Multistructural and Multiscale Instability Characterization of Gas–Liquid Two-Phase Flow with MRA-CMESSE

Characterizing instability in gas–liquid flows is difficult because flow dynamics interact across multiple scales. In this work, we develop an integrated framework that combines multi-resolution analysis with composite multiscale equiprobable symbolic sample entropy (MRA-CMESSE). This combination enables us to examine flow instability from a multistructural and multiscale perspective. A comprehensive evaluation across four distinct metrics shows that our method is more robust to changes in data length than multiscale sample entropy and composite multiscale sample entropy approaches. Furthermore, MRA-CMESSE is applied to analyze differential pressure time series from vertical air–water two-phase flow, providing a quantitative characterization of the instability of three flow patterns. Among these, bubble flow is the most unstable, with energy spread out and high complexity at small scales; slug flow is the most stable, with its energy focused at larger scales with low complexity, and churn flow falls in between. A central finding is that as superficial gas velocity increases, energy and complexity shift to the meso-scale and micro-scale. This quantitative analysis identifies increased agitation at the meso-scale and micro-scale as the primary driver of enhanced overall flow instability. This framework offers a new quantitative basis for analyzing gas–liquid two-phase flows and strengthens the physical foundation for the monitoring and control of related industrial systems.