Abstract: 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.

Key words: two-phase flow, complex networks, community structure, nonlinear dynamics