Nonlinear Dynamic Characteristics Of Two-Phase Flow In Complex Networks

Two-phase flow, as a complex nonlinear system, is commonly observed in many industrial applications, and its behaviors under a wide range of flow conditions and inclination angles constitute an outstanding interdisciplinary problem with significant applications to the petroleum industry. So far there has been no satisfactory understanding of the underlying dynamics leading to the formation and governing the evolution of two-phase fow structures. Therefore, a new theoretically method is strongly required to detect and describe the different flow structures and their nonlinear dynamics from the modern information processing perspective. Complex networks, which provide us with a new viewpoint and an effective tool for understanding a complex system from the relations between the elements in a global way, not only may be a powerful tool for revealing information embedded in time series but also can be used for studying nonlinear dynamic systems that can not be perfectly described by theoretical model, e.g., two-phase flow system. In this thesis, we focus our research on the vertical gas-liquid and water-dominated inclined oil-water two-phase flow. Based on the global and local conductance signals measured from vertical multi-electrode array sensor and mini-conductance probes, we propose and construct different types of complex networks, i.e., flow pattern complex network, fluid dynamic complex network, fluid structure complex network and directed weighted recurrence complex network. Furthermore, through investigating the different gas-liquid/oil-water two-phase complex networks, we make a systematic study on the complex two-phase flow structure and the nonlinear dynamics of the flow pattern transition. The effectiveness of the complex network method is be demonstrated and its broader applicability is articulated. The creative points of this thesis are as follows:1. We propose a method for constructing complex network from multiple measued signals, i.e., multiple-signals correlation complex network. In addition, we propose two effective network community-detection algorithms, i.e., community detection based on k-means clustering and community detection based on data fields. Based on the conductance fluctuating signals measured from gas-liquid/oil-water two-phase flow experiment, we construct gas-liquid/oil-water Flow Pattern Complex Network (FPCN). Through detecting the community structure of the FPCN by the community-detection algorithm based on K-means clustering, we achieve good identification of gas-liquid/oil-water two-phase flow pattern by finding the different communities correspond to different flow patterns. Hence, we have put forward a new method for identifying complex flow patterns by combining the community structure of FPCN. In order to study the nonlinear dynamics of gas-liquid/oil-water two-phase flow, we propose a Fluid Dynamic Complex Network (FDCN). Through analyzing the degree distributions, we find all the FDCNs present the small world and scale-free property. Moreover, based on the investigation of the statistical characteristics of FDCNs, we demonstrate that the power-law exponent and network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of gas-liquid/oil-water two-phase flow. The FDCN provides a new approach for uncovering the nonlinear dynamic characteristics of different flow patterns in two-phase flow.2. We propose a unique method for constructing complex networks from a time series based on phase space reconstruction, i.e., Phase Space Complex Network (PSCN). Through investigating an extensive range of network topology statistics, we find that the constructed network inherits main properties of the time series in its structure. Specifically, periodic series and noisy series convert into regular networks and random networks, respectively, and networks generated from chaotic time series typically exhibit small-world and scale-free features associated with unstable periodic orbits. Based the conductance fluctuating signals measured from two-phase flow experiment, we construct Fluid Structure Complex Network (FSCN) and exploit the network motifs to characterize inclined oil-water two-phase flow. Our main result is that motif distributions do exist in the constructed networks and, strikingly, they tend to be highly heterogeneous, a feature that has been found to be common for PSCNs constructed from low-dimensional, deterministic chaotic systems. Specifically, the D O/W PS flow pattern possesses low-dimensional chaotic property, and TF flow pattern indicates high-dimensional chaotic features, and D O/W CT flow pattern lies between them. The motif distribution can thus faithfully represent the distinct dynamical states of the inclined oil-water two-phase flow. For example, when a transition in the flow structure occurs, a characteristic change in the motif distribution arises. Moreover, we associate the fluid structure of gas-liquid two-phase flow with the topological indices of FSCN, and indicate that the assortative mixing property of FSCN can effectively reveal the bubble coalescence and bubble collapse in gas-liquid fluid structure. Our results suggest that the FSCN can potentially be a powerful tool for uncovering dynamical mechanisms generating various patterns in two-phase flows. 3. We put forward a new network concept and its construction method, i.e., Directed Weighted Recurrence Complex Network (DWRCN). Take the Tent map and 2x mod 1map as examples, we first theoretically demonstrate how to properly select the network recurrence threshold by using network maximum size of subgraph. Then we indicate that the coefficient of network recurrence threshold is an effective indicator for the existence of Unstable Periodic Orbits (UPOs). Furthermore, take the R?ssler chaotic system as an example, we associate the UPO dynamics with the indices of the DWRCN, and demonstrate how to detect different UPOs correlated with Lyapunov exponent. Using the the measured conductance fluctuating signals, we construct two-phase flow DWRCN, and the results indicate that: the coefficient of network recurrence threshold of slug flow is much smaller than that of bubble and churn flow, i.e., large numbers of UPOs do exist in the slug flow while bubble and churn flow not; the UPOs of slug flow are much more complex than that of typical chaotic system (R?ssler system); most of the UPOs of slug flow are mainly composed of interior small circle and exterior big circle; the orbit pass from interior small circle to exterior big circle represents the intermittent quasi-periodic oscillation motion in pipe between liquid slug contained gas bubbles and large gas slug. Thus, the DWRCN provides a new perspective for investigating detail properties in the formation of slug flow in terms of phase space orbits.