Search

Two-phase flow exists widely in the industrial field, and its research is of great significance for industrial production. In this brief, we design a wire-mesh sensor system with 256 measurement points and conduct vertical upward gas-liquid two-phase flow experiments to capture the flow information under different flow conditions. We find that flow structure can be characterized by the gas-liquid distribution imaging obtained through the wire-mesh sensor. To obtain more detailed imaging, we apply super-resolution methods based on deep learning to improve the imaging quality and choose No-Reference Structural Sharpness to evaluate the effects. The results show that compared with traditional interpolation method, the deep learning-based super resolution can restore more abundant details such as edges and textures, thereby characterizing the flow structure more finely. This provides an important support for further analysis of the flow characteristics and flow regularity, which can effectively optimize the industrial process.

Gas–liquid two-phase flow widely exists in petroleum, natural gas, and other industries. Recognition of flow structure is an important issue in the study of two-phase flow, and it is of great significance for the optimization of industrial processes. Therefore, how to recognize complex flow structures effectively represents a challenge. To cope with this problem, we develop a novel deep learning network to recognize flow structures under different flow conditions. In particular, we conduct vertical upward gas–liquid two-phase flow experiments to obtain the flow structure data set on the basis of images collected by a high-speed camera. Then, we design a branch-aggregation network (BAN), where the branch structure is utilized to increase the width of the network, and multilevel aggregation structure is used to fuse features of different levels. In recognition of flow structure, the proposed network achieves an accuracy of 99.60% with a fast convergence speed and shows the advantages in antinoise ability, which is significant for online recognition in industrial processes. The results indicate that BAN can be a feasible method to recognize complex flow structures.

Gas–liquid two-phase flow widely exits in production and transportation of petroleum industry. Characterizing gas–liquid flow and measuring flow parameters represent challenges of great importance, which contribute to the recognition of flow regime and the optimal design of industrial equipment. In this paper, we propose a novel complex network-based deep learning method for characterizing gas–liquid flow. Firstly, we map the multichannel measurements to multiple limited penetrable visibility graphs (LPVGs) and obtain their degree sequences as the graph representation. Based on the degree distribution, we analyze the complicated flow behavior under different flow structures. Then, we design a dual-input convolutional neural network to fuse the raw signals and the graph representation of LPVGs for the classification of flow structures and measurement of gas void fraction. We implement the model with two parallel branches with the same structure, each corresponding to one input. Each branch consists of a channel-projection convolutional part, a spatial–temporal convolutional part, a dense block and an attention module. The outputs of the two branches are concatenated and fed into several full connected layers for the classification and measurement. At last, our method achieves an accuracy of 95.3% for the classification of flow structures, and a mean squared error of 0.0038 and a mean absolute percent error of 6.3% for the measurement of gas void fraction. Our method provides a promising solution for characterizing gas–liquid flow and measuring flow parameters.

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.

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.

This paper presents the characteristics of a double helix capacitance sensor for measurement of the liquid holdup in horizontal oil–water two-phase flow. The finite element method is used to calculate the sensitivity field of the sensor in a pipe with 20 mm inner diameter and the effect of sensor geometry on the distribution of sensitivity field is presented. Then, a horizontal oil–water two-phase flow experiment is carried out to measure the response of the double helix capacitance sensor, in which a novel method is proposed to calibrate the liquid holdup based on three pairs of parallel-wire capacitance probes. The performance of the sensor is analyzed in terms of the flow structures detected by mini-conductance array probes.

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.

Due to the complex flow structures of horizontal oil–water flows, the liquid holdup measurement is still a challenging problem. In this paper, we using the finite element analysis build a two-dimensional model of the concave capacitance sensor and investigate the effect of sensor geometry on the distribution of the sensitivity field. Through calculating the sensor static response for different horizontal oil–water flow patterns, we figure out the optimum geometry of the concave capacitance sensor. In addition, we conduct experiment to obtain the measured response of the concave capacitance sensor and achieve the oil-holdup by using quick closing valve. The results indicate that the optimized concave capacitance sensor shows good performance for liquid holdup measurement of horizontal oil–water two-phase flow.

Horizontal oil–water two-phase flow widely exists in petroleum industry. The flow measurement in oil well, which is one of key production logging technologies, is becoming more and more important for horizontal well production management. The complicated flow structures happened in horizontal oil–water two-phase flow bring a great challenge to flow measurement. We employ a parallel–wire capacitance probe (PWCP) to compose the cross-correlation velocity measurement. Firstly, we investigate the distribution of sensitivity field of PWCP by using finite element method (FEM). Then, we carry out the flow loop test to figure out the cross-correlation velocity from the voltage fluctuation signals measured from upstream and downstream probes. The results indicate that the cross-correlation characteristic of PWCPs depends on the oil–water flow structures. Finally, we use the kinematic wave model to predict the homogeneous velocity for six different horizontal oil–water two-phase flow patterns.

This paper presents a novel capacitance probe, i.e. , parallel-wire capacitance probe (PWCP), for two-phase flow measurement. Using finite element method (FEM), the sensitivity field of the PWCP is investigated and the optimum sensor geometry is determiend in term of the characterisitc parameters. Then, the response of PWCP for the oil-water stratified flow is calculated, and it is found the PWCP has better linearity and sensitivity to the variation of water-layer thickness, and is almost independant of the angle between the oil-water interface and the sensor electrode. Finally, the static experiment for oil-water stratified flow is carried out and the calibration method of liquid holdup is presented.

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.

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.

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.

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.

In this paper, we first extract a nonlinear time series from the Weierestrass function as a toy model and investigate the anti-noise ability of six different fractal scale algorithm. The results indicate that the fractal scales calculated from Detrended Fluctuation Analysis(DFA) are robust with respect to variation in noise level. Based on the conductance fluctuating signals measured from vertical gas-liquid two phase flow experiment, we calculate the fractal scales of five typical flow patterns. The results show that when the water superficial velocity ranging from 0.0453ms−1 to 0.226 ms−1 and the gas superficial velocity ranging from 0.0043ms−1 to 3.43 ms−1, the values of the fractal scale of bubble flow are lowest corresponding to the random complex dynamic behavior, while the values of slug flow are highest corresponding to the alternatively periodic motions between gas slug and liquid slug, and the values of churn flow lies between them indicating the relatively complex dynamic behavior. Our main result is that the fractal scales obtained from conductance fluctuating signals can not only effectively characterize the dynamic characteristics of gas-liquid two phase flow patterns, but also further provide valuable reference for understanding the transitions of different gas-liquid two phase flow patterns.

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.

We experimentally investigate the inclined oil–water two phase flow characteristics in 125 mm 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 0.0052–0.3306 m/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.

Complex networks have established themselves in recent years as being particularly suitable and flexible for representing and modelling many complex natural and artificial systems. Oil–water two-phase flow is one of the most complex systems. In this paper, we use complex networks to study the inclined oil–water two-phase flow. Two different complex network construction methods are proposed to build two types of networks, i.e. the flow pattern complex network (FPCN) and fluid dynamic complex network (FDCN). Through detecting the community structure of FPCN by the community-detection algorithm based on K-means clustering, useful and interesting results are found which can be used for identifying three inclined oil–water flow patterns. To investigate the dynamic characteristics of the inclined oil–water two-phase flow, we construct 48 FDCNs under different flow conditions, and find that the power-law exponent and the network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of the inclined oil–water two-phase flow. In this paper, from a new perspective, we not only introduce a complex network theory into the study of the oil–water two-phase flow but also indicate that the complex network may be a powerful tool for exploring nonlinear time series in practice.

High water cut and low velocity vertical upward oil-water two-phase flow is a typical complex system with the features of multiscale, unstable and non-homogenous. We first measure local flow information by using distributed conductance sensor and then develop a multivariate multiscale complex network (MMCN) to reveal the dispersed oil-in-water local flow behavior. Specifically, we infer complex networks at different scales from multi-channel measurements for three typical vertical oil-in-water flow patterns. Then we characterize the generated multiscale complex networks in terms of network clustering measure. The results suggest that the clustering coefficient entropy from the MMCN not only allows indicating the oil-in-water flow pattern transition but also enables to probe the dynamical flow behavior governing the transitions of vertical oil-water two-phase flow.

Characterizing the flow structure underlying the evolution of oil-in-water bubbly flow remains a contemporary challenge of great interests and complexity. In particular, the oil droplets dispersing in a water continuum with diverse size make the study of oil-in-water bubbly flow really difficult. To study this issue, we first design a novel complex impedance sensor and systematically conduct vertical oil-water flow experiments. Based on the multivariate complex impedance measurements, we define modalities associated with the spatial transient flow structures and construct modality transition-based network for each flow condition to study the evolution of flow structures. In order to reveal the unique flow structures underlying the oil-in-water bubbly flow, we filter the inferred modality transition-based network by removing the edges with small weight and resulting isolated nodes. Then, the weighted clustering coefficient entropy and weighted average path length are employed for quantitatively assessing the original network and filtered network. The differences in network measures enable to efficiently characterize the evolution of the oil-in-water bubbly flow structures.

More recently, we have employed a Markov transition probability-based network to characterize the flow behavior underlying horizontal gas-liquid two-phase flow [1]. We here introduce methodology and obtained results as follows: A Markov chain is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states.

Characterizing complex patterns arising from horizontal oil-water two-phase flows is a contemporary and challenging problem of paramount importance. We design a new multisector conductance sensor and systematically carry out horizontal oil-water two-phase flow experiments for measuring multivariate signals of different flow patterns. We then infer multivariate recurrence networks from these experimental data and investigate local cross-network properties for each constructed network. Our results demonstrate that a cross-clustering coefficient from a multivariate recurrence network is very sensitive to transitions among different flow patterns and recovers quantitative insights into the flow behavior underlying horizontal oil-water flows. These properties render multivariate recurrence networks particularly powerful for investigating a horizontal oil-water two-phase flow system and its complex interacting components from a network perspective.

We carried out vertical upward oil-water two phase flow experiment and measured fluctuation signals from mini-conductance probes and the vertical multi-electrode array (VMEA). We first define three observed flow patterns in terms of mini-conductance probe. Then, based on the signals obtained from VMEA, we use Adaptive Optimal Kernel Time-Frequency Representation (AOK TFR) to investigate oil-water flow patterns from time-frequency perspective. Furthermore, we propose two characteristic parameters, i.e., total energy, and time-frequency entropy, to quantitatively characterize the dynamical characteristics of different flow patterns. The results indicate that AOK TFR is an effective tool for characterizing and distinguishing different oil-water flow patterns.

Due to the complicated distribution of local velocity and local phase hold up along the radial direction of pipe in horizontal oil-water two phase flow, it is difficult to measure the total flow rate and phase volume fraction. In this study, we carried out dynamic experiment in horizontal oil-water two phases flow simulation well by using combination measurement system including turbine flowmeter with petal type concentrating diverter, conductance sensor and flowpassing capacitance sensor. According to the response resolution ability of the conductance and capacitance sensor in different range of total flow rate and water-cut, we use drift flux model and statistical model to predict the partial phase flow rate, respectively. The results indicate that the variable coefficient drift flux model can self-adaptively tone the model parameter according to the oil-water two phase flow characteristic, and the prediction result of partial phase flow rate of oil-water two phase flow is of high accuracy.

The dynamics of two-phase flows have been a challenging problem in nonlinear dynamics and fluid mechanics. We propose a method to characterize and distinguish patterns from inclined water-oil flow experiments based on the concept of network motifs that have found great usage in network science and systems biology. In particular, we construct from measured time series phase-space complex networks and then calculate the distribution of a set of distinct network motifs. To gain insight, we first test the approach using time series from classical chaotic systems and find a universal feature: motif distributions from different chaotic systems are generally highly heterogeneous. Our main finding is that the distributions from experimental two-phase flows tend to be heterogeneous as well, suggesting the underlying chaotic nature of the flow patterns. Calculation of the maximal Lyapunov exponent provides further support for this. Motif distributions can thus be a feasible tool to understand the dynamics of realistic two-phase flow patterns.

The identification of flow pattern is a basic and important issue in multiphase systems. Because of the complexity of phase interaction in gas-liquid two-phase flow, it is difficult to discern its flow pattern objectively. In this paper, we make a systematic study on the vertical upward gas-liquid two-phase flow using complex network. Three unique network construction methods are proposed to build three types of networks, i.e., flow pattern complex network (FPCN), fluid dynamic complex network (FDCN), and fluid structure complex network (FSCN). Through detecting the community structure of FPCN by the community-detection algorithm based on K -mean clustering, useful and interesting results are found which can be used for identifying five vertical upward gas-liquid two-phase flow patterns. To investigate the dynamic characteristics of gas-liquid two-phase flow, we construct 50 FDCNs under different flow conditions, and find that the power-law exponent and the network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of gas-liquid two-phase flow. Furthermore, we construct FSCN and demonstrate how network statistic can be used to reveal the fluid structure of gas-liquid two-phase flow. In this paper, from a different perspective, we not only introduce complex network theory to the study of gas-liquid two-phase flow but also indicate that complex network may be a powerful tool for exploring nonlinear time series in practice.

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.

We propose an improved permutation entropy method, i.e., multi-scale permutation entropy (MSPE), for discriminating two-phase flow dynamics. We first take the signals from different typical dynamical systems as examples to demonstrate the effectiveness of the methods. In particular, we compute the MSPE values of sinusoidal signal, logistic, Lorenz and Chen chaotic signals and their signals with white Gaussian noise added. We find that the MSPE method can be an effective tool for analyzing the time series with distinct dynamics. We finally calculate the multi-scale permutation entropy and rate of MSPE from 66 groups of conductance fluctuating signals and find that these two measures can be used to identify different flow patterns and further explore dynamical characteristics of gas-liquid flow patterns. These results suggest that the MSPE can potentially be a useful tool for revealing the dynamical complexity of two-phase flow on different scales.

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.

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.

We optimize and design a new half-ring conductance sensor for measuring two-phase flow in a small diameter pipe. Based on the experimental signals measured from the designed sensor, we using the limited penetrable visibility graph we proposed construct complex networks for different flow patterns. Through analyzing the constructed networks, we find that the joint distribution of the allometric scaling exponent and the average degree of the network allows distinguishing different gas-liquid flow patterns in a small diameter pipe. The curve peak of the degree distribution allows uncovering the detailed features of the flow structure associated with the size of gas bubbles, the average degree of the network can reflect the macroscopic property of the flow behavior, The allometric scaling exponent is very sensitive to the complexity of fluid dynamics and allows characterizing the dynamic behaviors in the evolution of different flow patterns. In this regard, limited penetrable visibility graph analysis of fluid signals can provide a new perspective and a novel tool for uncovering the dynamical mechanisms governing the formation and evolution of different flow patterns.

In experiment we firstly define five typical horizontal oil-water flow patterns. Then we introduce an approach for analyzing signals by decomposing the original signals increment into magnitude and sign series and exploring their scaling properties. We characterize the nonlinear and linear properties of horizontal oil-water two-phase flow, which relate to magnitude and sign series respectively. We find that the joint distribution of different scaling exponents can effectively identify flow patterns, and the detrended fluctuation analysis (DFA) on magnitude and sign series can represent typical horizontal oil-water two-phase flow dynamics characteristics. The results indicate that the magnitude and sign decomposition method can be a helpful tool for characterizing complex dynamics of horizontal oil-water two-phase flow.

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.

We use finite element analysis method to optimize and design a new curve half-ring conductance sensor for gas-liquid two-phase flow system. Then we carry out gas-liquid two-phase flow experiment in multiphase flow loop facility, and use the designed sensor to measure multivariate time series corresponding to different flow patterns. According to the measured signals, we construct complex networks from multivariate time series for different flow patterns by a network inference method. Through investigating the community structures of the constructed networks, we find that different communities correspond to different flow patterns and the network statistics in community can be used to effectively characterize the dynamic behavior of different flow patterns. In this regard, our method can be a powerful tool for identifying flow patterns and uncovering the nonlinear dynamics governing the evolution of different flow patterns.

We extract the flow pattern complex network from the measured data. After detecting the community structure of the network through the community detection algorithm which is based on k-means clustering, we find that there are three communities in the network, which correspond to the bubble flow, slug flow and churn flow respectively, and the nodes of the network that are connected tightly between two communities correspond to the transitional flow. In this paper, from a new perspective, we not only achieve good identification of flow patterns in gas/liquid two-phase flow based on complex network theory, but also find the characteristics of flow pattern complex network that are sensitive to the flow parameters, which provide reference to the study of dynamic properties of two-phase flow.