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In order to better understand the variation of flow structure with delay time, we propose the element area (EA) of attractor morphology parameter in this paper. First, the conductance fluctuating signals and adaptive optimal kernel time-frequency representations of different gas-liquid flows are shown, we can find that flow pattern evolution is always accompanied by the numerical and frequency changes of large amplitude fluctuation (LAF). Then three kinds of signals, i. e., rossler signal, white noise and sinusoidal signal with multi-components, are used for analyzing the simulations, and the results indicate that the greater the frequency of LAF, the smaller the delay time of first crest of EA( peak ) is, and that the more the LAF, the bigger the peak value of first crest of EA(hpeak) is. Additionally, we use the above rule to analyze the conductance fluctuating signals measured from upward gas-liquid two-phase flow experiments and the signal length is selected to be 10 s for analysis. When the water superficial velocity is fixed to be 0.1138 m/s and the gas superficial velocity is gradually increased, we find that the peak is constant and hpeak changes up and down at bubble flow. When the flow pattern evolves into bubble-slug transition flow, the peak begins to turn bigger, and when the flow pattern evolves into slug flow, the peak becomes constant again while the hpeak increases monotonically with the gas flow rate increasing. The peak begins to become smaller as the flow pattern evolves from slug flow into churn flow, and we can find that the peak and hpeak of transition flow are alike. The peak and hpeak of bubble flow and churn flow are also alike because their dynamical mechanisms are similar but the downward trend of bubble flow is more gently than that of churn flow. When the water superficial velocity is fixed to be 0.2719 m/s, we can find similar variations of peak and hpeak to the above. Finally we determine the fall ratio (Rf) which is the ratio of the difference between the first crest and the first trough of EA and the hpeak, and then quantitatively distinguish three typical flow patterns, i.e., bubble flow, slug flow and churn flow by the Rf - peak distribution.
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Keywords:
- gas-liquid two-phase flow /
- flow patterns classification /
- attractor morphology /
- element area of attractor
[1] Hewitt G F 1980 Measurement of Two-phase Flow Parameters (London: Academic Press)
[2] Taitel Y, Barnea D, Dukler A E 1980 AICHEJ 26 345
[3] Pao W K S, Lewis R W 2002 Comput. Methods Appl. Mech. Engrg. 191 2631
[4] Padiala N T, VanderHeydena W B, Rauenzahna R M, Yarbrob S L 2000 Chem. Eng. Sci. 55 3261
[5] Jones J O C, Zuber N 1975 Int. J. Multiphase Flow 2 273
[6] Song C H, No H C, Chung M K 1995 Int. J. Multiphase Flow 21 381
[7] Sun B, Wang E P, Zheng Y J 2011 Acta Phys. Sin. 60 014701 (in Chinese) [孙斌, 王二朋, 郑永军 2011 物理学报 textbf60 014701]
[8] Du M, Jin N D, Gao Z K, Wang Z Y, Zhai L S 2012 Int. J. Multiphase Flow 41 91
[9] Daw C S, Finney C E A, Vasudevan M, van Goor N A, Nguyen K, Bruns D D, Kostelich E J, Grebogi C, Ott E, Yorke J A 1995 Phys. Rev. Lett. 75 2308
[10] 10 Gandhi A B, Joshi J B, Kulkarni A A, Jayaraman V K 2008 Int. J. Multiphase Flow 34 1099
[11] Wang Z Y, Jin N D, Gao Z K, Zong Y B, Wang T 2010 Chem. Eng. Sci. 65 5226
[12] Gao Z K, Zhang X W, Du M, Jin N D 2013 Phys. Lett. A 377 457
[13] Llaur F X, Llop M F 2006 Int. J. Multiphase Flow 32 1397
[14] Diks C, van Zwet W R, Takens F, DeGoede J 1996 Phys. Rev. E 53 2169
[15] van Ommen J R, Coppens M O, van den Bleek C M, Schouten J C 2000 AIChE J. 46 2183
[16] Nijenhuis J, Korbee R, Lensselink J, Kiel J H A, van Ommen J R 2007 Chem. Eng. Sci. 62 644
[17] Bartels M, Nijenhuis J, Lensselink J, Siedlecki M, de Jong W, Kapteijin F, van Ommen J R 2009 Energy Fuels 23 157
[18] Zhao J Ying, Jin N D, Gao Z K, Du M, Wang Z Y 2014 Chin. Phys. B 23 034702
[19] Zheng G B, Jin N D, Wang Z Y, Hu N N 2008 J. Tianjin Univ. 41 919 (in Chinese) [郑桂波, 金宁德, 王振亚, 胡娜娜 2008 天津大学学报 41 919]
[20] Zong Y B, Jin N D, Wang Z Y, Gao Z K, Wang C 2010 Int. J. Multiphase Flow 36 166
[21] Zong Y B, Jin N D, Wang Z Y 2009 Acta Phys. Sin. 57 7544 (in Chinese) [宗艳波, 金宁德, 王振亚 2009 物理学报 57 7544]
[22] Llop M F, Jand N, Gallucci K, Llaur F X 2012 Chem. Engineer. Sci. 71 252
[23] Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Berlin: Springer-Verlag) p366
[24] Zheng G B 2009 Ph. D. Dissertation (Tianjin: Tianjin University) (in Chinese) [郑桂波 2009 博士学位论文 (天津: 天津大学)]
[25] Rossler O E 1976 Phys. Lett. A 57 397
[26] You R Y, Chen Z, Xu S C, Wu B X 2004 Acta Phys. Sin. 53 2882 (in Chinese) [游荣义, 陈忠, 徐慎初, 吴伯僖 2004 物理学报 53 2882]
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[1] Hewitt G F 1980 Measurement of Two-phase Flow Parameters (London: Academic Press)
[2] Taitel Y, Barnea D, Dukler A E 1980 AICHEJ 26 345
[3] Pao W K S, Lewis R W 2002 Comput. Methods Appl. Mech. Engrg. 191 2631
[4] Padiala N T, VanderHeydena W B, Rauenzahna R M, Yarbrob S L 2000 Chem. Eng. Sci. 55 3261
[5] Jones J O C, Zuber N 1975 Int. J. Multiphase Flow 2 273
[6] Song C H, No H C, Chung M K 1995 Int. J. Multiphase Flow 21 381
[7] Sun B, Wang E P, Zheng Y J 2011 Acta Phys. Sin. 60 014701 (in Chinese) [孙斌, 王二朋, 郑永军 2011 物理学报 textbf60 014701]
[8] Du M, Jin N D, Gao Z K, Wang Z Y, Zhai L S 2012 Int. J. Multiphase Flow 41 91
[9] Daw C S, Finney C E A, Vasudevan M, van Goor N A, Nguyen K, Bruns D D, Kostelich E J, Grebogi C, Ott E, Yorke J A 1995 Phys. Rev. Lett. 75 2308
[10] 10 Gandhi A B, Joshi J B, Kulkarni A A, Jayaraman V K 2008 Int. J. Multiphase Flow 34 1099
[11] Wang Z Y, Jin N D, Gao Z K, Zong Y B, Wang T 2010 Chem. Eng. Sci. 65 5226
[12] Gao Z K, Zhang X W, Du M, Jin N D 2013 Phys. Lett. A 377 457
[13] Llaur F X, Llop M F 2006 Int. J. Multiphase Flow 32 1397
[14] Diks C, van Zwet W R, Takens F, DeGoede J 1996 Phys. Rev. E 53 2169
[15] van Ommen J R, Coppens M O, van den Bleek C M, Schouten J C 2000 AIChE J. 46 2183
[16] Nijenhuis J, Korbee R, Lensselink J, Kiel J H A, van Ommen J R 2007 Chem. Eng. Sci. 62 644
[17] Bartels M, Nijenhuis J, Lensselink J, Siedlecki M, de Jong W, Kapteijin F, van Ommen J R 2009 Energy Fuels 23 157
[18] Zhao J Ying, Jin N D, Gao Z K, Du M, Wang Z Y 2014 Chin. Phys. B 23 034702
[19] Zheng G B, Jin N D, Wang Z Y, Hu N N 2008 J. Tianjin Univ. 41 919 (in Chinese) [郑桂波, 金宁德, 王振亚, 胡娜娜 2008 天津大学学报 41 919]
[20] Zong Y B, Jin N D, Wang Z Y, Gao Z K, Wang C 2010 Int. J. Multiphase Flow 36 166
[21] Zong Y B, Jin N D, Wang Z Y 2009 Acta Phys. Sin. 57 7544 (in Chinese) [宗艳波, 金宁德, 王振亚 2009 物理学报 57 7544]
[22] Llop M F, Jand N, Gallucci K, Llaur F X 2012 Chem. Engineer. Sci. 71 252
[23] Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Berlin: Springer-Verlag) p366
[24] Zheng G B 2009 Ph. D. Dissertation (Tianjin: Tianjin University) (in Chinese) [郑桂波 2009 博士学位论文 (天津: 天津大学)]
[25] Rossler O E 1976 Phys. Lett. A 57 397
[26] You R Y, Chen Z, Xu S C, Wu B X 2004 Acta Phys. Sin. 53 2882 (in Chinese) [游荣义, 陈忠, 徐慎初, 吴伯僖 2004 物理学报 53 2882]
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