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We investigate the dynamic characteristics of vertical upward water-dominant oil-water two-phase flow by multiscale permutation entropy algorithm. We first measure the two-phase flow conductance fluctuation signals in a 20 mm inner-diameter pipe. Then we calculate the multiscale permutation entropies for different water-dominant flow patterns. The results indicate that multiscale permutation entropy rate and average of mutiscale permutation entropy can be used as quantitative parameters for measuring complexity of water dominant oil-water two-phase flow. In addition, we propose a new approach to identify different water-dominant flow patterns by using the joint distribution of multiscale permutation entropy rate and cumulant of increment series.
[1] Jana A K, Das G, Das P K 2006 Chem. Eng. Sci. 61 1500
[2] Lucas G P, Panagiotopoulos N 2009 Flow Meas. Instrum. 20 127
[3] Gao H, Gu H Y, Guo L J 2003 Int. J. Heat Mass Transf. 46 749
[4] Brauner N, Ullmann A 2002 Int. J. Multiphase Flow 28 1177
[5] Rouhani S Z, Sohal M S 1983 Prog. Nucl. Energ. 11 219
[6] Jones O C, Zuber N 1975 Int. J. Multiphase Flow 2 273
[7] Vincea M A, Lahey Jr R T 1982 Int. J. Multiphase Flow 8 93
[8] Chakrabarti D P, Das G, Das P K 2006 AIChE J. 52 3668
[9] Nguyen V T, Euh D J, Song C H 2010 Int. J. Multiphase Flow 36 755
[10] Ding H, Huang Z, Song Z, Yan Y 2007 Flow Meas. Instrum. 18 37
[11] He Z, Zhang D, Cheng B, Zhang W 1997 AIChE J. 43 345
[12] Sun B, Wang E P, Zheng Y J 2011 Acta Phys. Sin. 60 014701 (in Chinese) [孙斌, 王二鹏, 郑永军 2011 物理学报 60 014701]
[13] Sun B, Wang E P, Ding Y, Bai H Z, Huang Y M 2011 Chin. J. Chem. Eng. 19 243
[14] Li H W, Zhou Y L, Liu X, Sun B 2012 Acta Phys. Sin. 61 030508 (in Chinese) [李洪伟, 周云龙, 刘旭, 孙斌 2012 物理学报 61 030508]
[15] Sæther G, Bendiksen K, Müller J, Froland E 1990 Int. J. Multiphase Flow 16 1117
[16] Franca F, Acikgoz M, Lahey R T, Clausse A 1991 Int. J. Multiphase Flow 17 545
[17] Oddie G M 1991 Flow Meas. Instrum. 2 225
[18] Yuan Z L, Shen X L, Xu Y Q 1994 Science in China A 24 986 (in Chinese) [袁竹林, 沈湘林, 徐益谦 1994 中国科学(A辑) 24 986]
[19] 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]
[20] Lee J Y, Kim N S, Ishii M 2008 Nucl. Eng. Des. 238 945
[21] Govier G W, Sullivan G A, Wood R K 1961 Can. J. Chem. Eng. 4 67
[22] Flores J G, Chen X T, Sarica C, Brill J P 1999 SPE Prod. Facil. 14 102
[23] Du M, Jin N D, Gao Z K, Wang Z Y, Zhai L S 2012 Int. J. Multiphase Flow 41 91
[24] Cao B, Lü X Q, Zeng M, Wang Z M, Huang S S 2006 Acta Phys. Sin. 55 1696 (in Chinese) [曹彪, 吕小青, 曾敏, 王振民, 黄石生 2006 物理学报 55 1696]
[25] Li Q, Wang T Y, Leng Y G, He G Y, He H L 2007 Acta Phys. Sin. 56 6803 (in Chinese) [李强, 王太勇, 冷永刚, 何改云, 何慧龙 2007 物理学报 56 6803]
[26] Zhuang J J, Ning X B, Zou M, Sun B, Yang X 2008 Acta Phys. Sin. 57 2805 (in Chinese) [庄建军, 宁新宝, 邹鸣, 孙飙, 杨希 2008 物理学报 57 2805]
[27] Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese) [王启光, 张增平 2008 物理学报 57 1976]
[28] He W P, Wu Q, Zhang W, Wang Q G, Zhang Y 2009 Acta Phys. Sin. 58 2862 (in Chinese) [何文平, 吴琼, 张文, 王启光, 张勇 2009 物理学报 58 2862]
[29] Zhang C T, Ma Q L, Peng H 2010 Acta Phys. Sin. 59 7623 (in Chinese) [张春涛, 马千里, 彭宏 2010 物理学报 59 7623]
[30] Zhang C T, Ma Q L, Peng H, Jiang Y Y 2011 Acta Phys. Sin. 60 020508 (in Chinese) [张春涛, 马千里, 彭宏, 姜友谊 2010 物理学报 60 020508]
[31] Zhang W C, Yang L J, Lü X Q 2011 Acta Phys. Sin. 60 020601 (in Chinese) [张伟超, 杨立军, 吕小青 2011 物理学报 60 020601]
[32] He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin. 60 049202 (in Chinese) [何文平, 何涛, 成海英, 张文, 吴琼 2011 物理学报 60 049202]
[33] Shen W, Wang J 2011 Acta Phys. Sin. 60 118702 (in Chinese) [沈韡, 王俊 2011 物理学报 60 118702]
[34] Costa M, Goldberger A L, Peng C K 2002 Phys. Rev. Lett. 89 068102
[35] Costa M, Goldberger A L, Peng C K 2005 Phys. Rev. E 71 021906
[36] Zheng G B, Jin N D 2009 Acta Phys. Sin. 58 4485 (in Chinese) [郑桂波, 金宁德 2009 物理学报 58 4485]
[37] Costa M, Peng C K, Goldberger A L 2003 Physica A 330 53
[38] He L, Du L, Zhuang Y Q, Li W H, Chen J P 2008 Acta Phys. Sin. 57 6545 (in Chinese) [何亮, 杜磊, 庄奕琪, 李伟华, 陈建平 2008 物理学报 57 6545]
[39] Li Z W, Zhang Y K 2008 Stoch. Environ. Res. Risk. Assess. 22 507
[40] Huang X L, Cui S Z, Ning X B, Bian C H 2009 Acta Phys. Sin. 58 8160 (in Chinese) [黄晓林, 崔胜忠, 宁新宝, 卞春华 2009 物理学报 58 8160]
[41] Yan B G, Zhao T T 2011 Acta Phys. Sin. 60 078701 (in Chinese) [严碧歌, 赵婷婷 2011 物理学报 60 078701]
[42] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 174102
[43] Sun K H, Tan G Q, Sheng L Y 2008 Acta Phys. Sin. 57 3359 (in Chinese) [孙克辉, 谈国强, 盛利元 2008 物理学报 57 3359]
[44] Cao Y, Tung W, Gao J B 2004 Phys. Rev. E 70 046217
[45] Hou W, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 2663 (in Chinese) [侯威, 封国林, 董文杰, 李建平 2006 物理学报 55 2663]
[46] Zunino L, Zanin M, Tabak B M, Pérez D G, Rosso O A 2009 Physica A 388 2854
[47] Li D, Li X, Liang Z, Vossa L J, Sleigh J W 2010 J. Neural Eng. 7 046010
[48] Jin N D, Xin Z, Wang J, Wang Z Y, Jia X H, Chen W P 2008 Meas. Sci. Technol. 19 045403
[49] Ashkenazy Y, Ivanov P C, Havlin S, Peng C K, Goldberger A L, Stanley H E 2001 Phys. Rev. Lett. 86 1900
[50] Ashkenazy Y, Havlin S, Ivanov P C, Peng C K, Schulte-Frohlinde V, Stanley H E 2003 Physica A 323 19
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[1] Jana A K, Das G, Das P K 2006 Chem. Eng. Sci. 61 1500
[2] Lucas G P, Panagiotopoulos N 2009 Flow Meas. Instrum. 20 127
[3] Gao H, Gu H Y, Guo L J 2003 Int. J. Heat Mass Transf. 46 749
[4] Brauner N, Ullmann A 2002 Int. J. Multiphase Flow 28 1177
[5] Rouhani S Z, Sohal M S 1983 Prog. Nucl. Energ. 11 219
[6] Jones O C, Zuber N 1975 Int. J. Multiphase Flow 2 273
[7] Vincea M A, Lahey Jr R T 1982 Int. J. Multiphase Flow 8 93
[8] Chakrabarti D P, Das G, Das P K 2006 AIChE J. 52 3668
[9] Nguyen V T, Euh D J, Song C H 2010 Int. J. Multiphase Flow 36 755
[10] Ding H, Huang Z, Song Z, Yan Y 2007 Flow Meas. Instrum. 18 37
[11] He Z, Zhang D, Cheng B, Zhang W 1997 AIChE J. 43 345
[12] Sun B, Wang E P, Zheng Y J 2011 Acta Phys. Sin. 60 014701 (in Chinese) [孙斌, 王二鹏, 郑永军 2011 物理学报 60 014701]
[13] Sun B, Wang E P, Ding Y, Bai H Z, Huang Y M 2011 Chin. J. Chem. Eng. 19 243
[14] Li H W, Zhou Y L, Liu X, Sun B 2012 Acta Phys. Sin. 61 030508 (in Chinese) [李洪伟, 周云龙, 刘旭, 孙斌 2012 物理学报 61 030508]
[15] Sæther G, Bendiksen K, Müller J, Froland E 1990 Int. J. Multiphase Flow 16 1117
[16] Franca F, Acikgoz M, Lahey R T, Clausse A 1991 Int. J. Multiphase Flow 17 545
[17] Oddie G M 1991 Flow Meas. Instrum. 2 225
[18] Yuan Z L, Shen X L, Xu Y Q 1994 Science in China A 24 986 (in Chinese) [袁竹林, 沈湘林, 徐益谦 1994 中国科学(A辑) 24 986]
[19] 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]
[20] Lee J Y, Kim N S, Ishii M 2008 Nucl. Eng. Des. 238 945
[21] Govier G W, Sullivan G A, Wood R K 1961 Can. J. Chem. Eng. 4 67
[22] Flores J G, Chen X T, Sarica C, Brill J P 1999 SPE Prod. Facil. 14 102
[23] Du M, Jin N D, Gao Z K, Wang Z Y, Zhai L S 2012 Int. J. Multiphase Flow 41 91
[24] Cao B, Lü X Q, Zeng M, Wang Z M, Huang S S 2006 Acta Phys. Sin. 55 1696 (in Chinese) [曹彪, 吕小青, 曾敏, 王振民, 黄石生 2006 物理学报 55 1696]
[25] Li Q, Wang T Y, Leng Y G, He G Y, He H L 2007 Acta Phys. Sin. 56 6803 (in Chinese) [李强, 王太勇, 冷永刚, 何改云, 何慧龙 2007 物理学报 56 6803]
[26] Zhuang J J, Ning X B, Zou M, Sun B, Yang X 2008 Acta Phys. Sin. 57 2805 (in Chinese) [庄建军, 宁新宝, 邹鸣, 孙飙, 杨希 2008 物理学报 57 2805]
[27] Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese) [王启光, 张增平 2008 物理学报 57 1976]
[28] He W P, Wu Q, Zhang W, Wang Q G, Zhang Y 2009 Acta Phys. Sin. 58 2862 (in Chinese) [何文平, 吴琼, 张文, 王启光, 张勇 2009 物理学报 58 2862]
[29] Zhang C T, Ma Q L, Peng H 2010 Acta Phys. Sin. 59 7623 (in Chinese) [张春涛, 马千里, 彭宏 2010 物理学报 59 7623]
[30] Zhang C T, Ma Q L, Peng H, Jiang Y Y 2011 Acta Phys. Sin. 60 020508 (in Chinese) [张春涛, 马千里, 彭宏, 姜友谊 2010 物理学报 60 020508]
[31] Zhang W C, Yang L J, Lü X Q 2011 Acta Phys. Sin. 60 020601 (in Chinese) [张伟超, 杨立军, 吕小青 2011 物理学报 60 020601]
[32] He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin. 60 049202 (in Chinese) [何文平, 何涛, 成海英, 张文, 吴琼 2011 物理学报 60 049202]
[33] Shen W, Wang J 2011 Acta Phys. Sin. 60 118702 (in Chinese) [沈韡, 王俊 2011 物理学报 60 118702]
[34] Costa M, Goldberger A L, Peng C K 2002 Phys. Rev. Lett. 89 068102
[35] Costa M, Goldberger A L, Peng C K 2005 Phys. Rev. E 71 021906
[36] Zheng G B, Jin N D 2009 Acta Phys. Sin. 58 4485 (in Chinese) [郑桂波, 金宁德 2009 物理学报 58 4485]
[37] Costa M, Peng C K, Goldberger A L 2003 Physica A 330 53
[38] He L, Du L, Zhuang Y Q, Li W H, Chen J P 2008 Acta Phys. Sin. 57 6545 (in Chinese) [何亮, 杜磊, 庄奕琪, 李伟华, 陈建平 2008 物理学报 57 6545]
[39] Li Z W, Zhang Y K 2008 Stoch. Environ. Res. Risk. Assess. 22 507
[40] Huang X L, Cui S Z, Ning X B, Bian C H 2009 Acta Phys. Sin. 58 8160 (in Chinese) [黄晓林, 崔胜忠, 宁新宝, 卞春华 2009 物理学报 58 8160]
[41] Yan B G, Zhao T T 2011 Acta Phys. Sin. 60 078701 (in Chinese) [严碧歌, 赵婷婷 2011 物理学报 60 078701]
[42] Bandt C, Pompe B 2002 Phys. Rev. Lett. 88 174102
[43] Sun K H, Tan G Q, Sheng L Y 2008 Acta Phys. Sin. 57 3359 (in Chinese) [孙克辉, 谈国强, 盛利元 2008 物理学报 57 3359]
[44] Cao Y, Tung W, Gao J B 2004 Phys. Rev. E 70 046217
[45] Hou W, Feng G L, Dong W J, Li J P 2006 Acta Phys. Sin. 55 2663 (in Chinese) [侯威, 封国林, 董文杰, 李建平 2006 物理学报 55 2663]
[46] Zunino L, Zanin M, Tabak B M, Pérez D G, Rosso O A 2009 Physica A 388 2854
[47] Li D, Li X, Liang Z, Vossa L J, Sleigh J W 2010 J. Neural Eng. 7 046010
[48] Jin N D, Xin Z, Wang J, Wang Z Y, Jia X H, Chen W P 2008 Meas. Sci. Technol. 19 045403
[49] Ashkenazy Y, Ivanov P C, Havlin S, Peng C K, Goldberger A L, Stanley H E 2001 Phys. Rev. Lett. 86 1900
[50] Ashkenazy Y, Havlin S, Ivanov P C, Peng C K, Schulte-Frohlinde V, Stanley H E 2003 Physica A 323 19
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