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The identification and forecasting of chaos for natural circulation flow instabilities under rolling motion

Zhang Wen-Chao Tan Si-Chao Gao Pu-Zhen

The identification and forecasting of chaos for natural circulation flow instabilities under rolling motion

Zhang Wen-Chao, Tan Si-Chao, Gao Pu-Zhen
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  • Chaos identification and forecasting of the irregular complex flow oscillations in a two-phase natural circulation system under the rolling motion are performed. The irregular complex flow oscillation has chaotic characteristics by calculating the geometric invariants such as the correlation dimension, Kolmogorov entropy and the largest Lyapunov exponent. But the reliability of calculation result is liable to be influenced by data length and the interference of measurement noise, false judgment results may exist in the direct method. To avoid misjudgment for chaos flow oscillation, both the geometric invariants and chaos identification need to be calculated by surrogate-data method. The chaos is identified by the iterated-amplitude adjusted Fourier transform method. Chaotic forecasting for the irregular complex flow oscillation is carried out by adding weight one-rank local region method. By surrogate-data method, we can confirm that the irregular complex flow oscillation is chaotic oscillation from the deterministic system. Comparisons between the prediction results and experimental data indicate that the chaos forecasting based on adding weight one-rank local region method is an effective way for two-phase natural circulation flow instabilities, and a way of dynamical forecast to monitor flow oscillation is presented.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 50806014), the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. HEUCFZ1008), the Scientific Research Staring Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China (Grant No. 2012-1707), and the Heilongjiang Province Postdoctoral Sustentation Fund, China (Grant No. LBH-Q10131).
    [1]

    L J H, Murali K, Sinha S, Leung H, Aziz-Alaoui M A 2008 Phys. Lett. A 372 3234

    [2]

    L J H, Chen G R 2006 Int. J. Bifur. Chaos 16 775

    [3]

    Deng W H, L J H 2007 Phys. Lett. A 369 438

    [4]

    L J H 2008 Adv. in Mech. 38 713 (in Chinese) [吕金虎 2008 力学进展 38 713]

    [5]

    L J H, Chen G R 2005 IEEE Trans. Auto. Contr. 50 841

    [6]

    L J H, Yu X H, Chen G R, Cheng D 2004 IEEE Trans. Circ. Syst. I 51 787

    [7]

    Zhou J, Lu J A, L J H 2006 IEEE Trans. Automat. Contr. 51 652

    [8]

    Sachin B 2013 IEEE Trans. Circuits Syst. I 60 199

    [9]

    Chen Y, L J H, Lin Z L Automatica (in press)

    [10]

    Wu C Y, Wang S B, Pan C 1996 Nucl. Eng. Des. 162 223

    [11]

    Chang C J, Richard T, Lahey J 1997 Nucl. Eng. Des. 167 307

    [12]

    Kuang B, Chen H, Hu Z H, Lu L L, Xu J J 2005 J. Eng. Thermoph. 26 88 (in Chinese) [匡波, 陈宏, 胡志华, 陆柳柳, 徐济鋆 2005工程热物理学报 26 88]

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    Sun B, Zhou Y L 2006 J. Harb. Inst. Tech. 38 1963 (in Chinese) [孙斌, 周云龙 2006 哈尔滨工业大学学报 38 1963]

    [14]

    Xiao N, Jin N D 2007 Acta Phys. Sin. 56 5149 (in Chinese) [肖楠, 金宁德 2007 物理学报 56 5149]

    [15]

    Guo Y, Qiu S Z, Su G H, Jia D N 2008 Ann. Nucl. Energy 35 1598

    [16]

    Tan S, Su G H, Gao P Z 2009 Ann. Nucl. Energy 36 103

    [17]

    Tan S C, Pang F G 2005 Nuclear Power Engineering 26 140 (in Chinese) [谭思超, 庞凤阁 2005核动力工程 26 140]

    [18]

    Tan S C, Gao P Z, Su G H 2008 Atom. Energy. Sci. Tech. 42 1007 (in Chinese) [谭思超, 高璞珍, 苏光辉 2008原子能科学技术 42 1007]

    [19]

    Zhang W C, Tan S C, Gao P Z, Zhang H, Zhang H Y 2012 Atom. Energy Sci. Tech. 46 705 (in Chinese) [张文超, 谭思超, 高璞珍, 张虹, 张红岩 2012 原子能科学技术 46 705]

    [20]

    Theiler J, Euhank S, Longtin A, Caldrikian B, Farmer J D 1992 Physica D: Nonlinear Phenomena 58 77

    [21]

    Liu Y Z, Wen X S, Hu N Q 2001 Acta Phys. Sin. 50 1241 (in Chinese) [刘耀宗, 温熙森, 胡茑庆 2001 物理学报 50 1241]

    [22]

    Wu Y D, Xie H B 2007 Acta Phys. Sin. 56 6294 (in Chinese) [吴延东, 谢洪波 2007 物理学报 56 6294]

    [23]

    Ma W C, Jin N D, Gao Z K 2012 Acta Phys. Sin. 61 170510 (in Chinese) [马文聪, 金宁德, 高忠科 2012 物理学报 61 170510]

    [24]

    L J H, Zhang S C 2002 Control Theory and Application 19 767 (in Chinese) [吕金虎, 张锁春 2002 控制理论与应用 19 767]

    [25]

    Chen Y F, L J H, Zhou C B 2001 Chin. J. Rock Mech. Engin. 20 671 (in Chinese) [陈益峰, 吕金虎, 周创兵 2001 岩石力学与工程学报 20 671]

    [26]

    Yang Y F, Ren X M, Qin W Y, Wu Y F, Zhi X Z 2008 Acta Phys. Sin. 57 6139 (in Chinese) [杨永锋, 任兴民, 秦卫阳, 吴亚锋, 支希哲 2008物理学报 57 6139]

    [27]

    Tan S C, Su G H, Gao P Z 2009 Appl. Therm. Eng. 29 3160

    [28]

    Takens F 1981 Lecture Notes in Math. 898 361

    [29]

    L J H, Lu J A, Chen S H 2002 Chaotic Time Series Analysis and Application (Wuhan: Wuhan University Press) pp59, 60, 102 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉: 武汉大学出版) 第59, 60, 102 页]

    [30]

    Grassberger P, Procaccia I 1983 Physica D 9 189

    [31]

    Wang H Y, Lu S 2006 Nonlinear Time Scries Analysis and its Application (Beijing: Science Press) p30 (in Chinese) [王海燕, 卢山 2006非线性时间序列分析及其应用 (北京: 科学出版社) 第30页]

  • [1]

    L J H, Murali K, Sinha S, Leung H, Aziz-Alaoui M A 2008 Phys. Lett. A 372 3234

    [2]

    L J H, Chen G R 2006 Int. J. Bifur. Chaos 16 775

    [3]

    Deng W H, L J H 2007 Phys. Lett. A 369 438

    [4]

    L J H 2008 Adv. in Mech. 38 713 (in Chinese) [吕金虎 2008 力学进展 38 713]

    [5]

    L J H, Chen G R 2005 IEEE Trans. Auto. Contr. 50 841

    [6]

    L J H, Yu X H, Chen G R, Cheng D 2004 IEEE Trans. Circ. Syst. I 51 787

    [7]

    Zhou J, Lu J A, L J H 2006 IEEE Trans. Automat. Contr. 51 652

    [8]

    Sachin B 2013 IEEE Trans. Circuits Syst. I 60 199

    [9]

    Chen Y, L J H, Lin Z L Automatica (in press)

    [10]

    Wu C Y, Wang S B, Pan C 1996 Nucl. Eng. Des. 162 223

    [11]

    Chang C J, Richard T, Lahey J 1997 Nucl. Eng. Des. 167 307

    [12]

    Kuang B, Chen H, Hu Z H, Lu L L, Xu J J 2005 J. Eng. Thermoph. 26 88 (in Chinese) [匡波, 陈宏, 胡志华, 陆柳柳, 徐济鋆 2005工程热物理学报 26 88]

    [13]

    Sun B, Zhou Y L 2006 J. Harb. Inst. Tech. 38 1963 (in Chinese) [孙斌, 周云龙 2006 哈尔滨工业大学学报 38 1963]

    [14]

    Xiao N, Jin N D 2007 Acta Phys. Sin. 56 5149 (in Chinese) [肖楠, 金宁德 2007 物理学报 56 5149]

    [15]

    Guo Y, Qiu S Z, Su G H, Jia D N 2008 Ann. Nucl. Energy 35 1598

    [16]

    Tan S, Su G H, Gao P Z 2009 Ann. Nucl. Energy 36 103

    [17]

    Tan S C, Pang F G 2005 Nuclear Power Engineering 26 140 (in Chinese) [谭思超, 庞凤阁 2005核动力工程 26 140]

    [18]

    Tan S C, Gao P Z, Su G H 2008 Atom. Energy. Sci. Tech. 42 1007 (in Chinese) [谭思超, 高璞珍, 苏光辉 2008原子能科学技术 42 1007]

    [19]

    Zhang W C, Tan S C, Gao P Z, Zhang H, Zhang H Y 2012 Atom. Energy Sci. Tech. 46 705 (in Chinese) [张文超, 谭思超, 高璞珍, 张虹, 张红岩 2012 原子能科学技术 46 705]

    [20]

    Theiler J, Euhank S, Longtin A, Caldrikian B, Farmer J D 1992 Physica D: Nonlinear Phenomena 58 77

    [21]

    Liu Y Z, Wen X S, Hu N Q 2001 Acta Phys. Sin. 50 1241 (in Chinese) [刘耀宗, 温熙森, 胡茑庆 2001 物理学报 50 1241]

    [22]

    Wu Y D, Xie H B 2007 Acta Phys. Sin. 56 6294 (in Chinese) [吴延东, 谢洪波 2007 物理学报 56 6294]

    [23]

    Ma W C, Jin N D, Gao Z K 2012 Acta Phys. Sin. 61 170510 (in Chinese) [马文聪, 金宁德, 高忠科 2012 物理学报 61 170510]

    [24]

    L J H, Zhang S C 2002 Control Theory and Application 19 767 (in Chinese) [吕金虎, 张锁春 2002 控制理论与应用 19 767]

    [25]

    Chen Y F, L J H, Zhou C B 2001 Chin. J. Rock Mech. Engin. 20 671 (in Chinese) [陈益峰, 吕金虎, 周创兵 2001 岩石力学与工程学报 20 671]

    [26]

    Yang Y F, Ren X M, Qin W Y, Wu Y F, Zhi X Z 2008 Acta Phys. Sin. 57 6139 (in Chinese) [杨永锋, 任兴民, 秦卫阳, 吴亚锋, 支希哲 2008物理学报 57 6139]

    [27]

    Tan S C, Su G H, Gao P Z 2009 Appl. Therm. Eng. 29 3160

    [28]

    Takens F 1981 Lecture Notes in Math. 898 361

    [29]

    L J H, Lu J A, Chen S H 2002 Chaotic Time Series Analysis and Application (Wuhan: Wuhan University Press) pp59, 60, 102 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉: 武汉大学出版) 第59, 60, 102 页]

    [30]

    Grassberger P, Procaccia I 1983 Physica D 9 189

    [31]

    Wang H Y, Lu S 2006 Nonlinear Time Scries Analysis and its Application (Beijing: Science Press) p30 (in Chinese) [王海燕, 卢山 2006非线性时间序列分析及其应用 (北京: 科学出版社) 第30页]

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  • Received Date:  01 March 2013
  • Accepted Date:  02 April 2013
  • Published Online:  20 July 2013

The identification and forecasting of chaos for natural circulation flow instabilities under rolling motion

  • 1. National Defense Key Subject Laboratory for Nuclear Safety and Simulation Technology, Harbin Engineering University, Harbin 150001, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 50806014), the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. HEUCFZ1008), the Scientific Research Staring Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China (Grant No. 2012-1707), and the Heilongjiang Province Postdoctoral Sustentation Fund, China (Grant No. LBH-Q10131).

Abstract: Chaos identification and forecasting of the irregular complex flow oscillations in a two-phase natural circulation system under the rolling motion are performed. The irregular complex flow oscillation has chaotic characteristics by calculating the geometric invariants such as the correlation dimension, Kolmogorov entropy and the largest Lyapunov exponent. But the reliability of calculation result is liable to be influenced by data length and the interference of measurement noise, false judgment results may exist in the direct method. To avoid misjudgment for chaos flow oscillation, both the geometric invariants and chaos identification need to be calculated by surrogate-data method. The chaos is identified by the iterated-amplitude adjusted Fourier transform method. Chaotic forecasting for the irregular complex flow oscillation is carried out by adding weight one-rank local region method. By surrogate-data method, we can confirm that the irregular complex flow oscillation is chaotic oscillation from the deterministic system. Comparisons between the prediction results and experimental data indicate that the chaos forecasting based on adding weight one-rank local region method is an effective way for two-phase natural circulation flow instabilities, and a way of dynamical forecast to monitor flow oscillation is presented.

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