以上两个分析角度侧重点有所不同但可以相互印证，前者可以解释系统流动不稳定性的整个演化过程的机理，后者可以很好的解释复合型脉动的演化机理，特别是同步化现象。
根据混沌时序分析计算结果，证明所研究系统中存在混沌、同步化与分岔等典型非线性现象并解释其机理。首先，谱分析、吸引子重构、庞加莱截面图和几何不变量计算结果表明，不规则复合型脉动是典型的混沌振荡，这是因为发生不规则复合型脉动时，自然循环系统的各项影响因素都不能单独起主导作用，他们之间大小相差不大且存在着复杂的相互作用和反馈。本文还讨论了摇摆参数对系统混沌脉动的影响，通过分析发现，摇摆越剧烈，出现混沌时需要的无量纲功率越大。同时在分析中发现，在混沌脉动之前和之后都会出现规则复合型脉动，谱分析结果表明规则复合型脉动出现了新的公共周期，这是典型的同步化现象。从振子耦合的角度可以很好的说明同步化现象产生的机理，当线性振子或非线性振子其中之一单独起主要作用时，不占优的振子锁频到占优的振子频率之上，形成同步化现象，其公共周期是波谷型脉动与密度波型脉动周期的公倍数。最后，在发现了混沌脉动和同步化现象之后，分析了系统由同步化现象演变为混沌的道路，在谱分析图以及庞加莱截面图中发现了新的频率，说明摇摆条件下的自然循环系统出现了倍周期分岔现象。倍周期分岔是周期驱迫下的非线性系统通常出现的分岔方式，是通向混沌的一条重要路径。
通过频率谱演化、吸引子结构和几何不变量计算结果变化趋势等方面分析了摇摆条件下自然循环不稳定性的非线性演化特征与机理。通过分析发现：随着无量纲功率的增加，摇摆条件下自然循环系统经历周期性脉动→混沌脉动→周期性脉动→稳定流动的过程，在这个过程中，流量脉动的非线性特征先增强后减弱，这是因为当无量纲功率较小或者较大时，系统的某个影响因素单独起主要作用，系统在它们的单独作用下发生周期性脉动或稳态流动；当无量功率达到特定值时，力量处于此消彼长过程中的各因素都不能单独起主要作用且相互之间存在相互反馈与耦合，系统出现非线性特征最为强烈的混沌脉动。非线性演化特性分析展示了摇摆条件下自然循环系统流动不稳定性演化的“路线图”，从中可以发现各种非线性现象和他们之间的演变关系。
最后在证明不规则复合型脉动是混沌脉动的基础上，对其进行了混沌预测，预测效果较好，但可预测时间长度受最大Lyapunov指数的限制，这是由混沌脉动对初值的极端敏感性决定的。为了提高预测的实用性，本文提出了优化相空间重构参数和动态预测的方法，此方法可以提高预测精度并且可以实现持续预测，预测结果可以为核动力装置的安全运行提供参考。
本文相关研究成果可以为摇摆条件下自然循环系统流动不稳定性的现象分析和机理研究提供依据，为进一步深入研究提供基础。
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.
引文
[1]史永谦.核能发电的优点及世界核电发展动向[J].能源工程.2007(5):1-6.
[2]刘向阳.我国新能源发展现状及巨大在投资机遇[J].电力设备.2006,7(2):101-103.
[3]张力.日本福岛核电站事故对安全科学的启示[J].中国安全科学学报.2011,21(4):3-6.
[4]郭志锋. AP1000的非能动安全系统[J].国外核新闻.2005(9):14-20.
[5]谭思超，高文杰，高璞珍，苏光辉.摇摆运动对自然循环流动不稳定性的影响[J].核动力工程.2007,28(5):42-45.
[6] Wu C Y, Wang S B, Pan C. Chaotic oscillations in a low pressure two-phase naturalcirculation loop under low power and high inlet subcooling conditions[J]. Nucl. Eng.Des.1996.162(2–3):223-232.
[7]陈听宽.两相流与传热研究[M].西安:西安交通大学出版社,2004.
[8]徐济鋆.沸腾传热和气液两相流[M].北京市:原子能出版社,2001:388.
[9]王经.气液两相流动动态特性的研究[M].上海:上海交通大学出版社,2012.
[10] Vijayan P K, Sharma M, Pilkhwal D S. Experimental and numerical investigationson the nature of the unstable oscillatory flow in a single-phase natural circulationloop[Z]. Kalpakkam India:2004.
[11] Ishii M. Thermally induced flow instabilities in two phase mixture in thermalequilibrium[J]. PhD thesis, Georgia Institute of Technology.1971.
[12] Achard J L, Drew D A, Lahey Jr. R T. Effect of gravity and friction on the stabilityof boiling flow in a channel[J]. Chemical Engineering Communications.1981.11(1-3):59-79.
[13] Atkinson M J, Arcuri F W, Friedly J C. The use of a computer algebra system in theanalysis of chemical engineering problems[J]. Comput. Chem. Eng.1982.6(2):169-175.
[14] Lahey Jr., R. T. M F J. The thermal-hydraulics of a boiling water nuclear reactor[J].ANS Monograph.1993.
[15] Taleyarkhan R P, Podowski M Z, Lahey Jr. R T. Ventilated channel instabilityanalysis[J]. Journal of Heat Transfer.1985.107:175-181.
[16] Clausse A, Lahey Jr. R T. The analysis of periodic and strange attractors duringdensity wave oscillations in boiling flow[J]. Chaos Soliton. Fract.1991.1(2):167-178.
[17] Lin Y N, Pan C. Non-linear analysis for a natural circulation boiling channel[J].Nucl. Eng. Des.1994.152(1–3):349-360.
[18] Chin-Jang C, Lahey Jr. R T. Analysis of chaotic instabilities in boiling systems[J].Nucl. Eng. Des.1997.167(3):307-334.
[19] Zhou Z, Heusser, Kerntechnik P. Nonlinear analysis of low-quality density waveinstabilities in a natural circulation system at heating reactor conditions[J]. Fuel andEnergy Abstracts.1996.37(5):352.
[20] Ambrosini W, Di Marco P, Ferreri J C. Linear and nonlinear analysis of densitywave instability phenomena[J]. International Journal of Heat and Technology.2000.18(1):27-36.
[21] Karve A A, Uddin R, Dorning J J. Stability analysis of BWR nuclear-coupledthermal-hydraulics using a simple model[J]. Nucl. Eng. Des.1997.177(1–3):155-177.
[22] Lee J D, Pan C. Nonlinear analysis for a double-channel two-phase naturalcirculation loop under low-pressure conditions[J]. Ann. Nucl. Energy.2005.32(3):299-329.
[23] Dutta G, Doshi J B. Nonlinear analysis of nuclear coupled density wave instabilityin time domain for a boiling water reactor core undergoing core-wide and regionalmodes of oscillations[J]. Prog. Nucl. Energ.2009.51(8):769-787.
[24] Lee J D, Pan C. Periodic and chaotic oscillations in the nuclear-coupled boilingchannel system subject to strong void-reactivity feedbacks[J]. Ann. Nucl. Energy.2009.36(6):793-801.
[25] Lakshmanan S P, Pandey M. Analysis of startup oscillations in natural circulationboiling systems[J]. Nucl. Eng. Des.2009.239(11):2391-2398.
[26] Durga Prasad G V, Pandey M. Parametric effects on reactivity instabilities andnonlinear oscillations in a nuclear-coupled double channel natural circulation boilingsystem[J]. Nucl. Eng. Des.2010.240(5):1097-1110.
[27] Cammarata G, Fichera A, Pagano A. Nonlinear analysis of a rectangular naturalcirculation loop[J]. Int. Commun. Heat Mass.2000.27(8):1077-1089.
[28] Dokhane A, Hennig D, Rizwan-Uddin, Chawla R. Semi-analytical BifurcationAnalysis of Two phase Flow in a Heated Channel[J]. Retrieved from:http://docs.ksu.edu.sa/KSU_AFCs/adokhane/IJBC_paper.pdf.2003.
[29] Abdelhamid Dokhane, Dieter Hennig, Rizwan-Uddin, Chawla R. Interpretation of inphase and out-of-phase BWR oscillationsusing an extended reduced order model andsemi analytical bifurcation analysis[J]. Ann. Nucl. Energy.2007.34:271-287.
[30] Paruya S, Bhattacharya P. A moving boundary analysis for start up performance of anuclear steam generator[J]. Journal of Fluids Engineering.2008.130(5):1-11.
[31] Carsten Lange, Dieter Hennig, Antonio Hurtado. An advanced reduced order modelfor BWR stability analysis[J].2011.53:139-160.
[32]庞凤阁，高璞珍，王兆祥，刘殊一，丁洪河.海洋条件对自然循环影响的理论研究[J].核动力工程.1995,16(04):330-335.
[33]周云龙，赵建伟，衣晓青，王晓刚，洪文鹏.倾斜下降管内气（汽）─液两相流动特性研究[J].东北电力学院学报.1995,15(03):14-24.
[34]周云龙，孙斌，粱强，顾欣.倾斜下降管气液两相分层流截面含气率的计算与液层高度的预测[J].工程热物理学报.2002,23(02):238-240.
[35] Isshiki N. Effects of heaving and listing upon thermo-hydraulic performance andcritical heat flux of water-cooled marine reactors[J]. Nucl. Eng. Des.1966.4(2):138-162.
[36] Ozoe H, Sayama H, Churchill S W. Natural convection in an inclined rectangularchannel at various aspect ratios and angles—experimental measurements[J]. Int. J.Heat Mass Tran.1975.18(12):1425-1431.
[37] Ozoe H, Sayama H, Churchill S W. Natural convection patterns in a long inclinedrectangular box heated from below: Part I. Three-directional photography[J]. Int. J.Heat Mass Tran.1977.20(2):123-129.
[38] Hiroyuki O, Tsutomu S, Churchill S W. Natural convection in an inclined circularcylindrical annulus heated and cooled on its end plates[J]. Int. J. Heat Mass Tran.1981.24(4):727-737.
[39] Hiroyuki O, Kazumitsu Y, Hayatoshi S, Churchill S W. Natural circulation in aninclined rectangular channel heated on one side and cooled on the opposing side[J].Int. J. Heat Mass Tran.1974.17(10):1209-1217.
[40]宫厚军，杨星团，姜胜耀，刘志勇.海洋运动对自然循环流动影响的理论分析[J].核动力工程.2010,31(04):52-56.
[41] Iyori I, Aya I, Murata H, Kobayashi M, Nariai H. Natural circulation ofintegrated-type marine reactor at inclined attitude[J]. Nucl. Eng. Des.1987.99:423-430.
[42]苏光辉，张金玲，郭玉君，秋穗正，喻真烷，贾斗南.海洋条件对船用核动力堆余热排出系统特性的影响[J].原子能科学技术.1996,30(6):487-491.
[43]高璞珍，庞凤阁，刘殊一，彭敏俊.倾斜对强迫循环和自然循环影响的比较[J].核科学与工程.1997,17(02):179-183.
[44]曹夏昕，阎昌琪.倾斜管内气液两相流流型的实验研究[J].核动力工程.2005,26(06):572-575.
[45]曹夏昕，阎昌琪，孙立成.向上倾斜管内气-水两相流流型转变分析[J].核科学与工程.2005,25(01):45-49.
[46]高璞珍，王兆祥，刘顺隆.起伏对强制循环和自然循环的影响[J].核科学与工程.1999,19(02):116-120.
[47] Ishida T, Yoritsune T. Effects of ship motions on natural circulation of deep searesearch reactor DRX[J]. Nucl. Eng. Des.2002.215(1–2):51-67.
[48]于雷，鄢邴火，陈玉清.海基核动力装置自然循环数学模型的建立与运行特性研究[J].原子能科学技术.2008,42(Suppl.):116-122.
[49]张金玲，郭玉君，秋穗正，苏光辉，贾斗南，喻真烷，陈学俊.船用压水核反应堆系统自然循环分析[J].辐射防护通讯.1994,14(04):14-20.
[50]张金玲，郭玉君，秋穗正，苏光辉，贾斗南，喻真烷，陈学俊.船用核动力装置自然循环载热能力的分析与计算[J].西安交通大学学报.1994,28(6):35-42.
[51]洪钢，杨燕华，刘祥锋，闫晓，黄彦平，陈炳德.起伏运动对加热壁面汽泡受力的影响分析[J].核动力工程.2011,32(03):87-91.
[52]姜胜耀，杨星团，宫厚军，刘志勇，郝文涛，李军，葛裴.起伏因素影响自然循环流动的机理分析[J].原子能科学技术.2009,43(S1):92-96.
[53]孙德祥.船舶运动对反应堆热工水力的影响[C].核动力工程编辑部,1996.
[54] Ishida T, Kusunoki T. Effect by sea wave on thermal hydraulics of marine reactorsystem[J]. J. Nucl. Sci. Technol.1995.32(8):740-751.
[55] Murata H, Iyori I, Kobayashi M. Natural circulation characteristics of a marinereactor in rolling motion[J]. Nucl. Eng. Des.1990.118(2):141-154.
[56] Murata H, Sawada K, Kobayashi M. Natural circulation characteristics of a marinereactor in rolling motion and heat transfer in the core[J]. Nucl. Eng. Des.2002.215(1–2):69-85.
[57]高璞珍，刘顺隆，王兆祥.纵摇和横摇对自然循环的影响[J].核动力工程.1999,20(3):228-231.
[58]高璞珍，庞凤阁，王兆祥.核动力装置一回路冷却剂受海洋条件影响的数学模型[J].哈尔滨工程大学学报.1997,18(1):24-27.
[59]高璞珍，王兆祥，庞凤阁，丁洪河，彭敏俊，许岷.摇摆情况下水的自然循环临界热流密度实验研究[J].哈尔滨工程大学学报.1997,18(6):38-42.
[60]谭思超，高璞珍，苏光辉.摇摆运动条件下自然循环温度波动特性[J].原子能科学技术.2008,42(8):673-677.
[61]谭思超，高璞珍，苏光辉.摇摆运动条件下自然循环流动的实验和理论研究[J].哈尔滨工程大学学报.2007,28(11):1213-1217.
[62]谭思超，庞凤阁，高璞珍.摇摆对自然循环传热特性影响的实验研究[J].核动力工程.2006,27(5):33-36.
[63]谭思超，张红岩，庞凤阁，高璞珍.摇摆运动下单相自然循环流动特点[J].核动力工程.2005,26(6):554-558.
[64] Si-Chao T, Su G H, Pu-Zhen G. Heat transfer model of single-phase naturalcirculation flow under a rolling motion condition[J]. Nucl. Eng. Des.2009.239(10):2212-2216.
[65] Tan S, Su G H, Gao P. Experimental and theoretical study on single-phase naturalcirculation flow and heat transfer under rolling motion condition[J]. Appl. Therm.Eng.2009.29(14–15):3160-3168.
[66]谭思超，高璞珍，苏光辉.摇摆运动条件下自然循环复合型脉动的实验研究[J].原子能科学技术.2008,42(11):1007-1011.
[67]谭思超，庞凤阁.摇摆运动引起的波动与自然循环密度波型脉动的叠加[J].核动力工程.2005,26(2):140-143.
[68] Tan S, Su G H, Gao P. Experimental study on two-phase flow instability of naturalcirculation under rolling motion condition[J]. Ann. Nucl. Energy.2009.36(1):103-113.
[69]谭思超，高璞珍，苏光辉.摇摆运动下系统空间布置对自然循环流动特性的影响[J].西安交通大学学报.2008,42(11):1408-1412.
[70]栾锋，阎昌琪.摇摆状态下水平管内气-水两相流的流型研究[J].核动力工程.2007,28(2):19-23.
[71]栾锋，阎昌琪.摇摆状态下水平管内气-水两相流流型的判定方法[J].核动力工程.2008,29(4):39-43.
[72]栾锋，阎昌琪，曹夏昕.摇摆对竖直管内气-水两相流流型的影响分析[J].工程热物理学报.2007,28(Suppl.1):217-220.
[73]栾锋，阎昌琪，曹夏昕，姜兴伟.摇摆对垂直上升管内气液两相流截面含气率影响的研究[J].核科学与工程.2006,26(3):215-219.
[74]张金红，阎昌琪，曹夏昕，孙中宁.摇摆状态下水平管中单相水的摩擦阻力实验研究[J].核动力工程.2008,29(4):44-49.
[75]张金红，阎昌琪，方红宇，黄渭堂.摇摆对水平管内气液两相流流型的影响[J].核科学与工程.2007,27(3):206-212.
[76]张金红，阎昌琪，孙中宁.摇摆状态下水平管内气液两相流流型转换研究[J].哈尔滨工程大学学报.2008,29(10):1050-1053.
[77]杜思佳，张虹.海洋条件对单相强迫流动影响的理论研究[J].核动力工程.2009,30(5):60-64.
[78]杜思佳，张虹，贾宝山.海洋条件下竖直圆管内单相传热特性实验研究[J].核动力工程.2011,32(3):92-96.
[79] Yan B, Yu L. Theoretical research for natural circulation operational characteristicof ship nuclear machinery under ocean conditions[J]. Ann. Nucl. Energy.2009.36(6):733-741.
[80] Yan B, Gu H, Yang Y, Yu L. Theoretical models of turbulent flow in rollingmotion[J]. Prog. Nucl. Energ.2010.52(6):563-568.
[81] Yan B H, Yu L, Yang Y H. Theoretical model of laminar flow in a channel or tubeunder ocean conditions[J]. Energ. Convers. Manage.2011.52(7):2587-2597.
[82] Yan B H, Yu L. The development and validation of a thermal hydraulic code inrolling motion[J]. Ann. Nucl. Energy.2011.38(8):1728-1736.
[83] Bing-Huo Y, Han-Yang G, Yan-Hua Y, Lei Y. Numerical analysis of flowingcharacteristics of turbulent flow in rectangular channels in ocean environment[J].Prog. Nucl. Energ.2011.53(1):10-18.
[84] Yan B H, Yu L, Yang Y H. Effects of ship motions on laminar flow in tubes[J]. Ann.Nucl. Energy.2010.37(1):52-57.
[85] Yan B H, Yu L, Yang Y H. Effects of rolling on laminar frictional resistance intubes[J]. Ann. Nucl. Energy.2010.37(3):295-301.
[86] Yan B H, Gu H Y, Yang Y H, Yu L. Effect of rolling on the flowing and heattransfer characteristic of turbulent flow in sub-channels[J]. Prog. Nucl. Energ.2011.53(1):59-65.
[87]黄润生，黄浩.混沌分析及其应用[M].第二版.武汉:武汉大学出版社,2005.
[88]郝柏林.分岔、混沌、奇怪吸引子、湍流及其它——关于确定论系统中的内在随机性[J].物理学进展.1983,3(3):229-416.
[89] Lorenz E N. Deterministic nonperiofic flow[J]. J. Atoms. Sci.1963.20:130-141.
[90] Henon M. A two-dimentional mappling with a strange attractor[J]. Commun. Math.Phys.1976.50:69-77.
[91] Ruelle D, Takens F. On the natural of tubulence[J]. Commum Math Phys.1971.20(1):167-192.
[92] Li T Y, Yorke J A. Period three implies chaos[J]. Amer. Math. Monthly.1975.82(10):985-992.
[93] May R. Simple mathematical models with very complicated dynamic[J]. Nature.1976.261(10):459-475.
[94] Feigenbaum M J. Quantitative universality for a chass of nonlinear transformation[J].J. Stat. Phys.1978.19(1):25-52.
[95] Ott E, Grebogi C, Yorke J A. Controlling Chaos[J]. Phys. Rev. Lett.1990.64(11):1196-1199.
[96] Pecora L M, Carroll T L. Synchronization in chaotic systems[J]. Phys. Rev. Lett.1990.64(8):821-825.
[97]雷绍兰，孙才新，周湶，邓群，刘凡.电力短期负荷的多变量混沌预测方法[J].高电压技术.2005,31(12):69-72.
[98]王宝华，杨成梧，张强.电力系统分岔与混沌研究综述[J].电工技术学报.2005,20(7):1-10.
[99]王卫光，张仁铎.基于混沌理论的降雨量降尺度方法[J].华中科技大学学报(自然科学版).2008,36(6):129-132.
[100]蒙海花，王腊春，黄胜晔.鄱阳湖径流量时间序列的混沌特征分析[J].长江流域资源与环境.2011,20(5):540-545.
[101]王经民，柳建军，刘迎洲，赵斌.基于Lyapunov指数的树木年轮时间序列混沌特征分析[J].西北农林科技大学学报(自然科学版).2008,36(8):132-136.
[102]付义祥，刘志强.边坡位移的混沌时间序列分析方法及应用研究[J].武汉理工大学学报(交通科学与工程版).2003,27(4):473-476.
[103]丑纪范，郑志海，孙树鹏.10～30d延伸期数值天气预报的策略思考——直面混沌[J].气象科学.2010,30(5):569-573.
[104]贺太纲，卢广文，李建萍.脑电中的混沌[J].生物医学工程学杂志.2000,17(2):209-213.
[105]宁新宝，卞春华，王俊，陈颖.心脏电活动过程的非线性分析[J].科学通报.2006,54(7):764-771.
[106]施祖辉.传统经济学与混沌经济学的比较研究——兼论传统经济理论的局限性[J].外国经济与管理.2001,23(10):2-5.
[107]王凌，郑大钟，李清生.混沌优化方法的研究进展[J].计算技术与自动化.2001,20(1):1-5.
[108]石园丁，王建华.混沌神经网络的研究进展[J].微机发展.2002,12(6):33-39.
[109]黎娅，徐江峰.基于混沌的图像加密技术进展[J].河南师范大学学报(自然科学版).2005,33(3):150-151.
[110]庞春江，高婉青.基于模糊混沌神经网络的人脸识别算法[J].计算机应用.2008,28(6):1549-1558.
[111]王灵，俞金寿.混沌耗散离散粒子群算法及其在故障诊断中的应用[J].控制与决策.2007,22(10):1197-1200.
[112]杨靖，郭烈锦.气液两相流压差信号的非线性分析[J].中国电机工程学报.2002,22(9):134-139.
[113]孙斌，周云龙.水平管内空气-水两相流流型的混沌特征[J].哈尔滨工业大学学报.2006,38(11):1963-1967.
[114]顾丽莉，石炎福，余华瑞.气液两相流中压力波动信号的混沌分析[J].化学反应工程与工艺.1999,15(4):428-434.
[115]白博峰，杨靖，王学兴.气液两相流确定性混沌分析[J].石油化工设备.2003,32(6):1-4.
[116] Franca F, Acikgoz M, Lahey Jr R T, Clausse A. The use of fractal techniques forflow regime identification[J]. Int. J. Multiphas. Flow.1991.17(4):545-552.
[117]金宁德，郑桂波，胡凌云.垂直上升管中气液两相流电导波动信号的混沌特性分析[J].地球物理学报.2006,49(5):1552-1560.
[118] Biage M, Delliaye J M. The flooding transition：An experimental appraisal of thechaotic aspect of liquid film flow before the flooding point[Z]. Aiche Symposium:1989274-279.
[119] Kozma R, Kok H, Sakuma M, Djainal D D, Kitamura M. Characterization oftwo-phase flows using fractal analysis of local temperature fluctuations[J]. Int. J.Multiphas. Flow.1996.22(5):953-968.
[120]孙斌，许明飞，段晓松.水平管内气液两相泡状流的多尺度分形分析[J].中国电机工程学报.2011,31(14):77-83.
[121]周云龙，陈飞.水平气液两相流流型空间图像信息复杂性测度分析[J].化工学报.2008,59(1):64-69.
[122]谭思超.摇摆对自然循环热工水力特性的影响[D].哈尔滨:哈尔滨工程大学,2006.
[123]关新平，范正平，陈彩莲，华长春.混沌控制及其在保密通讯中的应用[M].北京:国防工业出版社,2002:1-30.
[124]曹建福，韩崇昭，方洋旺.非线性系统及应用[M].西安:西安交通大学出版社,2001:1-31.
[125]吕金虎，陆君安，陈士华.混沌时间序列分析及其应用[M].武汉:武汉大学出版社,2002.
[126]郜志英，沈允文，董海军，刘梦军.齿轮系统倍周期分岔和混沌层次结构的研究[J].机械工程学报.2005,41(4):44-48.
[127]张强，王宝华，杨成梧.电力系统倍周期分岔分析[J].电力自动化设备.2004,24(11):6-9.
[128]郑小武，谢建华.一类碰撞振动系统的倍周期分岔研究[J].四川大学学报(工程科学版).2006,38(2):30-33.
[129]郝柏林，张淑誉.研究强迫非线性振子中倍周期分岔和“混乱”现象的分频采样方法[J].物理学报.1983,32(2):198-208.
[130]孙红章，毛爱霞，苏向英，刘磊，魏荣慧，刘钢. Henon系统动力学行为的MATLAB仿真研究[J].商丘师范学院学报.2011,27(3):54-57.
[131] Takens F. Detecting strange attractors in turbulence[J]. Lecture Notes in Math.1981.898:361-381.
[132]王海燕，卢山.非线性时间序列分析及其应用[M].北京:科学出版社,2006.
[133] Grassberger P, Procaccia I. Measuring the strangeness of strange attractors[J].Physica D: Nonlinear Phenomena.1983.9(1–2):189-208.
[134] Grassberger P, Procaccia I. Estimation of the Kolmogorov entropy from a chaoticsignal[J]. Phys. Rev. A.1983.28(4):2591-2593.
[135] Wolf A, Swift J B, Swinney H L, Vastano J A. Determining Lyapunov exponentsfrom a time series[J]. Physica D.1985.16:285-317.
[136] Rosenstein M T, Collins J J, De Luca C J. A practical method for calculating largestLyapunov exponents from small data sets[J]. Physica D: Nonlinear Phenomena.1993.65(1–2):117-134.
[137] J T, S E, A L, B C, D F J. Testing for nonlinearity in time series-the method ofsurrogate data[J]. Physica D: Nonlinear Phenomena.1992.58(1-4):77-94.
[138]张文超，谭思超，高璞珍，张虹，张红岩.摇摆条件下自然循环流动不稳定性的混沌特性研究[J].原子能科学技术.2012,46(6):705-709.
[139]陆同兴，张季谦.非线性物理概论[M].第二版.合肥:中国科学技术大学出版社,2010.
[140]高璞珍，张文超，谭思超，张鹏飞.摇摆条件下自然循环复合型脉动的同步化分析[J].哈尔滨工程大学学报.2012,33(11):1346-1350.
[141]吴祥兴等.混沌学导论[M].上海市:上海科学技术文献出版社,1996:269.
[142]张文超，谭思超，高璞珍.摇摆参数对自然循环系统混沌脉动影响分析[J].哈尔滨工程大学学报.2012,33(6):796-800.
[143]王光瑞等.混沌的控制、同步与利用[M].北京市:国防工业出版社,2001:631.
[144] Goswami N, Paruya S. Advances on the research on nonlinear phenomena in boilingnatural circulation loop[J]. Prog. Nucl. Energ.2011.53(6):673-697.
[145] Yun G, Qiu S Z, Su G H, Jia D N. Theoretical investigations on two-phase flowinstability in parallel multichannel system[J]. Ann. Nucl. Energy.2008.35(4):665-676.
[146] Rizwan-Uddin. Turning points and sub-and supercritical bifurcations in a simpleBWR model[J]. Nucl. Eng. Des.2006.236(3):267-283.
[147]石教智，陈晓宏，林汝颜.东江流域降水时间序列的混沌特征分析[J].中山大学学报(自然科学版).2006,45(4):111-115.
[148]董超俊，刘智勇，邱祖廉.基于混沌理论的交通量实时预测[J].信息与控制.2004,33(5):518-522.
[149]梁志珊，王丽敏，付大鹏，张化光.基于Lyapunov指数的电力系统短期负荷预测[J].中国电机工程学报.1998,18(5):368-371.
[150]陆锦军，王执铨.一种基于混沌特性的网络流量改进预测算法[J].兵工学报.2007,28(11):1346-1350.
[151]李嘉，梁平.社会总用电量混沌全域法预测[J].广东教育学院学报.2008,28(5):60-63.
[152]孟庆芳，张强，牟文英.混沌时间序列多步自适应预测方法[J].物理学报.2006,55(4):1666-1671.
[153]陈瑛，罗鹏飞.基于神经网络的混沌时间序列建模及预测[J].计算机工程与应用.2005,49(11):77-80.
[154]张步涵，刘小华，万建平，刘沛，程时杰.基于混沌时间序列的负荷预测及其关键问题分析[J].电网技术.2004,28(13):32-36.
[2]刘向阳.我国新能源发展现状及巨大在投资机遇[J].电力设备.2006,7(2):101-103.
[3]张力.日本福岛核电站事故对安全科学的启示[J].中国安全科学学报.2011,21(4):3-6.
[4]郭志锋. AP1000的非能动安全系统[J].国外核新闻.2005(9):14-20.
[5]谭思超，高文杰，高璞珍，苏光辉.摇摆运动对自然循环流动不稳定性的影响[J].核动力工程.2007,28(5):42-45.
[6] Wu C Y, Wang S B, Pan C. Chaotic oscillations in a low pressure two-phase naturalcirculation loop under low power and high inlet subcooling conditions[J]. Nucl. Eng.Des.1996.162(2–3):223-232.
[7]陈听宽.两相流与传热研究[M].西安:西安交通大学出版社,2004.
[8]徐济鋆.沸腾传热和气液两相流[M].北京市:原子能出版社,2001:388.
[9]王经.气液两相流动动态特性的研究[M].上海:上海交通大学出版社,2012.
[10] Vijayan P K, Sharma M, Pilkhwal D S. Experimental and numerical investigationson the nature of the unstable oscillatory flow in a single-phase natural circulationloop[Z]. Kalpakkam India:2004.
[11] Ishii M. Thermally induced flow instabilities in two phase mixture in thermalequilibrium[J]. PhD thesis, Georgia Institute of Technology.1971.
[12] Achard J L, Drew D A, Lahey Jr. R T. Effect of gravity and friction on the stabilityof boiling flow in a channel[J]. Chemical Engineering Communications.1981.11(1-3):59-79.
[13] Atkinson M J, Arcuri F W, Friedly J C. The use of a computer algebra system in theanalysis of chemical engineering problems[J]. Comput. Chem. Eng.1982.6(2):169-175.
[14] Lahey Jr., R. T. M F J. The thermal-hydraulics of a boiling water nuclear reactor[J].ANS Monograph.1993.
[15] Taleyarkhan R P, Podowski M Z, Lahey Jr. R T. Ventilated channel instabilityanalysis[J]. Journal of Heat Transfer.1985.107:175-181.
[16] Clausse A, Lahey Jr. R T. The analysis of periodic and strange attractors duringdensity wave oscillations in boiling flow[J]. Chaos Soliton. Fract.1991.1(2):167-178.
[17] Lin Y N, Pan C. Non-linear analysis for a natural circulation boiling channel[J].Nucl. Eng. Des.1994.152(1–3):349-360.
[18] Chin-Jang C, Lahey Jr. R T. Analysis of chaotic instabilities in boiling systems[J].Nucl. Eng. Des.1997.167(3):307-334.
[19] Zhou Z, Heusser, Kerntechnik P. Nonlinear analysis of low-quality density waveinstabilities in a natural circulation system at heating reactor conditions[J]. Fuel andEnergy Abstracts.1996.37(5):352.
[20] Ambrosini W, Di Marco P, Ferreri J C. Linear and nonlinear analysis of densitywave instability phenomena[J]. International Journal of Heat and Technology.2000.18(1):27-36.
[21] Karve A A, Uddin R, Dorning J J. Stability analysis of BWR nuclear-coupledthermal-hydraulics using a simple model[J]. Nucl. Eng. Des.1997.177(1–3):155-177.
[22] Lee J D, Pan C. Nonlinear analysis for a double-channel two-phase naturalcirculation loop under low-pressure conditions[J]. Ann. Nucl. Energy.2005.32(3):299-329.
[23] Dutta G, Doshi J B. Nonlinear analysis of nuclear coupled density wave instabilityin time domain for a boiling water reactor core undergoing core-wide and regionalmodes of oscillations[J]. Prog. Nucl. Energ.2009.51(8):769-787.
[24] Lee J D, Pan C. Periodic and chaotic oscillations in the nuclear-coupled boilingchannel system subject to strong void-reactivity feedbacks[J]. Ann. Nucl. Energy.2009.36(6):793-801.
[25] Lakshmanan S P, Pandey M. Analysis of startup oscillations in natural circulationboiling systems[J]. Nucl. Eng. Des.2009.239(11):2391-2398.
[26] Durga Prasad G V, Pandey M. Parametric effects on reactivity instabilities andnonlinear oscillations in a nuclear-coupled double channel natural circulation boilingsystem[J]. Nucl. Eng. Des.2010.240(5):1097-1110.
[27] Cammarata G, Fichera A, Pagano A. Nonlinear analysis of a rectangular naturalcirculation loop[J]. Int. Commun. Heat Mass.2000.27(8):1077-1089.
[28] Dokhane A, Hennig D, Rizwan-Uddin, Chawla R. Semi-analytical BifurcationAnalysis of Two phase Flow in a Heated Channel[J]. Retrieved from:http://docs.ksu.edu.sa/KSU_AFCs/adokhane/IJBC_paper.pdf.2003.
[29] Abdelhamid Dokhane, Dieter Hennig, Rizwan-Uddin, Chawla R. Interpretation of inphase and out-of-phase BWR oscillationsusing an extended reduced order model andsemi analytical bifurcation analysis[J]. Ann. Nucl. Energy.2007.34:271-287.
[30] Paruya S, Bhattacharya P. A moving boundary analysis for start up performance of anuclear steam generator[J]. Journal of Fluids Engineering.2008.130(5):1-11.
[31] Carsten Lange, Dieter Hennig, Antonio Hurtado. An advanced reduced order modelfor BWR stability analysis[J].2011.53:139-160.
[32]庞凤阁，高璞珍，王兆祥，刘殊一，丁洪河.海洋条件对自然循环影响的理论研究[J].核动力工程.1995,16(04):330-335.
[33]周云龙，赵建伟，衣晓青，王晓刚，洪文鹏.倾斜下降管内气（汽）─液两相流动特性研究[J].东北电力学院学报.1995,15(03):14-24.
[34]周云龙，孙斌，粱强，顾欣.倾斜下降管气液两相分层流截面含气率的计算与液层高度的预测[J].工程热物理学报.2002,23(02):238-240.
[35] Isshiki N. Effects of heaving and listing upon thermo-hydraulic performance andcritical heat flux of water-cooled marine reactors[J]. Nucl. Eng. Des.1966.4(2):138-162.
[36] Ozoe H, Sayama H, Churchill S W. Natural convection in an inclined rectangularchannel at various aspect ratios and angles—experimental measurements[J]. Int. J.Heat Mass Tran.1975.18(12):1425-1431.
[37] Ozoe H, Sayama H, Churchill S W. Natural convection patterns in a long inclinedrectangular box heated from below: Part I. Three-directional photography[J]. Int. J.Heat Mass Tran.1977.20(2):123-129.
[38] Hiroyuki O, Tsutomu S, Churchill S W. Natural convection in an inclined circularcylindrical annulus heated and cooled on its end plates[J]. Int. J. Heat Mass Tran.1981.24(4):727-737.
[39] Hiroyuki O, Kazumitsu Y, Hayatoshi S, Churchill S W. Natural circulation in aninclined rectangular channel heated on one side and cooled on the opposing side[J].Int. J. Heat Mass Tran.1974.17(10):1209-1217.
[40]宫厚军，杨星团，姜胜耀，刘志勇.海洋运动对自然循环流动影响的理论分析[J].核动力工程.2010,31(04):52-56.
[41] Iyori I, Aya I, Murata H, Kobayashi M, Nariai H. Natural circulation ofintegrated-type marine reactor at inclined attitude[J]. Nucl. Eng. Des.1987.99:423-430.
[42]苏光辉，张金玲，郭玉君，秋穗正，喻真烷，贾斗南.海洋条件对船用核动力堆余热排出系统特性的影响[J].原子能科学技术.1996,30(6):487-491.
[43]高璞珍，庞凤阁，刘殊一，彭敏俊.倾斜对强迫循环和自然循环影响的比较[J].核科学与工程.1997,17(02):179-183.
[44]曹夏昕，阎昌琪.倾斜管内气液两相流流型的实验研究[J].核动力工程.2005,26(06):572-575.
[45]曹夏昕，阎昌琪，孙立成.向上倾斜管内气-水两相流流型转变分析[J].核科学与工程.2005,25(01):45-49.
[46]高璞珍，王兆祥，刘顺隆.起伏对强制循环和自然循环的影响[J].核科学与工程.1999,19(02):116-120.
[47] Ishida T, Yoritsune T. Effects of ship motions on natural circulation of deep searesearch reactor DRX[J]. Nucl. Eng. Des.2002.215(1–2):51-67.
[48]于雷，鄢邴火，陈玉清.海基核动力装置自然循环数学模型的建立与运行特性研究[J].原子能科学技术.2008,42(Suppl.):116-122.
[49]张金玲，郭玉君，秋穗正，苏光辉，贾斗南，喻真烷，陈学俊.船用压水核反应堆系统自然循环分析[J].辐射防护通讯.1994,14(04):14-20.
[50]张金玲，郭玉君，秋穗正，苏光辉，贾斗南，喻真烷，陈学俊.船用核动力装置自然循环载热能力的分析与计算[J].西安交通大学学报.1994,28(6):35-42.
[51]洪钢，杨燕华，刘祥锋，闫晓，黄彦平，陈炳德.起伏运动对加热壁面汽泡受力的影响分析[J].核动力工程.2011,32(03):87-91.
[52]姜胜耀，杨星团，宫厚军，刘志勇，郝文涛，李军，葛裴.起伏因素影响自然循环流动的机理分析[J].原子能科学技术.2009,43(S1):92-96.
[53]孙德祥.船舶运动对反应堆热工水力的影响[C].核动力工程编辑部,1996.
[54] Ishida T, Kusunoki T. Effect by sea wave on thermal hydraulics of marine reactorsystem[J]. J. Nucl. Sci. Technol.1995.32(8):740-751.
[55] Murata H, Iyori I, Kobayashi M. Natural circulation characteristics of a marinereactor in rolling motion[J]. Nucl. Eng. Des.1990.118(2):141-154.
[56] Murata H, Sawada K, Kobayashi M. Natural circulation characteristics of a marinereactor in rolling motion and heat transfer in the core[J]. Nucl. Eng. Des.2002.215(1–2):69-85.
[57]高璞珍，刘顺隆，王兆祥.纵摇和横摇对自然循环的影响[J].核动力工程.1999,20(3):228-231.
[58]高璞珍，庞凤阁，王兆祥.核动力装置一回路冷却剂受海洋条件影响的数学模型[J].哈尔滨工程大学学报.1997,18(1):24-27.
[59]高璞珍，王兆祥，庞凤阁，丁洪河，彭敏俊，许岷.摇摆情况下水的自然循环临界热流密度实验研究[J].哈尔滨工程大学学报.1997,18(6):38-42.
[60]谭思超，高璞珍，苏光辉.摇摆运动条件下自然循环温度波动特性[J].原子能科学技术.2008,42(8):673-677.
[61]谭思超，高璞珍，苏光辉.摇摆运动条件下自然循环流动的实验和理论研究[J].哈尔滨工程大学学报.2007,28(11):1213-1217.
[62]谭思超，庞凤阁，高璞珍.摇摆对自然循环传热特性影响的实验研究[J].核动力工程.2006,27(5):33-36.
[63]谭思超，张红岩，庞凤阁，高璞珍.摇摆运动下单相自然循环流动特点[J].核动力工程.2005,26(6):554-558.
[64] Si-Chao T, Su G H, Pu-Zhen G. Heat transfer model of single-phase naturalcirculation flow under a rolling motion condition[J]. Nucl. Eng. Des.2009.239(10):2212-2216.
[65] Tan S, Su G H, Gao P. Experimental and theoretical study on single-phase naturalcirculation flow and heat transfer under rolling motion condition[J]. Appl. Therm.Eng.2009.29(14–15):3160-3168.
[66]谭思超，高璞珍，苏光辉.摇摆运动条件下自然循环复合型脉动的实验研究[J].原子能科学技术.2008,42(11):1007-1011.
[67]谭思超，庞凤阁.摇摆运动引起的波动与自然循环密度波型脉动的叠加[J].核动力工程.2005,26(2):140-143.
[68] Tan S, Su G H, Gao P. Experimental study on two-phase flow instability of naturalcirculation under rolling motion condition[J]. Ann. Nucl. Energy.2009.36(1):103-113.
[69]谭思超，高璞珍，苏光辉.摇摆运动下系统空间布置对自然循环流动特性的影响[J].西安交通大学学报.2008,42(11):1408-1412.
[70]栾锋，阎昌琪.摇摆状态下水平管内气-水两相流的流型研究[J].核动力工程.2007,28(2):19-23.
[71]栾锋，阎昌琪.摇摆状态下水平管内气-水两相流流型的判定方法[J].核动力工程.2008,29(4):39-43.
[72]栾锋，阎昌琪，曹夏昕.摇摆对竖直管内气-水两相流流型的影响分析[J].工程热物理学报.2007,28(Suppl.1):217-220.
[73]栾锋，阎昌琪，曹夏昕，姜兴伟.摇摆对垂直上升管内气液两相流截面含气率影响的研究[J].核科学与工程.2006,26(3):215-219.
[74]张金红，阎昌琪，曹夏昕，孙中宁.摇摆状态下水平管中单相水的摩擦阻力实验研究[J].核动力工程.2008,29(4):44-49.
[75]张金红，阎昌琪，方红宇，黄渭堂.摇摆对水平管内气液两相流流型的影响[J].核科学与工程.2007,27(3):206-212.
[76]张金红，阎昌琪，孙中宁.摇摆状态下水平管内气液两相流流型转换研究[J].哈尔滨工程大学学报.2008,29(10):1050-1053.
[77]杜思佳，张虹.海洋条件对单相强迫流动影响的理论研究[J].核动力工程.2009,30(5):60-64.
[78]杜思佳，张虹，贾宝山.海洋条件下竖直圆管内单相传热特性实验研究[J].核动力工程.2011,32(3):92-96.
[79] Yan B, Yu L. Theoretical research for natural circulation operational characteristicof ship nuclear machinery under ocean conditions[J]. Ann. Nucl. Energy.2009.36(6):733-741.
[80] Yan B, Gu H, Yang Y, Yu L. Theoretical models of turbulent flow in rollingmotion[J]. Prog. Nucl. Energ.2010.52(6):563-568.
[81] Yan B H, Yu L, Yang Y H. Theoretical model of laminar flow in a channel or tubeunder ocean conditions[J]. Energ. Convers. Manage.2011.52(7):2587-2597.
[82] Yan B H, Yu L. The development and validation of a thermal hydraulic code inrolling motion[J]. Ann. Nucl. Energy.2011.38(8):1728-1736.
[83] Bing-Huo Y, Han-Yang G, Yan-Hua Y, Lei Y. Numerical analysis of flowingcharacteristics of turbulent flow in rectangular channels in ocean environment[J].Prog. Nucl. Energ.2011.53(1):10-18.
[84] Yan B H, Yu L, Yang Y H. Effects of ship motions on laminar flow in tubes[J]. Ann.Nucl. Energy.2010.37(1):52-57.
[85] Yan B H, Yu L, Yang Y H. Effects of rolling on laminar frictional resistance intubes[J]. Ann. Nucl. Energy.2010.37(3):295-301.
[86] Yan B H, Gu H Y, Yang Y H, Yu L. Effect of rolling on the flowing and heattransfer characteristic of turbulent flow in sub-channels[J]. Prog. Nucl. Energ.2011.53(1):59-65.
[87]黄润生，黄浩.混沌分析及其应用[M].第二版.武汉:武汉大学出版社,2005.
[88]郝柏林.分岔、混沌、奇怪吸引子、湍流及其它——关于确定论系统中的内在随机性[J].物理学进展.1983,3(3):229-416.
[89] Lorenz E N. Deterministic nonperiofic flow[J]. J. Atoms. Sci.1963.20:130-141.
[90] Henon M. A two-dimentional mappling with a strange attractor[J]. Commun. Math.Phys.1976.50:69-77.
[91] Ruelle D, Takens F. On the natural of tubulence[J]. Commum Math Phys.1971.20(1):167-192.
[92] Li T Y, Yorke J A. Period three implies chaos[J]. Amer. Math. Monthly.1975.82(10):985-992.
[93] May R. Simple mathematical models with very complicated dynamic[J]. Nature.1976.261(10):459-475.
[94] Feigenbaum M J. Quantitative universality for a chass of nonlinear transformation[J].J. Stat. Phys.1978.19(1):25-52.
[95] Ott E, Grebogi C, Yorke J A. Controlling Chaos[J]. Phys. Rev. Lett.1990.64(11):1196-1199.
[96] Pecora L M, Carroll T L. Synchronization in chaotic systems[J]. Phys. Rev. Lett.1990.64(8):821-825.
[97]雷绍兰，孙才新，周湶，邓群，刘凡.电力短期负荷的多变量混沌预测方法[J].高电压技术.2005,31(12):69-72.
[98]王宝华，杨成梧，张强.电力系统分岔与混沌研究综述[J].电工技术学报.2005,20(7):1-10.
[99]王卫光，张仁铎.基于混沌理论的降雨量降尺度方法[J].华中科技大学学报(自然科学版).2008,36(6):129-132.
[100]蒙海花，王腊春，黄胜晔.鄱阳湖径流量时间序列的混沌特征分析[J].长江流域资源与环境.2011,20(5):540-545.
[101]王经民，柳建军，刘迎洲，赵斌.基于Lyapunov指数的树木年轮时间序列混沌特征分析[J].西北农林科技大学学报(自然科学版).2008,36(8):132-136.
[102]付义祥，刘志强.边坡位移的混沌时间序列分析方法及应用研究[J].武汉理工大学学报(交通科学与工程版).2003,27(4):473-476.
[103]丑纪范，郑志海，孙树鹏.10～30d延伸期数值天气预报的策略思考——直面混沌[J].气象科学.2010,30(5):569-573.
[104]贺太纲，卢广文，李建萍.脑电中的混沌[J].生物医学工程学杂志.2000,17(2):209-213.
[105]宁新宝，卞春华，王俊，陈颖.心脏电活动过程的非线性分析[J].科学通报.2006,54(7):764-771.
[106]施祖辉.传统经济学与混沌经济学的比较研究——兼论传统经济理论的局限性[J].外国经济与管理.2001,23(10):2-5.
[107]王凌，郑大钟，李清生.混沌优化方法的研究进展[J].计算技术与自动化.2001,20(1):1-5.
[108]石园丁，王建华.混沌神经网络的研究进展[J].微机发展.2002,12(6):33-39.
[109]黎娅，徐江峰.基于混沌的图像加密技术进展[J].河南师范大学学报(自然科学版).2005,33(3):150-151.
[110]庞春江，高婉青.基于模糊混沌神经网络的人脸识别算法[J].计算机应用.2008,28(6):1549-1558.
[111]王灵，俞金寿.混沌耗散离散粒子群算法及其在故障诊断中的应用[J].控制与决策.2007,22(10):1197-1200.
[112]杨靖，郭烈锦.气液两相流压差信号的非线性分析[J].中国电机工程学报.2002,22(9):134-139.
[113]孙斌，周云龙.水平管内空气-水两相流流型的混沌特征[J].哈尔滨工业大学学报.2006,38(11):1963-1967.
[114]顾丽莉，石炎福，余华瑞.气液两相流中压力波动信号的混沌分析[J].化学反应工程与工艺.1999,15(4):428-434.
[115]白博峰，杨靖，王学兴.气液两相流确定性混沌分析[J].石油化工设备.2003,32(6):1-4.
[116] Franca F, Acikgoz M, Lahey Jr R T, Clausse A. The use of fractal techniques forflow regime identification[J]. Int. J. Multiphas. Flow.1991.17(4):545-552.
[117]金宁德，郑桂波，胡凌云.垂直上升管中气液两相流电导波动信号的混沌特性分析[J].地球物理学报.2006,49(5):1552-1560.
[118] Biage M, Delliaye J M. The flooding transition：An experimental appraisal of thechaotic aspect of liquid film flow before the flooding point[Z]. Aiche Symposium:1989274-279.
[119] Kozma R, Kok H, Sakuma M, Djainal D D, Kitamura M. Characterization oftwo-phase flows using fractal analysis of local temperature fluctuations[J]. Int. J.Multiphas. Flow.1996.22(5):953-968.
[120]孙斌，许明飞，段晓松.水平管内气液两相泡状流的多尺度分形分析[J].中国电机工程学报.2011,31(14):77-83.
[121]周云龙，陈飞.水平气液两相流流型空间图像信息复杂性测度分析[J].化工学报.2008,59(1):64-69.
[122]谭思超.摇摆对自然循环热工水力特性的影响[D].哈尔滨:哈尔滨工程大学,2006.
[123]关新平，范正平，陈彩莲，华长春.混沌控制及其在保密通讯中的应用[M].北京:国防工业出版社,2002:1-30.
[124]曹建福，韩崇昭，方洋旺.非线性系统及应用[M].西安:西安交通大学出版社,2001:1-31.
[125]吕金虎，陆君安，陈士华.混沌时间序列分析及其应用[M].武汉:武汉大学出版社,2002.
[126]郜志英，沈允文，董海军，刘梦军.齿轮系统倍周期分岔和混沌层次结构的研究[J].机械工程学报.2005,41(4):44-48.
[127]张强，王宝华，杨成梧.电力系统倍周期分岔分析[J].电力自动化设备.2004,24(11):6-9.
[128]郑小武，谢建华.一类碰撞振动系统的倍周期分岔研究[J].四川大学学报(工程科学版).2006,38(2):30-33.
[129]郝柏林，张淑誉.研究强迫非线性振子中倍周期分岔和“混乱”现象的分频采样方法[J].物理学报.1983,32(2):198-208.
[130]孙红章，毛爱霞，苏向英，刘磊，魏荣慧，刘钢. Henon系统动力学行为的MATLAB仿真研究[J].商丘师范学院学报.2011,27(3):54-57.
[131] Takens F. Detecting strange attractors in turbulence[J]. Lecture Notes in Math.1981.898:361-381.
[132]王海燕，卢山.非线性时间序列分析及其应用[M].北京:科学出版社,2006.
[133] Grassberger P, Procaccia I. Measuring the strangeness of strange attractors[J].Physica D: Nonlinear Phenomena.1983.9(1–2):189-208.
[134] Grassberger P, Procaccia I. Estimation of the Kolmogorov entropy from a chaoticsignal[J]. Phys. Rev. A.1983.28(4):2591-2593.
[135] Wolf A, Swift J B, Swinney H L, Vastano J A. Determining Lyapunov exponentsfrom a time series[J]. Physica D.1985.16:285-317.
[136] Rosenstein M T, Collins J J, De Luca C J. A practical method for calculating largestLyapunov exponents from small data sets[J]. Physica D: Nonlinear Phenomena.1993.65(1–2):117-134.
[137] J T, S E, A L, B C, D F J. Testing for nonlinearity in time series-the method ofsurrogate data[J]. Physica D: Nonlinear Phenomena.1992.58(1-4):77-94.
[138]张文超，谭思超，高璞珍，张虹，张红岩.摇摆条件下自然循环流动不稳定性的混沌特性研究[J].原子能科学技术.2012,46(6):705-709.
[139]陆同兴，张季谦.非线性物理概论[M].第二版.合肥:中国科学技术大学出版社,2010.
[140]高璞珍，张文超，谭思超，张鹏飞.摇摆条件下自然循环复合型脉动的同步化分析[J].哈尔滨工程大学学报.2012,33(11):1346-1350.
[141]吴祥兴等.混沌学导论[M].上海市:上海科学技术文献出版社,1996:269.
[142]张文超，谭思超，高璞珍.摇摆参数对自然循环系统混沌脉动影响分析[J].哈尔滨工程大学学报.2012,33(6):796-800.
[143]王光瑞等.混沌的控制、同步与利用[M].北京市:国防工业出版社,2001:631.
[144] Goswami N, Paruya S. Advances on the research on nonlinear phenomena in boilingnatural circulation loop[J]. Prog. Nucl. Energ.2011.53(6):673-697.
[145] Yun G, Qiu S Z, Su G H, Jia D N. Theoretical investigations on two-phase flowinstability in parallel multichannel system[J]. Ann. Nucl. Energy.2008.35(4):665-676.
[146] Rizwan-Uddin. Turning points and sub-and supercritical bifurcations in a simpleBWR model[J]. Nucl. Eng. Des.2006.236(3):267-283.
[147]石教智，陈晓宏，林汝颜.东江流域降水时间序列的混沌特征分析[J].中山大学学报(自然科学版).2006,45(4):111-115.
[148]董超俊，刘智勇，邱祖廉.基于混沌理论的交通量实时预测[J].信息与控制.2004,33(5):518-522.
[149]梁志珊，王丽敏，付大鹏，张化光.基于Lyapunov指数的电力系统短期负荷预测[J].中国电机工程学报.1998,18(5):368-371.
[150]陆锦军，王执铨.一种基于混沌特性的网络流量改进预测算法[J].兵工学报.2007,28(11):1346-1350.
[151]李嘉，梁平.社会总用电量混沌全域法预测[J].广东教育学院学报.2008,28(5):60-63.
[152]孟庆芳，张强，牟文英.混沌时间序列多步自适应预测方法[J].物理学报.2006,55(4):1666-1671.
[153]陈瑛，罗鹏飞.基于神经网络的混沌时间序列建模及预测[J].计算机工程与应用.2005,49(11):77-80.
[154]张步涵，刘小华，万建平，刘沛，程时杰.基于混沌时间序列的负荷预测及其关键问题分析[J].电网技术.2004,28(13):32-36.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |