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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 (I) and the global subnetwork clustering coefficient (C), 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. [ABSTRACT FROM AUTHOR]

Gas–liquid two-phase flow is polymorphic and unstable, and characterizing its flow behavior is a major challenge in the study of multiphase flow. We first conduct dynamic experiments on gas–liquid two-phase flow in a vertical tube and obtain multi-channel signals using a self-designed four-sector distributed conductivity sensor. In order to characterize the evolution of gas–liquid two-phase flow, we transform the obtained signals using the adaptive optimal kernel time-frequency representation and build a complex network based on the time-frequency energy distribution. As quantitative indicators, global clustering coefficients of the complex network at various sparsity levels are computed to analyze the dynamic behavior of various flow structures. The results demonstrate that the proposed approach enables effective analysis of multi-channel measurement information for revealing the evolutionary mechanisms of gas–liquid two-phase flow. Furthermore, for the purpose of flow structure recognition, we propose a temporal-spatio convolutional neural network and achieve a classification accuracy of 95.83%. [ABSTRACT FROM AUTHOR]

Characterizing nonlinear dynamic behaviors underlying multiphase flow has attracted considerable attention from the nonlinear research field. In this paper, the authors develop a novel multiple entropy-based multilayer network (MEMN) for exploring the complex gas-liquid two-phase flow. At first, we carry out the gas-liquid flow experiments to get the multichannel measurements. Then, MEMN is constructed based on the fusion of three nonlinear entropies, namely weighted permutation entropy (WPE), wavelet packet energy entropy (WPEE), and amplitude entropy (AE). For each derived projection network of MEMN, spectral radius and global clustering coefficient are both calculated and they allow effectively uncovering the nonlinear flow behaviors in the transition of different gas-liquid flow patterns. In addition, we perform wavelet time-frequency representation for the two typical flow patterns and the results support our findings well. All these demonstrate that our MEMN framework can effectively characterize the nonlinear evolution of gas-liquid flow from the perspective of complex network theory. And this also provides a novel idea for studying nonlinear complex systems from the observed multivariate time series. [ABSTRACT FROM AUTHOR]

We propose a complex network-based method to distinguish complex patterns arising from experimental horizontal oil–water two-phase flow. We first use the adaptive optimal kernel time–frequency representation (AOK TFR) to characterize flow pattern behaviors from the energy and frequency point of view. Then, we infer two-phase flow complex networks from experimental measurements and detect the community structures associated with flow patterns. The results suggest that the community detection in two-phase flow complex network allows objectively discriminating complex horizontal oil–water flow patterns, especially for the segregated and dispersed flow patterns, a task that existing method based on AOK TFR fails to work. [ABSTRACT FROM AUTHOR]

Charactering nonlinear dynamic behavior in gas–liquid two-phase flow is a contemporary and challenging problem of significant importance. We in this paper first systematically carry out gas–liquid two-phase flow experiments in a small diameter pipe for measuring local flow information from different flow patterns. Then, we propose a modality transition-based network for mapping the experimental multivariate measurements into a directed weighted complex network. In particular, we derive multivariate complex networks from different flow conditions and demonstrate that the generated networks corresponding to different flow patterns exhibit distinct topological structures. For each generated network, we exploit weighted clustering coefficient and closeness centrality to quantitatively probe the network topological properties associated with dynamic flow behavior. The results suggest that our multivariate complex network analysis allows quantitatively uncovering the transitions of distinct flow patterns and yields deep insights into the nonlinear dynamic behavior underlying gas–liquid flows. [ABSTRACT FROM AUTHOR]

Characterizing flow behavior underlying horizontal oil–water flows from experimental measurements is a challenging problem in the fields of time series analysis and fluid mechanics. We systematically conduct a horizontal oil–water two-phase flow experiment and use our designed distributed conductance sensor to measure multivariate signals from five different flow patterns. Taking two coupled Lorenz systems as examples, we first demonstrate that the multivariate multiscale entropy (MMSE) enables to uncover the one-way/both-way coupling structure of dynamic systems. Then we use MMSE method to analyze the experimental measurements and extract the slopes and mean values from low scales of MMSE to quantitatively characterize the flow behavior. The results suggest that the MMSE enables to quantitatively distinguish different horizontal oil–water flow patterns and further allows deeply uncovering dynamic flow behavior in the transitions of different flow patterns. [ABSTRACT FROM AUTHOR]

We generate a directed weighted complex network by a method based on Markov transition probability to represent an experimental two-phase flow. We first systematically carry out gas--liquid two-phase flow experiments for measuring the time series of flow signals. Then we construct directed weighted complex networks from various time series in terms of a network generation method based on Markov transition probability. We find that the generated network inherits the main features of the time series in the network structure. In particular, the networks from time series with different dynamics exhibit distinct topological properties. Finally, we construct two-phase flow directed weighted networks from experimental signals and associate the dynamic behavior of gas--liquid two-phase flow with the topological statistics of the generated networks. The results suggest that the topological statistics of two-phase flow networks allow quantitative characterization of the dynamic flow behavior in the transitions among different gas--liquid flow patterns. [ABSTRACT FROM AUTHOR]

Horizontal gas-liquid two-phase flow widely exists in many physical systems and chemical engineering processes. Compared with vertical upward gas-liquid two-phase flow, investigations on dynamic behavior underlying horizontal gas-liquid flows are quite limited. Complex network provides a powerful framework for time series analysis of complex dynamical systems. We use a network generation method based on Markov transition probability to infer directed weighted complex networks from signals measured from horizontal gas-liquid two-phase flow experiment and find that the networks corresponding to different flow patterns exhibit different network structure. To investigate the dynamic characteristics of horizontal gas-liquid flows, we construct a number of complex networks under different flow conditions, and explore the network indices for each constructed network. In addition, we investigate the sample entropy of different flow patterns. Our results suggest that the network statistic can well represent the complexity in the transition among different flow patterns and further allows characterizing the interface fluctuation behavior in horizontal gas-liquid two-phase flow. [ABSTRACT FROM AUTHOR]

Abstract: Characterizing complex dynamic behaviors arising from various inclined oil–water two-phase flow patterns is a challenging problem in the fields of nonlinear dynamics and fluid mechanics. We systematically carried out inclined oil–water two-phase flow experiments for measuring the time series conductance fluctuating signals of different flow patterns. We using the dynamic segmentation algorithm incorporating with phase space reconstruction analyze the measured experimental signals to uncover the dynamic behaviors underlying different flow patterns. Specifically, given a time series from a two-phase flow, we move a sliding pointer over the time series and for each position of the pointer we calculate the dynamic difference measure of the phase space orbits generated from the segment to the left and to the right of the pointer. A number of experimental signals under different flow conditions are investigated in order to reveal the dynamical characteristics of inclined oil–water flows. The results indicate that the heterogeneity of dynamic difference measure series is sensitive to the transition among different flow patterns and the standard deviation of dynamic difference measure series can yield quantitative insights into the nonlinear dynamics of the two-phase flow. These properties render the dynamic segmentation algorithm-based approach particularly useful for uncovering the dynamic behaviors of inclined oil–water two-phase flows. [Copyright &y& Elsevier]

Abstract: Based on the signals from oil–water two-phase flow experiment, we construct and analyze recurrence networks to characterize the dynamic behavior of different flow patterns. We first take a chaotic time series as an example to demonstrate that the local property of recurrence network allows characterizing chaotic dynamics. Then we construct recurrence networks for different oil-in-water flow patterns and investigate the local property of each constructed network, respectively. The results indicate that the local topological statistic of recurrence network is very sensitive to the transitions of flow patterns and allows uncovering the dynamic flow behavior associated with chaotic unstable periodic orbits. [Copyright &y& Elsevier]

Abstract: Understanding the nonlinear and complex dynamics underlying the gas–liquid slug flow is a significant but challenging problem. We systematically carried out gas–liquid two-phase flow experiments for measuring the time series of flow signals, which is studied in terms of the mapping from time series to complex networks. In particular, we construct directed weighted complex networks (DWCN) from time series and then associate different aspects of chaotic dynamics with the topological indices of the DWCN and further demonstrate that the DWCN can be exploited to detect unstable periodic orbits of low periods. Examples using time series from classical chaotic systems are provided to demonstrate the effectiveness of our approach. We construct and analyze numbers of DWCNs for different gas–liquid flow patterns and find that our approach can quantitatively distinguish different experimental gas–liquid flow patterns. Furthermore, the DWCN analysis indicates that slug flow shows obvious chaotic behavior and its unstable periodic orbits reflect the intermittent quasi-periodic oscillation behavior between liquid slug and large gas slug. These interesting and significant findings suggest that the directed weighted complex network can potentially be a powerful tool for uncovering the underlying dynamics leading to the formation of the gas–liquid slug flow. [Copyright &y& Elsevier]

Abstract: We propose a method to characterize and distinguish flow patterns in experimental two-phase (e.g., gas–liquid) flows. The basic idea is to calculate the instantaneous phase from the signal and to extract scaling behaviors associated with the phase fluctuations. The effectiveness of the method is demonstrated and its applicability is articulated. [ABSTRACT FROM AUTHOR]

• We measure gas-liquid two-phase flow via the four-sector distributed conductance sensor. • We propose a novel multilayer limited penetrable visibility graph to analyze multichannel measurements. • Our method allows characterizing the flow transition from bubble flow to slug flow. • Our proposed multilayer network measure is sensitive to the change of flow parameters. • Our analysis yields novel insights into the flow behavior underlying the formation of slug flow. The research of the dynamical flow behavior of gas-liquid two-phase flow remains a challenge of great importance. We first carry out the vertical upward gas-liquid two-phase flow experiment in a 50 mm inner-diameter pipe and capture flow information via four-sector distributed conductance sensor. Then, we develop multilayer limited penetrable visibility graph (MLPVG) to analyze multichannel measurements, aiming to characterize the complicated flow behavior. We calculate two projection networks of MLPVG from two different perspectives (i.e. the overlapping information and the whole information). The ratio between the global clustering coefficients of these two projection networks is calculated as a quantitative indicator to characterize the multilayer network. We find that the proposed multilayer network measure can effectively characterize the evolution of gas-liquid flow, from randomly dispersed bubbles to periodically arisen gas slugs. The results suggest that our method can effectively fuse multichannel measurements and reveal the evolution of the complicated flow behavior. [ABSTRACT FROM AUTHOR]

We first employ multi-scale time asymmetry (MSA) to analyze typical chaotic signals from Schuster maps and indicate that the MSA method can characterize the distinct time asymmetry of chaotic time series. Then we propose a modified MSA method, i.e., multi-scale weighted time asymmetry, and a novel time asymmetry index to investigate fractal Brownian motion signals and demonstrate its effects on discriminating between fractal signals with different Hurst exponents. Considering that the dynamic behavior of slug flow exhibits chaotic features, we apply the MSA method to analyze experimental signals from a gas-liquid two-phase flow and find that slug flow presents a unique time asymmetric structure. In addition, we further explore the mechanism leading to the formation of time asymmetry in terms of adaptive optimal kernel time-frequency representation. The results suggest that the MSA method can be a useful tool for detecting the complex flow structure underlying a gas-liquid two-phase flow. [ABSTRACT FROM AUTHOR]

We extend the complexity entropy causality plane (CECP) to propose a multi-scale complexity entropy causality plane (MS-CECP) and further use the proposed method to discriminate the deterministic characteristics of different oil-in-water flows. We first take several typical time series for example to investigate the characteristic of the MS-CECP and find that the MS-CECP not only describes the continuous loss of dynamical structure with the increase of scale, but also reflects the determinacy of the system. Then we calculate the MS-CECP for the conductance fluctuating signals measured from oil—water two-phase flow loop test facility. The results indicate that the MS-CECP could be an intrinsic measure for indicating oil-in-water two-phase flow structures. [ABSTRACT FROM AUTHOR]

Conductivity methods are commonly used in two-phase flow measurement due to their high sensitivity to the conductivity contrast between both phases. In this study, a dual-sensor probe array is newly designed to measure the local parameters of vertical upward gas–liquid two-phase flows in a small inner diameter pipe. Firstly, the measurements of gas volume fraction and gas velocity profiles are conducted using the dual-sensor probe array. Then series of bubble chord lengths at different locations are derived based on the rising velocities of the bubbles, and are compared with a model of maximum bubble diameter. Additionally, based on the simultaneously measured signals from the dual-sensor probe array, the structures of multiple bubble groups are visualized using a technology of phase density image. In view of the existence of the multiple bubble groups, the transformation from bubble chord length distribution to bubble size distribution is conducted based on the decomposition of the multiple bubble groups in the chord length distribution, and the evolution characteristics of the bubble size distributions at the pipe cross section are investigated as the flow condition changing. [ABSTRACT FROM AUTHOR]

Abstract: The oil–water two-phase flow experiment was carried out in a vertical upward pipe to study the responses of the pulsed ultrasonic sensor and vertical multiple electrode array sensor. Based on the finite element calculation, it is found that the calculated ultrasonic levels are very sensitive to the concentration variations of dispersed oil phase, and the oil droplet diameter can affect the ultrasonic field. Moreover, the technique of symbolic dynamic filtering is used to analyze the ultrasonic fluctuating signals, and extract the anomaly flow measure from the signals of ultrasonic sensor. The results show that, the anomaly flow measure linearly increases when the oil volume fraction y o is lower than 0.35. However, for higher oil volume fraction (y o >0.35) the variation of flow measure presents an irregular distribution with the change of oil volume fraction. These interesting and significant findings suggest that the pulsed ultrasonic technique can potentially be a powerful tool for measuring the high water volume fraction of dispersed oil-in-water two-phase flows. [Copyright &y& Elsevier]

Abstract: In this paper, we first make a simulation investigation to evaluate three time-frequency representation algorithms, i.e., Wigner–Ville distribution, Choi–Williams distribution and adaptive optimal kernel time-frequency representation (AOK TFR). The results indicate that AOK TFR can suppress the cross-term while keeping a high time-frequency concentration. In this regard, we use AOK TFR to analyze the fluctuating signals measured from vertical upward gas–liquid two-phase flow experiments. Moreover, we extract total energy and time-frequency entropy from the AOK TFR to characterize dynamic behaviors underlying different flow patterns. We find the total energy and entropy are sensitive to the flow pattern evolutions and the joint distribution of total energy and entropy can be a powerful tool for not only distinguishing different flow patterns but also revealing complex dynamic behaviors underlying gas–liquid flow patterns. [Copyright &y& Elsevier]

Abstract: We experimentally investigate vertical upward oil–water two-phase flow in a 20mm inner diameter pipe. We first using vertical multiple electrode array conductance sensor measure the water holdup, and using mini-conductance probes define five observed flow patterns, i.e., very fine dispersed oil-in-water (VFD O/W) flow, dispersed oil-in-water (D O/W) flow, oil-in-water slug (D OS/W) flow, water-in-oil (D W/O) and transition flow (TF). Then we present an experimental flow pattern map with oil and water superficial velocity ranging from 0.258m/s to 3.684m/s and 0.184m/s to 1.474m/s, respectively. In addition, we obtain the flow pattern transition boundaries in terms of water holdup. Finally, we propose an effective quadric time–frequency representation, i.e., the adaptive optimal kernel time–frequency representation (AOK TFR) to investigate the complex behavior underlying vertical upward oil–water flow. In particular, we extract total energy and time–frequency entropy to characterize the evolutions of flow patterns. The results suggest that AOK TFR based method could potentially be a powerful tool for characterizing the dynamical characteristics of different vertical upward water-dominant oil–water flow patterns. [Copyright &y& Elsevier]

Horizontal oil–water two-phase flows often exist in many industrial processes. Uncovering the dynamic mechanism of the flow pattern transition is of great significance for modeling the flow parameters. In this study we propose a method called multi-scale distribution entropy (MSDE) in a coupled 3D phase space, and use it to characterize the flow pattern transitions in horizontal oil–water two-phase flows. Firstly, the proposed MSDE is validated with Lorenz system and ARFIMA processes. Interestingly, it is found that the MSDE is dramatically associated with the cross-correlations of the coupled time series. Then, through conducting the experiment of horizontal oil–water two-phase flows, the upstream and downstream flow information is collected using a conductance cross-correlation velocity probe. The coupled cross-correlated signals are investigated using the MSDE method, and the results indicate that the MSDE is an effective tool uncovering the complex dynamic behaviors of flow pattern transitions. [ABSTRACT FROM AUTHOR]

Gas–liquid two-phase flows are widely encountered in many industrial applications, and the evolutionary dynamics of the flow patterns are fundamental knowledge for the establishment of the two-phase controlling system. In this work, we propose a symbolic complex network-based method for identifying the evolutionary dynamics of the gas–liquid​ two-phase flow system. First, we establish a series of symbolic networks with the derived gas–liquid two-phase flow symbolic series. Then we suggest a symbolic network index, which is the number of enumerated elementary cycles, to reveal the periodic oscillation properties of various gas–liquid flow patterns. In addition, we estimate the symbolic network average degree C and average shortest path length L to reveal the evolutionary dynamics of the flow patterns. The results suggest that our developed method is efficient for detecting the dynamics of the two-phase flow system, which can be further applied to other complex fluid systems. • A gas–liquid two-phase flow experimental is conducted in a 50 mm inner diameter pipe. • The fluid fluctuations are symbolized with a grammar defined in recurrence domain. • A novel symbolic complex network is proposed to characterize the fluid dynamics. • The two-phase flow oscillations are characterized with the network elementary cycles. • The flow pattern evolutionary dynamics are revealed with the network parameters. [ABSTRACT FROM AUTHOR]

We detect the flow structures of a horizontal oil–water two-phase flow in a 20 mm inner-diameter pipe using 8-channels radial mini-conductance probes. In particular, we present an experimental flow pattern map that includes 218 flow conditions and compare this map to the flow pattern transitional boundaries predicted by published models. In addition, using the Adaptive Optimal Kernel Time–Frequency Representation, we analyze the conductance fluctuating signals and characterize the flow pattern in terms of the total energy and dominant frequency. Based on the liquid holdup measurements using the quickly closing valve technology combined with three parallel-wire capacitance probes, we investigate the slip effect between the oil and water phases under various flow conditions. The results show that the flow structures greatly affect the slippage, and the slip ratio is sensitive to flow pattern variations. [ABSTRACT FROM AUTHOR]

Abstract: We experimentally investigate the inclined oil–water two phase flow characteristics in 125mm inner diameter pipe by using the vertical multi-electrode array (VMEA) conductance probe and mini-conductance probes. For the oil and water superficial velocities in the range of 0.0052–0.3306m/s and inclination angle at 15° and 45° from vertical, we observe the four typical inclined oil–water flow patterns, i.e., Dispersion of oil-in-water-Pseudoslugs, Dispersion oil-in-water-Countercurrent, Transitional Flow and Dispersion of water-in-oil flow pattern. Since the mini-conductance probes are sensitive to local change of flow pattern, with the help of high speed camera, we exactly identify different flow patterns under different flow conditions by analyzing the measured signals. In addition, we also propose the inclined oil–water two phase flow pattern maps for large diameter pipe. Furthermore, we further characterize the flow patterns by applying recurrence quantification analysis and chaotic attractor geometry morphological description to VMEA signals. The results show that the proposed nonlinear analysis method is an effective tool not only for classifying different water-dominated flow patterns but also for characterizing the complex flow structure of inclined oil–water two phase flow system. [Copyright &y& Elsevier]