The complex phase interactions of the two-phase flow are a key factor in understanding the flow pattern evolutional mechanisms, yet these complex flow behaviors have not been well understood. In this paper, we employ a series of gas–liquid two-phase flow multivariate fluctuation signals as observations and propose a novel interconnected ordinal pattern network to investigate the spatial coupling behaviors of the gas–liquid two-phase flow patterns. In addition, we use two network indices, which are the global subnetwork mutual information ( ) and the global subnetwork clustering coefficient ( ), to quantitatively measure the spatial coupling strength of different gas–liquid flow patterns. The gas–liquid two-phase flow pattern evolutionary behaviors are further characterized by calculating the two proposed coupling indices under different flow conditions. The proposed interconnected ordinal pattern network provides a novel tool for a deeper understanding of the evolutional mechanisms of the multi-phase flow system, and it can also be used to investigate the coupling behaviors of other complex systems with multiple observations.
REFERENCES
1.
Y. H.
Wu
, L. S.
Cheng
, S. J.
Huang
, Y. H.
Bai
, P.
Jia
, S. R.
Wang
, B. X.
Xu
, and L.
Chen
, “An approximate semianalytical method for two-phase flow analysis of liquid-rich shale gas and tight light-oil wells
,” J. Pet. Sci. Eng.
176
, 562
–572
(2019
). 2.
P. I.
Cano
, J.
Brito
, F.
Almenglo
, M.
Ramírez
, J. M.
Gómez
, and D.
Cantero
, “Influence of trickling liquid velocity, low molar ratio of nitrogen-sulfur and gas-liquid flow pattern in anoxic biotrickling filters for biogas desulfurization
,” Biochem. Eng. J.
148
, 205
–213
(2019
). 3.
Y. J.
Chang
, Q.
Xu
, Q. H.
Wu
, X. Y.
Zhao
, B.
Huang
, Y. C.
Wang
, and L. J.
Guo
, “Experimental study of the hydraulic jump phenomenon induced by the downstream riser structure in a pipeline–riser system
,” Chem. Eng. Sci.
256
, 117687
(2022
). 4.
L.
Zha
, M. J.
Shang
, M.
Qiu
, H.
Zhang
, and Y. H.
Su
, “Process intensification of mixing and chemical modification for polymer solutions in microreactors based on gas-liquid two-phase flow
,” Chem. Eng. Sci.
195
, 62
–73
(2019
). 5.
L. S.
Zhai
, J.
Yang
, and Y. Q.
Wang
, “An investigation of transition processes from transient gas–liquid plug to slug flow in horizontal pipe: Experiment and cost-based recurrence analysis
,” Nucl. Eng. Des.
379
, 111253
(2021
). 6.
B.
Wu
, M.
Firouzi
, T.
Mitchell
, T. E.
Rufford
, C.
Leonardi
, and B.
Towler
, “A critical review of flow maps for gas-liquid flows in vertical pipes and annuli
,” Chem. Eng. J.
326
, 350
–377
(2017
). 7.
F.
Dong
, L. H.
Li
, and S. M.
Zhang
, “Flow status identification based on multiple slow feature analysis of gas-liquid two-phase flow in horizontal pipes
,” Meas. Sci. Technol.
32
, 055301
(2021
). 8.
A. V.
Chinak
, A. E.
Gorelikova
, O. N.
Kashinsky
, M. A.
Pakhomov
, V. V.
Randin
, and V. I.
Terekhov
, “Hydrodynamics and heat transfer in an inclined bubbly flow
,” Int. J. Heat Mass Transfer
118
, 785
–801
(2018
). 9.
S.
Baragh
, H.
Shokouhmand
, and S. S. M.
Ajarostaghi
, “Experiments on mist flow and heat transfer in a tube fitted with porous media
,” Int. J. Therm. Sci.
137
, 388
–398
(2019
). 10.
C. S.
Daw
, C. E. A.
Finney
, M.
Vasudevan
, N. A.
Van Goor
, K.
Nguyen
, D. D.
Bruns
, E. J.
Kostelich
, C.
Grebogi
, E.
Ott
, and J. A.
Yorke
, “Self-organization and chaos in a fluidized bed
,” Phys. Rev. Lett.
75
, 2308
(1995
). 11.
Z.
Wu
, Z.
Cao
, and B.
Sunden
, “Flow patterns and slug scaling of liquid-liquid flow in square microchannels
,” Int. J. Multiphase Flow
112
, 27
–39
(2019
). 12.
N.
Zhao
, C. F.
Li
, H. J.
Jia
, F.
Wang
, Z. Y.
Zhao
, L. D.
Fang
, and X. T.
Li
, “Acoustic emission-based flow noise detection and mechanism analysis for gas-liquid two-phase flow
,” Measurement
179
, 109480
(2021
). 13.
H.
Ziaei-Halimejani
, S.
Kouzbour
, R.
Zarghami
, R.
Sotudeh-Gharebagh
, B.
Gourich
, N.
Mostoufi
, and Y.
Stiriba
, “Monitoring of the bubble columns hydrodynamics by recurrence quantification data analysis
,” Chem. Eng. Res. Des.
171
, 100
–110
(2021
). 14.
Z. K.
Gao
, D. M.
Lv
, W. D.
Dang
, M. X.
Liu
, and X. L.
Hong
, “Multilayer network from multiple entropies for characterizing gas-liquid nonlinear flow behavior
,” Int. J. Bifurcation Chaos
30
, 2050014
(2020
). 15.
Q. M.
Sun
and B.
Zhang
, “Nonlinear characterization of gas liquid two-phase flow in complex networks
,” Exp. Therm. Fluid Sci.
60
, 165
–172
(2015
). 16.
W. Z.
Liu
, Q.
Xu
, S. F.
Zou
, Y. J.
Chang
, and L. J.
Guo
, “Optimization of differential pressure signal acquisition for recognition of gas–liquid two-phase flow patterns in pipeline-riser system
,” Chem. Eng. Sci.
229
, 116043
(2021
). 17.
S.
Wijayanta
, Deendarlianto
, Indarto
, A.
Prasetyo
, and A. Z.
Hudaya
, “The effect of the liquid physical properties on the wave frequency and wave velocity of co-current gas-liquid stratified two-phase flow in a horizontal pipe
,” Int. J. Multiphase Flow
158
, 104300
(2023
). 18.
W. K.
Ren
, J. C.
Zhang
, and N. D.
Jin
, “Rescaled range permutation entropy: A method for quantifying the dynamical complexity of gas-liquid two-phase slug flow
,” Nonlinear Dyn.
104
, 4035
–4043
(2021
). 19.
D.
Li
, M.
Chen
, S.
Zhao
, and A. W.
Zeng
, “Entropy generation analysis of Rayleigh convection in gas–liquid mass transfer process
,” Chem. Eng. Res. Des.
134
, 359
–369
(2018
). 20.
A. V.
Cherdantsev
, S. A.
Zdornikov
, M. V.
Cherdantsev
, S. V.
Isaenkov
, and D. M.
Markovich
, “Stratified-to-annular gas-liquid flow patterns transition in a horizontal pipe
,” Exp. Therm. Fluid Sci.
132
, 110552
(2022
). 21.
L. S.
Zhai
, H. L.
Xie
, J.
Yang
, Y. L.
Wu
, and X. Z.
Lu
, “Characterizing dynamics of swirling film in gas-liquid cylindrical cyclone separator using multi-scale entropy analysis
,” Int. J. Mod. Phys. C
30
, 2050001
(2019
). 22.
B. A.
Khudayarov
and K. M.
Komilova
, “Vibration and dynamic stability of composite pipelines conveying a two-phase fluid flows
,” Eng. Fail. Anal.
104
, 500
–512
(2019
). 23.
M.
Du
, L.
Zhang
, X. Y.
Niu
, and C.
Grebogi
, “Detecting gas-liquid two-phase flow pattern determinism from experimental signals with missing ordinal patterns
,” Chaos
30
, 093102
(2020
). 24.
D.
Diego
, K. A.
Haaga
, and B.
Hannisdal
, “Transfer entropy computation using the Perron-Frobenius operator
,” Phys. Rev. E
99
, 042212
(2019
). 25.
P.
Sundaram
, M.
Luessi
, M.
Bianciardi
, S.
Stufflebeam
, M.
Hämäläinen
, and V.
Solo
, “Individual resting-state brain networks enabled by massive multivariate conditional mutual information
,” IEEE Trans. Med. Imaging
39
, 1957
–1966
(2019
). 26.
M.
Rosenblum
, M.
Frühwirth
, M.
Moser
, and A.
Pikovsky
, “Dynamical disentanglement in an analysis of oscillatory systems: An application to respiratory sinus arrhythmia
,” Philos. Trans. R. Soc. A
377
, 20190045
(2019
). 27.
J. L.
Neri
, P.
Depalle
, and R.
Badeau
, “Approximate inference and learning of state space models with Laplace noise
,” IEEE Trans. Signal Process.
69
, 3176
–3189
(2021
). 28.
D.
Wang
, D. T.
Ren
, K.
Li
, Y. M.
Feng
, D.
Ma
, X. G.
Yan
, and G.
Wang
, “Epileptic seizure detection in long-term EEG recordings by using wavelet-based directed transfer function
,” IEEE Trans. Biomed. Eng.
65
, 2591
–2599
(2018
). 29.
F.
Goetze
and P. Y.
Lai
, “Reconstructing positive and negative couplings in Ising spin networks by sorted local transfer entropy
,” Phys. Rev. E
100
, 012121
(2019
). 30.
R.
Malladi
, D. H.
Johnson
, G. P.
Kalamangalam
, N.
Tandon
, and B.
Aazhang
, “Mutual information in frequency and its application to measure cross-frequency coupling in epilepsy
,” IEEE Trans. Signal Process.
66
, 3008
–3023
(2018
). 31.
D.
Wen
, P. L.
Jia
, S. H.
Hsu
, Y. H.
Zhou
, X. F.
Lan
, D.
Cui
, G. L.
Li
, S. M.
Yin
, and L.
Wang
, “Estimating coupling strength between multivariate neural series with multivariate permutation conditional mutual information
,” Neural Netw.
110
, 159
–169
(2019
). 32.
J. F.
Fan
, J.
Meng
, J.
Ludescher
, X. S.
Chen
, Y.
Ashkenazy
, J.
Kurths
, S.
Havlin
, and H. J.
Schellnhuber
, “Statistical physics approaches to the complex earth system
,” Phys. Rep.
896
, 1
–84
(2021
). 33.
Y.
Zou
, R. V.
Donner
, N.
Marwan
, J. F.
Donges
, and J.
Kurths
, “Complex network approaches to nonlinear time series analysis
,” Phys. Rep.
787
, 1
–97
(2019
). 34.
T.
Kobayashi
, S.
Murayama
, T.
Hachijo
, and H.
Gotoda
, “Early detection of thermoacoustic combustion instability using a methodology combining complex networks and machine learning
,” Phys. Rev. Appl.
11
, 064034
(2019
). 35.
C.
Tan
, W. L.
Liu
, and F.
Dong
, “Characterizing the correlations between local phase fractions of gas–liquid two-phase flow with wire-mesh sensor
,” Philos. Trans. R. Soc. A
374
, 20150335
(2016
). 36.
C.
Ma
, Q. R.
Yang
, X. Q.
Wu
, and J. A.
Lu
, “Cluster synchronization: From single-layer to multi-layer networks
,” Chaos
29
, 123120
(2019
). 37.
K. W.
Li
, M. X.
Yu
, L.
Liu
, J. N.
Zhai
, and W. Y.
Liu
, “A novel reliability analysis approach for component-based software based on the complex network theory
,” Soft. Test. Verif. Rel.
28
, e1674
(2018
). 38.
O.
Cats
, G. J.
Koppenol
, and M.
Warnier
, “Robustness assessment of link capacity reduction for complex networks: Application for public transport systems
,” Reliab. Eng. Syst. Safe.
167
, 544
–553
(2017
). 39.
S.
Scarsoglio
, F.
Cazzato
, and L.
Ridolfi
, “From time-series to complex networks: Application to the cerebrovascular flow patterns in atrial fibrillation
,” Chaos
27
, 093107
(2017
). 40.
B.
Zarei
, M. R.
Meybodi
, and B.
Masoumi
, “Chaotic memetic algorithm and its application for detecting community structure in complex networks
,” Chaos
30
, 013125
(2020
). 41.
J. F.
Donges
, H. C. H.
Schultz
, N.
Marwan
, Y.
Zou
, and J.
Kurths
, “Investigating the topology of interacting networks
,” Eur. Phys. J. B
84
, 635
–651
(2011
). 42.
Z. K.
Gao
, M. X.
Liu
, W. D.
Dang
, C.
Ma
, L. H.
Hou
, and X. L.
Hong
, “Multilayer limited penetrable visibility graph for characterizing the gas-liquid flow behavior
,” Chem. Eng. J.
407
, 127229
(2021
). 43.
M.
Small
, “Complex networks from time series: Capturing dynamics,” in 2013 IEEE International Symposium on Circuits and Systems (ISCAS) (IEEE, 2013), pp. 2509–2512.44.
M.
Huang
, Z. K.
Sun
, R. V.
Donner
, J.
Zhang
, S. G.
Guan
, and Y.
Zou
, “Characterizing dynamical transitions by statistical complexity measures based on ordinal pattern transition networks
,” Chaos
31
, 033127
(2021
). 45.
C. W.
Kulp
, J. M.
Chobot
, H. R.
Freitas
, and G. D.
Sprechini
, “Using ordinal partition transition networks to analyze ECG data
,” Chaos
26
, 073114
(2016
). 46.
Y. J.
Ruan
, R. V.
Donner
, S. G.
Guan
, and Y.
Zou
, “Ordinal partition transition network based complexity measures for inferring coupling direction and delay from time series
,” Chaos
29
, 043111
(2019
). 47.
W.
Kobayashi
, H.
Gotoda
, S.
Kandani
, Y.
Ohmichi
, and S.
Matsuyama
, “Spatiotemporal dynamics of turbulent coaxial jet analyzed by symbolic information-theory quantifiers and complex-network approach
,” Chaos
29
, 123110
(2019
). 48.
Y.
Nomi
, H.
Gotoda
, S.
Fukuda
, and C.
Almarcha
, “Complex network analysis of spatiotemporal dynamics of premixed flame in a Hele–Shaw cell: A transition from chaos to stochastic state
,” Chaos
31
, 123133
(2021
). 49.
Y.
Nomi
, H.
Gotoda
, S.
Kandani
, and C.
Almarcha
, “Complex network analysis of the gravity effect on premixed flames propagating in a Hele-Shaw cell
,” Phys. Rev. E
103
, 022218
(2021
). 50.
Z. K.
Gao
, Y. X.
Yang
, L. S.
Zhai
, N. D.
Jin
, and G. R.
Chen
, “A four-sector conductance method for measuring and characterizing low-velocity oil–water two-phase flows
,” IEEE Trans. Instrum. Meas.
65
, 1690
–1697
(2016
). 51.
F.
Takens
, “Detecting strange attractors in turbulence,” in Dynamical systems and turbulence, Warwick 1980 (Springer, 1981), pp. 366–381.52.
C.
Bandt
and B.
Pompe
, “Permutation entropy: A natural complexity measure for time series
,” Phys. Rev. Lett.
88
, 174102
(2002
). 53.
M. B.
Kennel
, R.
Brown
, and H. D. I.
Abarbanel
, “Determining embedding dimension for phase-space reconstruction using a geometrical construction
,” Phys. Rev. A
45
, 3403
(1992
). 54.
H. S.
Kim
, R.
Eykholt
, and J. D.
Salas
, “Nonlinear dynamics, delay times, and embedding windows
,” Physica D
127
, 48
–60
(1999
). 55.
56.
Z. K.
Gao
and N. D.
Jin
, “Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks
,” Phys. Rev. E
79
, 066303
(2009
). © 2023 Author(s). Published under an exclusive license by AIP Publishing.
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