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Multi-scale cross-correlation characteristics of void fraction wave propagation for gas-liquid two-phase flows in small diameter pipe

Zhai Lu-Sheng Jin Ning-De

Multi-scale cross-correlation characteristics of void fraction wave propagation for gas-liquid two-phase flows in small diameter pipe

Zhai Lu-Sheng, Jin Ning-De
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  • The void fraction wave is a special physical phenomenon in a gas-liquid two-phase flow system. Understanding the propagation of the void fraction wave is of great significance for uncovering the physical mechanisms in both flow pattern transition and the fluid velocity measurement. In this study, detrended cross-correlation analysis (DCCA) is used to investigate the multi-scale cross-correlation characteristics of the coupled ARFIMA processes. It is found that the DCCA can effectively reveal the multi-scale cross-correlation dynamical behaviors of complex system. Then, we carry out the experimental test in a vertical gas-liquid two-phase flow pipe with small inner diameter. The DCCA is used to detect the cross-correlation characteristics of the void fraction wave on multiple time scales, and the growth rate of the cross-correlation level for the void fraction wave is observed on low time scales. Additionally, the spatial attenuation factor (SAF) of the void fraction wave is calculated to investigate the instability of the wave propagation. The SAF is close to zero under the transitional flow patterns, which means that the void fraction wave is in a stable propagating state. For bubble flows, the void fraction wave presents the attenuation characteristics, whilst the void fraction wave shows the amplification characteristics under the slug and churn flow patterns. Interestingly, the instability behaviors of the void fraction wave are always associated with its multi-scale cross-correlation characteristics. Specifically, the increasing rate of the wave cross-correlation level on low scales is much higher for transitional flow patterns, which is corresponding to the stable propagating characteristic of the void fraction wave. However, when the void fraction wave exhibits attenuation or amplification characteristics under other flow patterns, the increasing rate of the wave cross-correlation level on low scales is much lower.
      Corresponding author: Jin Ning-De, ndjin@tju.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 41504104, 51527805, 11572220), the Natural Science Foundation of Tianjin, China (Grant No. 14JCQNJC04200), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130032120042).
    [1]

    Liu L, Zhou F D, Li H X 1998 Adv. Mech. 28 227 (in Chinese) [刘磊, 周芳德, 李会雄 1998 力学进展 28 227]

    [2]

    Huang F, Zhang X M, Guo L J 2005 Prog. Nat. Sci. 15 459 (in Chinese) [黄飞, 张西民, 郭烈锦 2005 自然科学进展 15 459]

    [3]

    Bai B F, Huang F, Guo L J, Wang X Y 2005 Nucl. Power Eng. 26 323 (in Chinese) [白博峰, 黄飞, 郭烈锦, 王先元 2005 核动力工程 26 323]

    [4]

    Boure J A, Mercadier Y 1982 Appl. Sci. Re. 38 297

    [5]

    Matuszkiewicz A, Flamand J C, Boure J A 1987 Int. J. Multiphase Flow 13 199

    [6]

    Song C H, No H C, Chung M K 1995 Int. J. Multiphase Flow 21 381

    [7]

    Kytmaa H K, Brennen C E 1991 Int. J. Multiphase Flow 17 13

    [8]

    Lucas G P, Walton I C 1997 Flow Meas. Instrum. 8 133

    [9]

    Lucas G P, Jin N D 2001 Meas. Sci. Technol. 12 1529

    [10]

    Sun B J, Yan D C 2000 Acta Sci. Nat. Univ. Pekinensis 36 381 (in Chinese) [孙宝江, 颜大椿 2000 北京大学学报(自然科学版) 36 381]

    [11]

    Sun B J, Wang R H, Zhao X X, Gao Y H 2004 J. Hydrodyn. 19 246 (in Chinese) [孙宝江, 王瑞和, 赵欣欣, 高永海 2004 水动力学研究与进展 19 246]

    [12]

    Espinosa-Paredes G, Cazarez-Candia O, Garcia-Gutierrez A 2002 Ann. Nucl. Energy 29 1261

    [13]

    Jin N D, Nie X B, Wang J, Ren Y Y 2003 Flow Meas. Instrum. 14 177

    [14]

    Ami T, Umekawa H, Ozawa M, Shoji M 2009 Int. J. Heat Mass Transfer 52 5682

    [15]

    Yao W P, Liu T B, Dai J F, Wang J 2014 Acta Phys. Sin. 63 078704 (in Chinese) [姚文坡, 刘铁兵, 戴加飞, 王俊 2014 物理学报 63 078704]

    [16]

    Xiang Z T, Chen Y F, Li Y J, Xiong L 2014 Acta Phys. Sin. 63 038903 (in Chinese) [向郑涛, 陈宇峰, 李昱瑾, 熊励 2014 物理学报 63 038903]

    [17]

    Dou F X, Jin N D, Fan C L, Gao Z K, Sun B 2014 Chin. Phys. B 23 120502

    [18]

    Gou J, Liu J Y, Wei Z B, Taylor G, Liu Y B 2014 Acta Phys. Sin. 63 208402 (in Chinese) [苟竞, 刘俊勇, 魏震波, Taylor G, 刘友波 2014 物理学报 63 208402]

    [19]

    Hao Q Y, Jin N D, Han Y F, Gao Z K, Zhai L S 2014 Chin. Phys. Lett. 31 120501

    [20]

    Zhang M N, Li Z H, Chen X Y, Liu C X, Teng S Y, Cheng C F 2013 Chin. Phys. Lett. 30 044210

    [21]

    Jiang N, Zhang J 2005 Chin. Phys. Lett. 22 1968

    [22]

    Han J, Jiang N 2008 Chin. Phys. Lett. 25 1731

    [23]

    Zheng X B, Jiang N 2015 Chin. Phys. B 24 064702

    [24]

    Podobnik B, Stanley H E 2008 Phys. Rev. Lett. 100 084102

    [25]

    Horvatic D, Stanley H E, Podobnik B 2011 Europhys. Lett. 94 18007

    [26]

    Zebende G F 2011 Physica A 390 614

    [27]

    Vassoler R T, Zebende G F 2012 Physica A 391 2438

    [28]

    Zebende G F, da Silva M F, Filho A M 2013 Physica A 392 1756

    [29]

    Yuan N M, Fu Z 2014 Physica A 400 71

    [30]

    Cao G X, Han Y, Chen Y M, Yang C X 2014 Mod. Phys. Lett. B 28 1450090

    [31]

    de Silva M F, Pereira E J D A L, Filho A M D S, de Castro A P N, Miranda J G V, Zebende G F 2015 Physica A 424 124

    [32]

    Hajipour Sardouie S, Shamsollahi M B, Albera L, Merlet I 2015 IRBM 36 20

    [33]

    Zhai L S, Jin N D, Gao Z K, Chen P, Chi H 2011 MAPAN-J. Metrol. Soc. I. 26 255

    [34]

    Peng C K, Havlin S, Stanley H E, Goldberger A L 1995 Chaos 5 82

    [35]

    Hosking J 1981 Biometrica 68 165

    [36]

    Zhai L S, Jin N D, Zong Y B, Wang Z Y, Gu M 2012 Meas. Sci. Technol. 23 025304

    [37]

    Lucas G P, Mishra R 2005 Meas. Sci. Technol. 16 749

  • [1]

    Liu L, Zhou F D, Li H X 1998 Adv. Mech. 28 227 (in Chinese) [刘磊, 周芳德, 李会雄 1998 力学进展 28 227]

    [2]

    Huang F, Zhang X M, Guo L J 2005 Prog. Nat. Sci. 15 459 (in Chinese) [黄飞, 张西民, 郭烈锦 2005 自然科学进展 15 459]

    [3]

    Bai B F, Huang F, Guo L J, Wang X Y 2005 Nucl. Power Eng. 26 323 (in Chinese) [白博峰, 黄飞, 郭烈锦, 王先元 2005 核动力工程 26 323]

    [4]

    Boure J A, Mercadier Y 1982 Appl. Sci. Re. 38 297

    [5]

    Matuszkiewicz A, Flamand J C, Boure J A 1987 Int. J. Multiphase Flow 13 199

    [6]

    Song C H, No H C, Chung M K 1995 Int. J. Multiphase Flow 21 381

    [7]

    Kytmaa H K, Brennen C E 1991 Int. J. Multiphase Flow 17 13

    [8]

    Lucas G P, Walton I C 1997 Flow Meas. Instrum. 8 133

    [9]

    Lucas G P, Jin N D 2001 Meas. Sci. Technol. 12 1529

    [10]

    Sun B J, Yan D C 2000 Acta Sci. Nat. Univ. Pekinensis 36 381 (in Chinese) [孙宝江, 颜大椿 2000 北京大学学报(自然科学版) 36 381]

    [11]

    Sun B J, Wang R H, Zhao X X, Gao Y H 2004 J. Hydrodyn. 19 246 (in Chinese) [孙宝江, 王瑞和, 赵欣欣, 高永海 2004 水动力学研究与进展 19 246]

    [12]

    Espinosa-Paredes G, Cazarez-Candia O, Garcia-Gutierrez A 2002 Ann. Nucl. Energy 29 1261

    [13]

    Jin N D, Nie X B, Wang J, Ren Y Y 2003 Flow Meas. Instrum. 14 177

    [14]

    Ami T, Umekawa H, Ozawa M, Shoji M 2009 Int. J. Heat Mass Transfer 52 5682

    [15]

    Yao W P, Liu T B, Dai J F, Wang J 2014 Acta Phys. Sin. 63 078704 (in Chinese) [姚文坡, 刘铁兵, 戴加飞, 王俊 2014 物理学报 63 078704]

    [16]

    Xiang Z T, Chen Y F, Li Y J, Xiong L 2014 Acta Phys. Sin. 63 038903 (in Chinese) [向郑涛, 陈宇峰, 李昱瑾, 熊励 2014 物理学报 63 038903]

    [17]

    Dou F X, Jin N D, Fan C L, Gao Z K, Sun B 2014 Chin. Phys. B 23 120502

    [18]

    Gou J, Liu J Y, Wei Z B, Taylor G, Liu Y B 2014 Acta Phys. Sin. 63 208402 (in Chinese) [苟竞, 刘俊勇, 魏震波, Taylor G, 刘友波 2014 物理学报 63 208402]

    [19]

    Hao Q Y, Jin N D, Han Y F, Gao Z K, Zhai L S 2014 Chin. Phys. Lett. 31 120501

    [20]

    Zhang M N, Li Z H, Chen X Y, Liu C X, Teng S Y, Cheng C F 2013 Chin. Phys. Lett. 30 044210

    [21]

    Jiang N, Zhang J 2005 Chin. Phys. Lett. 22 1968

    [22]

    Han J, Jiang N 2008 Chin. Phys. Lett. 25 1731

    [23]

    Zheng X B, Jiang N 2015 Chin. Phys. B 24 064702

    [24]

    Podobnik B, Stanley H E 2008 Phys. Rev. Lett. 100 084102

    [25]

    Horvatic D, Stanley H E, Podobnik B 2011 Europhys. Lett. 94 18007

    [26]

    Zebende G F 2011 Physica A 390 614

    [27]

    Vassoler R T, Zebende G F 2012 Physica A 391 2438

    [28]

    Zebende G F, da Silva M F, Filho A M 2013 Physica A 392 1756

    [29]

    Yuan N M, Fu Z 2014 Physica A 400 71

    [30]

    Cao G X, Han Y, Chen Y M, Yang C X 2014 Mod. Phys. Lett. B 28 1450090

    [31]

    de Silva M F, Pereira E J D A L, Filho A M D S, de Castro A P N, Miranda J G V, Zebende G F 2015 Physica A 424 124

    [32]

    Hajipour Sardouie S, Shamsollahi M B, Albera L, Merlet I 2015 IRBM 36 20

    [33]

    Zhai L S, Jin N D, Gao Z K, Chen P, Chi H 2011 MAPAN-J. Metrol. Soc. I. 26 255

    [34]

    Peng C K, Havlin S, Stanley H E, Goldberger A L 1995 Chaos 5 82

    [35]

    Hosking J 1981 Biometrica 68 165

    [36]

    Zhai L S, Jin N D, Zong Y B, Wang Z Y, Gu M 2012 Meas. Sci. Technol. 23 025304

    [37]

    Lucas G P, Mishra R 2005 Meas. Sci. Technol. 16 749

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  • Received Date:  18 August 2015
  • Accepted Date:  11 October 2015
  • Published Online:  05 January 2016

Multi-scale cross-correlation characteristics of void fraction wave propagation for gas-liquid two-phase flows in small diameter pipe

    Corresponding author: Jin Ning-De, ndjin@tju.edu.cn
  • 1. School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 41504104, 51527805, 11572220), the Natural Science Foundation of Tianjin, China (Grant No. 14JCQNJC04200), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130032120042).

Abstract: The void fraction wave is a special physical phenomenon in a gas-liquid two-phase flow system. Understanding the propagation of the void fraction wave is of great significance for uncovering the physical mechanisms in both flow pattern transition and the fluid velocity measurement. In this study, detrended cross-correlation analysis (DCCA) is used to investigate the multi-scale cross-correlation characteristics of the coupled ARFIMA processes. It is found that the DCCA can effectively reveal the multi-scale cross-correlation dynamical behaviors of complex system. Then, we carry out the experimental test in a vertical gas-liquid two-phase flow pipe with small inner diameter. The DCCA is used to detect the cross-correlation characteristics of the void fraction wave on multiple time scales, and the growth rate of the cross-correlation level for the void fraction wave is observed on low time scales. Additionally, the spatial attenuation factor (SAF) of the void fraction wave is calculated to investigate the instability of the wave propagation. The SAF is close to zero under the transitional flow patterns, which means that the void fraction wave is in a stable propagating state. For bubble flows, the void fraction wave presents the attenuation characteristics, whilst the void fraction wave shows the amplification characteristics under the slug and churn flow patterns. Interestingly, the instability behaviors of the void fraction wave are always associated with its multi-scale cross-correlation characteristics. Specifically, the increasing rate of the wave cross-correlation level on low scales is much higher for transitional flow patterns, which is corresponding to the stable propagating characteristic of the void fraction wave. However, when the void fraction wave exhibits attenuation or amplification characteristics under other flow patterns, the increasing rate of the wave cross-correlation level on low scales is much lower.

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