# Multiscale Characterization of Flow Instability for Gas–Liquid Two-Phase Flow

## TL;DR

This paper introduces a new method to analyze gas-liquid flow instability, helping improve safety and efficiency in industrial systems.

## Contribution

A novel TMESE method is proposed and validated for characterizing multiscale flow instability in gas-liquid systems.

## Key findings

- TMESE distribution captures evolutionary features of different flow patterns effectively.
- Bubble flow shows the strongest instability, slug flow the least, and churn flow is intermediate.
- Higher gas or liquid velocity increases average TMESE and complexity index values.

## Abstract

Gas–liquid two-phase flow instability is a key issue affecting the safety and efficiency of industrial systems, and the accurate characterization of its multiscale dynamic characteristics remains a challenge. This study proposes a novel approach based on time-shift multiscale equiprobable symbolic sample entropy (TMESE) to characterize flow instability, which is validated using four evaluation metrics on eight typical time series. The TMESE method is applied to analyze the dynamic behaviors of bubble flow, slug flow, and churn flow both qualitatively and quantitatively. Results show that the TMESE distribution effectively captures evolutionary features of different flow patterns, and the joint distribution of average TMESE and complexity index (CI) provides a reliable quantitative measure of multiscale flow instability. Bubble flow exhibits the strongest instability, slug flow the least, and churn flow intermediate. Increasing gas or liquid superficial velocity raises average TMESE and CI values. These findings provide theoretical support for the prediction and control of gas–liquid two-phase flow systems in engineering applications.