Multilayer Visibility Graph-Based Ordinal Network for Revealing Gas–Liquid Nonlinear Dynamic Flow Behaviors

Characterizing the nonlinear dynamic behaviors of gas–liquid two-phase flow is a challenging but rewarding research topic. In this article, a novel multilayer visibility graph-based ordinal network (MVGON) is proposed for exploring the gas–liquid flow behaviors. In particular, the vertical upward gas–liquid flow experiments are first conducted in a 50 mm inner-diameter pipe, and multivariate measurement data is acquired. Then, MVGON is inferred from experimental signals. MVGON not only can effectively fuse multivariate time series but also enables to further excavate concise key information based on inheriting system features extracted by visibility graph (VG). For each derived projection network of MVGON, graph energy and average clustering coefficient (ACC) are calculated for quantitatively characterizing the topological structure of MVGON. In addition, permutation entropy (PE) and multivariate pseudo Wigner distribution-based time–frequency distribution are calculated for the three typical flow patterns to support our findings. The results indicate that our MVGON framework allows effectively characterizing the nonlinear dynamic behaviors during the evolution of different gas–liquid flow patterns. Meanwhile, it provides a novel approach for characterizing the complex system dynamics based on multivariate time series analysis.