Complex Network and Bidimensional Multiscale Permutation Entropy: A New Method for Characterizing Nonlinear Dynamic Behavior in Gas-Liquid Two-Phase Flow

Revealing the evolutionary mechanisms of gas-liquid two-phase flow patterns is vital for production and transport in industry. The resistance sensor array is used to collect gas-liquid two-phase flow information from the vertical upward pipeline. The data are encoded into 2-D images using a Gramian angular field (GAF). Based on the GAF images, we propose a framework for analyzing flow patterns by combining bidimensional multiscale permutation entropy (MPE2D) with interconnected pattern transition complex networks (IPTCNs). The MPE2D of GAF images is calculated to measure the multiscale spatial complexity of the flow patterns. In addition, a new image-based optimal scale IPTCN is proposed to analyze the spatial coupling behavior and evolutionary behavior of the four flow patterns using two network indices in the IPTCN. Finally, a 2-D scatter plot is constructed using the average value of MPE2D and the network indices from IPTCN. The K-nearest neighbor (KNN) algorithm is then applied to complete the flow pattern identification. The results show that the method can effectively analyze the nonlinear dynamic behavior of flow pattern at the optimal scale and reveal the evolutionary behavior between the flow patterns when the flow velocity changes.